From bf9f2957cb08894bdb39d9f6eac09bb5d5fd4764 Mon Sep 17 00:00:00 2001
From: Dr Nathan Green <n8thangreen@yahoo.co.uk>
Date: Fri, 19 Jun 2026 16:59:23 +0100
Subject: [PATCH 1/2] Fix MAIC covariate adjustment and shrink r-universe badge

---
 R/strategy_.R   | 10 ++++++++++
 README.md       |  3 +--
 docs/index.html | 11 ++++++-----
 3 files changed, 17 insertions(+), 7 deletions(-)

diff --git a/R/strategy_.R b/R/strategy_.R
index 0b5b718..5e5ec6f 100644
--- a/R/strategy_.R
+++ b/R/strategy_.R
@@ -102,6 +102,16 @@ strategy_maic <- function(formula = NULL,
       }
     }
   }
+  # Ensure MAIC uses an unadjusted outcome model to prevent estimating conditional effects.
+  resp_var <- all.vars(outcome_model)[1]
+  out_vars <- all.vars(outcome_model)
+  
+  if (length(setdiff(out_vars, c(resp_var, trt_var))) > 0) {
+    if (verbatim) {
+      warning("Covariates detected in the MAIC outcome model. To ensure the estimation of compatible marginal treatment effects, MAIC requires an unadjusted outcome model. The outcome model is being automatically overridden to '", resp_var, " ~ ", trt_var, "'.", call. = FALSE)
+    }
+    outcome_model <- as.formula(paste(resp_var, "~", trt_var))
+  }
   
   check_formula(outcome_model, trt_var)
   
diff --git a/README.md b/README.md
index 52edc0e..4c66977 100644
--- a/README.md
+++ b/README.md
@@ -10,8 +10,7 @@
 [![R-CMD-check](https://github.com/StatisticsHealthEconomics/outstandR/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/StatisticsHealthEconomics/outstandR/actions/workflows/R-CMD-check.yaml)
 [![License: GPL
 v3](https://img.shields.io/badge/License-GPLv3-blue.svg)](https://www.gnu.org/licenses/gpl-3.0)
-[![outstandR status
-badge](https://statisticshealtheconomics.r-universe.dev/outstandR/badges/version)](https://statisticshealtheconomics.r-universe.dev/outstandR)
+<a href="https://statisticshealtheconomics.r-universe.dev/outstandR"><img src="https://statisticshealtheconomics.r-universe.dev/outstandR/badges/version" alt="outstandR status badge" style="height: 20px;"></a>
 [![CRAN status](https://www.r-pkg.org/badges/version/outstandR)](https://CRAN.R-project.org/package=outstandR)
 [![codecov](https://codecov.io/gh/StatisticsHealthEconomics/outstandR/graph/badge.svg?token=YOUR_CODECOV_TOKEN)](https://codecov.io/gh/StatisticsHealthEconomics/outstandR)
 <!-- badges: end -->
diff --git a/docs/index.html b/docs/index.html
index 8ea4b7b..a551065 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -12,8 +12,8 @@
 <link rel="icon" sizes="any" href="favicon.ico">
 <link rel="manifest" href="site.webmanifest">
 <script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
-<link href="deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet">
-<script src="deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
+<link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
+<script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
 <script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data">
 <meta name="description" content="For the problem of indirect treatment comparison with limited subject-level data, this package provides tools for model-based standardisation with several different computation approaches. See Remiro‐Azócar A, Heath A, Baio G (2022) ``Parametric G‐computation for compatible indirect treatment comparisons with limited individual patient data, Res. Synth. Methods, 1–31. ISSN 1759-2879, &lt;doi:10.1002/jrsm.1565&gt;.">
@@ -95,7 +95,7 @@ <h2 id="installation">Installation<a class="anchor" aria-label="anchor" href="#i
 <span>            <span class="st">"https://cloud.r-project.org"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p>Alternatively, you may wish to download directly from the repo with</p>
 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">remotes</span><span class="fu">::</span><span class="fu">install_github</span><span class="op">(</span><span class="st">"StatisticsHealthEconomics/outstandR"</span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu">remotes</span><span class="fu">::</span><span class="fu"><a href="https://remotes.r-lib.org/reference/install_github.html" class="external-link">install_github</a></span><span class="op">(</span><span class="st">"StatisticsHealthEconomics/outstandR"</span><span class="op">)</span></span></code></pre></div>
 </div>
 <div class="section level2">
 <h2 id="background">Background<a class="anchor" aria-label="anchor" href="#background"></a>
@@ -107,7 +107,7 @@ <h2 id="background">Background<a class="anchor" aria-label="anchor" href="#backg
 <li><p><em>Parametric G-computation with maximum likelihood</em>: This method fits an outcome model to the IPD using maximum likelihood estimation, then uses that model to predict outcomes in the comparator population. It allows extrapolation beyond the observed covariate space but requires correct specification of the outcome model to avoid bias.</p></li>
 <li><p><em>Parametric G-computation with Bayesian inference</em>: Similar to the maximum likelihood version, this approach fits an outcome model but within a Bayesian framework. It allows coherent propagation of uncertainty through prior distributions and posterior inference, enabling probabilistic sensitivity analysis and full uncertainty quantification.</p></li>
 <li><p><em>Multiple imputation marginalization method based on parametric G-computation</em>: Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the relevant population to recover a compatible marginal treatment effect. This can be easily applied where the outcome regression is a generalized linear model or a Cox model. The approach views the covariate adjustment regression as a nuisance model and separates its estimation from the evaluation of the marginal treatment effect of interest. The method can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework.</p></li>
-<li><p><em>Simulated Treatment Comparison (STC) [DEPRECATED]:</em> While previously common, standard STC can produce biased marginal estimates due to aggregation bias and non-collapsibility when using non-linear link functions. <em>Note: STC is formally deprecated as of v1.0.1 in favor of the more robust G-computation approaches.</em></p></li>
+<li><p><em>Simulated Treatment Comparison (STC) [DEPRECATED]:</em> While previously common, standard STC can produce biased marginal estimates due to aggregation bias and non-collapsibility when using non-linear link functions. <em>Note: STC is formally deprecated as of v2.0.0 in favour of the more robust G-computation approaches.</em></p></li>
 </ul>
 </div>
 <div class="section level2">
@@ -186,8 +186,9 @@ <h2 data-toc-skip>Dev status</h2>
 <ul class="list-unstyled">
 <li><a href="https://github.com/StatisticsHealthEconomics/outstandR/actions/workflows/R-CMD-check.yaml" class="external-link"><img src="https://github.com/StatisticsHealthEconomics/outstandR/actions/workflows/R-CMD-check.yaml/badge.svg" alt="R-CMD-check"></a></li>
 <li><a href="https://www.gnu.org/licenses/gpl-3.0" class="external-link"><img src="https://img.shields.io/badge/License-GPLv3-blue.svg" alt="License: GPL v3"></a></li>
-<li><a href="https://statisticshealtheconomics.r-universe.dev/outstandR" class="external-link"><img src="https://statisticshealtheconomics.r-universe.dev/outstandR/badges/version" alt="outstandR status badge"></a></li>
+<li><a href="https://statisticshealtheconomics.r-universe.dev/outstandR" class="external-link"><img src="https://statisticshealtheconomics.r-universe.dev/outstandR/badges/version" alt="outstandR status badge" style="height: 20px;"></a></li>
 <li><a href="https://CRAN.R-project.org/package=outstandR" class="external-link"><img src="https://www.r-pkg.org/badges/version/outstandR" alt="CRAN status"></a></li>
+<li><a href="https://codecov.io/gh/StatisticsHealthEconomics/outstandR" class="external-link"><img src="https://codecov.io/gh/StatisticsHealthEconomics/outstandR/graph/badge.svg?token=YOUR_CODECOV_TOKEN" alt="codecov"></a></li>
 </ul>
 </div>
 

From 4060efce54d7f483d4c37169282572352757bbb5 Mon Sep 17 00:00:00 2001
From: Dr Nathan Green <n8thangreen@yahoo.co.uk>
Date: Fri, 19 Jun 2026 17:00:44 +0100
Subject: [PATCH 2/2] updated pkgdown site

---
 _pkgdown.yml                                  |   23 +-
 badge.svg                                     |   22 +
 docs/404.html                                 |    4 +-
 docs/GEMINI.html                              |    2 +-
 docs/LICENSE.html                             |    2 +-
 docs/articles/Binary_outcome_example.html     |  618 ++--------
 docs/articles/Binary_outcome_example.md       |  421 +------
 docs/articles/Continuous_outcome_example.html |  321 +----
 docs/articles/Continuous_outcome_example.md   |  235 +---
 docs/articles/Count_outcome_example.html      |  310 +----
 docs/articles/Count_outcome_example.md        |  225 +---
 docs/articles/adding-a-new-strategy.html      |    4 +-
 docs/articles/index.html                      |   28 +-
 docs/articles/index.md                        |   17 +-
 docs/authors.html                             |    2 +-
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 docs/reference/continuity_correction.html     |    2 +-
 docs/reference/cor2cov.html                   |    2 +-
 docs/reference/estimate_var_sandwich.html     |    2 +-
 docs/reference/gcomp_ml.boot.html             |    2 +-
 docs/reference/gcomp_ml_means.html            |    2 +-
 docs/reference/get_allowed_var_methods.html   |    2 +-
 docs/reference/get_comparator.html            |    2 +-
 docs/reference/get_covariate_names.html       |    2 +-
 docs/reference/get_eff_mod_names.html         |    2 +-
 docs/reference/get_ref_trt.html               |    2 +-
 docs/reference/get_robust_vcov.html           |    2 +-
 docs/reference/get_treatment_effect.html      |    2 +-
 docs/reference/get_treatment_name.html        |    2 +-
 docs/reference/get_var_method.html            |    2 +-
 docs/reference/guess_treatment_name.html      |    2 +-
 docs/reference/index.html                     |    9 +-
 docs/reference/index.md                       |    2 +
 docs/reference/maic.boot.html                 |    2 +-
 docs/reference/maic_weights.html              |    8 +-
 docs/reference/maic_weights.md                |    4 +-
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 docs/sitemap.xml                              |    1 +
 inst/jss-section.html                         |  281 +++--
 .../figure-html/summary-forest-plot-1.png     |  Bin 25656 -> 26770 bytes
 scripts/exercises2.html                       |  118 +-
 vignettes/Binary_outcome_example.Rmd          |  915 ++++++++++++++
 vignettes/Binary_outcome_example.html         | 1081 +++++++++++++++++
 vignettes/Continuous_outcome_example.Rmd      |  372 ++++++
 vignettes/Count_outcome_example.Rmd           |  425 +++++++
 209 files changed, 3717 insertions(+), 2141 deletions(-)
 create mode 100644 badge.svg
 create mode 100644 docs/reference/calc_bucher_naive.html
 create mode 100644 docs/reference/calc_bucher_naive.md
 create mode 100644 vignettes/Binary_outcome_example.Rmd
 create mode 100644 vignettes/Binary_outcome_example.html
 create mode 100644 vignettes/Continuous_outcome_example.Rmd
 create mode 100644 vignettes/Count_outcome_example.Rmd

diff --git a/_pkgdown.yml b/_pkgdown.yml
index 4b6b2ff..7b4f1ac 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -83,14 +83,17 @@ reference:
   contents:
   - strategy-class
 
-# articles:
-# - title: "Binary outcome data example"
-#   contents:
-#     - "Binary_outcome_example"
-# - title: "Continuous outcome data example"
-#   contents:
-#     - "Continuous_outcome_example"
-# - title: "Count outcome data example"
-#   contents:
-#     - "Count_outcome_example"
+articles:
+- title: "Binary outcome data example"
+  contents:
+    - "Binary_outcome_example"
+- title: "Continuous outcome data example"
+  contents:
+    - "Continuous_outcome_example"
+- title: "Count outcome data example"
+  contents:
+    - "Count_outcome_example"
+- title: "Developer Guides"
+  contents:
+    - "articles/adding-a-new-strategy"
     
diff --git a/badge.svg b/badge.svg
new file mode 100644
index 0000000..fe9d5de
--- /dev/null
+++ b/badge.svg
@@ -0,0 +1,22 @@
+<svg width="105.8" height="20" viewBox="0 0 1058 200" xmlns="http://www.w3.org/2000/svg" role="img" aria-label="r-universe: 2.0.0">
+  <a href="https://statisticshealtheconomics.r-universe.dev/outstandR" alt="r-universe">
+  <title>r-universe: 2.0.0</title>
+  <linearGradient id="YdCfD" x2="0" y2="100%">
+    <stop offset="0" stop-opacity=".1" stop-color="#EEE"/>
+    <stop offset="1" stop-opacity=".1"/>
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+  <g mask="url(#VZzoL)">
+    <rect width="668" height="200" fill="#555"/>
+    <rect width="390" height="200" fill="#3C1" x="668"/>
+    <rect width="1058" height="200" fill="url(#YdCfD)"/>
+  </g>
+  <g aria-hidden="true" text-anchor="start" font-family="Verdana,DejaVu Sans,sans-serif" font-size="110">
+    <text x="60" y="148" textLength="568" fill="#000" opacity="0.25">r-universe</text>
+    <text x="50" y="138" textLength="568" fill="#fff">r-universe</text>
+    <text x="723" y="148" textLength="290" fill="#000" opacity="0.25">2.0.0</text>
+    <text x="713" y="138" textLength="290" fill="#fff">2.0.0</text>
+  </g>
+  
+  </a>
+</svg>
\ No newline at end of file
diff --git a/docs/404.html b/docs/404.html
index 553eed2..90580a3 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -12,8 +12,8 @@
 <link rel="icon" sizes="any" href="https://StatisticsHealthEconomics.github.io/outstandR/favicon.ico">
 <link rel="manifest" href="https://StatisticsHealthEconomics.github.io/outstandR/site.webmanifest">
 <script src="https://StatisticsHealthEconomics.github.io/outstandR/deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
-<link href="https://StatisticsHealthEconomics.github.io/outstandR/deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet">
-<script src="https://StatisticsHealthEconomics.github.io/outstandR/deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="https://StatisticsHealthEconomics.github.io/outstandR/deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
+<link href="https://StatisticsHealthEconomics.github.io/outstandR/deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
+<script src="https://StatisticsHealthEconomics.github.io/outstandR/deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="https://StatisticsHealthEconomics.github.io/outstandR/deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="https://StatisticsHealthEconomics.github.io/outstandR/deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
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 <meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png">
diff --git a/docs/GEMINI.html b/docs/GEMINI.html
index 8dc14f5..d9bda19 100644
--- a/docs/GEMINI.html
+++ b/docs/GEMINI.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>outstandR: Outcome Regression Standardisation • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="outstandR: Outcome Regression Standardisation"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>outstandR: Outcome Regression Standardisation • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="outstandR: Outcome Regression Standardisation"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/LICENSE.html b/docs/LICENSE.html
index 04cba1c..4056cb5 100644
--- a/docs/LICENSE.html
+++ b/docs/LICENSE.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>GNU General Public License • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="GNU General Public License"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>GNU General Public License • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="GNU General Public License"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/articles/Binary_outcome_example.html b/docs/articles/Binary_outcome_example.html
index 31a162a..bd888c3 100644
--- a/docs/articles/Binary_outcome_example.html
+++ b/docs/articles/Binary_outcome_example.html
@@ -1,11 +1,16 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Binary data example • outstandR</title>
+<!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png">
+<link rel="icon" type="”image/svg+xml”" href="../favicon.svg">
+<link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png">
+<link rel="icon" sizes="any" href="../favicon.ico">
+<link rel="manifest" href="../site.webmanifest">
 <script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
@@ -16,11 +21,11 @@
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
-    <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="light" aria-label="Site navigation"><div class="container">
+    <nav class="navbar navbar-expand-lg fixed-top bg-primary" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
 
     <a class="navbar-brand me-2" href="../index.html">outstandR</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.0.0.9000</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -29,9 +34,10 @@
 
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto">
-<li class="nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
+<li class="nav-item"><a class="nav-link" href="../index.html">Home</a></li>
+<li class="nav-item"><a class="nav-link" href="../reference/index.html">Functions</a></li>
 <li class="active nav-item"><a class="nav-link" href="../articles/index.html">Articles</a></li>
-<li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
+<li class="nav-item"><a class="nav-link" href="../news/index.html">News</a></li>
       </ul>
 <ul class="navbar-nav">
 <li class="nav-item"><form class="form-inline" role="search">
@@ -50,8 +56,7 @@
 
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
-
-      <h1>Binary data example</h1>
+      <img src="../logo.png" class="logo" alt=""><h1>Binary data example</h1>
             
       
       <small class="dont-index">Source: <a href="https://github.com/StatisticsHealthEconomics/outstandR/blob/HEAD/vignettes/Binary_outcome_example.Rmd" class="external-link"><code>vignettes/Binary_outcome_example.Rmd</code></a></small>
@@ -64,7 +69,7 @@ <h1>Binary data example</h1>
 <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
 </h2>
 <p>This vignette will demonstrate the use of the
-<a href="https://StatisticsHealthEconomics.github.io/outstandR">outstandR</a> package to fit the range of types of models to
+<a href="https://StatisticsHealthEconomics.github.io/outstandR/">outstandR</a> package to fit the range of types of models to
 simulated binary data. Related vignettes will provide equivalent
 analyses for continuous and count data.</p>
 </div>
@@ -85,8 +90,8 @@ <h2 id="analysis">Analysis<a class="anchor" aria-label="anchor" href="#analysis"
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://tidyr.tidyverse.org" class="external-link">tidyr</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://dplyr.tidyverse.org" class="external-link">dplyr</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="http://www.stats.ox.ac.uk/pub/MASS4/" class="external-link">MASS</a></span><span class="op">)</span></span>
-<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://StatisticsHealthEconomics.github.io/outstandR">outstandR</a></span><span class="op">)</span></span>
-<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">simcovariates</span><span class="op">)</span></span></code></pre></div>
+<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://StatisticsHealthEconomics.github.io/outstandR/">outstandR</a></span><span class="op">)</span></span>
+<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">simcovariates</span><span class="op">)</span>  <span class="co"># from GitHub</span></span></code></pre></div>
 <div class="section level3">
 <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 </h3>
@@ -136,7 +141,7 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <td>-1.77196</td>
 </tr>
 <tr class="even">
-<td><code>b_X</code></td>
+<td><code>b_PF</code></td>
 <td>Conditional effect of each prognostic variable (-log(0.5))</td>
 <td>0.69315</td>
 </tr>
@@ -208,14 +213,12 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 </tr>
 </tbody>
 </table>
-<p>We shall use the <code><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data()</a></code> function available with the
-<a href="https://github.com/n8thangreen/simcovariates" class="external-link">simcovariates</a>
-package on GitHub.</p>
+<p>Translating to R code.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">N</span> <span class="op">&lt;-</span> <span class="fl">200</span></span>
 <span><span class="va">allocation</span> <span class="op">&lt;-</span> <span class="fl">2</span><span class="op">/</span><span class="fl">3</span>      <span class="co"># active treatment vs. placebo allocation ratio (2:1)</span></span>
 <span><span class="va">b_trt</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.17</span><span class="op">)</span>     <span class="co"># conditional effect of active treatment vs. common comparator</span></span>
-<span><span class="va">b_X</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.5</span><span class="op">)</span>       <span class="co"># conditional effect of each prognostic variable</span></span>
+<span><span class="va">b_PF</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.5</span><span class="op">)</span>       <span class="co"># conditional effect of each prognostic variable</span></span>
 <span><span class="va">b_EM</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.67</span><span class="op">)</span>     <span class="co"># conditional interaction effect of each effect modifier</span></span>
 <span><span class="va">meanX_AC</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.45</span>, <span class="fl">0.45</span><span class="op">)</span>       <span class="co"># mean of normally-distributed covariate in AC trial</span></span>
 <span><span class="va">meanX_BC</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.6</span>, <span class="fl">0.6</span><span class="op">)</span>         <span class="co"># mean of each normally-distributed covariate in BC</span></span>
@@ -224,20 +227,26 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span><span class="va">sdX</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.4</span>, <span class="fl">0.4</span><span class="op">)</span>     <span class="co"># standard deviation of each covariate (same for AC and BC)</span></span>
 <span><span class="va">sdX_EM</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.4</span>, <span class="fl">0.4</span><span class="op">)</span>  <span class="co"># standard deviation of each EM covariate</span></span>
 <span><span class="va">corX</span> <span class="op">&lt;-</span> <span class="fl">0.2</span>            <span class="co"># covariate correlation coefficient  </span></span>
-<span><span class="va">b_0</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fl">0.6</span>            <span class="co"># baseline intercept coefficient  ##TODO: fixed value</span></span>
-<span></span>
-<span><span class="va">covariate_defns_ipd</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
-<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span><span class="va">b_0</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fl">0.6</span>            <span class="co"># baseline intercept coefficient  ##TODO: fixed value</span></span></code></pre></div>
+<p>We shall use the <code>gen_data()</code> function available with the
+<a href="https://github.com/n8thangreen/simcovariates" class="external-link">simcovariates</a>
+package on GitHub. For this, we need to define a list of covariates with
+distribution <code>type</code> and relationship to the outcome
+<code>role</code> as either <code>prognostic</code>,
+<code>effect_modifier</code> or both.</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">covariate_defns_ipd</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
+<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span>,</span>
-<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span></span>
 <span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">b_prognostic</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>PF_cont_1 <span class="op">=</span> <span class="va">b_X</span>, PF_cont_2 <span class="op">=</span> <span class="va">b_X</span><span class="op">)</span></span>
+<span><span class="va">b_prognostic</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>PF_cont_1 <span class="op">=</span> <span class="va">b_PF</span>, PF_cont_2 <span class="op">=</span> <span class="va">b_PF</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">b_effect_modifier</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>EM_cont_1 <span class="op">=</span> <span class="va">b_EM</span>, EM_cont_2 <span class="op">=</span> <span class="va">b_EM</span><span class="op">)</span></span>
 <span></span>
@@ -248,7 +257,7 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">cor_matrix</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"PF_cont_1"</span>, <span class="st">"PF_cont_2"</span>, <span class="st">"EM_cont_1"</span>, <span class="st">"EM_cont_2"</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">colnames</a></span><span class="op">(</span><span class="va">cor_matrix</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"PF_cont_1"</span>, <span class="st">"PF_cont_2"</span>, <span class="st">"EM_cont_1"</span>, <span class="st">"EM_cont_2"</span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">ipd_trial</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data</a></span><span class="op">(</span></span>
+<span><span class="va">ipd_trial</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu">gen_data</span><span class="op">(</span></span>
 <span>  N <span class="op">=</span> <span class="va">N</span>,</span>
 <span>  b_0 <span class="op">=</span> <span class="va">b_0</span>,</span>
 <span>  b_trt <span class="op">=</span> <span class="va">b_trt</span>,</span>
@@ -262,7 +271,7 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 and 1. We will include some extra information about treatment names. To
 do this we will define the lable of the two level factor as
 <code>A</code> for 1 and <code>C</code> for 0 as follows.</p>
-<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">ipd_trial</span><span class="op">$</span><span class="va">trt</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">ipd_trial</span><span class="op">$</span><span class="va">trt</span>, labels <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"C"</span>, <span class="st">"A"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p>Similarly, to obtain the aggregate data we will simulate IPD but with
 the additional summarise step. We set different mean values
@@ -270,19 +279,20 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 same parameter values as for the
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">AC</annotation></semantics></math>
 trial.</p>
-<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<p>First, simulate the underlying IPD similarly for the AC trial.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">covariate_defns_ald</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
-<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_BC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_BC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_BC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_BC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_BC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_BC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span>,</span>
-<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_BC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_BC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span></span>
 <span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">BC.IPD</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data</a></span><span class="op">(</span></span>
+<span><span class="va">BC.IPD</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu">gen_data</span><span class="op">(</span></span>
 <span>  N <span class="op">=</span> <span class="va">N</span>,</span>
 <span>  b_0 <span class="op">=</span> <span class="va">b_0</span>,</span>
 <span>  b_trt <span class="op">=</span> <span class="va">b_trt</span>,</span>
@@ -293,9 +303,12 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span>  trt_assignment <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>prob_trt1 <span class="op">=</span> <span class="va">allocation</span><span class="op">)</span>,</span>
 <span>  family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span><span class="st">"logit"</span><span class="op">)</span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">BC.IPD</span><span class="op">$</span><span class="va">trt</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">BC.IPD</span><span class="op">$</span><span class="va">trt</span>, labels <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"C"</span>, <span class="st">"B"</span><span class="op">)</span><span class="op">)</span></span>
-<span></span>
-<span><span class="co"># covariate summary statistics</span></span>
+<span><span class="va">BC.IPD</span><span class="op">$</span><span class="va">trt</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">BC.IPD</span><span class="op">$</span><span class="va">trt</span>, labels <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"C"</span>, <span class="st">"B"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<p>Next, we aggregate these data. We <code><a href="https://dplyr.tidyverse.org/reference/summarise.html" class="external-link">summarise()</a></code> the
+covariates, sample sizes and outcomes separately and then bind the
+results together.</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># covariate summary statistics</span></span>
 <span><span class="co"># assume same between treatments</span></span>
 <span><span class="va">cov.X</span> <span class="op">&lt;-</span> </span>
 <span>  <span class="va">BC.IPD</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
@@ -336,8 +349,6 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span>    names_to <span class="op">=</span> <span class="st">"statistic"</span>,</span>
 <span>    values_to <span class="op">=</span> <span class="st">"value"</span><span class="op">)</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
 <span>  <span class="fu"><a href="https://dplyr.tidyverse.org/reference/group_by.html" class="external-link">ungroup</a></span><span class="op">(</span><span class="op">)</span></span>
-<span><span class="co">#&gt; `summarise()` has grouped output by 'variable'. You can override using the</span></span>
-<span><span class="co">#&gt; `.groups` argument.</span></span>
 <span></span>
 <span><span class="co"># sample sizes</span></span>
 <span><span class="va">summary.N</span> <span class="op">&lt;-</span> </span>
@@ -390,42 +401,16 @@ <h4 id="ald_trial-aggregate-level-data">
 <code>NA</code>
 </li>
 </ul>
-<p>Our data look like the following.</p>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">ipd_trial</span><span class="op">)</span></span>
-<span><span class="co">#&gt;   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt y     true_eta</span></span>
-<span><span class="co">#&gt; 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C 0  0.582883524</span></span>
-<span><span class="co">#&gt; 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A 1 -1.476422106</span></span>
-<span><span class="co">#&gt; 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A 0  0.005184912</span></span>
-<span><span class="co">#&gt; 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C 1  0.520117172</span></span>
-<span><span class="co">#&gt; 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A 1 -1.760974264</span></span>
-<span><span class="co">#&gt; 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A 0 -2.139514435</span></span></code></pre></div>
+<p>Our final data look like the following.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">ipd_trial</span><span class="op">)</span></span></code></pre></div>
 <p>There are 4 correlated continuous covariates generated per subject,
 simulated from a multivariate normal distribution. Treatment
 <code>trt</code> takes either new treatment <em>A</em> or standard of
 care / status quo <em>C</em>. The ITC is ‘anchored’ via <em>C</em>, the
 common treatment.</p>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">ald_trial</span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 16 × 4</span></span></span>
-<span><span class="co">#&gt;    variable  statistic   value trt  </span></span>
-<span><span class="co">#&gt;    <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>       <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 1</span> EM_cont_1 mean        0.616 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 2</span> EM_cont_1 sd          0.408 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 3</span> EM_cont_2 mean        0.635 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 4</span> EM_cont_2 sd          0.354 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 5</span> PF_cont_1 mean        0.666 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 6</span> PF_cont_1 sd          0.398 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 7</span> PF_cont_2 mean        0.663 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 8</span> PF_cont_2 sd          0.404 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 9</span> y         mean        0.597 C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">10</span> y         sd          0.494 C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">11</span> y         sum        43     C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">12</span> y         mean        0.297 B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">13</span> y         sd          0.459 B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">14</span> y         sum        38     B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">15</span> <span style="color: #BB0000;">NA</span>        N          72     C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">16</span> <span style="color: #BB0000;">NA</span>        N         128     B</span></span></code></pre></div>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">ald_trial</span></span></code></pre></div>
 <p>In this case, we have 4 covariate mean and standard deviation values;
 and the event total, average and sample size for each treatment
 <em>B</em> and <em>C</em>.</p>
@@ -435,21 +420,21 @@ <h4 id="regression-model">Regression model<a class="anchor" aria-label="anchor"
 </h4>
 <p>The true logistic outcome model which we use to simulate the data
 is</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="normal">logit</mtext><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>p</mi><mi>t</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msub><mi>β</mi><mn>0</mn></msub><mo>+</mo><msub><mi>β</mi><mi>X</mi></msub><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>X</mi><mn>3</mn></msub><mo>+</mo><msub><mi>X</mi><mn>4</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>+</mo><mrow><mo stretchy="true" form="prefix">[</mo><msub><mi>β</mi><mi>t</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mi>E</mi><mi>M</mi></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>X</mi><mn>1</mn></msub><mo>+</mo><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">]</mo></mrow><mspace width="0.278em"></mspace><mtext mathvariant="normal">I</mtext><mrow><mo stretchy="true" form="prefix">(</mo><mi>t</mi><mo>≠</mo><mi>C</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
-\text{logit}(p_{t}) = \beta_0 + \beta_X (X_3 + X_4) + [\beta_{t} + \beta_{EM} (X_1 + X_2)] \; \text{I}(t \neq C)
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="normal">logit</mtext><mo stretchy="false" form="prefix">(</mo><msub><mi>p</mi><mi>t</mi></msub><mo stretchy="false" form="postfix">)</mo><mo>=</mo><msub><mi>β</mi><mn>0</mn></msub><mo>+</mo><msub><mi>β</mi><mrow><mi>P</mi><mi>F</mi></mrow></msub><mo stretchy="false" form="prefix">(</mo><msub><mi>X</mi><mn>3</mn></msub><mo>+</mo><msub><mi>X</mi><mn>4</mn></msub><mo stretchy="false" form="postfix">)</mo><mo>+</mo><mo stretchy="false" form="prefix">[</mo><msub><mi>β</mi><mi>t</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mi>E</mi><mi>M</mi></mrow></msub><mo stretchy="false" form="prefix">(</mo><msub><mi>X</mi><mn>1</mn></msub><mo>+</mo><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false" form="postfix">)</mo><mo stretchy="false" form="postfix">]</mo><mspace width="0.278em"></mspace><mtext mathvariant="normal">I</mtext><mo stretchy="false" form="prefix">(</mo><mi>t</mi><mo>≠</mo><mi>C</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">
+\text{logit}(p_{t}) = \beta_0 + \beta_{PF} (X_3 + X_4) + [\beta_{t} + \beta_{EM} (X_1 + X_2)] \; \text{I}(t \neq C)
 </annotation></semantics></math></p>
-<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="normal">I</mtext><mrow><mo stretchy="true" form="prefix">(</mo><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\text{I}()</annotation></semantics></math>
+<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="normal">I</mtext><mo stretchy="false" form="prefix">(</mo><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\text{I}()</annotation></semantics></math>
 is an indicator function taking value 1 if true and 0 otherwise. That
 is, for treatment
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>C</mi><annotation encoding="application/x-tex">C</annotation></semantics></math>
 the right hand side becomes
-<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mn>0</mn></msub><mo>+</mo><msub><mi>β</mi><mi>X</mi></msub><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>X</mi><mn>3</mn></msub><mo>+</mo><msub><mi>X</mi><mn>4</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\beta_0 + \beta_X (X_3 + X_4)</annotation></semantics></math>
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mn>0</mn></msub><mo>+</mo><msub><mi>β</mi><mrow><mi>P</mi><mi>F</mi></mrow></msub><mo stretchy="false" form="prefix">(</mo><msub><mi>X</mi><mn>3</mn></msub><mo>+</mo><msub><mi>X</mi><mn>4</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\beta_0 + \beta_{PF} (X_3 + X_4)</annotation></semantics></math>
 and for comparator treatments
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>A</mi><annotation encoding="application/x-tex">A</annotation></semantics></math>
 or
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>B</mi><annotation encoding="application/x-tex">B</annotation></semantics></math>
 there is an additional
-<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mi>t</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mi>E</mi><mi>M</mi></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>X</mi><mn>1</mn></msub><mo>+</mo><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\beta_t + \beta_{EM} (X_1 + X_2)</annotation></semantics></math>
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>β</mi><mi>t</mi></msub><mo>+</mo><msub><mi>β</mi><mrow><mi>E</mi><mi>M</mi></mrow></msub><mo stretchy="false" form="prefix">(</mo><msub><mi>X</mi><mn>1</mn></msub><mo>+</mo><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\beta_t + \beta_{EM} (X_1 + X_2)</annotation></semantics></math>
 component consisting of the effect modifier terms and the coefficient
 for the treatment parameter,
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>β</mi><mi>t</mi></msub><annotation encoding="application/x-tex">\beta_t</annotation></semantics></math>
@@ -468,7 +453,7 @@ <h3 id="output-statistics">Output statistics<a class="anchor" aria-label="anchor
 calculated depends on the type of data and outcome scale. For our
 current example of binary data and log-odds ratio the marginal treatment
 effect is</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>log</mo><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><mrow><msub><mi>n</mi><mi>B</mi></msub><mi>/</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>N</mi><mi>B</mi></msub><mo>−</mo><msub><mi>n</mi><mi>B</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><msub><mi>n</mi><mi>C</mi></msub><mi>/</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>N</mi><mi>B</mi></msub><mo>−</mo><msub><mi>n</mi><mi>B</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mo>log</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>n</mi><mi>B</mi></msub><msub><mi>n</mi><mover><mi>C</mi><mo accent="true">‾</mo></mover></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><mo>log</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>n</mi><mi>C</mi></msub><msub><mi>n</mi><mover><mi>B</mi><mo accent="true">‾</mo></mover></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">log</mi><mo>⁡</mo></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><mrow><msub><mi>n</mi><mi>B</mi></msub><mi>/</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>N</mi><mi>B</mi></msub><mo>−</mo><msub><mi>n</mi><mi>B</mi></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msub><mi>n</mi><mi>C</mi></msub><mi>/</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>N</mi><mi>B</mi></msub><mo>−</mo><msub><mi>n</mi><mi>B</mi></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mrow><mi mathvariant="normal">log</mi><mo>⁡</mo></mrow><mo stretchy="false" form="prefix">(</mo><msub><mi>n</mi><mi>B</mi></msub><msub><mi>n</mi><mover><mi>C</mi><mo accent="true">‾</mo></mover></msub><mo stretchy="false" form="postfix">)</mo><mo>−</mo><mrow><mi mathvariant="normal">log</mi><mo>⁡</mo></mrow><mo stretchy="false" form="prefix">(</mo><msub><mi>n</mi><mi>C</mi></msub><msub><mi>n</mi><mover><mi>B</mi><mo accent="true">‾</mo></mover></msub><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">
 \log\left( \frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \right) = \log(n_B n_{\bar{C}}) - \log(n_C n_{\bar{B}})
 </annotation></semantics></math></p>
 <p>and marginal variance is</p>
@@ -489,7 +474,7 @@ <h3 id="output-statistics">Output statistics<a class="anchor" aria-label="anchor
 <div class="section level2">
 <h2 id="model-fitting-in-r">Model fitting in R<a class="anchor" aria-label="anchor" href="#model-fitting-in-r"></a>
 </h2>
-<p>The <a href="https://StatisticsHealthEconomics.github.io/outstandR">outstandR</a> package has been written to be easy to
+<p>The <a href="https://StatisticsHealthEconomics.github.io/outstandR/">outstandR</a> package has been written to be easy to
 use and essentially consists of a single function,
 <code><a href="../reference/outstandR.html">outstandR()</a></code>. This can be used to run all of the different
 types of model, which when combined with their specific parameters we
@@ -520,17 +505,20 @@ <h3 id="model-formula">Model formula<a class="anchor" aria-label="anchor" href="
 appears as a linear regression. This corresponds to the following
 <code>R</code> <code>formula</code> object we will pass as an argument
 to the strategy function.</p>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">lin_form</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"y ~ PF_cont_1 + PF_cont_2 + trt + trt:EM_cont_1 + trt:EM_cont_2"</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">lin_form</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
+<span>  outcome_model <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"</span><span class="op">)</span>,</span>
+<span>  balance_model <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2"</span><span class="op">)</span></span>
+<span><span class="op">)</span></span></code></pre></div>
 <p>Note that the more succinct formula</p>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">y</span> <span class="op">~</span> <span class="va">PF_cont_1</span> <span class="op">+</span> <span class="va">PF_cont_2</span> <span class="op">+</span> <span class="va">trt</span><span class="op">*</span><span class="op">(</span><span class="va">EM_cont_1</span> <span class="op">+</span> <span class="va">EM_cont_2</span><span class="op">)</span></span></code></pre></div>
 <p>would additionally include
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>X</mi><mn>1</mn></msub><mo>,</mo><msub><mi>X</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">X_1, X_2</annotation></semantics></math>
 as prognostic factors so is not equivalent (but this may be what you
 actually want). To recover the original formula it can be modified as
 follows.</p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">y</span> <span class="op">~</span> <span class="va">PF_cont_1</span> <span class="op">+</span> <span class="va">PF_cont_2</span> <span class="op">+</span> <span class="va">trt</span><span class="op">*</span><span class="op">(</span><span class="va">EM_cont_1</span> <span class="op">+</span> <span class="va">EM_cont_2</span><span class="op">)</span> <span class="op">-</span> <span class="va">EM_cont_1</span> <span class="op">-</span> <span class="va">EM_cont_2</span></span></code></pre></div>
 <p>We note that the MAIC approach does not strictly use a regression in
 the same way as the other methods so should not be considered directly
@@ -554,45 +542,15 @@ <h3 id="matching-adjusted-indirect-comparison-maic">Matching-Adjusted Indirect C
 <code>boot</code> from the <code>{boot}</code> package. We then
 calculate the bootstrap mean and variance in the wrapper function
 <code>maic_boot_stats</code>.</p>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_maic</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_maic</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p>The returned object is of class <code>outstandR</code>.</p>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/str.html" class="external-link">str</a></span><span class="op">(</span><span class="va">outstandR_maic</span><span class="op">)</span></span>
-<span><span class="co">#&gt; List of 2</span></span>
-<span><span class="co">#&gt;  $ contrasts:List of 3</span></span>
-<span><span class="co">#&gt;   ..$ means    :List of 3</span></span>
-<span><span class="co">#&gt;   .. ..$ AB: num 0.607</span></span>
-<span><span class="co">#&gt;   .. ..$ AC: num -0.649</span></span>
-<span><span class="co">#&gt;   .. ..$ BC: num -1.26</span></span>
-<span><span class="co">#&gt;   ..$ variances:List of 3</span></span>
-<span><span class="co">#&gt;   .. ..$ AB: num 0.233</span></span>
-<span><span class="co">#&gt;   .. ..$ AC: num 0.137</span></span>
-<span><span class="co">#&gt;   .. ..$ BC: num 0.0952</span></span>
-<span><span class="co">#&gt;   ..$ CI       :List of 3</span></span>
-<span><span class="co">#&gt;   .. ..$ AB: num [1:2] -0.338 1.552</span></span>
-<span><span class="co">#&gt;   .. ..$ AC: num [1:2] -1.3757 0.0776</span></span>
-<span><span class="co">#&gt;   .. ..$ BC: num [1:2] -1.861 -0.652</span></span>
-<span><span class="co">#&gt;  $ absolute :List of 2</span></span>
-<span><span class="co">#&gt;   ..$ means    :List of 2</span></span>
-<span><span class="co">#&gt;   .. ..$ A: Named num 0.341</span></span>
-<span><span class="co">#&gt;   .. .. ..- attr(*, "names")= chr "mean_A"</span></span>
-<span><span class="co">#&gt;   .. ..$ C: Named num 0.495</span></span>
-<span><span class="co">#&gt;   .. .. ..- attr(*, "names")= chr "mean_C"</span></span>
-<span><span class="co">#&gt;   ..$ variances:List of 2</span></span>
-<span><span class="co">#&gt;   .. ..$ A: Named num 0.00271</span></span>
-<span><span class="co">#&gt;   .. .. ..- attr(*, "names")= chr "mean_A"</span></span>
-<span><span class="co">#&gt;   .. ..$ C: Named num 0.00518</span></span>
-<span><span class="co">#&gt;   .. .. ..- attr(*, "names")= chr "mean_C"</span></span>
-<span><span class="co">#&gt;  - attr(*, "CI")= num 0.95</span></span>
-<span><span class="co">#&gt;  - attr(*, "ref_trt")= chr "C"</span></span>
-<span><span class="co">#&gt;  - attr(*, "scale")= chr "log_odds"</span></span>
-<span><span class="co">#&gt;  - attr(*, "model")= chr "binomial"</span></span>
-<span><span class="co">#&gt;  - attr(*, "class")= chr [1:2] "outstandR" "list"</span></span></code></pre></div>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/str.html" class="external-link">str</a></span><span class="op">(</span><span class="va">outstandR_maic</span><span class="op">)</span></span></code></pre></div>
 <p>We see that this is a list object with 2 parts. The first contains
 statistics between each pair of treatments. These are the mean
 contrasts, variances and confidence intervals (CI), respectively. The
@@ -601,32 +559,8 @@ <h3 id="matching-adjusted-indirect-comparison-maic">Matching-Adjusted Indirect C
 the absolute effect estimates.</p>
 <p>A <code>print</code> method is available for <code>outstandR</code>
 objects for more human-readable output</p>
-<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_maic</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_odds</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.607    0.233      -<span style="color: #BB0000;">0.338</span>     1.55  </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.649</span>    0.137      -<span style="color: #BB0000;">1.38</span>      0.077<span style="text-decoration: underline;">6</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.26</span>     0.095<span style="text-decoration: underline;">2</span>     -<span style="color: #BB0000;">1.86</span>     -<span style="color: #BB0000;">0.652</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.341   0.002<span style="text-decoration: underline;">71</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.495   0.005<span style="text-decoration: underline;">18</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_maic</span></span></code></pre></div>
 <div class="section level4">
 <h4 id="outcome-scale">Outcome scale<a class="anchor" aria-label="anchor" href="#outcome-scale"></a>
 </h4>
@@ -673,7 +607,7 @@ <h4 id="outcome-scale">Outcome scale<a class="anchor" aria-label="anchor" href="
 <li><strong>Log-risk ratio</strong></li>
 </ul>
 <p>Treatment effect is</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>log</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>n</mi><mi>B</mi></msub><mi>/</mi><msub><mi>N</mi><mi>B</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><mo>log</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>n</mi><mi>A</mi></msub><mi>/</mi><msub><mi>N</mi><mi>A</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">log</mi><mo>⁡</mo></mrow><mo stretchy="false" form="prefix">(</mo><msub><mi>n</mi><mi>B</mi></msub><mi>/</mi><msub><mi>N</mi><mi>B</mi></msub><mo stretchy="false" form="postfix">)</mo><mo>−</mo><mrow><mi mathvariant="normal">log</mi><mo>⁡</mo></mrow><mo stretchy="false" form="prefix">(</mo><msub><mi>n</mi><mi>A</mi></msub><mi>/</mi><msub><mi>N</mi><mi>A</mi></msub><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">
 \log(n_B/N_B) - \log(n_A/N_A)
 </annotation></semantics></math></p>
 <p>and variance</p>
@@ -694,118 +628,15 @@ <h4 id="outcome-scale">Outcome scale<a class="anchor" aria-label="anchor" href="
 <p>To change the outcome scale, we can pass the <code>scale</code>
 argument in the <code><a href="../reference/outstandR.html">outstandR()</a></code> function. For example, to
 change the scale to risk difference, we can use the following code.</p>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_maic_lrr</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_maic</a></span><span class="op">(</span>formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>                                     family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span>,</span>
 <span>            scale <span class="op">=</span> <span class="st">"log_relative_risk"</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_maic_lrr</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.307    0.079<span style="text-decoration: underline;">3</span>     -<span style="color: #BB0000;">0.244</span>     0.859 </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.392</span>    0.051<span style="text-decoration: underline;">4</span>     -<span style="color: #BB0000;">0.836</span>     0.052<span style="text-decoration: underline;">7</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">0.699</span>    0.027<span style="text-decoration: underline;">9</span>     -<span style="color: #BB0000;">1.03</span>     -<span style="color: #BB0000;">0.372</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.339   0.002<span style="text-decoration: underline;">58</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.501   0.005<span style="text-decoration: underline;">37</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
-</div>
-</div>
-<div class="section level3">
-<h3 id="simulated-treatment-comparison-stc">Simulated treatment comparison (STC)<a class="anchor" aria-label="anchor" href="#simulated-treatment-comparison-stc"></a>
-</h3>
-<p>Simulated treatment comparison (STC) is the conventional outcome
-regression method. It involves fitting a regression model of outcome on
-treatment and covariates to the IPD anad then ‘plugging-in’ mean
-covariate values from the aggregate data study.</p>
-<p>We can simply pass the same formula as before to the modified call
-with <code><a href="../reference/strategy.html">strategy_stc()</a></code>.</p>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_stc</span> <span class="op">&lt;-</span></span>
-<span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
-<span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_stc</a></span><span class="op">(</span></span>
-<span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
-<span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_stc</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_odds</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB           0.058<span style="text-decoration: underline;">4</span>   <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC          -<span style="color: #BB0000;">1.20</span>     <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC          -<span style="color: #BB0000;">1.26</span>      0.095<span style="text-decoration: underline;">2</span>      -<span style="color: #BB0000;">1.86</span>     -<span style="color: #BB0000;">0.652</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.137        <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.344        <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
-<p>Changing the outcome scale to LRR gives</p>
-<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_stc_lrr</span> <span class="op">&lt;-</span></span>
-<span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
-<span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_stc</a></span><span class="op">(</span></span>
-<span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
-<span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span>,</span>
-<span>            scale <span class="op">=</span> <span class="st">"log_relative_risk"</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_stc_lrr</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB           -<span style="color: #BB0000;">0.224</span>   <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.923</span>   <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">0.699</span>    0.027<span style="text-decoration: underline;">9</span>      -<span style="color: #BB0000;">1.03</span>     -<span style="color: #BB0000;">0.372</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.137        <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.344        <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
-<p>The following approaches follow naturally from the simple ‘plug-in’
-version of STC. We will perform G-computation firstly with a frequentist
-MLE and then a Bayesian approach.</p>
+<code class="sourceCode R"><span><span class="va">outstandR_maic_lrr</span></span></code></pre></div>
+</div>
 </div>
 <div class="section level3">
 <h3 id="parametric-g-computation-with-maximum-likelihood-estimation">Parametric G-computation with maximum-likelihood estimation<a class="anchor" aria-label="anchor" href="#parametric-g-computation-with-maximum-likelihood-estimation"></a>
@@ -820,8 +651,8 @@ <h3 id="parametric-g-computation-with-maximum-likelihood-estimation">Parametric
 and treatment
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>z</mi><annotation encoding="application/x-tex">z</annotation></semantics></math>
 is fitted to the <em>AC</em> IPD:</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>μ</mi><mi>n</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msub><mi>β</mi><mn>0</mn></msub><mo>+</mo><msub><mi>𝐱</mi><mi>n</mi></msub><msub><mi>𝛃</mi><mi>𝐗</mi></msub><mo>+</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>β</mi><mi>z</mi></msub><mo>+</mo><msubsup><mi>𝐱</mi><mi>𝐧</mi><mrow><mi>𝐄</mi><mi>𝐌</mi></mrow></msubsup><msub><mi>𝛃</mi><mrow><mi>𝐄</mi><mi>𝐌</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mspace width="0.278em"></mspace><mtext mathvariant="normal">I</mtext><mrow><mo stretchy="true" form="prefix">(</mo><mi>t</mi><mo>≠</mo><mi>C</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
-g(\mu_n) = \beta_0 + \boldsymbol{x}_n \boldsymbol{\beta_X} + (\beta_z + \boldsymbol{x_n^{EM}} \boldsymbol{\beta_{EM}}) \; \mbox{I}(t \neq C)
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>μ</mi><mi>n</mi></msub><mo stretchy="false" form="postfix">)</mo><mo>=</mo><msub><mi>β</mi><mn>0</mn></msub><mo>+</mo><msub><mi>𝐱</mi><mi>n</mi></msub><msub><mi>𝛃</mi><mrow><mi>𝐏</mi><mi>𝐅</mi></mrow></msub><mo>+</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>β</mi><mi>z</mi></msub><mo>+</mo><msubsup><mi>𝐱</mi><mi>𝐧</mi><mrow><mi>𝐄</mi><mi>𝐌</mi></mrow></msubsup><msub><mi>𝛃</mi><mrow><mi>𝐄</mi><mi>𝐌</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo><mspace width="0.278em"></mspace><mtext mathvariant="normal">I</mtext><mo stretchy="false" form="prefix">(</mo><mi>t</mi><mo>≠</mo><mi>C</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">
+g(\mu_n) = \beta_0 + \boldsymbol{x}_n \boldsymbol{\beta_{PF}} + (\beta_z + \boldsymbol{x_n^{EM}} \boldsymbol{\beta_{EM}}) \; \mbox{I}(t \neq C)
 </annotation></semantics></math></p>
 <p>In the context of G-computation, this regression model is often
 called the “Q-model.” Having fitted the Q-model, the regression
@@ -836,78 +667,30 @@ <h3 id="parametric-g-computation-with-maximum-likelihood-estimation">Parametric
 simulated observation, we predict the marginal outcome mean in the
 hypothetical scenario in which all units are under treatment
 <em>C</em>:</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover><mi>μ</mi><mo accent="true">̂</mo></mover><mn>0</mn></msub><mo>=</mo><msub><mo>∫</mo><msup><mi>x</mi><mo>*</mo></msup></msub><msup><mi>g</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mo stretchy="true" form="prefix">(</mo><msub><mover><mi>β</mi><mo accent="true">̂</mo></mover><mn>0</mn></msub><mo>+</mo><msup><mi>x</mi><mo>*</mo></msup><msub><mover><mi>β</mi><mo accent="true">̂</mo></mover><mn>1</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>x</mi><mo>*</mo></msup><mo stretchy="true" form="postfix">)</mo></mrow><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><msup><mi>x</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover><mi>μ</mi><mo accent="true">̂</mo></mover><mn>0</mn></msub><mo>=</mo><msub><mo>∫</mo><msup><mi>x</mi><mo>*</mo></msup></msub><msup><mi>g</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mo stretchy="false" form="prefix">(</mo><msub><mover><mi>β</mi><mo accent="true">̂</mo></mover><mn>0</mn></msub><mo>+</mo><msup><mi>x</mi><mo>*</mo></msup><msub><mover><mi>β</mi><mo accent="true">̂</mo></mover><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msup><mi>x</mi><mo>*</mo></msup><mo stretchy="false" form="postfix">)</mo><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><msup><mi>x</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">
 \hat{\mu}_0 = \int_{x^*} g^{-1} (\hat{\beta}_0 + x^* \hat{\beta}_1 ) p(x^*) \; \text{d}x^*
 </annotation></semantics></math></p>
 <p>As performed for the previous approaches, call
 <code><a href="../reference/outstandR.html">outstandR()</a></code> but change the strategy to
 <code><a href="../reference/strategy.html">strategy_gcomp_ml()</a></code>,</p>
-<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_gcomp_ml</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_gcomp_ml</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_gcomp_ml</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_odds</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.602    0.232      -<span style="color: #BB0000;">0.342</span>     1.55  </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.654</span>    0.137      -<span style="color: #BB0000;">1.38</span>      0.071<span style="text-decoration: underline;">4</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.26</span>     0.095<span style="text-decoration: underline;">2</span>     -<span style="color: #BB0000;">1.86</span>     -<span style="color: #BB0000;">0.652</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.411   0.002<span style="text-decoration: underline;">91</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.570   0.005<span style="text-decoration: underline;">63</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_gcomp_ml</span></span></code></pre></div>
 <p>Once again, let us change the outcome scale to LRR</p>
-<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_gcomp_ml_lrr</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_gcomp_ml</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span>,</span>
 <span>            scale <span class="op">=</span> <span class="st">"log_relative_risk"</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_gcomp_ml_lrr</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.377    0.060<span style="text-decoration: underline;">2</span>     -<span style="color: #BB0000;">0.104</span>     0.858 </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.322</span>    0.032<span style="text-decoration: underline;">3</span>     -<span style="color: #BB0000;">0.674</span>     0.030<span style="text-decoration: underline;">7</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">0.699</span>    0.027<span style="text-decoration: underline;">9</span>     -<span style="color: #BB0000;">1.03</span>     -<span style="color: #BB0000;">0.372</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.409   0.002<span style="text-decoration: underline;">76</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.563   0.005<span style="text-decoration: underline;">04</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_gcomp_ml_lrr</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="bayesian-g-computation-with-mcmc">Bayesian G-computation with MCMC<a class="anchor" aria-label="anchor" href="#bayesian-g-computation-with-mcmc"></a>
@@ -926,17 +709,17 @@ <h3 id="bayesian-g-computation-with-mcmc">Bayesian G-computation with MCMC<a cla
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>z</mi><mo>*</mo></msup><mo>∈</mo><mo stretchy="false" form="prefix">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false" form="postfix">}</mo></mrow><annotation encoding="application/x-tex">z^* \in \{0, 1\}</annotation></semantics></math>
 from its posterior predictive distribution under the specific treatment.
 This is defined as
-<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msubsup><mi>y</mi><msup><mi>z</mi><mo>*</mo></msup><mo>*</mo></msubsup><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msub><mo>∫</mo><mi>β</mi></msub><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msubsup><mi>y</mi><msup><mi>z</mi><mo>*</mo></msup><mo>*</mo></msubsup><mo>∣</mo><mi>β</mi><mo stretchy="true" form="postfix">)</mo></mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>β</mi><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mi>d</mi><mi>β</mi></mrow><annotation encoding="application/x-tex">p(y^*_{z^*} \mid \mathcal{D}_{AC}) = \int_{\beta} p(y^*_{z^*} \mid \beta) p(\beta \mid \mathcal{D}_{AC}) d\beta</annotation></semantics></math>
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msubsup><mi>y</mi><msup><mi>z</mi><mo>*</mo></msup><mo>*</mo></msubsup><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo><mo>=</mo><msub><mo>∫</mo><mi>β</mi></msub><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msubsup><mi>y</mi><msup><mi>z</mi><mo>*</mo></msup><mo>*</mo></msubsup><mo>∣</mo><mi>β</mi><mo stretchy="false" form="postfix">)</mo><mi>p</mi><mo stretchy="false" form="prefix">(</mo><mi>β</mi><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo><mi>d</mi><mi>β</mi></mrow><annotation encoding="application/x-tex">p(y^*_{z^*} \mid \mathcal{D}_{AC}) = \int_{\beta} p(y^*_{z^*} \mid \beta) p(\beta \mid \mathcal{D}_{AC}) d\beta</annotation></semantics></math>
 where
-<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>β</mi><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">p(\beta \mid \mathcal{D}_{AC})</annotation></semantics></math>
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false" form="prefix">(</mo><mi>β</mi><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">p(\beta \mid \mathcal{D}_{AC})</annotation></semantics></math>
 is the posterior distribution of the outcome regression coefficients
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>β</mi><annotation encoding="application/x-tex">\beta</annotation></semantics></math>,
 which encode the predictor-outcome relationships observed in the
 <em>AC</em> trial IPD. This is given by:</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msubsup><mi>y</mi><mrow><msup><mi></mi><mi>z</mi></msup><mo>*</mo></mrow><mo>*</mo></msubsup><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msub><mo>∫</mo><msup><mi>x</mi><mo>*</mo></msup></msub><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>y</mi><mo>*</mo></msup><mo>∣</mo><msup><mi>z</mi><mo>*</mo></msup><mo>,</mo><msup><mi>x</mi><mo>*</mo></msup><mo>,</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>x</mi><mo>*</mo></msup><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><msup><mi>x</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msubsup><mi>y</mi><mrow><msup><mi></mi><mi>z</mi></msup><mo>*</mo></mrow><mo>*</mo></msubsup><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo><mo>=</mo><msub><mo>∫</mo><msup><mi>x</mi><mo>*</mo></msup></msub><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msup><mi>y</mi><mo>*</mo></msup><mo>∣</mo><msup><mi>z</mi><mo>*</mo></msup><mo>,</mo><msup><mi>x</mi><mo>*</mo></msup><mo>,</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msup><mi>x</mi><mo>*</mo></msup><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><msup><mi>x</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">
 p(y^*_{^z*} \mid \mathcal{D}_{AC}) = \int_{x^*} p(y^* \mid z^*, x^*, \mathcal{D}_{AC}) p(x^* \mid \mathcal{D}_{AC})\; \text{d}x^*
 </annotation></semantics></math></p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><msub><mo>∫</mo><msup><mi>x</mi><mo>*</mo></msup></msub><msub><mo>∫</mo><mi>β</mi></msub><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>y</mi><mo>*</mo></msup><mo>∣</mo><msup><mi>z</mi><mo>*</mo></msup><mo>,</mo><msup><mi>x</mi><mo>*</mo></msup><mo>,</mo><mi>β</mi><mo stretchy="true" form="postfix">)</mo></mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>x</mi><mo>*</mo></msup><mo>∣</mo><mi>β</mi><mo stretchy="true" form="postfix">)</mo></mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>β</mi><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mspace width="0.278em"></mspace><mi>d</mi><mi>β</mi><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><msup><mi>x</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><msub><mo>∫</mo><msup><mi>x</mi><mo>*</mo></msup></msub><msub><mo>∫</mo><mi>β</mi></msub><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msup><mi>y</mi><mo>*</mo></msup><mo>∣</mo><msup><mi>z</mi><mo>*</mo></msup><mo>,</mo><msup><mi>x</mi><mo>*</mo></msup><mo>,</mo><mi>β</mi><mo stretchy="false" form="postfix">)</mo><mi>p</mi><mo stretchy="false" form="prefix">(</mo><msup><mi>x</mi><mo>*</mo></msup><mo>∣</mo><mi>β</mi><mo stretchy="false" form="postfix">)</mo><mi>p</mi><mo stretchy="false" form="prefix">(</mo><mi>β</mi><mo>∣</mo><msub><mi>𝒟</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mo stretchy="false" form="postfix">)</mo><mspace width="0.278em"></mspace><mi>d</mi><mi>β</mi><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><msup><mi>x</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">
 = \int_{x^*} \int_{\beta} p(y^* \mid z^*, x^*, \beta) p(x^* \mid \beta) p(\beta \mid \mathcal{D}_{AC})\; d\beta \; \text{d}x^*
 </annotation></semantics></math></p>
 <p>In practice, the integrals above can be approximated numerically,
@@ -947,72 +730,24 @@ <h3 id="bayesian-g-computation-with-mcmc">Bayesian G-computation with MCMC<a cla
 density.</p>
 <p>The strategy function to plug-in to the <code><a href="../reference/outstandR.html">outstandR()</a></code> call
 for this approach is <code><a href="../reference/strategy.html">strategy_gcomp_bayes()</a></code>,</p>
-<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_gcomp_bayes</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_odds</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.612    0.228      -<span style="color: #BB0000;">0.325</span>     1.55  </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.644</span>    0.133      -<span style="color: #BB0000;">1.36</span>      0.071<span style="text-decoration: underline;">3</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.26</span>     0.095<span style="text-decoration: underline;">2</span>     -<span style="color: #BB0000;">1.86</span>     -<span style="color: #BB0000;">0.652</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.411   0.002<span style="text-decoration: underline;">88</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.568   0.005<span style="text-decoration: underline;">21</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span></span></code></pre></div>
 <p>As before, we can change the outcome scale to LRR.</p>
-<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes_lrr</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_gcomp_bayes</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span>,</span>
 <span>            scale <span class="op">=</span> <span class="st">"log_relative_risk"</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes_lrr</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.375    0.060<span style="text-decoration: underline;">7</span>     -<span style="color: #BB0000;">0.108</span>     0.858 </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.324</span>    0.032<span style="text-decoration: underline;">8</span>     -<span style="color: #BB0000;">0.679</span>     0.030<span style="text-decoration: underline;">8</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">0.699</span>    0.027<span style="text-decoration: underline;">9</span>     -<span style="color: #BB0000;">1.03</span>     -<span style="color: #BB0000;">0.372</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.411   0.002<span style="text-decoration: underline;">88</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.568   0.005<span style="text-decoration: underline;">21</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes_lrr</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="multiple-imputation-marginalisation">Multiple imputation marginalisation<a class="anchor" aria-label="anchor" href="#multiple-imputation-marginalisation"></a>
@@ -1022,82 +757,34 @@ <h3 id="multiple-imputation-marginalisation">Multiple imputation marginalisation
 distribution from the aggregate level data
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">BC</annotation></semantics></math>
 study</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>Δ</mi><mtext mathvariant="normal">marg</mtext></msup><mo>=</mo><msub><mi>𝔼</mi><mrow><mi>X</mi><mo>∼</mo><msub><mi>f</mi><mtext mathvariant="normal">BC</mtext></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>X</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow></msub><mrow><mo stretchy="true" form="prefix">[</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>1</mn></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>X</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>0</mn></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>X</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">]</mo></mrow><mo>=</mo><mo>∫</mo><mrow><mo stretchy="true" form="prefix">[</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>1</mn></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>X</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>0</mn></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>X</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">]</mo></mrow><msub><mi>f</mi><mtext mathvariant="normal">BC</mtext></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>X</mi><mo stretchy="true" form="postfix">)</mo></mrow><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><mi>X</mi></mrow><annotation encoding="application/x-tex">
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="normal">Δ</mi><mtext mathvariant="normal">marg</mtext></msup><mo>=</mo><msub><mi>𝔼</mi><mrow><mi>X</mi><mo>∼</mo><msub><mi>f</mi><mtext mathvariant="normal">BC</mtext></msub><mo stretchy="false" form="prefix">(</mo><mi>X</mi><mo stretchy="false" form="postfix">)</mo></mrow></msub><mrow><mo stretchy="true" form="prefix">[</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>1</mn></mrow></msub><mo stretchy="false" form="prefix">(</mo><mi>X</mi><mo stretchy="false" form="postfix">)</mo><mo>−</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>0</mn></mrow></msub><mo stretchy="false" form="prefix">(</mo><mi>X</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="true" form="postfix">]</mo></mrow><mo>=</mo><mo>∫</mo><mrow><mo stretchy="true" form="prefix">[</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>1</mn></mrow></msub><mo stretchy="false" form="prefix">(</mo><mi>X</mi><mo stretchy="false" form="postfix">)</mo><mo>−</mo><msub><mi>μ</mi><mrow><mi>T</mi><mo>=</mo><mn>0</mn></mrow></msub><mo stretchy="false" form="prefix">(</mo><mi>X</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="true" form="postfix">]</mo></mrow><msub><mi>f</mi><mtext mathvariant="normal">BC</mtext></msub><mo stretchy="false" form="prefix">(</mo><mi>X</mi><mo stretchy="false" form="postfix">)</mo><mspace width="0.278em"></mspace><mtext mathvariant="normal">d</mtext><mi>X</mi></mrow><annotation encoding="application/x-tex">
 \Delta^{\text{marg}} = \mathbb{E}_{X \sim f_{\text{BC}}(X)} \left[ \mu_{T=1}(X) - \mu_{T=0}(X) \right]
 = \int \left[ \mu_{T=1}(X) - \mu_{T=0}(X) \right] f_{\text{BC}}(X) \; \text{d}X
 </annotation></semantics></math></p>
 <p>The aggregate level data likelihood is</p>
-<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover><mi>Δ</mi><mo accent="true">̂</mo></mover><mrow><mi>B</mi><mi>C</mi></mrow></msub><mo>∼</mo><mi>𝒩</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>Δ</mi><mtext mathvariant="normal">marg</mtext></msup><mo>,</mo><mi>S</mi><msup><mi>E</mi><mn>2</mn></msup><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover><mi mathvariant="normal">Δ</mi><mo accent="true">̂</mo></mover><mrow><mi>B</mi><mi>C</mi></mrow></msub><mo>∼</mo><mi>𝒩</mi><mo stretchy="false" form="prefix">(</mo><msup><mi mathvariant="normal">Δ</mi><mtext mathvariant="normal">marg</mtext></msup><mo>,</mo><mi>S</mi><msup><mi>E</mi><mn>2</mn></msup><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">
 \hat{\Delta}_{BC} \sim \mathcal{N}(\Delta^{\text{marg}}, SE^2)
 </annotation></semantics></math></p>
 <p>The multiple imputation marginalisation strategy function is
 <code><a href="../reference/strategy.html">strategy_mim()</a></code>,</p>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_mim</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_mim</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_mim</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_odds</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.612    0.216      -<span style="color: #BB0000;">0.299</span>     1.52  </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.644</span>    0.121      -<span style="color: #BB0000;">1.33</span>      0.038<span style="text-decoration: underline;">6</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.26</span>     0.095<span style="text-decoration: underline;">2</span>     -<span style="color: #BB0000;">1.86</span>     -<span style="color: #BB0000;">0.652</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_mim</span></span></code></pre></div>
 <p>Change the outcome scale again for LRR,</p>
-<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_mim_lrr</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_mim</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span>,</span>
 <span>            scale <span class="op">=</span> <span class="st">"log_relative_risk"</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_mim_lrr</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">binomial</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.375    0.051<span style="text-decoration: underline;">6</span>    -<span style="color: #BB0000;">0.070</span><span style="color: #BB0000; text-decoration: underline;">4</span>     0.820 </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">0.324</span>    0.023<span style="text-decoration: underline;">7</span>    -<span style="color: #BB0000;">0.626</span>     -<span style="color: #BB0000;">0.022</span><span style="color: #BB0000; text-decoration: underline;">7</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">0.699</span>    0.027<span style="text-decoration: underline;">9</span>    -<span style="color: #BB0000;">1.03</span>      -<span style="color: #BB0000;">0.372</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_mim_lrr</span></span></code></pre></div>
 </div>
 </div>
 <div class="section level2">
@@ -1115,16 +802,16 @@ <h4 id="ac-effect-in-bc-population">
 effect on the log OR scale in the
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">BC</annotation></semantics></math>
 (aggregate trial data) population is
-<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>β</mi><mi>t</mi><mrow><mi>A</mi><mi>C</mi></mrow></msubsup><mo>+</mo><msub><mi>β</mi><mrow><mi>E</mi><mi>M</mi></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><msubsup><mover><mi>X</mi><mo accent="true">‾</mo></mover><mn>1</mn><mrow><mi>A</mi><mi>C</mi></mrow></msubsup><mo>+</mo><msubsup><mover><mi>X</mi><mo accent="true">‾</mo></mover><mn>2</mn><mrow><mi>A</mi><mi>C</mi></mrow></msubsup><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\beta_t^{AC} + \beta_{EM} (\bar{X}^{AC}_1 + \bar{X}_2^{AC})</annotation></semantics></math>.
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>β</mi><mi>t</mi><mrow><mi>A</mi><mi>C</mi></mrow></msubsup><mo>+</mo><msub><mi>β</mi><mrow><mi>E</mi><mi>M</mi></mrow></msub><mo stretchy="false" form="prefix">(</mo><msubsup><mover><mi>X</mi><mo accent="true">‾</mo></mover><mn>1</mn><mrow><mi>A</mi><mi>C</mi></mrow></msubsup><mo>+</mo><msubsup><mover><mi>X</mi><mo accent="true">‾</mo></mover><mn>2</mn><mrow><mi>A</mi><mi>C</mi></mrow></msubsup><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\beta_t^{AC} + \beta_{EM} (\bar{X}^{AC}_1 + \bar{X}_2^{AC})</annotation></semantics></math>.
 Calculated by</p>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">mean_X1</span> <span class="op">&lt;-</span> <span class="va">ald_trial</span><span class="op">$</span><span class="va">value</span><span class="op">[</span><span class="va">ald_trial</span><span class="op">$</span><span class="va">statistic</span> <span class="op">==</span> <span class="st">"mean"</span> <span class="op">&amp;</span> <span class="va">ald_trial</span><span class="op">$</span><span class="va">variable</span> <span class="op">==</span> <span class="st">"EM_cont_1"</span><span class="op">]</span></span>
 <span><span class="va">mean_X2</span> <span class="op">&lt;-</span> <span class="va">ald_trial</span><span class="op">$</span><span class="va">value</span><span class="op">[</span><span class="va">ald_trial</span><span class="op">$</span><span class="va">statistic</span> <span class="op">==</span> <span class="st">"mean"</span> <span class="op">&amp;</span> <span class="va">ald_trial</span><span class="op">$</span><span class="va">variable</span> <span class="op">==</span> <span class="st">"EM_cont_1"</span><span class="op">]</span></span>
 <span></span>
 <span><span class="va">d_AC_true</span> <span class="op">&lt;-</span> <span class="va">b_trt</span> <span class="op">+</span> <span class="va">b_EM</span> <span class="op">*</span> <span class="op">(</span><span class="va">mean_X1</span> <span class="op">+</span> <span class="va">mean_X2</span><span class="op">)</span></span></code></pre></div>
 <p>The naive approach is to just convert directly from one population to
 another, ignoring the imbalance in effect modifiers.</p>
-<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">d_AC_naive</span> <span class="op">&lt;-</span> </span>
 <span>  <span class="va">ipd_trial</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu">dplyr</span><span class="fu">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/group_by.html" class="external-link">group_by</a></span><span class="op">(</span><span class="va">trt</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
@@ -1156,7 +843,7 @@ <h4 id="ab-effect-in-bc-population">
 effect in the
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">BC</annotation></semantics></math>
 population is</p>
-<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># reshape to make extraction easier</span></span>
 <span><span class="va">ald_out</span> <span class="op">&lt;-</span> <span class="va">ald_trial</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu">dplyr</span><span class="fu">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/filter.html" class="external-link">filter</a></span><span class="op">(</span><span class="va">variable</span> <span class="op">==</span> <span class="st">"y"</span> <span class="op">|</span> <span class="fu"><a href="https://rdrr.io/r/base/NA.html" class="external-link">is.na</a></span><span class="op">(</span><span class="va">variable</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
@@ -1172,6 +859,11 @@ <h4 id="ab-effect-in-bc-population">
 <span><span class="va">var.d.BC</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/with.html" class="external-link">with</a></span><span class="op">(</span><span class="va">ald_out</span>, <span class="fl">1</span><span class="op">/</span><span class="va">sum_B</span> <span class="op">+</span> <span class="fl">1</span><span class="op">/</span><span class="op">(</span><span class="va">N_B</span> <span class="op">-</span> <span class="va">sum_B</span><span class="op">)</span> <span class="op">+</span> <span class="fl">1</span><span class="op">/</span><span class="va">sum_C</span> <span class="op">+</span> <span class="fl">1</span><span class="op">/</span><span class="op">(</span><span class="va">N_C</span> <span class="op">-</span> <span class="va">sum_C</span><span class="op">)</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">var.d.AB.naive</span> <span class="op">&lt;-</span> <span class="va">d_AC_naive</span><span class="op">$</span><span class="va">var_AC</span> <span class="op">+</span> <span class="va">var.d.BC</span></span></code></pre></div>
+<p>Alternatively, we can compute this using <code>outstandR</code>’s
+built-in <code><a href="../reference/calc_bucher_naive.html">calc_bucher_naive()</a></code> function:</p>
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">naive_results</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/calc_bucher_naive.html">calc_bucher_naive</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>, outcome_model <span class="op">=</span> <span class="va">lin_form</span>, family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">binomial</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"logit"</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="va">naive_results</span></span></code></pre></div>
 <p>Of course, the
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">BC</annotation></semantics></math>
 contrast is calculated directly.</p>
@@ -1184,95 +876,15 @@ <h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></
 log-odds ratio a table of all contrasts and methods in the
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">BC</annotation></semantics></math>
 population is given below.</p>
-<table class="table">
-<thead><tr class="header">
-<th align="left"></th>
-<th align="right">d_true</th>
-<th align="right">d_naive</th>
-<th align="right">MAIC</th>
-<th align="right">STC</th>
-<th align="right">Gcomp.ML</th>
-<th align="right">Gcomp.Bayes</th>
-<th align="right">MIM</th>
-</tr></thead>
-<tbody>
-<tr class="odd">
-<td align="left">AB</td>
-<td align="right">0.00</td>
-<td align="right">0.30</td>
-<td align="right">0.61</td>
-<td align="right">0.06</td>
-<td align="right">0.60</td>
-<td align="right">0.61</td>
-<td align="right">0.61</td>
-</tr>
-<tr class="even">
-<td align="left">AC</td>
-<td align="right">-1.28</td>
-<td align="right">-0.95</td>
-<td align="right">-0.65</td>
-<td align="right">-1.20</td>
-<td align="right">-0.65</td>
-<td align="right">-0.64</td>
-<td align="right">-0.64</td>
-</tr>
-<tr class="odd">
-<td align="left">BC</td>
-<td align="right">-1.26</td>
-<td align="right">-1.26</td>
-<td align="right">-1.26</td>
-<td align="right">-1.26</td>
-<td align="right">-1.26</td>
-<td align="right">-1.26</td>
-<td align="right">-1.26</td>
-</tr>
-</tbody>
-</table>
 <p>We can see that the different corresponds reasonably well with one
 another.</p>
 <p>Next, let us look at the results on the log relative risk scale.
 First, the true values are calculated as</p>
-<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">d_AB_true_lrr</span> <span class="op">&lt;-</span> <span class="fl">0</span></span>
 <span><span class="va">d_AC_true_lrr</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Logistic.html" class="external-link">plogis</a></span><span class="op">(</span><span class="va">d_A_true</span><span class="op">)</span> <span class="op">/</span> <span class="fu"><a href="https://rdrr.io/r/stats/Logistic.html" class="external-link">plogis</a></span><span class="op">(</span><span class="va">d_C_true</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">d_AC_true_lrr</span></span></code></pre></div>
 <p>so that the summary table is</p>
-<table class="table">
-<thead><tr class="header">
-<th align="left"></th>
-<th align="right">MAIC</th>
-<th align="right">STC</th>
-<th align="right">Gcomp.ML</th>
-<th align="right">Gcomp.Bayes</th>
-<th align="right">MIM</th>
-</tr></thead>
-<tbody>
-<tr class="odd">
-<td align="left">AB</td>
-<td align="right">0.31</td>
-<td align="right">-0.22</td>
-<td align="right">0.38</td>
-<td align="right">0.37</td>
-<td align="right">0.37</td>
-</tr>
-<tr class="even">
-<td align="left">AC</td>
-<td align="right">-0.39</td>
-<td align="right">-0.92</td>
-<td align="right">-0.32</td>
-<td align="right">-0.32</td>
-<td align="right">-0.32</td>
-</tr>
-<tr class="odd">
-<td align="left">BC</td>
-<td align="right">-0.70</td>
-<td align="right">-0.70</td>
-<td align="right">-0.70</td>
-<td align="right">-0.70</td>
-<td align="right">-0.70</td>
-</tr>
-</tbody>
-</table>
 <div class="section level4">
 <h4 id="plots">Plots<a class="anchor" aria-label="anchor" href="#plots"></a>
 </h4>
@@ -1282,8 +894,6 @@ <h4 id="plots">Plots<a class="anchor" aria-label="anchor" href="#plots"></a>
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">BC</annotation></semantics></math>
 population. The log-odds ratio and log risk ratio plot are given
 below.</p>
-<p><img src="Binary_outcome_example_files/figure-html/forest-lor-1.png" width="768"></p>
-<p><img src="Binary_outcome_example_files/figure-html/forest-rr-1.png" width="768"></p>
 </div>
 </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
@@ -1293,11 +903,11 @@ <h4 id="plots">Plots<a class="anchor" aria-label="anchor" href="#plots"></a>
 
 
     <footer><div class="pkgdown-footer-left">
-  <p>Developed by Nathan Green, Chengyang Gao, Antonio Remiro-Azocar.</p>
+  <p>Developed by <a href="https://n8thangreen.github.io/" class="external-link">Nathan Green</a>, Chengyang Gao, Antonio Remiro-Azocar.</p>
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.3.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.2.0.</p>
 </div>
 
     </footer>
diff --git a/docs/articles/Binary_outcome_example.md b/docs/articles/Binary_outcome_example.md
index c11f4ae..00d900a 100644
--- a/docs/articles/Binary_outcome_example.md
+++ b/docs/articles/Binary_outcome_example.md
@@ -3,7 +3,7 @@
 ## Introduction
 
 This vignette will demonstrate the use of the
-[outstandR](https://StatisticsHealthEconomics.github.io/outstandR)
+[outstandR](https://StatisticsHealthEconomics.github.io/outstandR/)
 package to fit the range of types of models to simulated binary data.
 Related vignettes will provide equivalent analyses for continuous and
 count data.
@@ -27,7 +27,7 @@ library(tidyr)
 library(dplyr)
 library(MASS)
 library(outstandR)
-library(simcovariates)
+library(simcovariates)  # from GitHub
 ```
 
 ### Data
@@ -53,7 +53,7 @@ The simulation input parameters are given below.
 | `N` | Sample size | 200 |
 | `allocation` | Active treatment vs. placebo allocation ratio (2:1) | 2/3 |
 | `b_trt` | Conditional effect of active treatment vs. comparator (log(0.17)) | -1.77196 |
-| `b_X` | Conditional effect of each prognostic variable (-log(0.5)) | 0.69315 |
+| `b_PF` | Conditional effect of each prognostic variable (-log(0.5)) | 0.69315 |
 | `b_EM` | Conditional interaction effect of each effect modifier (-log(0.67)) | 0.40048 |
 | `meanX_AC[1]` | Mean of prognostic factor in AC trial | 0.45 |
 | `meanX_AC[2]` | Mean of prognostic factor in AC trial | 0.45 |
@@ -68,18 +68,14 @@ The simulation input parameters are given below.
 | `corX` | Covariate correlation coefficient | 0.2 |
 | `b_0` | Baseline intercept | -0.6 |
 
-We shall use the
-[`gen_data()`](https://rdrr.io/pkg/simcovariates/man/gen_data.html)
-function available with the
-[simcovariates](https://github.com/n8thangreen/simcovariates) package on
-GitHub.
+Translating to R code.
 
 ``` r
 
 N <- 200
 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1)
 b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator
-b_X <- -log(0.5)       # conditional effect of each prognostic variable
+b_PF <- -log(0.5)       # conditional effect of each prognostic variable
 b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier
 meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial
 meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC
@@ -89,6 +85,15 @@ sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and B
 sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate
 corX <- 0.2            # covariate correlation coefficient  
 b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value
+```
+
+We shall use the `gen_data()` function available with the
+[simcovariates](https://github.com/n8thangreen/simcovariates) package on
+GitHub. For this, we need to define a list of covariates with
+distribution `type` and relationship to the outcome `role` as either
+`prognostic`, `effect_modifier` or both.
+
+``` r
 
 covariate_defns_ipd <- list(
   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),
@@ -101,7 +106,7 @@ covariate_defns_ipd <- list(
                     role = "effect_modifier")
 )
 
-b_prognostic <- c(PF_cont_1 = b_X, PF_cont_2 = b_X)
+b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)
 
 b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)
 
@@ -139,6 +144,8 @@ the additional summarise step. We set different mean values `meanX_BC`
 and `meanX_EM_BC` but otherwise use the same parameter values as for the
 $`AC`$ trial.
 
+First, simulate the underlying IPD similarly for the AC trial.
+
 ``` r
 
 covariate_defns_ald <- list(
@@ -164,6 +171,14 @@ BC.IPD <- simcovariates::gen_data(
   family = binomial("logit"))
 
 BC.IPD$trt <- factor(BC.IPD$trt, labels = c("C", "B"))
+```
+
+Next, we aggregate these data. We
+[`summarise()`](https://dplyr.tidyverse.org/reference/summarise.html)
+the covariates, sample sizes and outcomes separately and then bind the
+results together.
+
+``` r
 
 # covariate summary statistics
 # assume same between treatments
@@ -206,8 +221,6 @@ summary.y <-
     names_to = "statistic",
     values_to = "value") %>%
   ungroup()
-#> `summarise()` has grouped output by 'variable'. You can override using the
-#> `.groups` argument.
 
 # sample sizes
 summary.N <- 
@@ -244,18 +257,11 @@ the following.
 - `trt`: Treatment label. Because we assume a common covariate
   distribution between treatment arms this is `NA`
 
-Our data look like the following.
+Our final data look like the following.
 
 ``` r
 
 head(ipd_trial)
-#>   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt y     true_eta
-#> 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C 0  0.582883524
-#> 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A 1 -1.476422106
-#> 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A 0  0.005184912
-#> 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C 1  0.520117172
-#> 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A 1 -1.760974264
-#> 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A 0 -2.139514435
 ```
 
 There are 4 correlated continuous covariates generated per subject,
@@ -266,25 +272,6 @@ is ‘anchored’ via *C*, the common treatment.
 ``` r
 
 ald_trial
-#> # A tibble: 16 × 4
-#>    variable  statistic   value trt  
-#>    <chr>     <chr>       <dbl> <chr>
-#>  1 EM_cont_1 mean        0.616 NA   
-#>  2 EM_cont_1 sd          0.408 NA   
-#>  3 EM_cont_2 mean        0.635 NA   
-#>  4 EM_cont_2 sd          0.354 NA   
-#>  5 PF_cont_1 mean        0.666 NA   
-#>  6 PF_cont_1 sd          0.398 NA   
-#>  7 PF_cont_2 mean        0.663 NA   
-#>  8 PF_cont_2 sd          0.404 NA   
-#>  9 y         mean        0.597 C    
-#> 10 y         sd          0.494 C    
-#> 11 y         sum        43     C    
-#> 12 y         mean        0.297 B    
-#> 13 y         sd          0.459 B    
-#> 14 y         sum        38     B    
-#> 15 NA        N          72     C    
-#> 16 NA        N         128     B
 ```
 
 In this case, we have 4 covariate mean and standard deviation values;
@@ -296,13 +283,13 @@ and the event total, average and sample size for each treatment *B* and
 The true logistic outcome model which we use to simulate the data is
 
 ``` math
-\text{logit}(p_{t}) = \beta_0 + \beta_X (X_3 + X_4) + [\beta_{t} + \beta_{EM} (X_1 + X_2)] \; \text{I}(t \neq C)
+\text{logit}(p_{t}) = \beta_0 + \beta_{PF} (X_3 + X_4) + [\beta_{t} + \beta_{EM} (X_1 + X_2)] \; \text{I}(t \neq C)
 ```
 
 $`\text{I}()`$ is an indicator function taking value 1 if true and 0
 otherwise. That is, for treatment $`C`$ the right hand side becomes
-$`\beta_0 + \beta_X (X_3 + X_4)`$ and for comparator treatments $`A`$ or
-$`B`$ there is an additional $`\beta_t + \beta_{EM} (X_1 + X_2)`$
+$`\beta_0 + \beta_{PF} (X_3 + X_4)`$ and for comparator treatments $`A`$
+or $`B`$ there is an additional $`\beta_t + \beta_{EM} (X_1 + X_2)`$
 component consisting of the effect modifier terms and the coefficient
 for the treatment parameter, $`\beta_t`$ (or `b_trt` in the R code),
 i.e. the log odds-ratio (LOR) for the logit model. Finally, $`p_{t}`$ is
@@ -332,7 +319,7 @@ outcome scales will be discussed below.
 
 ## Model fitting in R
 
-The [outstandR](https://StatisticsHealthEconomics.github.io/outstandR)
+The [outstandR](https://StatisticsHealthEconomics.github.io/outstandR/)
 package has been written to be easy to use and essentially consists of a
 single function,
 [`outstandR()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.md).
@@ -366,7 +353,10 @@ appears as a linear regression. This corresponds to the following `R`
 
 ``` r
 
-lin_form <- as.formula("y ~ PF_cont_1 + PF_cont_2 + trt + trt:EM_cont_1 + trt:EM_cont_2")
+lin_form <- list(
+  outcome_model = as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"),
+  balance_model = as.formula("~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2")
+)
 ```
 
 Note that the more succinct formula
@@ -420,36 +410,6 @@ The returned object is of class `outstandR`.
 ``` r
 
 str(outstandR_maic)
-#> List of 2
-#>  $ contrasts:List of 3
-#>   ..$ means    :List of 3
-#>   .. ..$ AB: num 0.607
-#>   .. ..$ AC: num -0.649
-#>   .. ..$ BC: num -1.26
-#>   ..$ variances:List of 3
-#>   .. ..$ AB: num 0.233
-#>   .. ..$ AC: num 0.137
-#>   .. ..$ BC: num 0.0952
-#>   ..$ CI       :List of 3
-#>   .. ..$ AB: num [1:2] -0.338 1.552
-#>   .. ..$ AC: num [1:2] -1.3757 0.0776
-#>   .. ..$ BC: num [1:2] -1.861 -0.652
-#>  $ absolute :List of 2
-#>   ..$ means    :List of 2
-#>   .. ..$ A: Named num 0.341
-#>   .. .. ..- attr(*, "names")= chr "mean_A"
-#>   .. ..$ C: Named num 0.495
-#>   .. .. ..- attr(*, "names")= chr "mean_C"
-#>   ..$ variances:List of 2
-#>   .. ..$ A: Named num 0.00271
-#>   .. .. ..- attr(*, "names")= chr "mean_A"
-#>   .. ..$ C: Named num 0.00518
-#>   .. .. ..- attr(*, "names")= chr "mean_C"
-#>  - attr(*, "CI")= num 0.95
-#>  - attr(*, "ref_trt")= chr "C"
-#>  - attr(*, "scale")= chr "log_odds"
-#>  - attr(*, "model")= chr "binomial"
-#>  - attr(*, "class")= chr [1:2] "outstandR" "list"
 ```
 
 We see that this is a list object with 2 parts. The first contains
@@ -465,30 +425,6 @@ human-readable output
 ``` r
 
 outstandR_maic
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_odds 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.607    0.233      -0.338     1.55  
-#> 2 AC           -0.649    0.137      -1.38      0.0776
-#> 3 BC           -1.26     0.0952     -1.86     -0.652 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.341   0.00271 NA         NA        
-#> 2 C             0.495   0.00518 NA         NA
 ```
 
 #### Outcome scale
@@ -558,125 +494,8 @@ outstandR_maic_lrr <-
 ``` r
 
 outstandR_maic_lrr
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.307    0.0793     -0.244     0.859 
-#> 2 AC           -0.392    0.0514     -0.836     0.0527
-#> 3 BC           -0.699    0.0279     -1.03     -0.372 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.339   0.00258 NA         NA        
-#> 2 C             0.501   0.00537 NA         NA
 ```
 
-### Simulated treatment comparison (STC)
-
-Simulated treatment comparison (STC) is the conventional outcome
-regression method. It involves fitting a regression model of outcome on
-treatment and covariates to the IPD anad then ‘plugging-in’ mean
-covariate values from the aggregate data study.
-
-We can simply pass the same formula as before to the modified call with
-[`strategy_stc()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.md).
-
-``` r
-
-outstandR_stc <-
-  outstandR(ipd_trial, ald_trial,
-            strategy = strategy_stc(
-              formula = lin_form,
-              family = binomial(link = "logit")))
-```
-
-``` r
-
-outstandR_stc
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_odds 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB           0.0584   NA           NA        NA    
-#> 2 AC          -1.20     NA           NA        NA    
-#> 3 BC          -1.26      0.0952      -1.86     -0.652
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.137        NA NA         NA        
-#> 2 C             0.344        NA NA         NA
-```
-
-Changing the outcome scale to LRR gives
-
-``` r
-
-outstandR_stc_lrr <-
-  outstandR(ipd_trial, ald_trial,
-            strategy = strategy_stc(
-              formula = lin_form,
-              family = binomial(link = "logit")),
-            scale = "log_relative_risk")
-```
-
-``` r
-
-outstandR_stc_lrr
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB           -0.224   NA           NA        NA    
-#> 2 AC           -0.923   NA           NA        NA    
-#> 3 BC           -0.699    0.0279      -1.03     -0.372
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.137        NA NA         NA        
-#> 2 C             0.344        NA NA         NA
-```
-
-The following approaches follow naturally from the simple ‘plug-in’
-version of STC. We will perform G-computation firstly with a frequentist
-MLE and then a Bayesian approach.
-
 ### Parametric G-computation with maximum-likelihood estimation
 
 G-computation marginalizes the conditional estimates by separating the
@@ -686,7 +505,7 @@ outcome $`y`$ on the covariates $`x`$ and treatment $`z`$ is fitted to
 the *AC* IPD:
 
 ``` math
-g(\mu_n) = \beta_0 + \boldsymbol{x}_n \boldsymbol{\beta_X} + (\beta_z + \boldsymbol{x_n^{EM}} \boldsymbol{\beta_{EM}}) \; \mbox{I}(t \neq C)
+g(\mu_n) = \beta_0 + \boldsymbol{x}_n \boldsymbol{\beta_{PF}} + (\beta_z + \boldsymbol{x_n^{EM}} \boldsymbol{\beta_{EM}}) \; \mbox{I}(t \neq C)
 ```
 
 In the context of G-computation, this regression model is often called
@@ -722,30 +541,6 @@ outstandR_gcomp_ml <-
 ``` r
 
 outstandR_gcomp_ml
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_odds 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.602    0.232      -0.342     1.55  
-#> 2 AC           -0.654    0.137      -1.38      0.0714
-#> 3 BC           -1.26     0.0952     -1.86     -0.652 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.411   0.00291 NA         NA        
-#> 2 C             0.570   0.00563 NA         NA
 ```
 
 Once again, let us change the outcome scale to LRR
@@ -763,30 +558,6 @@ outstandR_gcomp_ml_lrr <-
 ``` r
 
 outstandR_gcomp_ml_lrr
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.377    0.0602     -0.104     0.858 
-#> 2 AC           -0.322    0.0323     -0.674     0.0307
-#> 3 BC           -0.699    0.0279     -1.03     -0.372 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.409   0.00276 NA         NA        
-#> 2 C             0.563   0.00504 NA         NA
 ```
 
 ### Bayesian G-computation with MCMC
@@ -837,30 +608,6 @@ outstandR_gcomp_bayes <-
 ``` r
 
 outstandR_gcomp_bayes
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_odds 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.612    0.228      -0.325     1.55  
-#> 2 AC           -0.644    0.133      -1.36      0.0713
-#> 3 BC           -1.26     0.0952     -1.86     -0.652 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.411   0.00288 NA         NA        
-#> 2 C             0.568   0.00521 NA         NA
 ```
 
 As before, we can change the outcome scale to LRR.
@@ -878,30 +625,6 @@ outstandR_gcomp_bayes_lrr <-
 ``` r
 
 outstandR_gcomp_bayes_lrr
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.375    0.0607     -0.108     0.858 
-#> 2 AC           -0.324    0.0328     -0.679     0.0308
-#> 3 BC           -0.699    0.0279     -1.03     -0.372 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.411   0.00288 NA         NA        
-#> 2 C             0.568   0.00521 NA         NA
 ```
 
 ### Multiple imputation marginalisation
@@ -936,30 +659,6 @@ outstandR_mim <-
 ``` r
 
 outstandR_mim
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_odds 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.612    0.216      -0.299     1.52  
-#> 2 AC           -0.644    0.121      -1.33      0.0386
-#> 3 BC           -1.26     0.0952     -1.86     -0.652 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>     
-#> 1 A          NA       NA        NA         NA        
-#> 2 C          NA       NA        NA         NA
 ```
 
 Change the outcome scale again for LRR,
@@ -977,30 +676,6 @@ outstandR_mim_lrr <-
 ``` r
 
 outstandR_mim_lrr
-#> Object of class 'outstandR' 
-#> Model: binomial 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.375    0.0516    -0.0704     0.820 
-#> 2 AC           -0.324    0.0237    -0.626     -0.0227
-#> 3 BC           -0.699    0.0279    -1.03      -0.372 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>     
-#> 1 A          NA       NA        NA         NA        
-#> 2 C          NA       NA        NA         NA
 ```
 
 ## Model comparison
@@ -1067,6 +742,16 @@ var.d.BC <- with(ald_out, 1/sum_B + 1/(N_B - sum_B) + 1/sum_C + 1/(N_C - sum_C))
 var.d.AB.naive <- d_AC_naive$var_AC + var.d.BC
 ```
 
+Alternatively, we can compute this using `outstandR`’s built-in
+[`calc_bucher_naive()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.md)
+function:
+
+``` r
+
+naive_results <- calc_bucher_naive(ipd_trial, ald_trial, outcome_model = lin_form, family = binomial(link = "logit"))
+naive_results
+```
+
 Of course, the $`BC`$ contrast is calculated directly.
 
 ## Results
@@ -1075,12 +760,6 @@ We now combine all outputs and present in plots and tables. For a
 log-odds ratio a table of all contrasts and methods in the $`BC`$
 population is given below.
 
-|     | d_true | d_naive |  MAIC |   STC | Gcomp.ML | Gcomp.Bayes |   MIM |
-|:----|-------:|--------:|------:|------:|---------:|------------:|------:|
-| AB  |   0.00 |    0.30 |  0.61 |  0.06 |     0.60 |        0.61 |  0.61 |
-| AC  |  -1.28 |   -0.95 | -0.65 | -1.20 |    -0.65 |       -0.64 | -0.64 |
-| BC  |  -1.26 |   -1.26 | -1.26 | -1.26 |    -1.26 |       -1.26 | -1.26 |
-
 We can see that the different corresponds reasonably well with one
 another.
 
@@ -1096,19 +775,9 @@ d_AC_true_lrr
 
 so that the summary table is
 
-|     |  MAIC |   STC | Gcomp.ML | Gcomp.Bayes |   MIM |
-|:----|------:|------:|---------:|------------:|------:|
-| AB  |  0.31 | -0.22 |     0.38 |        0.37 |  0.37 |
-| AC  | -0.39 | -0.92 |    -0.32 |       -0.32 | -0.32 |
-| BC  | -0.70 | -0.70 |    -0.70 |       -0.70 | -0.70 |
-
 #### Plots
 
 The same output can be presented in forest plots is as follows. Each
 horizontal bar represent a different method and the facets group these
 by treatment comparison for the $`BC`$ population. The log-odds ratio
 and log risk ratio plot are given below.
-
-![](Binary_outcome_example_files/figure-html/forest-lor-1.png)
-
-![](Binary_outcome_example_files/figure-html/forest-rr-1.png)
diff --git a/docs/articles/Continuous_outcome_example.html b/docs/articles/Continuous_outcome_example.html
index 5eb0d56..7411133 100644
--- a/docs/articles/Continuous_outcome_example.html
+++ b/docs/articles/Continuous_outcome_example.html
@@ -1,11 +1,16 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Continuous data example • outstandR</title>
+<!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png">
+<link rel="icon" type="”image/svg+xml”" href="../favicon.svg">
+<link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png">
+<link rel="icon" sizes="any" href="../favicon.ico">
+<link rel="manifest" href="../site.webmanifest">
 <script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
@@ -16,11 +21,11 @@
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
-    <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="light" aria-label="Site navigation"><div class="container">
+    <nav class="navbar navbar-expand-lg fixed-top bg-primary" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
 
     <a class="navbar-brand me-2" href="../index.html">outstandR</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.0.0.9000</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -29,9 +34,10 @@
 
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto">
-<li class="nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
+<li class="nav-item"><a class="nav-link" href="../index.html">Home</a></li>
+<li class="nav-item"><a class="nav-link" href="../reference/index.html">Functions</a></li>
 <li class="active nav-item"><a class="nav-link" href="../articles/index.html">Articles</a></li>
-<li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
+<li class="nav-item"><a class="nav-link" href="../news/index.html">News</a></li>
       </ul>
 <ul class="navbar-nav">
 <li class="nav-item"><form class="form-inline" role="search">
@@ -50,8 +56,7 @@
 
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
-
-      <h1>Continuous data example</h1>
+      <img src="../logo.png" class="logo" alt=""><h1>Continuous data example</h1>
             
       
       <small class="dont-index">Source: <a href="https://github.com/StatisticsHealthEconomics/outstandR/blob/HEAD/vignettes/Continuous_outcome_example.Rmd" class="external-link"><code>vignettes/Continuous_outcome_example.Rmd</code></a></small>
@@ -66,11 +71,10 @@ <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#i
 <p>This is the vignette for performing population adjustment methods
 with continuous data, in order to compare marginal treatment effects
 when there are cross-trial differences in effect modifiers and limited
-patient-level data. We will demonstrate how to apply MAIC, STC,
-G-computation with ML, G-computation with Bayesian inference and
-multiple imputation marginalisation. The document structure follow the
-binary data example vignette which should be referred to for more
-details.</p>
+patient-level data. We will demonstrate how to apply MAIC, G-computation
+with ML, G-computation with Bayesian inference and multiple imputation
+marginalisation. The document structure follow the binary data example
+vignette which should be referred to for more details.</p>
 </div>
 <div class="section level2">
 <h2 id="example-analysis">Example analysis<a class="anchor" aria-label="anchor" href="#example-analysis"></a>
@@ -89,24 +93,18 @@ <h2 id="example-analysis">Example analysis<a class="anchor" aria-label="anchor"
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://tidyr.tidyverse.org" class="external-link">tidyr</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://dplyr.tidyverse.org" class="external-link">dplyr</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="http://www.stats.ox.ac.uk/pub/MASS4/" class="external-link">MASS</a></span><span class="op">)</span></span>
-<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://StatisticsHealthEconomics.github.io/outstandR">outstandR</a></span><span class="op">)</span></span>
+<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://StatisticsHealthEconomics.github.io/outstandR/">outstandR</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">simcovariates</span><span class="op">)</span></span></code></pre></div>
 <div class="section level3">
 <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 </h3>
 <p>We first simulate both the IPD and ALD data. See the binary data
-example vignette for more details on how this is implemented. The
-difference with that example is that we change the <code>family</code>
-argument in <code><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data()</a></code> to
-<code>gaussian(link = "identity")</code>, corresponding to the
-continuous data case. The <code><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data()</a></code> function is available
-in the <a href="https://github.com/n8thangreen/simcovariates" class="external-link">simcovariates</a>
-package on GitHub.</p>
+example vignette for more details on how this is implemented.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">N</span> <span class="op">&lt;-</span> <span class="fl">200</span></span>
 <span><span class="va">allocation</span> <span class="op">&lt;-</span> <span class="fl">2</span><span class="op">/</span><span class="fl">3</span>      <span class="co"># active treatment vs. placebo allocation ratio (2:1)</span></span>
 <span><span class="va">b_trt</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.17</span><span class="op">)</span>     <span class="co"># conditional effect of active treatment vs. common comparator</span></span>
-<span><span class="va">b_X</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.5</span><span class="op">)</span>       <span class="co"># conditional effect of each prognostic variable</span></span>
+<span><span class="va">b_PF</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.5</span><span class="op">)</span>      <span class="co"># conditional effect of each prognostic variable</span></span>
 <span><span class="va">b_EM</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.67</span><span class="op">)</span>     <span class="co"># conditional interaction effect of each effect modifier</span></span>
 <span><span class="va">meanX_AC</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.45</span>, <span class="fl">0.45</span><span class="op">)</span>       <span class="co"># mean of normally-distributed covariate in AC trial</span></span>
 <span><span class="va">meanX_BC</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.6</span>, <span class="fl">0.6</span><span class="op">)</span>         <span class="co"># mean of each normally-distributed covariate in BC</span></span>
@@ -115,20 +113,26 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span><span class="va">sdX</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.4</span>, <span class="fl">0.4</span><span class="op">)</span>     <span class="co"># standard deviation of each covariate (same for AC and BC)</span></span>
 <span><span class="va">sdX_EM</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.4</span>, <span class="fl">0.4</span><span class="op">)</span>  <span class="co"># standard deviation of each EM covariate</span></span>
 <span><span class="va">corX</span> <span class="op">&lt;-</span> <span class="fl">0.2</span>            <span class="co"># covariate correlation coefficient  </span></span>
-<span><span class="va">b_0</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fl">0.6</span>            <span class="co"># baseline intercept coefficient  ##TODO: fixed value</span></span>
-<span></span>
-<span><span class="va">covariate_defns_ipd</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
-<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span><span class="va">b_0</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fl">0.6</span>            <span class="co"># baseline intercept coefficient  ##TODO: fixed value</span></span></code></pre></div>
+<p>The difference with that example is that we change the
+<code>family</code> argument in <code>gen_data()</code> to
+<code>gaussian(link = "identity")</code>, corresponding to the
+continuous data case. The <code>gen_data()</code> function is available
+in the <a href="https://github.com/n8thangreen/simcovariates" class="external-link">simcovariates</a>
+package on GitHub.</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">covariate_defns_ipd</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
+<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span>,</span>
-<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span></span>
 <span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">b_prognostic</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>PF_cont_1 <span class="op">=</span> <span class="va">b_X</span>, PF_cont_2 <span class="op">=</span> <span class="va">b_X</span><span class="op">)</span></span>
+<span><span class="va">b_prognostic</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>PF_cont_1 <span class="op">=</span> <span class="va">b_PF</span>, PF_cont_2 <span class="op">=</span> <span class="va">b_PF</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">b_effect_modifier</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>EM_cont_1 <span class="op">=</span> <span class="va">b_EM</span>, EM_cont_2 <span class="op">=</span> <span class="va">b_EM</span><span class="op">)</span></span>
 <span></span>
@@ -139,7 +143,7 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">cor_matrix</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"PF_cont_1"</span>, <span class="st">"PF_cont_2"</span>, <span class="st">"EM_cont_1"</span>, <span class="st">"EM_cont_2"</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">colnames</a></span><span class="op">(</span><span class="va">cor_matrix</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"PF_cont_1"</span>, <span class="st">"PF_cont_2"</span>, <span class="st">"EM_cont_1"</span>, <span class="st">"EM_cont_2"</span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">ipd_trial</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data</a></span><span class="op">(</span></span>
+<span><span class="va">ipd_trial</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu">gen_data</span><span class="op">(</span></span>
 <span>  N <span class="op">=</span> <span class="va">N</span>,</span>
 <span>  b_0 <span class="op">=</span> <span class="va">b_0</span>,</span>
 <span>  b_trt <span class="op">=</span> <span class="va">b_trt</span>,</span>
@@ -191,54 +195,28 @@ <h4 id="ald_trial-aggregate-level-data">
 </li>
 </ul>
 <p>Our data look like the following.</p>
-<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">ipd_trial</span><span class="op">)</span></span>
-<span><span class="co">#&gt;   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt          y     true_eta</span></span>
-<span><span class="co">#&gt; 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C  1.9634929  0.582883524</span></span>
-<span><span class="co">#&gt; 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A  0.1985888 -1.476422106</span></span>
-<span><span class="co">#&gt; 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A  1.1820915  0.005184912</span></span>
-<span><span class="co">#&gt; 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C  0.3712188  0.520117172</span></span>
-<span><span class="co">#&gt; 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A -1.9387976 -1.760974264</span></span>
-<span><span class="co">#&gt; 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A -1.3363926 -2.139514435</span></span></code></pre></div>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">ipd_trial</span><span class="op">)</span></span></code></pre></div>
 <p>There are 4 correlated continuous covariates generated per subject,
 simulated from a multivariate normal distribution. Treatment
 <code>trt</code> takes either new treatment <em>A</em> or standard of
 care / status quo <em>C</em>. The ITC is ‘anchored’ via <em>C</em>, the
 common treatment.</p>
-<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">ald_trial</span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 16 × 4</span></span></span>
-<span><span class="co">#&gt;    variable  statistic    value trt  </span></span>
-<span><span class="co">#&gt;    <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>        <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 1</span> EM_cont_1 mean         0.618 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 2</span> EM_cont_1 sd           0.406 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 3</span> EM_cont_2 mean         0.649 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 4</span> EM_cont_2 sd           0.376 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 5</span> PF_cont_1 mean         0.662 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 6</span> PF_cont_1 sd           0.370 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 7</span> PF_cont_2 mean         0.623 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 8</span> PF_cont_2 sd           0.389 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 9</span> y         mean         0.437 C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">10</span> y         sd           1.13  C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">11</span> y         sum         28.0   C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">12</span> y         mean        -<span style="color: #BB0000;">1.04</span>  B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">13</span> y         sd           1.16  B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">14</span> y         sum       -<span style="color: #BB0000;">142.</span>    B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">15</span> <span style="color: #BB0000;">NA</span>        N           64     C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">16</span> <span style="color: #BB0000;">NA</span>        N          136     B</span></span></code></pre></div>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">ald_trial</span></span></code></pre></div>
 <p>In this case, we have 4 covariate mean and standard deviation values;
 and the total, average and sample size for each treatment <em>B</em> and
 <em>C</em>.</p>
-<p>In the following we will implement for MAIC, STC, and G-computation
-methods to obtain the <em>marginal variance</em> and the <em>marginal
-treatment effect</em>.</p>
+<p>In the following we will implement for MAIC and G-computation methods
+to obtain the <em>marginal variance</em> and the <em>marginal treatment
+effect</em>.</p>
 </div>
 </div>
 </div>
 <div class="section level2">
 <h2 id="model-fitting-in-r">Model fitting in R<a class="anchor" aria-label="anchor" href="#model-fitting-in-r"></a>
 </h2>
-<p>The <a href="https://StatisticsHealthEconomics.github.io/outstandR">outstandR</a> package has been written to be easy to
+<p>The <a href="https://StatisticsHealthEconomics.github.io/outstandR/">outstandR</a> package has been written to be easy to
 use and essential consists of a single function,
 <code><a href="../reference/outstandR.html">outstandR()</a></code>. This can be used to run all of the different
 types of model, which we will call <em>strategies</em>. The first two
@@ -251,126 +229,26 @@ <h2 id="model-fitting-in-r">Model fitting in R<a class="anchor" aria-label="anch
 example is provided below.</p>
 <p>The formula used in this model, passed as an argument to the strategy
 function is</p>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">lin_form</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">lin_form</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
+<span>  outcome_model <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"</span><span class="op">)</span>,</span>
+<span>  balance_model <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2"</span><span class="op">)</span></span>
+<span><span class="op">)</span></span></code></pre></div>
 <div class="section level3">
 <h3 id="maic">MAIC<a class="anchor" aria-label="anchor" href="#maic"></a>
 </h3>
 <p>As mentioned above, pass the model specific strategy function to the
 main <code><a href="../reference/outstandR.html">outstandR()</a></code> function, in this case use
 <code><a href="../reference/strategy.html">strategy_maic()</a></code>.</p>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_maic</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_maic</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">gaussian</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"identity"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p>The returned object is of class <code>outstandR</code>.</p>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_maic</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">gaussian</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">mean_difference</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.199    0.079<span style="text-decoration: underline;">8</span>     -<span style="color: #BB0000;">0.354</span>      0.753</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">1.28</span>     0.049<span style="text-decoration: underline;">7</span>     -<span style="color: #BB0000;">1.72</span>      -<span style="color: #BB0000;">0.845</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.48</span>     0.030<span style="text-decoration: underline;">1</span>     -<span style="color: #BB0000;">1.82</span>      -<span style="color: #BB0000;">1.14</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A            -<span style="color: #BB0000;">1.14</span>     0.017<span style="text-decoration: underline;">4</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.139    0.030<span style="text-decoration: underline;">3</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
-</div>
-<div class="section level3">
-<h3 id="simulated-treatment-comparison-stc">Simulated Treatment Comparison (STC)<a class="anchor" aria-label="anchor" href="#simulated-treatment-comparison-stc"></a>
-</h3>
-<p>STC is the conventional outcome regression method. It involves
-fitting a regression model of outcome on treatment and covariates to the
-IPD. Simply pass the same as formula as before with the
-<code><a href="../reference/strategy.html">strategy_stc()</a></code> strategy function.</p>
 <div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_stc</span> <span class="op">&lt;-</span></span>
-<span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
-<span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_stc</a></span><span class="op">(</span></span>
-<span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
-<span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">gaussian</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"identity"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
-<span><span class="va">outstandR_stc</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">gaussian</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">mean_difference</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB           <span style="color: #BB0000;">NaN</span>      <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           <span style="color: #BB0000;">NaN</span>      <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC            -<span style="color: #BB0000;">1.48</span>    0.030<span style="text-decoration: underline;">1</span>      -<span style="color: #BB0000;">1.82</span>      -<span style="color: #BB0000;">1.14</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A            <span style="color: #BB0000;">NaN</span>           <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             -<span style="color: #BB0000;">1.57</span>        <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
-</div>
-<div class="section level3">
-<h3 id="parametric-g-computation-with-maximum-likelihood-estimation">Parametric G-computation with maximum-likelihood estimation<a class="anchor" aria-label="anchor" href="#parametric-g-computation-with-maximum-likelihood-estimation"></a>
-</h3>
-<p>G-computation marginalizes the conditional estimates by separating
-the regression modelling from the estimation of the marginal treatment
-effect for <em>A</em> versus <em>C</em>. Pass the
-<code><a href="../reference/strategy.html">strategy_gcomp_ml()</a></code> strategy function.</p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_gcomp_ml</span> <span class="op">&lt;-</span></span>
-<span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
-<span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_gcomp_ml</a></span><span class="op">(</span></span>
-<span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
-<span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">gaussian</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"identity"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
-<span></span>
-<span><span class="va">outstandR_gcomp_ml</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">gaussian</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">mean_difference</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.314    0.069<span style="text-decoration: underline;">3</span>     -<span style="color: #BB0000;">0.202</span>      0.830</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">1.17</span>     0.039<span style="text-decoration: underline;">2</span>     -<span style="color: #BB0000;">1.56</span>      -<span style="color: #BB0000;">0.779</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.48</span>     0.030<span style="text-decoration: underline;">1</span>     -<span style="color: #BB0000;">1.82</span>      -<span style="color: #BB0000;">1.14</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A            -<span style="color: #BB0000;">0.889</span>    0.013<span style="text-decoration: underline;">4</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.278    0.029<span style="text-decoration: underline;">6</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">outstandR_maic</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="bayesian-g-computation-with-mcmc">Bayesian G-computation with MCMC<a class="anchor" aria-label="anchor" href="#bayesian-g-computation-with-mcmc"></a>
@@ -382,38 +260,14 @@ <h3 id="bayesian-g-computation-with-mcmc">Bayesian G-computation with MCMC<a cla
 nuisance parameters of the outcome regression, as well as the joint
 covariate distribution.</p>
 <p>Pass the <code><a href="../reference/strategy.html">strategy_gcomp_bayes()</a></code> strategy function.</p>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_gcomp_bayes</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">gaussian</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"identity"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">gaussian</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">mean_difference</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.311    0.076<span style="text-decoration: underline;">0</span>     -<span style="color: #BB0000;">0.229</span>      0.852</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">1.17</span>     0.045<span style="text-decoration: underline;">9</span>     -<span style="color: #BB0000;">1.59</span>      -<span style="color: #BB0000;">0.750</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.48</span>     0.030<span style="text-decoration: underline;">1</span>     -<span style="color: #BB0000;">1.82</span>      -<span style="color: #BB0000;">1.14</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A            -<span style="color: #BB0000;">0.888</span>    0.016<span style="text-decoration: underline;">5</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.282    0.030<span style="text-decoration: underline;">5</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="multiple-imputation-marginalisation">Multiple imputation marginalisation<a class="anchor" aria-label="anchor" href="#multiple-imputation-marginalisation"></a>
@@ -421,81 +275,20 @@ <h3 id="multiple-imputation-marginalisation">Multiple imputation marginalisation
 <p>Finally, the strategy function to pass to <code><a href="../reference/outstandR.html">outstandR()</a></code>
 for multiple imputation marginalisation is
 <code><a href="../reference/strategy.html">strategy_mim()</a></code>,</p>
-<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_mim</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_mim</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">gaussian</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"identity"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_mim</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">gaussian</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">mean_difference</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB            0.312    0.072<span style="text-decoration: underline;">4</span>     -<span style="color: #BB0000;">0.215</span>      0.839</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC           -<span style="color: #BB0000;">1.17</span>     0.042<span style="text-decoration: underline;">3</span>     -<span style="color: #BB0000;">1.57</span>      -<span style="color: #BB0000;">0.766</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">1.48</span>     0.030<span style="text-decoration: underline;">1</span>     -<span style="color: #BB0000;">1.82</span>      -<span style="color: #BB0000;">1.14</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_mim</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="model-comparison">Model comparison<a class="anchor" aria-label="anchor" href="#model-comparison"></a>
 </h3>
 <p>Combine all outputs for relative effects table of all contrasts and
 methods.</p>
-<table class="table">
-<thead><tr class="header">
-<th align="left"></th>
-<th align="right">MAIC</th>
-<th align="right">STC</th>
-<th align="right">Gcomp.ML</th>
-<th align="right">Gcomp.Bayes</th>
-<th align="right">MIM</th>
-</tr></thead>
-<tbody>
-<tr class="odd">
-<td align="left">AB</td>
-<td align="right">0.20</td>
-<td align="right">NaN</td>
-<td align="right">0.31</td>
-<td align="right">0.31</td>
-<td align="right">0.31</td>
-</tr>
-<tr class="even">
-<td align="left">AC</td>
-<td align="right">-1.28</td>
-<td align="right">NaN</td>
-<td align="right">-1.17</td>
-<td align="right">-1.17</td>
-<td align="right">-1.17</td>
-</tr>
-<tr class="odd">
-<td align="left">BC</td>
-<td align="right">-1.48</td>
-<td align="right">-1.48</td>
-<td align="right">-1.48</td>
-<td align="right">-1.48</td>
-<td align="right">-1.48</td>
-</tr>
-</tbody>
-</table>
-<p><img src="Continuous_outcome_example_files/figure-html/forest-res-1.png" width="768"></p>
 </div>
 </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
@@ -505,11 +298,11 @@ <h3 id="model-comparison">Model comparison<a class="anchor" aria-label="anchor"
 
 
     <footer><div class="pkgdown-footer-left">
-  <p>Developed by Nathan Green, Chengyang Gao, Antonio Remiro-Azocar.</p>
+  <p>Developed by <a href="https://n8thangreen.github.io/" class="external-link">Nathan Green</a>, Chengyang Gao, Antonio Remiro-Azocar.</p>
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.3.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.2.0.</p>
 </div>
 
     </footer>
diff --git a/docs/articles/Continuous_outcome_example.md b/docs/articles/Continuous_outcome_example.md
index 929d66e..c2e9db2 100644
--- a/docs/articles/Continuous_outcome_example.md
+++ b/docs/articles/Continuous_outcome_example.md
@@ -5,11 +5,10 @@
 This is the vignette for performing population adjustment methods with
 continuous data, in order to compare marginal treatment effects when
 there are cross-trial differences in effect modifiers and limited
-patient-level data. We will demonstrate how to apply MAIC, STC,
-G-computation with ML, G-computation with Bayesian inference and
-multiple imputation marginalisation. The document structure follow the
-binary data example vignette which should be referred to for more
-details.
+patient-level data. We will demonstrate how to apply MAIC, G-computation
+with ML, G-computation with Bayesian inference and multiple imputation
+marginalisation. The document structure follow the binary data example
+vignette which should be referred to for more details.
 
 ## Example analysis
 
@@ -36,22 +35,14 @@ library(simcovariates)
 ### Data
 
 We first simulate both the IPD and ALD data. See the binary data example
-vignette for more details on how this is implemented. The difference
-with that example is that we change the `family` argument in
-[`gen_data()`](https://rdrr.io/pkg/simcovariates/man/gen_data.html) to
-`gaussian(link = "identity")`, corresponding to the continuous data
-case. The
-[`gen_data()`](https://rdrr.io/pkg/simcovariates/man/gen_data.html)
-function is available in the
-[simcovariates](https://github.com/n8thangreen/simcovariates) package on
-GitHub.
+vignette for more details on how this is implemented.
 
 ``` r
 
 N <- 200
 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1)
 b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator
-b_X <- -log(0.5)       # conditional effect of each prognostic variable
+b_PF <- -log(0.5)      # conditional effect of each prognostic variable
 b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier
 meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial
 meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC
@@ -61,6 +52,15 @@ sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and B
 sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate
 corX <- 0.2            # covariate correlation coefficient  
 b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value
+```
+
+The difference with that example is that we change the `family` argument
+in `gen_data()` to `gaussian(link = "identity")`, corresponding to the
+continuous data case. The `gen_data()` function is available in the
+[simcovariates](https://github.com/n8thangreen/simcovariates) package on
+GitHub.
+
+``` r
 
 covariate_defns_ipd <- list(
   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),
@@ -73,7 +73,7 @@ covariate_defns_ipd <- list(
                     role = "effect_modifier")
 )
 
-b_prognostic <- c(PF_cont_1 = b_X, PF_cont_2 = b_X)
+b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)
 
 b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)
 
@@ -126,13 +126,6 @@ Our data look like the following.
 ``` r
 
 head(ipd_trial)
-#>   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt          y     true_eta
-#> 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C  1.9634929  0.582883524
-#> 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A  0.1985888 -1.476422106
-#> 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A  1.1820915  0.005184912
-#> 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C  0.3712188  0.520117172
-#> 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A -1.9387976 -1.760974264
-#> 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A -1.3363926 -2.139514435
 ```
 
 There are 4 correlated continuous covariates generated per subject,
@@ -143,37 +136,17 @@ is ‘anchored’ via *C*, the common treatment.
 ``` r
 
 ald_trial
-#> # A tibble: 16 × 4
-#>    variable  statistic    value trt  
-#>    <chr>     <chr>        <dbl> <chr>
-#>  1 EM_cont_1 mean         0.618 NA   
-#>  2 EM_cont_1 sd           0.406 NA   
-#>  3 EM_cont_2 mean         0.649 NA   
-#>  4 EM_cont_2 sd           0.376 NA   
-#>  5 PF_cont_1 mean         0.662 NA   
-#>  6 PF_cont_1 sd           0.370 NA   
-#>  7 PF_cont_2 mean         0.623 NA   
-#>  8 PF_cont_2 sd           0.389 NA   
-#>  9 y         mean         0.437 C    
-#> 10 y         sd           1.13  C    
-#> 11 y         sum         28.0   C    
-#> 12 y         mean        -1.04  B    
-#> 13 y         sd           1.16  B    
-#> 14 y         sum       -142.    B    
-#> 15 NA        N           64     C    
-#> 16 NA        N          136     B
 ```
 
 In this case, we have 4 covariate mean and standard deviation values;
 and the total, average and sample size for each treatment *B* and *C*.
 
-In the following we will implement for MAIC, STC, and G-computation
-methods to obtain the *marginal variance* and the *marginal treatment
-effect*.
+In the following we will implement for MAIC and G-computation methods to
+obtain the *marginal variance* and the *marginal treatment effect*.
 
 ## Model fitting in R
 
-The [outstandR](https://StatisticsHealthEconomics.github.io/outstandR)
+The [outstandR](https://StatisticsHealthEconomics.github.io/outstandR/)
 package has been written to be easy to use and essential consists of a
 single function,
 [`outstandR()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.md).
@@ -193,7 +166,10 @@ function is
 
 ``` r
 
-lin_form <- as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2")
+lin_form <- list(
+  outcome_model = as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"),
+  balance_model = as.formula("~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2")
+)
 ```
 
 ### MAIC
@@ -218,115 +194,6 @@ The returned object is of class `outstandR`.
 ``` r
 
 outstandR_maic
-#> Object of class 'outstandR' 
-#> Model: gaussian 
-#> Scale: mean_difference 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.199    0.0798     -0.354      0.753
-#> 2 AC           -1.28     0.0497     -1.72      -0.845
-#> 3 BC           -1.48     0.0301     -1.82      -1.14 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A            -1.14     0.0174 NA         NA        
-#> 2 C             0.139    0.0303 NA         NA
-```
-
-### Simulated Treatment Comparison (STC)
-
-STC is the conventional outcome regression method. It involves fitting a
-regression model of outcome on treatment and covariates to the IPD.
-Simply pass the same as formula as before with the
-[`strategy_stc()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.md)
-strategy function.
-
-``` r
-
-outstandR_stc <-
-  outstandR(ipd_trial, ald_trial,
-            strategy = strategy_stc(
-              formula = lin_form,
-              family = gaussian(link = "identity")))
-outstandR_stc
-#> Object of class 'outstandR' 
-#> Model: gaussian 
-#> Scale: mean_difference 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB           NaN      NA           NA         NA   
-#> 2 AC           NaN      NA           NA         NA   
-#> 3 BC            -1.48    0.0301      -1.82      -1.14
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A            NaN           NA NA         NA        
-#> 2 C             -1.57        NA NA         NA
-```
-
-### Parametric G-computation with maximum-likelihood estimation
-
-G-computation marginalizes the conditional estimates by separating the
-regression modelling from the estimation of the marginal treatment
-effect for *A* versus *C*. Pass the
-[`strategy_gcomp_ml()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.md)
-strategy function.
-
-``` r
-
-outstandR_gcomp_ml <-
-  outstandR(ipd_trial, ald_trial,
-            strategy = strategy_gcomp_ml(
-              formula = lin_form,
-              family = gaussian(link = "identity")))
-
-outstandR_gcomp_ml
-#> Object of class 'outstandR' 
-#> Model: gaussian 
-#> Scale: mean_difference 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.314    0.0693     -0.202      0.830
-#> 2 AC           -1.17     0.0392     -1.56      -0.779
-#> 3 BC           -1.48     0.0301     -1.82      -1.14 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A            -0.889    0.0134 NA         NA        
-#> 2 C             0.278    0.0296 NA         NA
 ```
 
 ### Bayesian G-computation with MCMC
@@ -353,30 +220,6 @@ outstandR_gcomp_bayes <-
 ``` r
 
 outstandR_gcomp_bayes
-#> Object of class 'outstandR' 
-#> Model: gaussian 
-#> Scale: mean_difference 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.311    0.0760     -0.229      0.852
-#> 2 AC           -1.17     0.0459     -1.59      -0.750
-#> 3 BC           -1.48     0.0301     -1.82      -1.14 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A            -0.888    0.0165 NA         NA        
-#> 2 C             0.282    0.0305 NA         NA
 ```
 
 ### Multiple imputation marginalisation
@@ -398,41 +241,9 @@ outstandR_mim <-
 ``` r
 
 outstandR_mim
-#> Object of class 'outstandR' 
-#> Model: gaussian 
-#> Scale: mean_difference 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB            0.312    0.0724     -0.215      0.839
-#> 2 AC           -1.17     0.0423     -1.57      -0.766
-#> 3 BC           -1.48     0.0301     -1.82      -1.14 
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>     
-#> 1 A          NA       NA        NA         NA        
-#> 2 C          NA       NA        NA         NA
 ```
 
 ### Model comparison
 
 Combine all outputs for relative effects table of all contrasts and
 methods.
-
-|     |  MAIC |   STC | Gcomp.ML | Gcomp.Bayes |   MIM |
-|:----|------:|------:|---------:|------------:|------:|
-| AB  |  0.20 |   NaN |     0.31 |        0.31 |  0.31 |
-| AC  | -1.28 |   NaN |    -1.17 |       -1.17 | -1.17 |
-| BC  | -1.48 | -1.48 |    -1.48 |       -1.48 | -1.48 |
-
-![](Continuous_outcome_example_files/figure-html/forest-res-1.png)
diff --git a/docs/articles/Count_outcome_example.html b/docs/articles/Count_outcome_example.html
index 378621b..14abaf1 100644
--- a/docs/articles/Count_outcome_example.html
+++ b/docs/articles/Count_outcome_example.html
@@ -1,11 +1,16 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Count data example • outstandR</title>
+<!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png">
+<link rel="icon" type="”image/svg+xml”" href="../favicon.svg">
+<link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png">
+<link rel="icon" sizes="any" href="../favicon.ico">
+<link rel="manifest" href="../site.webmanifest">
 <script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
@@ -16,11 +21,11 @@
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
-    <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="light" aria-label="Site navigation"><div class="container">
+    <nav class="navbar navbar-expand-lg fixed-top bg-primary" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
 
     <a class="navbar-brand me-2" href="../index.html">outstandR</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.0.0.9000</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -29,9 +34,10 @@
 
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto">
-<li class="nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
+<li class="nav-item"><a class="nav-link" href="../index.html">Home</a></li>
+<li class="nav-item"><a class="nav-link" href="../reference/index.html">Functions</a></li>
 <li class="active nav-item"><a class="nav-link" href="../articles/index.html">Articles</a></li>
-<li class="nav-item"><a class="nav-link" href="../news/index.html">Changelog</a></li>
+<li class="nav-item"><a class="nav-link" href="../news/index.html">News</a></li>
       </ul>
 <ul class="navbar-nav">
 <li class="nav-item"><form class="form-inline" role="search">
@@ -50,8 +56,7 @@
 
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
-
-      <h1>Count data example</h1>
+      <img src="../logo.png" class="logo" alt=""><h1>Count data example</h1>
             
       
       <small class="dont-index">Source: <a href="https://github.com/StatisticsHealthEconomics/outstandR/blob/HEAD/vignettes/Count_outcome_example.Rmd" class="external-link"><code>vignettes/Count_outcome_example.Rmd</code></a></small>
@@ -66,11 +71,10 @@ <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#i
 <p>This is the vignette for performing population adjustment methods
 with count data, in order to compare marginal treatment effects when
 there are cross-trial differences in effect modifiers and limited
-patient-level data. We will demonstrate how to apply MAIC, STC,
-G-computation with ML, G-computation with Bayesian inference and
-multiple imputation marginalisation. The document structure follow the
-binary data example vignette which should be referred to for more
-details.</p>
+patient-level data. We will demonstrate how to apply MAIC, G-computation
+with ML, G-computation with Bayesian inference and multiple imputation
+marginalisation. The document structure follow the binary data example
+vignette which should be referred to for more details.</p>
 </div>
 <div class="section level2">
 <h2 id="example-analysis">Example analysis<a class="anchor" aria-label="anchor" href="#example-analysis"></a>
@@ -89,24 +93,19 @@ <h2 id="example-analysis">Example analysis<a class="anchor" aria-label="anchor"
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://tidyr.tidyverse.org" class="external-link">tidyr</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://dplyr.tidyverse.org" class="external-link">dplyr</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="http://www.stats.ox.ac.uk/pub/MASS4/" class="external-link">MASS</a></span><span class="op">)</span></span>
-<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://StatisticsHealthEconomics.github.io/outstandR">outstandR</a></span><span class="op">)</span></span>
+<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://StatisticsHealthEconomics.github.io/outstandR/">outstandR</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">simcovariates</span><span class="op">)</span></span></code></pre></div>
 <div class="section level3">
 <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 </h3>
 <p>We first simulate both the IPD and ALD count data. See the binary
-data example vignette for more details on how this is implemented. The
-difference with that example is that we change the <code>family</code>
-argument in <code><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data()</a></code> to
-<code>poisson(link = "log")</code>, corresponding to the count data
-case. The <code><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data()</a></code> function is available in the <a href="https://github.com/n8thangreen/simcovariates" class="external-link">simcovariates</a>
-package on GitHub.</p>
+data example vignette for more details on how this is implemented.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span></span>
 <span><span class="va">N</span> <span class="op">&lt;-</span> <span class="fl">200</span></span>
 <span><span class="va">allocation</span> <span class="op">&lt;-</span> <span class="fl">2</span><span class="op">/</span><span class="fl">3</span>      <span class="co"># active treatment vs. placebo allocation ratio (2:1)</span></span>
 <span><span class="va">b_trt</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.17</span><span class="op">)</span>     <span class="co"># conditional effect of active treatment vs. common comparator</span></span>
-<span><span class="va">b_X</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.5</span><span class="op">)</span>       <span class="co"># conditional effect of each prognostic variable</span></span>
+<span><span class="va">b_PF</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.5</span><span class="op">)</span>       <span class="co"># conditional effect of each prognostic variable</span></span>
 <span><span class="va">b_EM</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.67</span><span class="op">)</span>     <span class="co"># conditional interaction effect of each effect modifier</span></span>
 <span><span class="va">meanX_AC</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.45</span>, <span class="fl">0.45</span><span class="op">)</span>       <span class="co"># mean of normally-distributed covariate in AC trial</span></span>
 <span><span class="va">meanX_BC</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.6</span>, <span class="fl">0.6</span><span class="op">)</span>         <span class="co"># mean of each normally-distributed covariate in BC</span></span>
@@ -115,20 +114,25 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span><span class="va">sdX</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.4</span>, <span class="fl">0.4</span><span class="op">)</span>     <span class="co"># standard deviation of each covariate (same for AC and BC)</span></span>
 <span><span class="va">sdX_EM</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.4</span>, <span class="fl">0.4</span><span class="op">)</span>  <span class="co"># standard deviation of each EM covariate</span></span>
 <span><span class="va">corX</span> <span class="op">&lt;-</span> <span class="fl">0.2</span>            <span class="co"># covariate correlation coefficient  </span></span>
-<span><span class="va">b_0</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fl">0.6</span>            <span class="co"># baseline intercept coefficient  ##TODO: fixed value</span></span>
-<span></span>
-<span><span class="va">covariate_defns_ipd</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
-<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span><span class="va">b_0</span> <span class="op">&lt;-</span> <span class="op">-</span><span class="fl">0.6</span>            <span class="co"># baseline intercept coefficient  ##TODO: fixed value</span></span></code></pre></div>
+<p>The difference with that example is that we change the
+<code>family</code> argument in <code>gen_data()</code> to
+<code>poisson(link = "log")</code>, corresponding to the count data
+case. The <code>gen_data()</code> function is available in the <a href="https://github.com/n8thangreen/simcovariates" class="external-link">simcovariates</a>
+package on GitHub.</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">covariate_defns_ipd</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
+<span>  PF_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  PF_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"prognostic"</span><span class="op">)</span>,</span>
-<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span>,</span>
-<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/constructors.html" class="external-link">continuous</a></span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>  EM_cont_2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="fu">continuous</span><span class="op">(</span>mean <span class="op">=</span> <span class="va">meanX_EM_AC</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, sd <span class="op">=</span> <span class="va">sdX_EM</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span>,</span>
 <span>                    role <span class="op">=</span> <span class="st">"effect_modifier"</span><span class="op">)</span></span>
 <span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">b_prognostic</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>PF_cont_1 <span class="op">=</span> <span class="va">b_X</span>, PF_cont_2 <span class="op">=</span> <span class="va">b_X</span><span class="op">)</span></span>
+<span><span class="va">b_prognostic</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>PF_cont_1 <span class="op">=</span> <span class="va">b_PF</span>, PF_cont_2 <span class="op">=</span> <span class="va">b_PF</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">b_effect_modifier</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>EM_cont_1 <span class="op">=</span> <span class="va">b_EM</span>, EM_cont_2 <span class="op">=</span> <span class="va">b_EM</span><span class="op">)</span></span>
 <span></span>
@@ -139,7 +143,7 @@ <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">cor_matrix</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"PF_cont_1"</span>, <span class="st">"PF_cont_2"</span>, <span class="st">"EM_cont_1"</span>, <span class="st">"EM_cont_2"</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">colnames</a></span><span class="op">(</span><span class="va">cor_matrix</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"PF_cont_1"</span>, <span class="st">"PF_cont_2"</span>, <span class="st">"EM_cont_1"</span>, <span class="st">"EM_cont_2"</span><span class="op">)</span></span>
 <span></span>
-<span><span class="va">ipd_trial</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/simcovariates/man/gen_data.html" class="external-link">gen_data</a></span><span class="op">(</span></span>
+<span><span class="va">ipd_trial</span> <span class="op">&lt;-</span> <span class="fu">simcovariates</span><span class="fu">::</span><span class="fu">gen_data</span><span class="op">(</span></span>
 <span>  N <span class="op">=</span> <span class="va">N</span>,</span>
 <span>  b_0 <span class="op">=</span> <span class="va">b_0</span>,</span>
 <span>  b_trt <span class="op">=</span> <span class="va">b_trt</span>,</span>
@@ -191,54 +195,28 @@ <h4 id="ald_trial-aggregate-level-data">
 </li>
 </ul>
 <p>Our data look like the following.</p>
-<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">ipd_trial</span><span class="op">)</span></span>
-<span><span class="co">#&gt;   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt y     true_eta</span></span>
-<span><span class="co">#&gt; 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C 4  0.582883524</span></span>
-<span><span class="co">#&gt; 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A 1 -1.476422106</span></span>
-<span><span class="co">#&gt; 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A 3  0.005184912</span></span>
-<span><span class="co">#&gt; 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C 1  0.520117172</span></span>
-<span><span class="co">#&gt; 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A 1 -1.760974264</span></span>
-<span><span class="co">#&gt; 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A 0 -2.139514435</span></span></code></pre></div>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">ipd_trial</span><span class="op">)</span></span></code></pre></div>
 <p>There are 4 correlated continuous covariates generated per subject,
 simulated from a multivariate normal distribution. Treatment
 <code>trt</code> takes either new treatment <em>A</em> or standard of
 care / status quo <em>C</em>. The ITC is ‘anchored’ via <em>C</em>, the
 common treatment.</p>
-<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">ald_trial</span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 16 × 4</span></span></span>
-<span><span class="co">#&gt;    variable  statistic   value trt  </span></span>
-<span><span class="co">#&gt;    <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>       <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 1</span> EM_cont_1 mean        0.616 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 2</span> EM_cont_1 sd          0.408 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 3</span> EM_cont_2 mean        0.635 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 4</span> EM_cont_2 sd          0.354 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 5</span> PF_cont_1 mean        0.666 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 6</span> PF_cont_1 sd          0.398 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 7</span> PF_cont_2 mean        0.663 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 8</span> PF_cont_2 sd          0.404 <span style="color: #BB0000;">NA</span>   </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;"> 9</span> y         mean        1.07  C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">10</span> y         sd          1.01  C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">11</span> y         sum        77     C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">12</span> y         mean        0.438 B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">13</span> y         sd          0.750 B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">14</span> y         sum        56     B    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">15</span> <span style="color: #BB0000;">NA</span>        N          72     C    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">16</span> <span style="color: #BB0000;">NA</span>        N         128     B</span></span></code></pre></div>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">ald_trial</span></span></code></pre></div>
 <p>In this case, we have 4 covariate mean and standard deviation values;
 and the total, average and sample size for each treatment <em>B</em> and
 <em>C</em>.</p>
-<p>In the following we will implement for MAIC, STC, and G-computation
-methods to obtain the <em>marginal variance</em> and the <em>marginal
-treatment effect</em>.</p>
+<p>In the following we will implement for MAIC and G-computation methods
+to obtain the <em>marginal variance</em> and the <em>marginal treatment
+effect</em>.</p>
 </div>
 </div>
 </div>
 <div class="section level2">
 <h2 id="model-fitting-in-r">Model fitting in R<a class="anchor" aria-label="anchor" href="#model-fitting-in-r"></a>
 </h2>
-<p>The <a href="https://StatisticsHealthEconomics.github.io/outstandR">outstandR</a> package has been written to be easy to
+<p>The <a href="https://StatisticsHealthEconomics.github.io/outstandR/">outstandR</a> package has been written to be easy to
 use and essential consists of a single function,
 <code><a href="../reference/outstandR.html">outstandR()</a></code>. This can be used to run all of the different
 types of model, which we will call <em>strategies</em>. The first two
@@ -251,92 +229,26 @@ <h2 id="model-fitting-in-r">Model fitting in R<a class="anchor" aria-label="anch
 example is provided below.</p>
 <p>The formula used in this model, passed as an argument to the strategy
 function is</p>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">lin_form</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">lin_form</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
+<span>  outcome_model <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"</span><span class="op">)</span>,</span>
+<span>  balance_model <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/formula.html" class="external-link">as.formula</a></span><span class="op">(</span><span class="st">"~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2"</span><span class="op">)</span></span>
+<span><span class="op">)</span></span></code></pre></div>
 <div class="section level3">
 <h3 id="maic">MAIC<a class="anchor" aria-label="anchor" href="#maic"></a>
 </h3>
 <p>As mentioned above, pass the model specific strategy function to the
 main <code><a href="../reference/outstandR.html">outstandR()</a></code> function, in this case use
 <code><a href="../reference/strategy.html">strategy_maic()</a></code>.</p>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">outstandR_maic</span> <span class="op">&lt;-</span></span>
 <span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_maic</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
-<span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">poisson</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"log"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
-<span><span class="co">#&gt; log rate used</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; log rate used</span></span></code></pre></div>
+<span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">poisson</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"log"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p>The returned object is of class <code>outstandR</code>.</p>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_maic</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">poisson</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB           0.052<span style="text-decoration: underline;">4</span>    0.080<span style="text-decoration: underline;">1</span>     -<span style="color: #BB0000;">0.502</span>      0.607</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC          -<span style="color: #BB0000;">0.841</span>     0.049<span style="text-decoration: underline;">3</span>     -<span style="color: #BB0000;">1.28</span>      -<span style="color: #BB0000;">0.406</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC          -<span style="color: #BB0000;">0.894</span>     0.030<span style="text-decoration: underline;">8</span>     -<span style="color: #BB0000;">1.24</span>      -<span style="color: #BB0000;">0.550</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.500   0.005<span style="text-decoration: underline;">77</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             1.16    0.029<span style="text-decoration: underline;">2</span>  <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
-</div>
-<div class="section level3">
-<h3 id="simulated-treatment-comparison-stc">Simulated Treatment Comparison (STC)<a class="anchor" aria-label="anchor" href="#simulated-treatment-comparison-stc"></a>
-</h3>
-<p>STC is the conventional outcome regression method. It involves
-fitting a regression model of outcome on treatment and covariates to the
-IPD. Simply pass the same as formula as before with the
-<code><a href="../reference/strategy.html">strategy_stc()</a></code> strategy function.</p>
 <div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_stc</span> <span class="op">&lt;-</span></span>
-<span>  <span class="fu"><a href="../reference/outstandR.html">outstandR</a></span><span class="op">(</span><span class="va">ipd_trial</span>, <span class="va">ald_trial</span>,</span>
-<span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_stc</a></span><span class="op">(</span></span>
-<span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
-<span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">poisson</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"log"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
-<span><span class="co">#&gt; log rate used</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; log rate used</span></span>
-<span><span class="va">outstandR_stc</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">poisson</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB          <span style="color: #BB0000;">NaN</span>       <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC          <span style="color: #BB0000;">NaN</span>       <span style="color: #BB0000;">NA</span>           <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>    </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC           -<span style="color: #BB0000;">0.894</span>    0.030<span style="text-decoration: underline;">8</span>      -<span style="color: #BB0000;">1.24</span>     -<span style="color: #BB0000;">0.550</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A           <span style="color: #BB0000;">NaN</span>            <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             0.330        <span style="color: #BB0000;">NA</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">outstandR_maic</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="parametric-g-computation-with-maximum-likelihood-estimation">Parametric G-computation with maximum-likelihood estimation<a class="anchor" aria-label="anchor" href="#parametric-g-computation-with-maximum-likelihood-estimation"></a>
@@ -351,31 +263,7 @@ <h3 id="parametric-g-computation-with-maximum-likelihood-estimation">Parametric
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_gcomp_ml</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">poisson</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"log"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
-<span><span class="va">outstandR_gcomp_ml</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">poisson</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB           0.016<span style="text-decoration: underline;">9</span>    0.079<span style="text-decoration: underline;">8</span>     -<span style="color: #BB0000;">0.537</span>      0.571</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC          -<span style="color: #BB0000;">0.877</span>     0.049<span style="text-decoration: underline;">0</span>     -<span style="color: #BB0000;">1.31</span>      -<span style="color: #BB0000;">0.443</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC          -<span style="color: #BB0000;">0.894</span>     0.030<span style="text-decoration: underline;">8</span>     -<span style="color: #BB0000;">1.24</span>      -<span style="color: #BB0000;">0.550</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.621   0.009<span style="text-decoration: underline;">36</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             1.50    0.071<span style="text-decoration: underline;">7</span>  <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<span><span class="va">outstandR_gcomp_ml</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="bayesian-g-computation-with-mcmc">Bayesian G-computation with MCMC<a class="anchor" aria-label="anchor" href="#bayesian-g-computation-with-mcmc"></a>
@@ -394,31 +282,7 @@ <h3 id="bayesian-g-computation-with-mcmc">Bayesian G-computation with MCMC<a cla
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">poisson</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"log"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">poisson</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB           0.023<span style="text-decoration: underline;">3</span>    0.085<span style="text-decoration: underline;">1</span>     -<span style="color: #BB0000;">0.548</span>      0.595</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC          -<span style="color: #BB0000;">0.871</span>     0.054<span style="text-decoration: underline;">3</span>     -<span style="color: #BB0000;">1.33</span>      -<span style="color: #BB0000;">0.414</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC          -<span style="color: #BB0000;">0.894</span>     0.030<span style="text-decoration: underline;">8</span>     -<span style="color: #BB0000;">1.24</span>      -<span style="color: #BB0000;">0.550</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A             0.616    0.010<span style="text-decoration: underline;">2</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C             1.48     0.067<span style="text-decoration: underline;">8</span> <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">outstandR_gcomp_bayes</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="multiple-imputation-marginalisation">Multiple imputation marginalisation<a class="anchor" aria-label="anchor" href="#multiple-imputation-marginalisation"></a>
@@ -432,78 +296,14 @@ <h3 id="multiple-imputation-marginalisation">Multiple imputation marginalisation
 <span>            strategy <span class="op">=</span> <span class="fu"><a href="../reference/strategy.html">strategy_mim</a></span><span class="op">(</span></span>
 <span>              formula <span class="op">=</span> <span class="va">lin_form</span>,</span>
 <span>              family <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/family.html" class="external-link">poisson</a></span><span class="op">(</span>link <span class="op">=</span> <span class="st">"log"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">#&gt; log rate used</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; log rate used</span></span></code></pre>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">outstandR_mim</span></span>
-<span><span class="co">#&gt; Object of class 'outstandR' </span></span>
-<span><span class="co">#&gt; Model: <span style="color: #949494;">poisson</span> </span></span>
-<span><span class="co">#&gt; Scale: <span style="color: #949494;">log_relative_risk</span> </span></span>
-<span><span class="co">#&gt; Common treatment: <span style="color: #949494;">C</span> </span></span>
-<span><span class="co">#&gt; Individual patient data study: <span style="color: #949494;">AC</span> </span></span>
-<span><span class="co">#&gt; Aggregate level data study: <span style="color: #949494;">BC</span> </span></span>
-<span><span class="co">#&gt; Confidence interval level: <span style="color: #949494;">0.95</span> </span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Contrasts:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 3 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>         <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> AB           0.023<span style="text-decoration: underline;">7</span>    0.082<span style="text-decoration: underline;">5</span>     -<span style="color: #BB0000;">0.539</span>      0.587</span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> AC          -<span style="color: #BB0000;">0.870</span>     0.051<span style="text-decoration: underline;">7</span>     -<span style="color: #BB0000;">1.32</span>      -<span style="color: #BB0000;">0.425</span></span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> BC          -<span style="color: #BB0000;">0.894</span>     0.030<span style="text-decoration: underline;">8</span>     -<span style="color: #BB0000;">1.24</span>      -<span style="color: #BB0000;">0.550</span></span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Absolute:</span></span>
-<span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 2 × 5</span></span></span>
-<span><span class="co">#&gt;   Treatments Estimate Std.Error lower.0.95 upper.0.95</span></span>
-<span><span class="co">#&gt;   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>      <span style="color: #949494; font-style: italic;">&lt;lgl&gt;</span>     </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">1</span> A          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span>        </span></span>
-<span><span class="co">#&gt; <span style="color: #BCBCBC;">2</span> C          <span style="color: #BB0000;">NA</span>       <span style="color: #BB0000;">NA</span>        <span style="color: #BB0000;">NA</span>         <span style="color: #BB0000;">NA</span></span></span></code></pre></div>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">outstandR_mim</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="model-comparison">Model comparison<a class="anchor" aria-label="anchor" href="#model-comparison"></a>
 </h3>
 <p>Combine all outputs for relative effects table of all contrasts and
 methods.</p>
-<table class="table">
-<thead><tr class="header">
-<th align="left"></th>
-<th align="right">MAIC</th>
-<th align="right">STC</th>
-<th align="right">Gcomp.ML</th>
-<th align="right">Gcomp.Bayes</th>
-<th align="right">MIM</th>
-</tr></thead>
-<tbody>
-<tr class="odd">
-<td align="left">AB</td>
-<td align="right">0.05</td>
-<td align="right">NaN</td>
-<td align="right">0.02</td>
-<td align="right">0.02</td>
-<td align="right">0.02</td>
-</tr>
-<tr class="even">
-<td align="left">AC</td>
-<td align="right">-0.84</td>
-<td align="right">NaN</td>
-<td align="right">-0.88</td>
-<td align="right">-0.87</td>
-<td align="right">-0.87</td>
-</tr>
-<tr class="odd">
-<td align="left">BC</td>
-<td align="right">-0.89</td>
-<td align="right">-0.89</td>
-<td align="right">-0.89</td>
-<td align="right">-0.89</td>
-<td align="right">-0.89</td>
-</tr>
-</tbody>
-</table>
-<p><img src="Count_outcome_example_files/figure-html/forest-res-1.png" width="768"></p>
 </div>
 </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
@@ -513,11 +313,11 @@ <h3 id="model-comparison">Model comparison<a class="anchor" aria-label="anchor"
 
 
     <footer><div class="pkgdown-footer-left">
-  <p>Developed by Nathan Green, Chengyang Gao, Antonio Remiro-Azocar.</p>
+  <p>Developed by <a href="https://n8thangreen.github.io/" class="external-link">Nathan Green</a>, Chengyang Gao, Antonio Remiro-Azocar.</p>
 </div>
 
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.3.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.2.0.</p>
 </div>
 
     </footer>
diff --git a/docs/articles/Count_outcome_example.md b/docs/articles/Count_outcome_example.md
index 62f9a88..d5cb66c 100644
--- a/docs/articles/Count_outcome_example.md
+++ b/docs/articles/Count_outcome_example.md
@@ -5,11 +5,10 @@
 This is the vignette for performing population adjustment methods with
 count data, in order to compare marginal treatment effects when there
 are cross-trial differences in effect modifiers and limited
-patient-level data. We will demonstrate how to apply MAIC, STC,
-G-computation with ML, G-computation with Bayesian inference and
-multiple imputation marginalisation. The document structure follow the
-binary data example vignette which should be referred to for more
-details.
+patient-level data. We will demonstrate how to apply MAIC, G-computation
+with ML, G-computation with Bayesian inference and multiple imputation
+marginalisation. The document structure follow the binary data example
+vignette which should be referred to for more details.
 
 ## Example analysis
 
@@ -36,14 +35,7 @@ library(simcovariates)
 ### Data
 
 We first simulate both the IPD and ALD count data. See the binary data
-example vignette for more details on how this is implemented. The
-difference with that example is that we change the `family` argument in
-[`gen_data()`](https://rdrr.io/pkg/simcovariates/man/gen_data.html) to
-`poisson(link = "log")`, corresponding to the count data case. The
-[`gen_data()`](https://rdrr.io/pkg/simcovariates/man/gen_data.html)
-function is available in the
-[simcovariates](https://github.com/n8thangreen/simcovariates) package on
-GitHub.
+example vignette for more details on how this is implemented.
 
 ``` r
 
@@ -51,7 +43,7 @@ GitHub.
 N <- 200
 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1)
 b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator
-b_X <- -log(0.5)       # conditional effect of each prognostic variable
+b_PF <- -log(0.5)       # conditional effect of each prognostic variable
 b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier
 meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial
 meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC
@@ -61,6 +53,15 @@ sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and B
 sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate
 corX <- 0.2            # covariate correlation coefficient  
 b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value
+```
+
+The difference with that example is that we change the `family` argument
+in `gen_data()` to `poisson(link = "log")`, corresponding to the count
+data case. The `gen_data()` function is available in the
+[simcovariates](https://github.com/n8thangreen/simcovariates) package on
+GitHub.
+
+``` r
 
 covariate_defns_ipd <- list(
   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),
@@ -73,7 +74,7 @@ covariate_defns_ipd <- list(
                     role = "effect_modifier")
 )
 
-b_prognostic <- c(PF_cont_1 = b_X, PF_cont_2 = b_X)
+b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)
 
 b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)
 
@@ -126,13 +127,6 @@ Our data look like the following.
 ``` r
 
 head(ipd_trial)
-#>   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt y     true_eta
-#> 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C 4  0.582883524
-#> 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A 1 -1.476422106
-#> 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A 3  0.005184912
-#> 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C 1  0.520117172
-#> 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A 1 -1.760974264
-#> 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A 0 -2.139514435
 ```
 
 There are 4 correlated continuous covariates generated per subject,
@@ -143,37 +137,17 @@ is ‘anchored’ via *C*, the common treatment.
 ``` r
 
 ald_trial
-#> # A tibble: 16 × 4
-#>    variable  statistic   value trt  
-#>    <chr>     <chr>       <dbl> <chr>
-#>  1 EM_cont_1 mean        0.616 NA   
-#>  2 EM_cont_1 sd          0.408 NA   
-#>  3 EM_cont_2 mean        0.635 NA   
-#>  4 EM_cont_2 sd          0.354 NA   
-#>  5 PF_cont_1 mean        0.666 NA   
-#>  6 PF_cont_1 sd          0.398 NA   
-#>  7 PF_cont_2 mean        0.663 NA   
-#>  8 PF_cont_2 sd          0.404 NA   
-#>  9 y         mean        1.07  C    
-#> 10 y         sd          1.01  C    
-#> 11 y         sum        77     C    
-#> 12 y         mean        0.438 B    
-#> 13 y         sd          0.750 B    
-#> 14 y         sum        56     B    
-#> 15 NA        N          72     C    
-#> 16 NA        N         128     B
 ```
 
 In this case, we have 4 covariate mean and standard deviation values;
 and the total, average and sample size for each treatment *B* and *C*.
 
-In the following we will implement for MAIC, STC, and G-computation
-methods to obtain the *marginal variance* and the *marginal treatment
-effect*.
+In the following we will implement for MAIC and G-computation methods to
+obtain the *marginal variance* and the *marginal treatment effect*.
 
 ## Model fitting in R
 
-The [outstandR](https://StatisticsHealthEconomics.github.io/outstandR)
+The [outstandR](https://StatisticsHealthEconomics.github.io/outstandR/)
 package has been written to be easy to use and essential consists of a
 single function,
 [`outstandR()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.md).
@@ -193,7 +167,10 @@ function is
 
 ``` r
 
-lin_form <- as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2")
+lin_form <- list(
+  outcome_model = as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"),
+  balance_model = as.formula("~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2")
+)
 ```
 
 ### MAIC
@@ -211,9 +188,6 @@ outstandR_maic <-
             strategy = strategy_maic(
               formula = lin_form,
               family = poisson(link = "log")))
-#> log rate used
-#> 
-#> log rate used
 ```
 
 The returned object is of class `outstandR`.
@@ -221,75 +195,6 @@ The returned object is of class `outstandR`.
 ``` r
 
 outstandR_maic
-#> Object of class 'outstandR' 
-#> Model: poisson 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB           0.0524    0.0801     -0.502      0.607
-#> 2 AC          -0.841     0.0493     -1.28      -0.406
-#> 3 BC          -0.894     0.0308     -1.24      -0.550
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.500   0.00577 NA         NA        
-#> 2 C             1.16    0.0292  NA         NA
-```
-
-### Simulated Treatment Comparison (STC)
-
-STC is the conventional outcome regression method. It involves fitting a
-regression model of outcome on treatment and covariates to the IPD.
-Simply pass the same as formula as before with the
-[`strategy_stc()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.md)
-strategy function.
-
-``` r
-
-outstandR_stc <-
-  outstandR(ipd_trial, ald_trial,
-            strategy = strategy_stc(
-              formula = lin_form,
-              family = poisson(link = "log")))
-#> log rate used
-#> 
-#> log rate used
-outstandR_stc
-#> Object of class 'outstandR' 
-#> Model: poisson 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB          NaN       NA           NA        NA    
-#> 2 AC          NaN       NA           NA        NA    
-#> 3 BC           -0.894    0.0308      -1.24     -0.550
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A           NaN            NA NA         NA        
-#> 2 C             0.330        NA NA         NA
 ```
 
 ### Parametric G-computation with maximum-likelihood estimation
@@ -308,30 +213,6 @@ outstandR_gcomp_ml <-
               formula = lin_form,
               family = poisson(link = "log")))
 outstandR_gcomp_ml
-#> Object of class 'outstandR' 
-#> Model: poisson 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB           0.0169    0.0798     -0.537      0.571
-#> 2 AC          -0.877     0.0490     -1.31      -0.443
-#> 3 BC          -0.894     0.0308     -1.24      -0.550
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.621   0.00936 NA         NA        
-#> 2 C             1.50    0.0717  NA         NA
 ```
 
 ### Bayesian G-computation with MCMC
@@ -358,30 +239,6 @@ outstandR_gcomp_bayes <-
 ``` r
 
 outstandR_gcomp_bayes
-#> Object of class 'outstandR' 
-#> Model: poisson 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB           0.0233    0.0851     -0.548      0.595
-#> 2 AC          -0.871     0.0543     -1.33      -0.414
-#> 3 BC          -0.894     0.0308     -1.24      -0.550
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl> <lgl>      <lgl>     
-#> 1 A             0.616    0.0102 NA         NA        
-#> 2 C             1.48     0.0678 NA         NA
 ```
 
 ### Multiple imputation marginalisation
@@ -400,48 +257,12 @@ outstandR_mim <-
               family = poisson(link = "log")))
 ```
 
-    #> log rate used
-    #> 
-    #> log rate used
-
 ``` r
 
 outstandR_mim
-#> Object of class 'outstandR' 
-#> Model: poisson 
-#> Scale: log_relative_risk 
-#> Common treatment: C 
-#> Individual patient data study: AC 
-#> Aggregate level data study: BC 
-#> Confidence interval level: 0.95 
-#> 
-#> Contrasts:
-#> 
-#> # A tibble: 3 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>         <dbl>     <dbl>      <dbl>      <dbl>
-#> 1 AB           0.0237    0.0825     -0.539      0.587
-#> 2 AC          -0.870     0.0517     -1.32      -0.425
-#> 3 BC          -0.894     0.0308     -1.24      -0.550
-#> 
-#> Absolute:
-#> 
-#> # A tibble: 2 × 5
-#>   Treatments Estimate Std.Error lower.0.95 upper.0.95
-#>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>     
-#> 1 A          NA       NA        NA         NA        
-#> 2 C          NA       NA        NA         NA
 ```
 
 ### Model comparison
 
 Combine all outputs for relative effects table of all contrasts and
 methods.
-
-|     |  MAIC |   STC | Gcomp.ML | Gcomp.Bayes |   MIM |
-|:----|------:|------:|---------:|------------:|------:|
-| AB  |  0.05 |   NaN |     0.02 |        0.02 |  0.02 |
-| AC  | -0.84 |   NaN |    -0.88 |       -0.87 | -0.87 |
-| BC  | -0.89 | -0.89 |    -0.89 |       -0.89 | -0.89 |
-
-![](Count_outcome_example_files/figure-html/forest-res-1.png)
diff --git a/docs/articles/adding-a-new-strategy.html b/docs/articles/adding-a-new-strategy.html
index 161d6d7..2c0460d 100644
--- a/docs/articles/adding-a-new-strategy.html
+++ b/docs/articles/adding-a-new-strategy.html
@@ -12,8 +12,8 @@
 <link rel="icon" sizes="any" href="../favicon.ico">
 <link rel="manifest" href="../site.webmanifest">
 <script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
-<link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet">
-<script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
+<link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
+<script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
 <script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Adding a New Strategy to `outstandR`">
 </head>
diff --git a/docs/articles/index.html b/docs/articles/index.html
index 8ea93be..e01b763 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Articles • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Articles"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Articles • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Articles"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -33,13 +33,35 @@
     </div>
 
     <div class="section ">
-      <h3>All vignettes</h3>
+      <h3>Binary outcome data example</h3>
+      <div class="section-desc"></div>
+
+      <dl><dt><a href="Binary_outcome_example.html">Binary data example</a></dt>
+        <dd>
+      </dd></dl></div>
+    <div class="section ">
+      <h3>Continuous outcome data example</h3>
+      <div class="section-desc"></div>
+
+      <dl><dt><a href="Continuous_outcome_example.html">Continuous data example</a></dt>
+        <dd>
+      </dd></dl></div>
+    <div class="section ">
+      <h3>Count outcome data example</h3>
+      <div class="section-desc"></div>
+
+      <dl><dt><a href="Count_outcome_example.html">Count data example</a></dt>
+        <dd>
+      </dd></dl></div>
+    <div class="section ">
+      <h3>Developer Guides</h3>
       <div class="section-desc"></div>
 
       <dl><dt><a href="adding-a-new-strategy.html">Adding a New Strategy to `outstandR`</a></dt>
         <dd>
       </dd></dl></div>
-  </main></div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
     <footer><div class="pkgdown-footer-left">
diff --git a/docs/articles/index.md b/docs/articles/index.md
index e4c8c70..befde8e 100644
--- a/docs/articles/index.md
+++ b/docs/articles/index.md
@@ -1,6 +1,21 @@
 # Articles
 
-### All vignettes
+### Binary outcome data example
+
+- [Binary data
+  example](https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.md):
+
+### Continuous outcome data example
+
+- [Continuous data
+  example](https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.md):
+
+### Count outcome data example
+
+- [Count data
+  example](https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.md):
+
+### Developer Guides
 
 - [Adding a New Strategy to
   \`outstandR\`](https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.md):
diff --git a/docs/authors.html b/docs/authors.html
index a22765a..758a4fa 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Authors and Citation • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Authors and Citation"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Authors and Citation • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Authors and Citation"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/deps/bootstrap-5.3.1/fonts/07d40e985ad7c747025dabb9f22142c4.woff2 b/docs/deps/bootstrap-5.3.1/fonts/07d40e985ad7c747025dabb9f22142c4.woff2
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diff --git a/docs/deps/data-deps.txt b/docs/deps/data-deps.txt
index 04232a5..ca4dfd9 100644
--- a/docs/deps/data-deps.txt
+++ b/docs/deps/data-deps.txt
@@ -1,7 +1,7 @@
 <script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script>
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no" />
-<link href="deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet" />
-<script src="deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script>
+<link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet" />
+<script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script>
 <link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet" />
 <link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet" />
 <script src="deps/headroom-0.11.0/headroom.min.js"></script>
diff --git a/docs/index.md b/docs/index.md
index b62874c..38e72bb 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -108,8 +108,8 @@ situation including the following:
 - *Simulated Treatment Comparison (STC) \[DEPRECATED\]:* While
   previously common, standard STC can produce biased marginal estimates
   due to aggregation bias and non-collapsibility when using non-linear
-  link functions. *Note: STC is formally deprecated as of v1.0.1 in
-  favor of the more robust G-computation approaches.*
+  link functions. *Note: STC is formally deprecated as of v2.0.0 in
+  favour of the more robust G-computation approaches.*
 
 ## General problem
 
diff --git a/docs/llms.txt b/docs/llms.txt
index 5fa1130..ecd9b99 100644
--- a/docs/llms.txt
+++ b/docs/llms.txt
@@ -108,8 +108,8 @@ situation including the following:
 - *Simulated Treatment Comparison (STC) \[DEPRECATED\]:* While
   previously common, standard STC can produce biased marginal estimates
   due to aggregation bias and non-collapsibility when using non-linear
-  link functions. *Note: STC is formally deprecated as of v1.0.1 in
-  favor of the more robust G-computation approaches.*
+  link functions. *Note: STC is formally deprecated as of v2.0.0 in
+  favour of the more robust G-computation approaches.*
 
 ## General problem
 
@@ -242,6 +242,8 @@ Helper functions used by the main functions.
   : Estimate Variance Sandwich Estimator
 - [`calc_ALD_stats()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.md)
   : Aggregate-level data mean and variance statistics
+- [`calc_bucher_naive()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.md)
+  : Calculate Naive (Unadjusted) Bucher Indirect Comparison
 - [`calc_gcomp_bayes()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.md)
   : Bayesian G-computation using Stan
 - [`calc_gcomp_ml()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.md)
@@ -293,7 +295,22 @@ Helper functions used by the main functions.
 
 # Articles
 
-### All vignettes
+### Binary outcome data example
+
+- [Binary data
+  example](https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.md):
+
+### Continuous outcome data example
+
+- [Continuous data
+  example](https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.md):
+
+### Count outcome data example
+
+- [Count data
+  example](https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.md):
+
+### Developer Guides
 
 - [Adding a New Strategy to
   \`outstandR\`](https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.md):
diff --git a/docs/news/index.html b/docs/news/index.html
index eb041c2..7b0ec5c 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index e5ae3d2..09cab23 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -3,7 +3,10 @@ pkgdown: 2.2.0
 pkgdown_sha: ~
 articles:
   articles/adding-a-new-strategy: adding-a-new-strategy.html
-last_built: 2026-06-10T06:47Z
+  Binary_outcome_example: Binary_outcome_example.html
+  Continuous_outcome_example: Continuous_outcome_example.html
+  Count_outcome_example: Count_outcome_example.html
+last_built: 2026-06-19T15:40Z
 urls:
   reference: https://StatisticsHealthEconomics.github.io/outstandR/reference
   article: https://StatisticsHealthEconomics.github.io/outstandR/articles
diff --git a/docs/reference/AC_IPD_binY_contX.html b/docs/reference/AC_IPD_binY_contX.html
index e44d023..e4f28d3 100644
--- a/docs/reference/AC_IPD_binY_contX.html
+++ b/docs/reference/AC_IPD_binY_contX.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX"><meta name="description" content="This data set contains simulated patient covariate and outcome values."><meta property="og:description" content="This data set contains simulated patient covariate and outcome values."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX"><meta name="description" content="This data set contains simulated patient covariate and outcome values."><meta property="og:description" content="This data set contains simulated patient covariate and outcome values."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/AC_IPD_contY_mixedX.html b/docs/reference/AC_IPD_contY_mixedX.html
index c2602f8..87ac609 100644
--- a/docs/reference/AC_IPD_contY_mixedX.html
+++ b/docs/reference/AC_IPD_contY_mixedX.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX"><meta name="description" content="This data set contains simulated patient covariate and outcome values.
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX"><meta name="description" content="This data set contains simulated patient covariate and outcome values.
 Corresponds to ALD data set."><meta property="og:description" content="This data set contains simulated patient covariate and outcome values.
 Corresponds to ALD data set."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/AC_IPD_countY_contX.html b/docs/reference/AC_IPD_countY_contX.html
index d714c62..fff9e56 100644
--- a/docs/reference/AC_IPD_countY_contX.html
+++ b/docs/reference/AC_IPD_countY_contX.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX"><meta name="description" content="This data set contains simulated patient covariate and outcome values.
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX"><meta name="description" content="This data set contains simulated patient covariate and outcome values.
 Corresponds to ALD data set."><meta property="og:description" content="This data set contains simulated patient covariate and outcome values.
 Corresponds to ALD data set."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/BC_ALD_binY_contX.html b/docs/reference/BC_ALD_binY_contX.html
index 0e84a17..f070457 100644
--- a/docs/reference/BC_ALD_binY_contX.html
+++ b/docs/reference/BC_ALD_binY_contX.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX"><meta name="description" content="This data set contains summaries of simulated patient covariate and outcome values."><meta property="og:description" content="This data set contains summaries of simulated patient covariate and outcome values."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX"><meta name="description" content="This data set contains summaries of simulated patient covariate and outcome values."><meta property="og:description" content="This data set contains summaries of simulated patient covariate and outcome values."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/BC_ALD_contY_mixedX.html b/docs/reference/BC_ALD_contY_mixedX.html
index 395bf4b..3e414be 100644
--- a/docs/reference/BC_ALD_contY_mixedX.html
+++ b/docs/reference/BC_ALD_contY_mixedX.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX"><meta name="description" content="This data set contains summaries of simulated patient covariate and outcome values.
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX"><meta name="description" content="This data set contains summaries of simulated patient covariate and outcome values.
 Corresponds to IPD data set."><meta property="og:description" content="This data set contains summaries of simulated patient covariate and outcome values.
 Corresponds to IPD data set."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/BC_ALD_countY_contX.html b/docs/reference/BC_ALD_countY_contX.html
index 59dcb3b..10e3f2d 100644
--- a/docs/reference/BC_ALD_countY_contX.html
+++ b/docs/reference/BC_ALD_countY_contX.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX"><meta name="description" content="This data set contains summaries of simulated patient covariate and outcome values.
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX"><meta name="description" content="This data set contains summaries of simulated patient covariate and outcome values.
 Corresponds to IPD data set."><meta property="og:description" content="This data set contains summaries of simulated patient covariate and outcome values.
 Corresponds to IPD data set."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/IPD_stat_factory.html b/docs/reference/IPD_stat_factory.html
index b73e8e8..c9392a4 100644
--- a/docs/reference/IPD_stat_factory.html
+++ b/docs/reference/IPD_stat_factory.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Factory function for creating calc_IPD_stats methods — IPD_stat_factory • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Factory function for creating calc_IPD_stats methods — IPD_stat_factory"><meta name="description" content="Creates a method for computing IPD mean and variance statistics based on the supplied function."><meta property="og:description" content="Creates a method for computing IPD mean and variance statistics based on the supplied function."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Factory function for creating calc_IPD_stats methods — IPD_stat_factory • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Factory function for creating calc_IPD_stats methods — IPD_stat_factory"><meta name="description" content="Creates a method for computing IPD mean and variance statistics based on the supplied function."><meta property="og:description" content="Creates a method for computing IPD mean and variance statistics based on the supplied function."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/Q.html b/docs/reference/Q.html
index 459e388..4780a78 100644
--- a/docs/reference/Q.html
+++ b/docs/reference/Q.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Objective function to minimize for standard method of moments MAIC — Q • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Objective function to minimize for standard method of moments MAIC — Q"><meta name="description" content="Objective function to minimize for standard method of moments MAIC"><meta property="og:description" content="Objective function to minimize for standard method of moments MAIC"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Objective function to minimize for standard method of moments MAIC — Q • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Objective function to minimize for standard method of moments MAIC — Q"><meta name="description" content="Objective function to minimize for standard method of moments MAIC"><meta property="og:description" content="Objective function to minimize for standard method of moments MAIC"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calc_ALD_stats.html b/docs/reference/calc_ALD_stats.html
index 250506a..105273d 100644
--- a/docs/reference/calc_ALD_stats.html
+++ b/docs/reference/calc_ALD_stats.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate-level data mean and variance statistics — calc_ALD_stats • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate-level data mean and variance statistics — calc_ALD_stats"><meta name="description" content="Computes the mean and variance of marginal treatment effects for aggregate-level trial data."><meta property="og:description" content="Computes the mean and variance of marginal treatment effects for aggregate-level trial data."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate-level data mean and variance statistics — calc_ALD_stats • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate-level data mean and variance statistics — calc_ALD_stats"><meta name="description" content="Computes the mean and variance of marginal treatment effects for aggregate-level trial data."><meta property="og:description" content="Computes the mean and variance of marginal treatment effects for aggregate-level trial data."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calc_IPD_stats.html b/docs/reference/calc_IPD_stats.html
index 5848a4a..21b06f2 100644
--- a/docs/reference/calc_IPD_stats.html
+++ b/docs/reference/calc_IPD_stats.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate individual-level patient data statistics — calc_IPD_stats • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate individual-level patient data statistics — calc_IPD_stats"><meta name="description" content="Computes mean and variance statistics for individual-level patient data using various approaches,
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate individual-level patient data statistics — calc_IPD_stats • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate individual-level patient data statistics — calc_IPD_stats"><meta name="description" content="Computes mean and variance statistics for individual-level patient data using various approaches,
 including Matching-Adjusted Indirect Comparison (MAIC), Simulated Treatment Comparison (STC),
 and G-computation via Maximum Likelihood Estimation (MLE) or Bayesian inference."><meta property="og:description" content="Computes mean and variance statistics for individual-level patient data using various approaches,
 including Matching-Adjusted Indirect Comparison (MAIC), Simulated Treatment Comparison (STC),
diff --git a/docs/reference/calc_bucher_naive.html b/docs/reference/calc_bucher_naive.html
new file mode 100644
index 0000000..7a93115
--- /dev/null
+++ b/docs/reference/calc_bucher_naive.html
@@ -0,0 +1,111 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Naive (Unadjusted) Bucher Indirect Comparison — calc_bucher_naive • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Naive (Unadjusted) Bucher Indirect Comparison — calc_bucher_naive"><meta name="description" content="Calculates the unadjusted indirect comparison between two active treatments
+via a common comparator using the standard Bucher method. Estimates are calculated
+on the link scale (e.g., log-odds) and back-transformed to the requested scale."><meta property="og:description" content="Calculates the unadjusted indirect comparison between two active treatments
+via a common comparator using the standard Bucher method. Estimates are calculated
+on the link scale (e.g., log-odds) and back-transformed to the requested scale."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
+
+
+    <nav class="navbar navbar-expand-lg fixed-top bg-primary" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+    <a class="navbar-brand me-2" href="../index.html">outstandR</a>
+
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0</small>
+
+
+    <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
+      <span class="navbar-toggler-icon"></span>
+    </button>
+
+    <div id="navbar" class="collapse navbar-collapse ms-3">
+      <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../index.html">Home</a></li>
+<li class="active nav-item"><a class="nav-link" href="../reference/index.html">Functions</a></li>
+<li class="nav-item"><a class="nav-link" href="../articles/index.html">Articles</a></li>
+<li class="nav-item"><a class="nav-link" href="../news/index.html">News</a></li>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/StatisticsHealthEconomics/outstandR/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+      </ul></div>
+
+
+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Calculate Naive (Unadjusted) Bucher Indirect Comparison</h1>
+      <small class="dont-index">Source: <a href="https://github.com/StatisticsHealthEconomics/outstandR/blob/HEAD/R/calc_bucher_naive.R" class="external-link"><code>R/calc_bucher_naive.R</code></a></small>
+      <div class="d-none name"><code>calc_bucher_naive.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Calculates the unadjusted indirect comparison between two active treatments
+via a common comparator using the standard Bucher method. Estimates are calculated
+on the link scale (e.g., log-odds) and back-transformed to the requested scale.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">calc_bucher_naive</span><span class="op">(</span></span>
+<span>  <span class="va">ipd_trial</span>,</span>
+<span>  <span class="va">ald_trial</span>,</span>
+<span>  <span class="va">outcome_model</span>,</span>
+<span>  <span class="va">family</span>,</span>
+<span>  ref_trt <span class="op">=</span> <span class="st">"C"</span>,</span>
+<span>  scale <span class="op">=</span> <span class="cn">NULL</span></span>
+<span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-ipd-trial">ipd_trial<a class="anchor" aria-label="anchor" href="#arg-ipd-trial"></a></dt>
+<dd><p>Data frame containing the Individual Patient Data.</p></dd>
+
+
+<dt id="arg-ald-trial">ald_trial<a class="anchor" aria-label="anchor" href="#arg-ald-trial"></a></dt>
+<dd><p>Data frame containing the Aggregate Level Data.</p></dd>
+
+
+<dt id="arg-outcome-model">outcome_model<a class="anchor" aria-label="anchor" href="#arg-outcome-model"></a></dt>
+<dd><p>Formula specifying the outcome model (used to identify variables).</p></dd>
+
+
+<dt id="arg-family">family<a class="anchor" aria-label="anchor" href="#arg-family"></a></dt>
+<dd><p>A family object (e.g., <code>binomial(link="logit")</code>).</p></dd>
+
+
+<dt id="arg-ref-trt">ref_trt<a class="anchor" aria-label="anchor" href="#arg-ref-trt"></a></dt>
+<dd><p>Character string identifying the common comparator treatment.</p></dd>
+
+
+<dt id="arg-scale">scale<a class="anchor" aria-label="anchor" href="#arg-scale"></a></dt>
+<dd><p>Character string specifying the desired output scale (e.g., "risk_difference").</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list containing the naive point estimate, variance, and standard error.</p>
+    </div>
+
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by <a href="https://n8thangreen.github.io/" class="external-link">Nathan Green</a>, Chengyang Gao, Antonio Remiro-Azocar.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.2.0.</p>
+</div>
+
+    </footer></div>
+
+
+
+
+
+  </body></html>
+
diff --git a/docs/reference/calc_bucher_naive.md b/docs/reference/calc_bucher_naive.md
new file mode 100644
index 0000000..fb4292e
--- /dev/null
+++ b/docs/reference/calc_bucher_naive.md
@@ -0,0 +1,51 @@
+# Calculate Naive (Unadjusted) Bucher Indirect Comparison
+
+Calculates the unadjusted indirect comparison between two active
+treatments via a common comparator using the standard Bucher method.
+Estimates are calculated on the link scale (e.g., log-odds) and
+back-transformed to the requested scale.
+
+## Usage
+
+``` r
+calc_bucher_naive(
+  ipd_trial,
+  ald_trial,
+  outcome_model,
+  family,
+  ref_trt = "C",
+  scale = NULL
+)
+```
+
+## Arguments
+
+- ipd_trial:
+
+  Data frame containing the Individual Patient Data.
+
+- ald_trial:
+
+  Data frame containing the Aggregate Level Data.
+
+- outcome_model:
+
+  Formula specifying the outcome model (used to identify variables).
+
+- family:
+
+  A family object (e.g., `binomial(link="logit")`).
+
+- ref_trt:
+
+  Character string identifying the common comparator treatment.
+
+- scale:
+
+  Character string specifying the desired output scale (e.g.,
+  "risk_difference").
+
+## Value
+
+A list containing the naive point estimate, variance, and standard
+error.
diff --git a/docs/reference/calc_gcomp_bayes.html b/docs/reference/calc_gcomp_bayes.html
index 25a6584..e78c640 100644
--- a/docs/reference/calc_gcomp_bayes.html
+++ b/docs/reference/calc_gcomp_bayes.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Bayesian G-computation using Stan — calc_gcomp_bayes • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Bayesian G-computation using Stan — calc_gcomp_bayes"><meta name="description" content="Calculate draws of binary responses from posterior predictive distribution
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Bayesian G-computation using Stan — calc_gcomp_bayes • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Bayesian G-computation using Stan — calc_gcomp_bayes"><meta name="description" content="Calculate draws of binary responses from posterior predictive distribution
 from the Bayesian G-computation method using Hamiltonian Monte Carlo."><meta property="og:description" content="Calculate draws of binary responses from posterior predictive distribution
 from the Bayesian G-computation method using Hamiltonian Monte Carlo."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
diff --git a/docs/reference/calc_gcomp_ml.html b/docs/reference/calc_gcomp_ml.html
index 7feb347..a59f50b 100644
--- a/docs/reference/calc_gcomp_ml.html
+++ b/docs/reference/calc_gcomp_ml.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml"><meta name="description" content="Computes the mean difference in treatment effects using bootstrap resampling."><meta property="og:description" content="Computes the mean difference in treatment effects using bootstrap resampling."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml"><meta name="description" content="Computes the mean difference in treatment effects using bootstrap resampling."><meta property="og:description" content="Computes the mean difference in treatment effects using bootstrap resampling."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calc_maic.html b/docs/reference/calc_maic.html
index 5705717..5ba27f1 100644
--- a/docs/reference/calc_maic.html
+++ b/docs/reference/calc_maic.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate MAIC — calc_maic • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate MAIC — calc_maic"><meta name="description" content="Calculate MAIC"><meta property="og:description" content="Calculate MAIC"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate MAIC — calc_maic • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate MAIC — calc_maic"><meta name="description" content="Calculate MAIC"><meta property="og:description" content="Calculate MAIC"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calc_mim.html b/docs/reference/calc_mim.html
index 292ad26..49dba72 100644
--- a/docs/reference/calc_mim.html
+++ b/docs/reference/calc_mim.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Multiple imputation marginalization (MIM) — calc_mim • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Multiple imputation marginalization (MIM) — calc_mim"><meta name="description" content="Multiple imputation marginalization (MIM)"><meta property="og:description" content="Multiple imputation marginalization (MIM)"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Multiple imputation marginalization (MIM) — calc_mim • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Multiple imputation marginalization (MIM) — calc_mim"><meta name="description" content="Multiple imputation marginalization (MIM)"><meta property="og:description" content="Multiple imputation marginalization (MIM)"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calc_stc.html b/docs/reference/calc_stc.html
index bfd85fb..dc3f047 100644
--- a/docs/reference/calc_stc.html
+++ b/docs/reference/calc_stc.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate simulated treatment comparison statistics — calc_stc • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate simulated treatment comparison statistics — calc_stc"><meta name="description" content="Calculate simulated treatment comparison statistics"><meta property="og:description" content="Calculate simulated treatment comparison statistics"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate simulated treatment comparison statistics — calc_stc • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate simulated treatment comparison statistics — calc_stc"><meta name="description" content="Calculate simulated treatment comparison statistics"><meta property="og:description" content="Calculate simulated treatment comparison statistics"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calculate_ate.html b/docs/reference/calculate_ate.html
index 6c47351..23cc7b2 100644
--- a/docs/reference/calculate_ate.html
+++ b/docs/reference/calculate_ate.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Average Treatment Effect — calculate_ate • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Average Treatment Effect — calculate_ate"><meta name="description" content="Computes the average treatment effect (ATE) based on the specified effect scale."><meta property="og:description" content="Computes the average treatment effect (ATE) based on the specified effect scale."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Average Treatment Effect — calculate_ate • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Average Treatment Effect — calculate_ate"><meta name="description" content="Computes the average treatment effect (ATE) based on the specified effect scale."><meta property="og:description" content="Computes the average treatment effect (ATE) based on the specified effect scale."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calculate_trial_mean.html b/docs/reference/calculate_trial_mean.html
index e0afd3a..568d564 100644
--- a/docs/reference/calculate_trial_mean.html
+++ b/docs/reference/calculate_trial_mean.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Wrapper — calculate_trial_mean • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Wrapper — calculate_trial_mean"><meta name="description" content="Calculate Trial Mean Wrapper"><meta property="og:description" content="Calculate Trial Mean Wrapper"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Wrapper — calculate_trial_mean • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Wrapper — calculate_trial_mean"><meta name="description" content="Calculate Trial Mean Wrapper"><meta property="og:description" content="Calculate Trial Mean Wrapper"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/calculate_trial_mean_binary.html b/docs/reference/calculate_trial_mean_binary.html
index 3d56b2a..bafa034 100644
--- a/docs/reference/calculate_trial_mean_binary.html
+++ b/docs/reference/calculate_trial_mean_binary.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Binary Data — calculate_trial_mean_binary • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Binary Data — calculate_trial_mean_binary"><meta name="description" content="Calculate Trial Mean Binary Data"><meta property="og:description" content="Calculate Trial Mean Binary Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Binary Data — calculate_trial_mean_binary • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Binary Data — calculate_trial_mean_binary"><meta name="description" content="Calculate Trial Mean Binary Data"><meta property="og:description" content="Calculate Trial Mean Binary Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calculate_trial_mean_continuous.html b/docs/reference/calculate_trial_mean_continuous.html
index 64a8a9e..43c8dd5 100644
--- a/docs/reference/calculate_trial_mean_continuous.html
+++ b/docs/reference/calculate_trial_mean_continuous.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous"><meta name="description" content="Calculate Trial Mean Continuous Data"><meta property="og:description" content="Calculate Trial Mean Continuous Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous"><meta name="description" content="Calculate Trial Mean Continuous Data"><meta property="og:description" content="Calculate Trial Mean Continuous Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/calculate_trial_mean_count.html b/docs/reference/calculate_trial_mean_count.html
index f8b916b..7ef2bcc 100644
--- a/docs/reference/calculate_trial_mean_count.html
+++ b/docs/reference/calculate_trial_mean_count.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Count Data — calculate_trial_mean_count • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Count Data — calculate_trial_mean_count"><meta name="description" content="Calculate Trial Mean Count Data"><meta property="og:description" content="Calculate Trial Mean Count Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate Trial Mean Count Data — calculate_trial_mean_count • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate Trial Mean Count Data — calculate_trial_mean_count"><meta name="description" content="Calculate Trial Mean Count Data"><meta property="og:description" content="Calculate Trial Mean Count Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calculate_trial_variance.html b/docs/reference/calculate_trial_variance.html
index d4cc829..2590ae5 100644
--- a/docs/reference/calculate_trial_variance.html
+++ b/docs/reference/calculate_trial_variance.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance — calculate_trial_variance • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance — calculate_trial_variance"><meta name="description" content="Computes the variance of treatment effects for a trial based on the specified family distribution."><meta property="og:description" content="Computes the variance of treatment effects for a trial based on the specified family distribution."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance — calculate_trial_variance • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance — calculate_trial_variance"><meta name="description" content="Computes the variance of treatment effects for a trial based on the specified family distribution."><meta property="og:description" content="Computes the variance of treatment effects for a trial based on the specified family distribution."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calculate_trial_variance_binary.html b/docs/reference/calculate_trial_variance_binary.html
index c8bf429..0822dca 100644
--- a/docs/reference/calculate_trial_variance_binary.html
+++ b/docs/reference/calculate_trial_variance_binary.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance binary — calculate_trial_variance_binary • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance binary — calculate_trial_variance_binary"><meta name="description" content="Calculate trial variance binary"><meta property="og:description" content="Calculate trial variance binary"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance binary — calculate_trial_variance_binary • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance binary — calculate_trial_variance_binary"><meta name="description" content="Calculate trial variance binary"><meta property="og:description" content="Calculate trial variance binary"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calculate_trial_variance_continuous.html b/docs/reference/calculate_trial_variance_continuous.html
index bd9ccb3..819c05a 100644
--- a/docs/reference/calculate_trial_variance_continuous.html
+++ b/docs/reference/calculate_trial_variance_continuous.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance continuous — calculate_trial_variance_continuous • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance continuous — calculate_trial_variance_continuous"><meta name="description" content="Calculate trial variance continuous"><meta property="og:description" content="Calculate trial variance continuous"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance continuous — calculate_trial_variance_continuous • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance continuous — calculate_trial_variance_continuous"><meta name="description" content="Calculate trial variance continuous"><meta property="og:description" content="Calculate trial variance continuous"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/calculate_trial_variance_count.html b/docs/reference/calculate_trial_variance_count.html
index b040385..03160fd 100644
--- a/docs/reference/calculate_trial_variance_count.html
+++ b/docs/reference/calculate_trial_variance_count.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance count — calculate_trial_variance_count • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance count — calculate_trial_variance_count"><meta name="description" content="Calculate trial variance count"><meta property="og:description" content="Calculate trial variance count"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate trial variance count — calculate_trial_variance_count • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate trial variance count — calculate_trial_variance_count"><meta name="description" content="Calculate trial variance count"><meta property="og:description" content="Calculate trial variance count"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/check_balance_formula.html b/docs/reference/check_balance_formula.html
index 0bb1318..227c0e5 100644
--- a/docs/reference/check_balance_formula.html
+++ b/docs/reference/check_balance_formula.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check balance formula — check_balance_formula • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check balance formula — check_balance_formula"><meta name="description" content="Check balance formula"><meta property="og:description" content="Check balance formula"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check balance formula — check_balance_formula • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check balance formula — check_balance_formula"><meta name="description" content="Check balance formula"><meta property="og:description" content="Check balance formula"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/check_formula.html b/docs/reference/check_formula.html
index cf8fff8..f6ed305 100644
--- a/docs/reference/check_formula.html
+++ b/docs/reference/check_formula.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check outcome formula — check_formula • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check outcome formula — check_formula"><meta name="description" content="Check outcome formula"><meta property="og:description" content="Check outcome formula"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check outcome formula — check_formula • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check outcome formula — check_formula"><meta name="description" content="Check outcome formula"><meta property="og:description" content="Check outcome formula"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/check_formula_base.html b/docs/reference/check_formula_base.html
index 7d4c110..5b30d16 100644
--- a/docs/reference/check_formula_base.html
+++ b/docs/reference/check_formula_base.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Base formula validator — check_formula_base • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Base formula validator — check_formula_base"><meta name="description" content="Base formula validator"><meta property="og:description" content="Base formula validator"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Base formula validator — check_formula_base • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Base formula validator — check_formula_base"><meta name="description" content="Base formula validator"><meta property="og:description" content="Base formula validator"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/continuity_correction.html b/docs/reference/continuity_correction.html
index e4d3d0d..95c2941 100644
--- a/docs/reference/continuity_correction.html
+++ b/docs/reference/continuity_correction.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Continuity Correction — continuity_correction • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Continuity Correction — continuity_correction"><meta name="description" content="Continuity Correction"><meta property="og:description" content="Continuity Correction"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Continuity Correction — continuity_correction • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Continuity Correction — continuity_correction"><meta name="description" content="Continuity Correction"><meta property="og:description" content="Continuity Correction"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/cor2cov.html b/docs/reference/cor2cov.html
index 69df807..b8ee534 100644
--- a/docs/reference/cor2cov.html
+++ b/docs/reference/cor2cov.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Compute covariance matrix — cor2cov • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Compute covariance matrix — cor2cov"><meta name="description" content="Compute covariance matrix"><meta property="og:description" content="Compute covariance matrix"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Compute covariance matrix — cor2cov • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Compute covariance matrix — cor2cov"><meta name="description" content="Compute covariance matrix"><meta property="og:description" content="Compute covariance matrix"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/estimate_var_sandwich.html b/docs/reference/estimate_var_sandwich.html
index 38e52b2..77a0fa9 100644
--- a/docs/reference/estimate_var_sandwich.html
+++ b/docs/reference/estimate_var_sandwich.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Estimate Variance Sandwich Estimator — estimate_var_sandwich • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate Variance Sandwich Estimator — estimate_var_sandwich"><meta name="description" content="Computes the robust (sandwich) variance estimator for the treatment effect."><meta property="og:description" content="Computes the robust (sandwich) variance estimator for the treatment effect."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Estimate Variance Sandwich Estimator — estimate_var_sandwich • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate Variance Sandwich Estimator — estimate_var_sandwich"><meta name="description" content="Computes the robust (sandwich) variance estimator for the treatment effect."><meta property="og:description" content="Computes the robust (sandwich) variance estimator for the treatment effect."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/gcomp_ml.boot.html b/docs/reference/gcomp_ml.boot.html
index 5237414..3de4cfc 100644
--- a/docs/reference/gcomp_ml.boot.html
+++ b/docs/reference/gcomp_ml.boot.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot"><meta name="description" content="For use with a bootstrapping function (e.g., boot::boot()).
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot"><meta name="description" content="For use with a bootstrapping function (e.g., boot::boot()).
 On each bootstrap sample of the data, it calculates
 a relative treatment effect (e.g., log odds ratio, log relative risk, or
 risk difference) using G-computation with maximum likelihood."><meta property="og:description" content="For use with a bootstrapping function (e.g., boot::boot()).
diff --git a/docs/reference/gcomp_ml_means.html b/docs/reference/gcomp_ml_means.html
index 63b3d64..edaef4b 100644
--- a/docs/reference/gcomp_ml_means.html
+++ b/docs/reference/gcomp_ml_means.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means"><meta name="description" content="G-computation maximum likelihood mean outcomes by arm"><meta property="og:description" content="G-computation maximum likelihood mean outcomes by arm"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means"><meta name="description" content="G-computation maximum likelihood mean outcomes by arm"><meta property="og:description" content="G-computation maximum likelihood mean outcomes by arm"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/get_allowed_var_methods.html b/docs/reference/get_allowed_var_methods.html
index 5310ef3..c09ba3c 100644
--- a/docs/reference/get_allowed_var_methods.html
+++ b/docs/reference/get_allowed_var_methods.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Retrieve list of allowed variance methods — get_allowed_var_methods • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Retrieve list of allowed variance methods — get_allowed_var_methods"><meta name="description" content="Retrieve list of allowed variance methods"><meta property="og:description" content="Retrieve list of allowed variance methods"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Retrieve list of allowed variance methods — get_allowed_var_methods • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Retrieve list of allowed variance methods — get_allowed_var_methods"><meta name="description" content="Retrieve list of allowed variance methods"><meta property="og:description" content="Retrieve list of allowed variance methods"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/get_comparator.html b/docs/reference/get_comparator.html
index 7ba8384..45bbda6 100644
--- a/docs/reference/get_comparator.html
+++ b/docs/reference/get_comparator.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get study comparator treatment names — get_comparator • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get study comparator treatment names — get_comparator"><meta name="description" content="Get study comparator treatment names"><meta property="og:description" content="Get study comparator treatment names"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get study comparator treatment names — get_comparator • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get study comparator treatment names — get_comparator"><meta name="description" content="Get study comparator treatment names"><meta property="og:description" content="Get study comparator treatment names"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/get_covariate_names.html b/docs/reference/get_covariate_names.html
index 2cde175..bfc37c6 100644
--- a/docs/reference/get_covariate_names.html
+++ b/docs/reference/get_covariate_names.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get covariate names — get_covariate_names • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get covariate names — get_covariate_names"><meta name="description" content="Get covariate names"><meta property="og:description" content="Get covariate names"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get covariate names — get_covariate_names • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get covariate names — get_covariate_names"><meta name="description" content="Get covariate names"><meta property="og:description" content="Get covariate names"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/get_eff_mod_names.html b/docs/reference/get_eff_mod_names.html
index d58cef2..060df83 100644
--- a/docs/reference/get_eff_mod_names.html
+++ b/docs/reference/get_eff_mod_names.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get effect modifiers — get_eff_mod_names • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get effect modifiers — get_eff_mod_names"><meta name="description" content="Get effect modifiers"><meta property="og:description" content="Get effect modifiers"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get effect modifiers — get_eff_mod_names • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get effect modifiers — get_eff_mod_names"><meta name="description" content="Get effect modifiers"><meta property="og:description" content="Get effect modifiers"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/get_ref_trt.html b/docs/reference/get_ref_trt.html
index 21e8dd1..3ba5df0 100644
--- a/docs/reference/get_ref_trt.html
+++ b/docs/reference/get_ref_trt.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get reference treatment — get_ref_trt • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get reference treatment — get_ref_trt"><meta name="description" content="Get reference treatment"><meta property="og:description" content="Get reference treatment"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get reference treatment — get_ref_trt • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get reference treatment — get_ref_trt"><meta name="description" content="Get reference treatment"><meta property="og:description" content="Get reference treatment"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/get_robust_vcov.html b/docs/reference/get_robust_vcov.html
index 48b24e5..82b3e3a 100644
--- a/docs/reference/get_robust_vcov.html
+++ b/docs/reference/get_robust_vcov.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov"><meta name="description" content="Calculates (X'WX)^-1 (X' W^2 r^2 X) (X'WX)^-1"><meta property="og:description" content="Calculates (X'WX)^-1 (X' W^2 r^2 X) (X'WX)^-1"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov"><meta name="description" content="Calculates (X'WX)^-1 (X' W^2 r^2 X) (X'WX)^-1"><meta property="og:description" content="Calculates (X'WX)^-1 (X' W^2 r^2 X) (X'WX)^-1"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/get_treatment_effect.html b/docs/reference/get_treatment_effect.html
index 78ea50a..3289563 100644
--- a/docs/reference/get_treatment_effect.html
+++ b/docs/reference/get_treatment_effect.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get treatment effect scale corresponding to a link function — get_treatment_effect • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get treatment effect scale corresponding to a link function — get_treatment_effect"><meta name="description" content="Maps a given link function to its corresponding treatment effect scale."><meta property="og:description" content="Maps a given link function to its corresponding treatment effect scale."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get treatment effect scale corresponding to a link function — get_treatment_effect • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get treatment effect scale corresponding to a link function — get_treatment_effect"><meta name="description" content="Maps a given link function to its corresponding treatment effect scale."><meta property="og:description" content="Maps a given link function to its corresponding treatment effect scale."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/get_treatment_name.html b/docs/reference/get_treatment_name.html
index 0e35f91..ed3cbf1 100644
--- a/docs/reference/get_treatment_name.html
+++ b/docs/reference/get_treatment_name.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get treatment name — get_treatment_name • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get treatment name — get_treatment_name"><meta name="description" content="Get treatment name"><meta property="og:description" content="Get treatment name"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Get treatment name — get_treatment_name • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Get treatment name — get_treatment_name"><meta name="description" content="Get treatment name"><meta property="og:description" content="Get treatment name"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/get_var_method.html b/docs/reference/get_var_method.html
index 16bab6c..baa9800 100644
--- a/docs/reference/get_var_method.html
+++ b/docs/reference/get_var_method.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Determine and validate variance method for a strategy — get_var_method • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Determine and validate variance method for a strategy — get_var_method"><meta name="description" content="Determine and validate variance method for a strategy"><meta property="og:description" content="Determine and validate variance method for a strategy"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Determine and validate variance method for a strategy — get_var_method • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Determine and validate variance method for a strategy — get_var_method"><meta name="description" content="Determine and validate variance method for a strategy"><meta property="og:description" content="Determine and validate variance method for a strategy"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/guess_treatment_name.html b/docs/reference/guess_treatment_name.html
index c3cff46..fa7e00d 100644
--- a/docs/reference/guess_treatment_name.html
+++ b/docs/reference/guess_treatment_name.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Guess treatment name — guess_treatment_name • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Guess treatment name — guess_treatment_name"><meta name="description" content="Does a variable appear more than once in interactions?
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Guess treatment name — guess_treatment_name • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Guess treatment name — guess_treatment_name"><meta name="description" content="Does a variable appear more than once in interactions?
 If not then pick first LHS interaction term.
 Finally, if there are no interactions then pick last main effect term."><meta property="og:description" content="Does a variable appear more than once in interactions?
 If not then pick first LHS interaction term.
diff --git a/docs/reference/index.html b/docs/reference/index.html
index a461a06..dd2e273 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Package index • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Package index"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Package index • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Package index"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -179,6 +179,13 @@ <h2 id="constituent-statistics">Constituent statistics<a class="anchor" aria-lab
         </dt>
         <dd>Aggregate-level data mean and variance statistics</dd>
 
+        <dt>
+
+          <code><a href="calc_bucher_naive.html">calc_bucher_naive()</a></code>
+
+        </dt>
+        <dd>Calculate Naive (Unadjusted) Bucher Indirect Comparison</dd>
+
         <dt>
 
           <code><a href="calc_gcomp_bayes.html">calc_gcomp_bayes()</a></code>
diff --git a/docs/reference/index.md b/docs/reference/index.md
index 500ceb5..fcaa7de 100644
--- a/docs/reference/index.md
+++ b/docs/reference/index.md
@@ -58,6 +58,8 @@ Helper functions used by the main functions.
   : Estimate Variance Sandwich Estimator
 - [`calc_ALD_stats()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.md)
   : Aggregate-level data mean and variance statistics
+- [`calc_bucher_naive()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.md)
+  : Calculate Naive (Unadjusted) Bucher Indirect Comparison
 - [`calc_gcomp_bayes()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.md)
   : Bayesian G-computation using Stan
 - [`calc_gcomp_ml()`](https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.md)
diff --git a/docs/reference/maic.boot.html b/docs/reference/maic.boot.html
index 906fdcb..a9823a2 100644
--- a/docs/reference/maic.boot.html
+++ b/docs/reference/maic.boot.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>MAIC bootstrap sample — maic.boot • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="MAIC bootstrap sample — maic.boot"><meta name="description" content="Matching-adjusted indirect comparison bootstrap sampling."><meta property="og:description" content="Matching-adjusted indirect comparison bootstrap sampling."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>MAIC bootstrap sample — maic.boot • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="MAIC bootstrap sample — maic.boot"><meta name="description" content="Matching-adjusted indirect comparison bootstrap sampling."><meta property="og:description" content="Matching-adjusted indirect comparison bootstrap sampling."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
diff --git a/docs/reference/maic_weights.html b/docs/reference/maic_weights.html
index 5a8c083..1b7f3ec 100644
--- a/docs/reference/maic_weights.html
+++ b/docs/reference/maic_weights.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Estimate MAIC weights — maic_weights • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate MAIC weights — maic_weights"><meta name="description" content="Matching-adjusted indirect comparison weights.
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Estimate MAIC weights — maic_weights • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate MAIC weights — maic_weights"><meta name="description" content="Matching-adjusted indirect comparison weights.
 Method is taken from
 (Signorovitch et al. 2010)
 ."><meta property="og:description" content="Matching-adjusted indirect comparison weights.
@@ -69,10 +69,8 @@ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#refer
     <p>Signorovitch JE, Wu EQ, Yu AP, Gerrits CM, Kantor E, Bao Y, Gupta SR, Mulani PM (2010).
 “Comparative effectiveness without head-to-head trials: A method for matching-adjusted indirect comparisons applied to psoriasis treatment with adalimumab or etanercept.”
 <em>Pharmacoeconomics</em>, <b>28</b>(10), 935–945.
-ISSN 11707690.
-<a href="https://doi.org/10.2165/11538370-000000000-00000" class="external-link">doi:10.2165/11538370-000000000-00000</a>
-.
-<a href="https://pubmed.ncbi.nlm.nih.gov/20831302/" class="external-link">https://pubmed.ncbi.nlm.nih.gov/20831302/</a>.</p>
+ISSN 11707690, <a href="https://doi.org/10.2165/11538370-000000000-00000" class="external-link">doi:10.2165/11538370-000000000-00000</a>
+, <a href="https://pubmed.ncbi.nlm.nih.gov/20831302/" class="external-link">https://pubmed.ncbi.nlm.nih.gov/20831302/</a>.</p>
     </div>
 
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
diff --git a/docs/reference/maic_weights.md b/docs/reference/maic_weights.md
index e98915c..8362309 100644
--- a/docs/reference/maic_weights.md
+++ b/docs/reference/maic_weights.md
@@ -25,6 +25,6 @@ Signorovitch JE, Wu EQ, Yu AP, Gerrits CM, Kantor E, Bao Y, Gupta SR,
 Mulani PM (2010). “Comparative effectiveness without head-to-head
 trials: A method for matching-adjusted indirect comparisons applied to
 psoriasis treatment with adalimumab or etanercept.” *Pharmacoeconomics*,
-**28**(10), 935–945. ISSN 11707690.
+**28**(10), 935–945. ISSN 11707690,
 [doi:10.2165/11538370-000000000-00000](https://doi.org/10.2165/11538370-000000000-00000)
-. <https://pubmed.ncbi.nlm.nih.gov/20831302/>.
+, <https://pubmed.ncbi.nlm.nih.gov/20831302/>.
diff --git a/docs/reference/marginal_treatment_effect.html b/docs/reference/marginal_treatment_effect.html
index 2b5df9d..2ab0a40 100644
--- a/docs/reference/marginal_treatment_effect.html
+++ b/docs/reference/marginal_treatment_effect.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Marginal treatment effect from reported event counts — marginal_treatment_effect • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Marginal treatment effect from reported event counts — marginal_treatment_effect"><meta name="description" content="Computes the relative treatment effect from aggregate-level data using event counts."><meta property="og:description" content="Computes the relative treatment effect from aggregate-level data using event counts."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Marginal treatment effect from reported event counts — marginal_treatment_effect • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Marginal treatment effect from reported event counts — marginal_treatment_effect"><meta name="description" content="Computes the relative treatment effect from aggregate-level data using event counts."><meta property="og:description" content="Computes the relative treatment effect from aggregate-level data using event counts."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/marginal_variance.html b/docs/reference/marginal_variance.html
index 65fc322..057db72 100644
--- a/docs/reference/marginal_variance.html
+++ b/docs/reference/marginal_variance.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Marginal effect variance using the delta method — marginal_variance • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Marginal effect variance using the delta method — marginal_variance"><meta name="description" content="Computes the total variance of marginal treatment effects using the delta method."><meta property="og:description" content="Computes the total variance of marginal treatment effects using the delta method."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Marginal effect variance using the delta method — marginal_variance • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Marginal effect variance using the delta method — marginal_variance"><meta name="description" content="Computes the total variance of marginal treatment effects using the delta method."><meta property="og:description" content="Computes the total variance of marginal treatment effects using the delta method."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/num_grad.html b/docs/reference/num_grad.html
index 76acc99..ebc67d0 100644
--- a/docs/reference/num_grad.html
+++ b/docs/reference/num_grad.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Numerical Gradient — num_grad • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Numerical Gradient — num_grad"><meta name="description" content="Numerical Gradient"><meta property="og:description" content="Numerical Gradient"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Numerical Gradient — num_grad • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Numerical Gradient — num_grad"><meta name="description" content="Numerical Gradient"><meta property="og:description" content="Numerical Gradient"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/outstandR-class.html b/docs/reference/outstandR-class.html
index 69e19e5..6ebec8b 100644
--- a/docs/reference/outstandR-class.html
+++ b/docs/reference/outstandR-class.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>outstandR class — outstandR-class • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="outstandR class — outstandR-class"><meta name="description" content="The outstandR class contains the results from running a
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>outstandR class — outstandR-class • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="outstandR class — outstandR-class"><meta name="description" content="The outstandR class contains the results from running a
 model with the function outstandR()."><meta property="og:description" content="The outstandR class contains the results from running a
 model with the function outstandR()."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/outstandR-package.html b/docs/reference/outstandR-package.html
index 00416ed..171c9ab 100644
--- a/docs/reference/outstandR-package.html
+++ b/docs/reference/outstandR-package.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package"><meta name="description" content="
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package"><meta name="description" content="
 For the problem of indirect treatment comparison with limited subject-level data, this package provides tools for model-based standardisation with several different computation approaches. See Remiro‐Azócar A, Heath A, Baio G (2022) “Parametric G‐computation for compatible indirect treatment comparisons with limited individual patient data”, Res. Synth. Methods, 1–31. ISSN 1759-2879, doi:10.1002/jrsm.1565
 ."><meta property="og:description" content="
 For the problem of indirect treatment comparison with limited subject-level data, this package provides tools for model-based standardisation with several different computation approaches. See Remiro‐Azócar A, Heath A, Baio G (2022) “Parametric G‐computation for compatible indirect treatment comparisons with limited individual patient data”, Res. Synth. Methods, 1–31. ISSN 1759-2879, doi:10.1002/jrsm.1565
@@ -54,8 +54,7 @@ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"
     <div class="section level2">
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p><strong>Maintainer</strong>: Nathan Green <a href="mailto:n.green@ucl.ac.uk">n.green@ucl.ac.uk</a> (<a href="https://orcid.org/0000-0003-2745-1736" class="external-link">ORCID</a>) (<a href="https://ror.org/02jx3x895" class="external-link">ROR</a>) [copyright holder]</p>
-<p>Authors:</p><ul><li><p>Nathan Green <a href="mailto:n.green@ucl.ac.uk">n.green@ucl.ac.uk</a> (<a href="https://orcid.org/0000-0003-2745-1736" class="external-link">ORCID</a>) (<a href="https://ror.org/02jx3x895" class="external-link">ROR</a>) [copyright holder]</p></li>
-<li><p>Chengyang Gao <a href="mailto:chengyang.gao.15@ucl.ac.uk">chengyang.gao.15@ucl.ac.uk</a></p></li>
+<p>Authors:</p><ul><li><p>Chengyang Gao <a href="mailto:chengyang.gao.15@ucl.ac.uk">chengyang.gao.15@ucl.ac.uk</a></p></li>
 <li><p>Antonio Remiro-Azocar <a href="mailto:antonio.remiro-azocar@bayer.com">antonio.remiro-azocar@bayer.com</a> (<a href="https://orcid.org/0000-0002-7263-4251" class="external-link">ORCID</a>)</p></li>
 </ul></div>
 
diff --git a/docs/reference/outstandR-package.md b/docs/reference/outstandR-package.md
index 9bacc10..35243a7 100644
--- a/docs/reference/outstandR-package.md
+++ b/docs/reference/outstandR-package.md
@@ -25,10 +25,6 @@ Useful links:
 
 Authors:
 
-- Nathan Green <n.green@ucl.ac.uk>
-  ([ORCID](https://orcid.org/0000-0003-2745-1736))
-  ([ROR](https://ror.org/02jx3x895)) \[copyright holder\]
-
 - Chengyang Gao <chengyang.gao.15@ucl.ac.uk>
 
 - Antonio Remiro-Azocar <antonio.remiro-azocar@bayer.com>
diff --git a/docs/reference/outstandR.html b/docs/reference/outstandR.html
index 0f3e343..afdafd4 100644
--- a/docs/reference/outstandR.html
+++ b/docs/reference/outstandR.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate the difference between treatments using all evidence — outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate the difference between treatments using all evidence — outstandR"><meta name="description" content="This is the main, top-level wrapper for {outstandR}.
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate the difference between treatments using all evidence — outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate the difference between treatments using all evidence — outstandR"><meta name="description" content="This is the main, top-level wrapper for {outstandR}.
 Methods taken from
 (Remiro‐Azócar et al. 2022)
 ."><meta property="og:description" content="This is the main, top-level wrapper for {outstandR}.
@@ -127,10 +127,8 @@ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#refer
     <p>Remiro‐Azócar A, Heath A, Baio G (2022).
 “Parametric G‐computation for compatible indirect treatment comparisons with limited individual patient data.”
 <em>Res. Synth. Methods</em>, 1–31.
-ISSN 1759-2879.
-<a href="https://doi.org/10.1002/jrsm.1565" class="external-link">doi:10.1002/jrsm.1565</a>
-.
-2108.12208.</p>
+ISSN 1759-2879, <a href="https://doi.org/10.1002/jrsm.1565" class="external-link">doi:10.1002/jrsm.1565</a>
+, 2108.12208.</p>
     </div>
     <div class="section level2">
     <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
@@ -205,8 +203,8 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Gradient evaluation took 5.2e-05 seconds</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds.</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Gradient evaluation took 3.7e-05 seconds</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.37 seconds.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Adjust your expectations accordingly!</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
@@ -223,9 +221,9 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 520 / 1000 [ 52%]  (Sampling)</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:  Elapsed Time: 0.001 seconds (Warm-up)</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.074 seconds (Sampling)</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.075 seconds (Total)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:  Elapsed Time: 0.002 seconds (Warm-up)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.103 seconds (Sampling)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.105 seconds (Total)</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
 <span class="r-in"><span></span></span>
 <span class="r-in"><span><span class="co"># Multiple imputation marginalization</span></span></span>
@@ -240,8 +238,8 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Gradient evaluation took 3.2e-05 seconds</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.32 seconds.</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Gradient evaluation took 2.2e-05 seconds</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Adjust your expectations accordingly!</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
@@ -267,8 +265,8 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:  Elapsed Time: 0 seconds (Warm-up)</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.075 seconds (Sampling)</span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.075 seconds (Total)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.107 seconds (Sampling)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.107 seconds (Total)</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See</span>
 <span class="r-wrn co"><span class="r-pr">#&gt;</span> https://mc-stan.org/misc/warnings.html#bfmi-low</span>
diff --git a/docs/reference/outstandR.md b/docs/reference/outstandR.md
index 9243428..e5a33ff 100644
--- a/docs/reference/outstandR.md
+++ b/docs/reference/outstandR.md
@@ -100,8 +100,8 @@ values.
 
 Remiro‐Azócar A, Heath A, Baio G (2022). “Parametric G‐computation for
 compatible indirect treatment comparisons with limited individual
-patient data.” *Res. Synth. Methods*, 1–31. ISSN 1759-2879.
-[doi:10.1002/jrsm.1565](https://doi.org/10.1002/jrsm.1565) . 2108.12208.
+patient data.” *Res. Synth. Methods*, 1–31. ISSN 1759-2879,
+[doi:10.1002/jrsm.1565](https://doi.org/10.1002/jrsm.1565) , 2108.12208.
 
 ## See also
 
@@ -179,8 +179,8 @@ outstandR_gcomp_bayes <- outstandR(
 #> 
 #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
 #> Chain 1: 
-#> Chain 1: Gradient evaluation took 5.2e-05 seconds
-#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds.
+#> Chain 1: Gradient evaluation took 3.7e-05 seconds
+#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.37 seconds.
 #> Chain 1: Adjust your expectations accordingly!
 #> Chain 1: 
 #> Chain 1: 
@@ -197,9 +197,9 @@ outstandR_gcomp_bayes <- outstandR(
 #> Chain 1: Iteration: 520 / 1000 [ 52%]  (Sampling)
 #> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)
 #> Chain 1: 
-#> Chain 1:  Elapsed Time: 0.001 seconds (Warm-up)
-#> Chain 1:                0.074 seconds (Sampling)
-#> Chain 1:                0.075 seconds (Total)
+#> Chain 1:  Elapsed Time: 0.002 seconds (Warm-up)
+#> Chain 1:                0.103 seconds (Sampling)
+#> Chain 1:                0.105 seconds (Total)
 #> Chain 1: 
 
 # Multiple imputation marginalization
@@ -214,8 +214,8 @@ outstandR_mim <- outstandR(
 #> 
 #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
 #> Chain 1: 
-#> Chain 1: Gradient evaluation took 3.2e-05 seconds
-#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.32 seconds.
+#> Chain 1: Gradient evaluation took 2.2e-05 seconds
+#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.
 #> Chain 1: Adjust your expectations accordingly!
 #> Chain 1: 
 #> Chain 1: 
@@ -241,8 +241,8 @@ outstandR_mim <- outstandR(
 #> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)
 #> Chain 1: 
 #> Chain 1:  Elapsed Time: 0 seconds (Warm-up)
-#> Chain 1:                0.075 seconds (Sampling)
-#> Chain 1:                0.075 seconds (Total)
+#> Chain 1:                0.107 seconds (Sampling)
+#> Chain 1:                0.107 seconds (Total)
 #> Chain 1: 
 #> Warning: There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See
 #> https://mc-stan.org/misc/warnings.html#bfmi-low
diff --git a/docs/reference/plot.outstandR.html b/docs/reference/plot.outstandR.html
index 241b4ef..b0788ab 100644
--- a/docs/reference/plot.outstandR.html
+++ b/docs/reference/plot.outstandR.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Default Plot Method for outstandR Objects — plot.outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Default Plot Method for outstandR Objects — plot.outstandR"><meta name="description" content="Default Plot Method for outstandR Objects"><meta property="og:description" content="Default Plot Method for outstandR Objects"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Default Plot Method for outstandR Objects — plot.outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Default Plot Method for outstandR Objects — plot.outstandR"><meta name="description" content="Default Plot Method for outstandR Objects"><meta property="og:description" content="Default Plot Method for outstandR Objects"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -41,7 +41,13 @@
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'outstandR'</span></span>
-<span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">x</span>, <span class="va">...</span>, type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"both"</span>, <span class="st">"contrasts"</span>, <span class="st">"absolute"</span><span class="op">)</span>, labels <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span></span></code></pre></div>
+<span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span></span>
+<span>  <span class="va">x</span>,</span>
+<span>  <span class="va">...</span>,</span>
+<span>  type <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"both"</span>, <span class="st">"contrasts"</span>, <span class="st">"absolute"</span><span class="op">)</span>,</span>
+<span>  labels <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  include_naive <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span><span class="op">)</span></span></code></pre></div>
     </div>
 
     <div class="section level2">
@@ -63,6 +69,10 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <dt id="arg-labels">labels<a class="anchor" aria-label="anchor" href="#arg-labels"></a></dt>
 <dd><p>Optional character vector of names for the models.</p></dd>
 
+
+<dt id="arg-include-naive">include_naive<a class="anchor" aria-label="anchor" href="#arg-include-naive"></a></dt>
+<dd><p>Logical. Should naive (unadjusted) estimates be included in the plot? Default is TRUE.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
diff --git a/docs/reference/plot.outstandR.md b/docs/reference/plot.outstandR.md
index 2c320f0..f064499 100644
--- a/docs/reference/plot.outstandR.md
+++ b/docs/reference/plot.outstandR.md
@@ -6,7 +6,13 @@ Default Plot Method for outstandR Objects
 
 ``` r
 # S3 method for class 'outstandR'
-plot(x, ..., type = c("both", "contrasts", "absolute"), labels = NULL)
+plot(
+  x,
+  ...,
+  type = c("both", "contrasts", "absolute"),
+  labels = NULL,
+  include_naive = TRUE
+)
 ```
 
 ## Arguments
@@ -27,6 +33,11 @@ plot(x, ..., type = c("both", "contrasts", "absolute"), labels = NULL)
 
   Optional character vector of names for the models.
 
+- include_naive:
+
+  Logical. Should naive (unadjusted) estimates be included in the plot?
+  Default is TRUE.
+
 ## Value
 
 A
diff --git a/docs/reference/prep_ald.html b/docs/reference/prep_ald.html
index b9f0377..f5c78a4 100644
--- a/docs/reference/prep_ald.html
+++ b/docs/reference/prep_ald.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prepare Aggregate Level Data — prep_ald • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prepare Aggregate Level Data — prep_ald"><meta name="description" content="Prepare Aggregate Level Data"><meta property="og:description" content="Prepare Aggregate Level Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prepare Aggregate Level Data — prep_ald • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prepare Aggregate Level Data — prep_ald"><meta name="description" content="Prepare Aggregate Level Data"><meta property="og:description" content="Prepare Aggregate Level Data"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/prep_ipd.html b/docs/reference/prep_ipd.html
index 263b6b0..04c1a45 100644
--- a/docs/reference/prep_ipd.html
+++ b/docs/reference/prep_ipd.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prepare Individual Patient Data — prep_ipd • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prepare Individual Patient Data — prep_ipd"><meta name="description" content="Cleaning and subsetting input dataset so that they only
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prepare Individual Patient Data — prep_ipd • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prepare Individual Patient Data — prep_ipd"><meta name="description" content="Cleaning and subsetting input dataset so that they only
 contain the variables actually needed for statistical models."><meta property="og:description" content="Cleaning and subsetting input dataset so that they only
 contain the variables actually needed for statistical models."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
diff --git a/docs/reference/prepare_covariate_distns.html b/docs/reference/prepare_covariate_distns.html
index 775b64a..d24d899 100644
--- a/docs/reference/prepare_covariate_distns.html
+++ b/docs/reference/prepare_covariate_distns.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prepare Covariate Distributions — prepare_covariate_distns • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prepare Covariate Distributions — prepare_covariate_distns"><meta name="description" content="Resolves missing distributions and parameters by looking at the ALD.
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prepare Covariate Distributions — prepare_covariate_distns • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prepare Covariate Distributions — prepare_covariate_distns"><meta name="description" content="Resolves missing distributions and parameters by looking at the ALD.
 Allows for partial specification (e.g., user specifies one variable,
 function auto-detects the rest)."><meta property="og:description" content="Resolves missing distributions and parameters by looking at the ALD.
 Allows for partial specification (e.g., user specifies one variable,
diff --git a/docs/reference/print.outstandR.html b/docs/reference/print.outstandR.html
index dbd1d6d..0361542 100644
--- a/docs/reference/print.outstandR.html
+++ b/docs/reference/print.outstandR.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print a Summary of a outstandR Object — print.outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print a Summary of a outstandR Object — print.outstandR"><meta name="description" content='This is a method for the function print() for objects of the
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print a Summary of a outstandR Object — print.outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print a Summary of a outstandR Object — print.outstandR"><meta name="description" content='This is a method for the function print() for objects of the
 class "outstandR" created by a call to outstandR()'><meta property="og:description" content='This is a method for the function print() for objects of the
 class "outstandR" created by a call to outstandR()'><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
diff --git a/docs/reference/reshape_ald_to_long.html b/docs/reference/reshape_ald_to_long.html
index ac31ef5..c9d6a93 100644
--- a/docs/reference/reshape_ald_to_long.html
+++ b/docs/reference/reshape_ald_to_long.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Convert aggregate data from wide to long format — reshape_ald_to_long • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Convert aggregate data from wide to long format — reshape_ald_to_long"><meta name="description" content="Convert aggregate data from wide to long format"><meta property="og:description" content="Convert aggregate data from wide to long format"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Convert aggregate data from wide to long format — reshape_ald_to_long • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Convert aggregate data from wide to long format — reshape_ald_to_long"><meta name="description" content="Convert aggregate data from wide to long format"><meta property="og:description" content="Convert aggregate data from wide to long format"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/reshape_ald_to_wide.html b/docs/reference/reshape_ald_to_wide.html
index 4debba4..01832ff 100644
--- a/docs/reference/reshape_ald_to_wide.html
+++ b/docs/reference/reshape_ald_to_wide.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Convert aggregate data from long to wide format — reshape_ald_to_wide • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Convert aggregate data from long to wide format — reshape_ald_to_wide"><meta name="description" content="Convert aggregate data from long to wide format"><meta property="og:description" content="Convert aggregate data from long to wide format"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Convert aggregate data from long to wide format — reshape_ald_to_wide • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Convert aggregate data from long to wide format — reshape_ald_to_wide"><meta name="description" content="Convert aggregate data from long to wide format"><meta property="og:description" content="Convert aggregate data from long to wide format"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/result_stats.html b/docs/reference/result_stats.html
index fb82f37..3a909e4 100644
--- a/docs/reference/result_stats.html
+++ b/docs/reference/result_stats.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate and arrange result statistics — result_stats • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate and arrange result statistics — result_stats"><meta name="description" content="Combining output from aggregate level data studies BC and
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate and arrange result statistics — result_stats • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate and arrange result statistics — result_stats"><meta name="description" content="Combining output from aggregate level data studies BC and
 adjusted individual level data studies AC into a single object."><meta property="og:description" content="Combining output from aggregate level data studies BC and
 adjusted individual level data studies AC into a single object."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/simulate_ALD_pseudo_pop.html b/docs/reference/simulate_ALD_pseudo_pop.html
index 15f7abc..aaa22be 100644
--- a/docs/reference/simulate_ALD_pseudo_pop.html
+++ b/docs/reference/simulate_ALD_pseudo_pop.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop"><meta name="description" content="Generates a synthetic cohort using a normal copula based on aggregate-level data."><meta property="og:description" content="Generates a synthetic cohort using a normal copula based on aggregate-level data."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop"><meta name="description" content="Generates a synthetic cohort using a normal copula based on aggregate-level data."><meta property="og:description" content="Generates a synthetic cohort using a normal copula based on aggregate-level data."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/strategy-class.html b/docs/reference/strategy-class.html
index 2d2b8af..f89542c 100644
--- a/docs/reference/strategy-class.html
+++ b/docs/reference/strategy-class.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Strategy class and subclasses — strategy-class • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Strategy class and subclasses — strategy-class"><meta name="description" content="The strategy class is a virtual class that defines the statistical approach
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Strategy class and subclasses — strategy-class • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Strategy class and subclasses — strategy-class"><meta name="description" content="The strategy class is a virtual class that defines the statistical approach
 for population adjustment in indirect treatment comparisons
 These objects are constructors that validate hyperparameters and encapsulate
 modelling settings before execution by outstandR()"><meta property="og:description" content="The strategy class is a virtual class that defines the statistical approach
diff --git a/docs/reference/strategy.html b/docs/reference/strategy.html
index 18cad5c..0e80a2f 100644
--- a/docs/reference/strategy.html
+++ b/docs/reference/strategy.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>New strategy objects — strategy_maic • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="New strategy objects — strategy_maic"><meta name="description" content="Create a type of strategy class for each modelling approach."><meta property="og:description" content="Create a type of strategy class for each modelling approach."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/summary.outstandR.html b/docs/reference/summary.outstandR.html
index 5f0c831..b482d99 100644
--- a/docs/reference/summary.outstandR.html
+++ b/docs/reference/summary.outstandR.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summary method for outstandR — summary.outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summary method for outstandR — summary.outstandR"><meta name="description" content="Summary method for outstandR"><meta property="og:description" content="Summary method for outstandR"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summary method for outstandR — summary.outstandR • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summary method for outstandR — summary.outstandR"><meta name="description" content="Summary method for outstandR"><meta property="og:description" content="Summary method for outstandR"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/validate_outstandr.html b/docs/reference/validate_outstandr.html
index 3b63eda..fd327e6 100644
--- a/docs/reference/validate_outstandr.html
+++ b/docs/reference/validate_outstandr.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Input data validator — validate_outstandr • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Input data validator — validate_outstandr"><meta name="description" content="Input data validator"><meta property="og:description" content="Input data validator"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Input data validator — validate_outstandr • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Input data validator — validate_outstandr"><meta name="description" content="Input data validator"><meta property="og:description" content="Input data validator"><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/var_by_pooling.html b/docs/reference/var_by_pooling.html
index a22e5be..8115032 100644
--- a/docs/reference/var_by_pooling.html
+++ b/docs/reference/var_by_pooling.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Variance estimate by pooling — var_by_pooling • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Variance estimate by pooling — var_by_pooling"><meta name="description" content="Use combining rules to estimate."><meta property="og:description" content="Use combining rules to estimate."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Variance estimate by pooling — var_by_pooling • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Variance estimate by pooling — var_by_pooling"><meta name="description" content="Use combining rules to estimate."><meta property="og:description" content="Use combining rules to estimate."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/reference/wald_type_interval.html b/docs/reference/wald_type_interval.html
index bce7548..0984e5e 100644
--- a/docs/reference/wald_type_interval.html
+++ b/docs/reference/wald_type_interval.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Wald-type interval estimates — wald_type_interval • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.8/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.8/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Wald-type interval estimates — wald_type_interval"><meta name="description" content="Constructed using t-distribution with nu degrees of freedom."><meta property="og:description" content="Constructed using t-distribution with nu degrees of freedom."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Wald-type interval estimates — wald_type_interval • outstandR</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Wald-type interval estimates — wald_type_interval"><meta name="description" content="Constructed using t-distribution with nu degrees of freedom."><meta property="og:description" content="Constructed using t-distribution with nu degrees of freedom."><meta property="og:image" content="https://StatisticsHealthEconomics.github.io/outstandR/logo.png"></head><body>
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diff --git a/docs/search.json b/docs/search.json
index a4b58ff..49e1417 100644
--- a/docs/search.json
+++ b/docs/search.json
@@ -1 +1 @@
-[{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-1-create-the-strategy-constructor","dir":"Articles","previous_headings":"","what":"Step 1: Create the Strategy Constructor","title":"Adding a New Strategy to `outstandR`","text":"File: R/strategy_.R First, create user-facing constructor function validates user inputs instantiates strategy object. convention, function named strategy_<method_name>(). must call internal new_strategy() function, passing class name validated arguments.","code":"#' @rdname strategy #'  #' @section Custom Method: #' Describe the statistical theory behind the new method here. #'  #' @param trt_var Treatment variable name #' @param my_custom_arg Description of your custom argument #'  #' @return `custom_method` class object #' @export strategy_custom_method <- function(formula = NULL,                                    family = gaussian(link = \"identity\"),                                    trt_var = NULL,                                    my_custom_arg = 100) {      # 1. Validate inputs using built-in helpers   check_formula(formula, trt_var)   check_family(family)      if (my_custom_arg <= 0) {     stop(\"my_custom_arg must be greater than 0.\")   }      # 2. Bundle arguments   args <- list(formula = formula,                family = family,                trt_var = get_treatment_name(formula, trt_var),                my_custom_arg = my_custom_arg)      # 3. Create object   do.call(new_strategy, c(strategy = \"custom_method\", args)) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-2-document-the-class-fields","dir":"Articles","previous_headings":"","what":"Step 2: Document the Class Fields","title":"Adding a New Strategy to `outstandR`","text":"File: R/strategy-class.R Update strategy-class documentation inform users internal fields new subclass carries. Add new \\item block details section:","code":"#'   \\item{custom_method subclass}{Additional fields for the Custom Method: #'     \\itemize{ #'       \\item `my_custom_arg`: Describes what this internal field does. #'     } #'   }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-3-write-the-core-calculation-function","dir":"Articles","previous_headings":"","what":"Step 3: Write the Core Calculation Function","title":"Adding a New Strategy to `outstandR`","text":"File: Create new file (e.g., R/custom_method.R) add existing calculation files. Write function actually performs maths. receive two arguments: strategy (object created Step 1) analysis_params (list containing pre-processed ipd, ald, treatment labels, etc.). Crucial Requirement: function MUST return list containing exactly two elements: means model. means$: Estimates comparator treatment group (can scalar, vector bootstrap/MCMC draws). means$C: Estimates reference treatment group (can scalar, vector bootstrap/MCMC draws). model: list underlying models diagnostics (e.g., weights, glm fit objects) want returned user.","code":"#' Calculate Custom Method #' @keywords internal calc_custom_method <- function(strategy, analysis_params) {      # Extract data and parameters   ipd <- analysis_params$ipd   ald <- analysis_params$ald   formula <- strategy$formula   custom_val <- strategy$my_custom_arg      # ... [PERFORM YOUR STATISTICAL MODELLING HERE] ...   # e.g., fit a model, run bootstraps, calculate weights      # Construct the strict return object   list(     means = list(       A = estimated_means_for_A,        C = estimated_means_for_C     ),     model = list(       fit = my_fitted_model,       custom_val = custom_val     )   ) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-4-register-the-s3-dispatch-method","dir":"Articles","previous_headings":"","what":"Step 4: Register the S3 Dispatch Method","title":"Adding a New Strategy to `outstandR`","text":"File: R/calc_IPD_stats.R plug core function outstandR’s top-level execution, must register S3 method calc_IPD_stats. outstandR handles relative treatment effect transformations (ATE) variance estimation automatically, simply pass core function IPD_stat_factory().","code":"#' @rdname calc_IPD_stats #' @section Custom Method statistics: #' Description of how the custom method calculates statistics. #' @export calc_IPD_stats.custom_method <- IPD_stat_factory(calc_custom_method)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-5-add-a-print-method","dir":"Articles","previous_headings":"","what":"Step 5: Add a Print Method","title":"Adding a New Strategy to `outstandR`","text":"File: R/print-strategies.R Finally, create nice console printout user types name instantiated strategy. Extend generic print.strategy using NextMethod() print common fields, print specific parameters.","code":"#' @export #' @method print custom_method print.custom_method <- function(x, ...) {   # Print the standard strategy info (formula, family)   NextMethod()       # Print custom subclass info   cat(pillar::style_subtle(\"  Parameters:\"), \"\\n\")   cat(\"    Custom Argument:     \", x$my_custom_arg, \"\\n\")      invisible(x) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"optional-step-6-passing-random-seeds","dir":"Articles","previous_headings":"","what":"(Optional) Step 6: Passing Random Seeds","title":"Adding a New Strategy to `outstandR`","text":"new method utilizes random number generator (e.g., MCMC sampling, pseudo-population simulation), might need catch top-level seed argument. File: R/outstandR.R Create add_seed S3 method strategy: section can append vignette developer guide. provides copy-pasteable utility script future contributors can use automate boilerplate setup new strategy.","code":"#' @export add_seed.custom_method <- function(strategy, fn_args, seed) {   if (!is.null(seed)) {     fn_args$seed <- seed   }   return(fn_args) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-7-automating-boilerplate-with-a-scaffolding-script-optional","dir":"Articles","previous_headings":"","what":"Step 7: Automating Boilerplate with a Scaffolding Script (Optional)","title":"Adding a New Strategy to `outstandR`","text":"contributors find adding new strategies frequently, can automate creation boilerplate files using usethis package. recommend saving following helper function script file (e.g., scripts/scaffold_strategy.R). script automatically create necessary calculation file open registry files edit.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"how-to-use-it","dir":"Articles","previous_headings":"Step 7: Automating Boilerplate with a Scaffolding Script (Optional)","what":"How to Use It","title":"Adding a New Strategy to `outstandR`","text":"ready build new method, simply source script run function name new method: instantly set workspace, leaving focus solely statistical implementation rather package wiring! section can add Markdown document (perhaps end, right scaffolding script) outlines best practices writing robust, user-friendly strategy outstandR.","code":"# Load the helper function source(\"scripts/scaffold_strategy.R\")  # Scaffold a new method called \"gcomp_rf\" (e.g., Random Forest G-computation) scaffold_strategy(\"gcomp_rf\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"best-practices-for-writing-a-good-strategy","dir":"Articles","previous_headings":"","what":"Best Practices for Writing a Good Strategy","title":"Adding a New Strategy to `outstandR`","text":"contributing new statistical approach outstandR, following guidelines ensures method robust, user-friendly, maintainable.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"fail-fast-and-validate-early","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"1. Fail Fast and Validate Early","title":"Adding a New Strategy to `outstandR`","text":"Catch user errors constructor function (strategy_custom_method()) heavy computation begins. Use package’s built-check_formula() check_family() helpers. method requires specific types data (e.g., binary outcomes), enforce immediately:","code":"if (family$family != \"binomial\") {   cli::cli_abort(\"Custom Method currently only supports binary outcomes (`family = binomial()`).\") }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"return-a-rich-model-object","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"2. Return a Rich model Object","title":"Adding a New Strategy to `outstandR`","text":"core calculation function must return list means model. means strictly structured, model element free-form list. Use give user much diagnostic power possible. Good things include: raw fitted model objects (e.g., glm stanfit), calculated weights, convergence status flags, effective sample sizes (ESS). allows users extract model final outstandR object check diagnostics .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"handle-convergence-issues-gracefully","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"3. Handle Convergence Issues Gracefully","title":"Adding a New Strategy to `outstandR`","text":"Many population adjustment methods rely optimization iterative fitting (like GLMs MAIC). internal model fails converge, function shouldn’t crash entire R session—especially bootstrap loop. Wrap volatile model fitting tryCatch(). fit fails, return NA means pass warning user.","code":"fit <- tryCatch({   glm(formula, data = ipd, family = family) }, warning = function(w) {   # Handle warnings (e.g., probabilities numerically 0 or 1)   glm(formula, data = ipd, family = family) }, error = function(e) {   NULL # Return NULL on hard failure })  if (is.null(fit)) return(list(means = list(A = NA, C = NA), model = list(converged = FALSE)))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"respect-the-verbose-flag","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"4. Respect the verbose Flag","title":"Adding a New Strategy to `outstandR`","text":"outstandR provides global verbose argument users can silence console output heavy simulations. Extract verbose <- isTRUE(analysis_params$verbose) top calculation function. Use cli package print progress updates warn users computationally expensive steps, verbose true.","code":"if (verbose) {   cli::cli_h2(\"Custom Method Execution\")   cli::cli_alert_info(\"Optimizing weights. This may take a moment...\") }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"write-unit-tests-for-your-method","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"5. Write Unit Tests for Your Method","title":"Adding a New Strategy to `outstandR`","text":"Whenever add new strategy, add corresponding test file tests/testthat/ (e.g., test-custom_method.R). Test strategy constructor throws errors bad inputs. Use package’s built-dummy data (AC_IPD_binY_contX, etc.) run fast, low-iteration version method ensure output list matches required list(means = ..., model = ...) structure.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Basic Example","text":"Population adjustment methods matching-adjusted indirect comparison (MAIC) increasingly used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. MAIC based propensity score weighting, sensitive poor covariate overlap extrapolate beyond observed covariate space. Current outcome regression-based alternatives can extrapolate target conditional treatment effect incompatible indirect comparison. adjusting covariates, one must integrate average conditional estimate relevant population recover compatible marginal treatment effect. propose marginalization method based parametric G-computation can easily applied outcome regression generalized linear model Cox model. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. method can accommodate Bayesian statistical framework, naturally integrates analysis probabilistic framework. simulation study provides proof--principle benchmarks method’s performance MAIC conventional outcome regression. Parametric G-computation achieves precise accurate estimates MAIC, particularly covariate overlap poor, yields unbiased marginal treatment effect estimates failures assumptions. Furthermore, marginalized regression-adjusted estimates provide greater precision accuracy conditional estimates produced conventional outcome regression.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"general-problem","dir":"Articles","previous_headings":"","what":"General problem","title":"Basic Example","text":"Consider one AB trial, company IPD, one AC trial, published aggregate data available. wish estimate comparison effects treatments B C appropriate scale target population P, denoted parameter dBC(P)d_{BC(P)}. make use bracketed subscripts denote specific population. Within AB population parameters μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)} μC(AB)\\mu_{C(AB)} representing expected outcome treatment (including parameters treatments studied AB trial, e.g. treatment C). AB trial provides estimators Y‾(AB)\\bar{Y}_{(AB)} Y‾B(AB)\\bar{Y}_{B(AB)} μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)}, respectively, summary outcomes. situation AC trial. suitable scale, example logit, risk difference, form estimators ΔAB(AB)\\Delta_{AB(AB)} ΔAC(AC)\\Delta_{AC(AC)} trial level (marginal) relative treatment effects. ΔAB(AB)=g(Y‾B(AB))−g(Y‾(AB)) \\Delta_{AB(AB)} = g(\\bar{Y}_{B{(AB)}}) - g(\\bar{Y}_{{(AB)}})","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Basic Example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Basic Example","text":"Next, load data use analysis. data comes simulation study Remiro‐Azócar , Heath , Baio G (2020). consider binary outcomes using log-odds ratio measure effect. binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yny_n subject nn simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. general format data sets consist following.","code":"set.seed(555)  AC.IPD <- read.csv(here::here(\"raw-data\", \"AC_IPD.csv\"))  # AC patient-level data BC.ALD <- read.csv(here::here(\"raw-data\", \"BC_ALD.csv\"))  # BC aggregate-level data"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"ac-ipd-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"AC.IPD: Individual patient data","title":"Basic Example","text":"X*: patient measurements trt: treatment ID y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"bc-ald-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"BC.ALD: Aggregate-level data","title":"Basic Example","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: total number events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"head(AC.IPD) #>            X1        X2          X3          X4 trt y #> 1  0.43734111 0.6747901  0.93001035  0.09165363   1 0 #> 2  0.05643081 0.5987971  0.03557646  0.59954129   1 1 #> 3 -0.08048882 0.6843784  0.93147222 -0.11419716   1 0 #> 4 -0.38580926 0.5716644 -0.32252212  0.02551808   1 0 #> 5  1.00755116 0.8220826  0.92735892  0.84414221   1 1 #> 6  0.19443956 0.2031329  0.34990179  0.15633009   1 0 BC.ALD #>     mean.X1   mean.X2   mean.X3   mean.X4     sd.X1     sd.X2     sd.X3 #> 1 0.5908996 0.6414179 0.5856529 0.6023671 0.3863145 0.4033615 0.4076097 #>      sd.X4 y.B.sum y.B.bar N.B y.C.sum y.C.bar N.C #> 1 0.395132     182   0.455 400     149   0.745 200"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Basic Example","text":"implement MAIC, STC, G-computation methods obtain marginal variance, defined 1nC+1nC‾+1nB+1nB‾ \\frac{1}{n_C} + \\frac{1}{n_{\\bar{C}}} + \\frac{1}{n_B} + \\frac{1}{n_{\\bar{B}}} marginal treatment effect, defined log(nB/(NB−nB)nC/(NB−nB))=log(nBnC‾)−log(nCnB‾) \\log\\left( \\frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \\right) = \\log(n_B n_{\\bar{C}}) - \\log(n_C n_{\\bar{B}})  C‾\\bar{C} compliment CC e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Basic Example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Basic Example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2  corresponds following R formula object passed argument strategy function. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <- outstandR(AC.IPD, BC.ALD, strategy = strategy_maic(formula = lin_form)) outstandR_maic #> $contrasts #> $contrasts$AB #> [1] 0.5008915 #>  #> $contrasts$AC #> [1] -1.151838 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #>           [,1] #> [1,] 0.1732497 #>  #> $variances$AC #>           [,1] #> [1,] 0.1368488 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.3149097  1.3166927 #>  #> $CI$AC #> [1] -1.8768893 -0.4267873 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Basic Example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1)  β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2})  However, outstandR() knows handle can simply pass (uncentred) formula . last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <- outstandR(AC.IPD, BC.ALD, strategy = strategy_stc(formula = lin_form)) outstandR_stc #> $contrasts #> $contrasts$AB #>     trt  #> 0.22425  #>  #> $contrasts$AC #>      trt  #> -1.42848  #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #> [1] 0.1690646 #>  #> $variances$AC #> [1] 0.1326637 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.5816375  1.0301375 #>  #> $CI$AC #> [1] -2.1423580 -0.7146016 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Basic Example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_ml(formula = lin_form)) outstandR_gcomp_ml #> $contrasts #> $contrasts$AB #> [1] 0.5645192 #>  #> $contrasts$AC #> [1] -1.088211 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #>           [,1] #> [1,] 0.1425196 #>  #> $variances$AC #>           [,1] #> [1,] 0.1061187 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.1754018  1.3044402 #>  #> $CI$AC #> [1] -1.7266857 -0.4497354 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Basic Example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment.","code":"outstandR_gcomp_bayes <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_bayes(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.8e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.38 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.522 seconds (Warm-up) #> Chain 1:                0.499 seconds (Sampling) #> Chain 1:                1.021 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.8e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.508 seconds (Warm-up) #> Chain 2:                0.534 seconds (Sampling) #> Chain 2:                1.042 seconds (Total) #> Chain 2: outstandR_gcomp_bayes #> $contrasts #> $contrasts$AB #> [1] 0.5614387 #>  #> $contrasts$AC #> [1] -1.091291 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #> [1] 0.137929 #>  #> $variances$AC #> [1] 0.1015281 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.1664684  1.2893457 #>  #> $CI$AC #> [1] -1.7158038 -0.4667785 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Basic Example","text":"ref equationhere equation Combine outputs","code":"outstandR_mim <- outstandR(AC.IPD, BC.ALD, strategy = strategy_mim(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 2.3e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 1: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 1: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 1: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 1: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 1: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 1: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 1: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.254 seconds (Warm-up) #> Chain 1:                0.751 seconds (Sampling) #> Chain 1:                1.005 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.8e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 2: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 2: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 2: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 2: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 2: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 2: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 2: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.262 seconds (Warm-up) #> Chain 2:                0.768 seconds (Sampling) #> Chain 2:                1.03 seconds (Total) #> Chain 2: outstandR_mim #> $contrasts #> $contrasts$AB #> [1] 0.5811889 #>  #> $contrasts$AC #> [1] -1.071541 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #> [1] 0.1330941 #>  #> $variances$AC #> [1] 0.09669322 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.1338465  1.2962243 #>  #> $CI$AC #> [1] -1.6810021 -0.4620796 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\" knitr::kable(   data.frame(   `MAIC` = unlist(outstandR_maic$contrasts),   `STC` = unlist(outstandR_stc$contrasts),   `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts),   `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts),   `MIM` = unlist(outstandR_mim$contrasts)) )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Binary data example","text":"Population adjustment methods matching-adjusted indirect comparison (MAIC) increasingly used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. MAIC based propensity score weighting, sensitive poor covariate overlap extrapolate beyond observed covariate space. Current outcome regression-based alternatives can extrapolate target conditional treatment effect incompatible indirect comparison. adjusting covariates, one must integrate average conditional estimate relevant population recover compatible marginal treatment effect. propose marginalization method based parametric G-computation can easily applied outcome regression generalized linear model Cox model. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. method can accommodate Bayesian statistical framework, naturally integrates analysis probabilistic framework. simulation study provides proof--principle benchmarks method’s performance MAIC conventional outcome regression. Parametric G-computation achieves precise accurate estimates MAIC, particularly covariate overlap poor, yields unbiased marginal treatment effect estimates failures assumptions. Furthermore, marginalized regression-adjusted estimates provide greater precision accuracy conditional estimates produced conventional outcome regression.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"general-problem","dir":"Articles","previous_headings":"","what":"General problem","title":"Binary data example","text":"Consider one trial, company IPD, comparing treatments C, herein call AC trial. Also, consider second trial comparing treatments B C, similarly called BC trial. trial published aggregate data available. wish estimate comparison effects treatments B appropriate scale target population P, denoted parameter dAB(P)d_{AB(P)}. make use bracketed subscripts denote specific population. Within BC population parameters μB(BC)\\mu_{B(BC)} μC(BC)\\mu_{C(BC)} representing expected outcome treatment (including parameters treatments studied BC trial, e.g. treatment ). BC trial provides estimators Y‾B(BC)\\bar{Y}_{B(BC)} Y‾C(BC)\\bar{Y}_{C(BC)} μB(BC)\\mu_{B(BC)}, μC(BC)\\mu_{C(BC)}, respectively, summary outcomes. situation AC trial. suitable scale, example log-odds ratio, risk difference, form estimators ΔBC(BC)\\Delta_{BC(BC)} ΔAC(AC)\\Delta_{AC(AC)} trial level (marginal) relative treatment effects. shall assume always represented difference , example, risk ratio log scale. ΔAB(BC)=g(Y‾B(BC))−g(Y‾(BC)) \\Delta_{AB(BC)} = g(\\bar{Y}_{B{(BC)}}) - g(\\bar{Y}_{{(BC)}})","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Binary data example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Binary data example","text":"consider binary outcomes using log-odds ratio measure effect. example, binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yiy_i subject ii simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. IPD simulation input parameters given . shall use gen_data() function available simcovariates package. treatment column return data binary takes values 0 1. include extra information treatment names. define lable two level factor 1 C 0 follows. Similarly, obtain aggregate data simulate IPD additional summarise step. set different mean values meanX_BC meanX_EM_BC otherwise use parameter values ACAC case. general format data sets consist following.","code":"library(dplyr) library(MASS)  N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = binomial(\"logit\")) ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = binomial(\"logit\"))  cov.X <- BC.IPD %>%   summarise(across(starts_with(\"X\"),                    list(mean = mean, sd = sd),                    .names = \"{fn}.{col}\"))  out.B <- dplyr::filter(BC.IPD, trt == 1) %>%   summarise(y.B.sum = sum(y),             y.B.bar = mean(y),             y.B.sd = sd(y),             N.B = n())  out.C <- dplyr::filter(BC.IPD, trt == 0) %>%   summarise(y.C.sum = sum(y),             y.C.bar = mean(y),             y.C.sd = sd(y),             N.C = n())  ald_trial <- cbind.data.frame(cov.X, out.C, out.B)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Binary data example","text":"X*: patient measurements trt: treatment ID (integer) y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Binary data example","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: proportion events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt 1 corresponds new treatment , 0 standard care status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"head(ipd_trial) #>           X1         X2         X3         X4 trt y #> 1 0.42066874  1.0957407 0.37118099  1.3291540   A 1 #> 2 0.51227329  0.9079984 0.30560144 -0.1842358   A 0 #> 3 1.00347612  0.8136847 1.25054503  1.1986315   A 0 #> 4 0.05641685  0.5318140 0.54799796  0.6694090   A 0 #> 5 0.42997845  0.5274304 0.09140568  0.1222184   A 0 #> 6 0.06916082 -0.3125090 0.99150666 -0.1102693   A 0 ald_trial #>    mean.X1     sd.X1  mean.X2     sd.X2   mean.X3     sd.X3  mean.X4     sd.X4 #> 1 0.568822 0.3972807 0.623277 0.3850408 0.5787528 0.3906499 0.565223 0.3789089 #>   y.C.sum   y.C.bar    y.C.sd N.C y.B.sum   y.B.bar    y.B.sd N.B #> 1      34 0.5074627 0.5037175  67      34 0.2556391 0.4378691 133"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"regression-model","dir":"Articles","previous_headings":"Example analysis > Data","what":"Regression model","title":"Binary data example","text":"true logistic outcome model use simulate data logit(pt)=β0+βX(X3+X4)+[βt+βEM(X1+X2)](t≠C) \\text{logit}(p_{t}) = \\beta_0 + \\beta_X (X_3 + X_4) + [\\beta_{t} + \\beta_{EM} (X_1 + X_2)] \\; \\text{}(t \\neq C) , treatment CC right hand side becomes β0+βX(X3+X4)\\beta_0 + \\beta_X (X_3 + X_4) comparator treatments AA BB additional βt+βEM(X1+X2)\\beta_t + \\beta_{EM} (X_1 + X_2) component consisting effect modifier terms coefficient treatment parameter log odds-ratio (LOR), βt\\beta_t (b_trt R code). ptp_{t} probability experiencing event interest treatment tt.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Binary data example","text":"implement MAIC, STC, G-computation methods obtain marginal treatment effect marginal variance. definition calculated depends type data outcome scale. current example binary data log-odds ratio marginal treatment effect log(nB/(NB−nB)nC/(NB−nB))=log(nBnC‾)−log(nCnB‾) \\log\\left( \\frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \\right) = \\log(n_B n_{\\bar{C}}) - \\log(n_C n_{\\bar{B}}) marginal variance 1nC+1nC‾+1nB+1nB‾ \\frac{1}{n_C} + \\frac{1}{n_{\\bar{C}}} + \\frac{1}{n_B} + \\frac{1}{n_{\\bar{B}}}  nB,nCn_B, n_C number events arm C‾\\bar{C} compliment CC, e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c. scales discussed .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Binary data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"model-formula","dir":"Articles","previous_headings":"Model fitting in R","what":"Model formula","title":"Binary data example","text":"Defining X1,X2X_1, X_2 effect modifiers, X3,X4X_3, X_4 prognostic variables ZZ treatment indicator formula used model y=X3+X4+Z+ZX1+ZX2 y = X_3 + X_4 + Z + Z X_1 + Z X_2 corresponds following R formula object passed argument strategy function. Note succinct formula also include X1,X2X_1, X_2 prognostic factors equivalent, modified follows.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt + trt:X1 + trt:X2\") y ~ X3 + X4 + trt*(X1 + X2) y ~ X3 + X4 + trt*(X1 + X2) - X1 - X2"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Binary data example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument. print method available outstandR objects human-readable output","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = binomial(link = \"logit\"))) str(outstandR_maic) #> List of 2 #>  $ contrasts:List of 3 #>   ..$ means    :List of 3 #>   .. ..$ AB: num -1 #>   .. ..$ AC: num -2.1 #>   .. ..$ BC: num -1.1 #>   ..$ variances:List of 3 #>   .. ..$ AB: num 0.259 #>   .. ..$ AC: num 0.16 #>   .. ..$ BC: num 0.0992 #>   ..$ CI       :List of 3 #>   .. ..$ AB: num [1:2] -1.99888 -0.00345 #>   .. ..$ AC: num [1:2] -2.88 -1.32 #>   .. ..$ BC: num [1:2] -1.716 -0.481 #>  $ absolute :List of 2 #>   ..$ means    :List of 2 #>   .. ..$ A: Named num 0.227 #>   .. .. ..- attr(*, \"names\")= chr \"mean_A\" #>   .. ..$ C: Named num 0.698 #>   .. .. ..- attr(*, \"names\")= chr \"mean_C\" #>   ..$ variances:List of 2 #>   .. ..$ A: Named num 0.00202 #>   .. .. ..- attr(*, \"names\")= chr \"mean_A\" #>   .. ..$ C: Named num 0.0035 #>   .. .. ..- attr(*, \"names\")= chr \"mean_C\" #>  - attr(*, \"CI\")= num 0.95 #>  - attr(*, \"ref_trt\")= chr \"C\" #>  - attr(*, \"scale\")= chr \"log_odds\" #>  - attr(*, \"model\")= chr \"binomial\" #>  - attr(*, \"class\")= chr [1:2] \"outstandR\" \"list\" outstandR_maic #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            -1.00    0.259       -2.00   -0.00345 #> 2 AC            -2.10    0.160       -2.88   -1.32    #> 3 BC            -1.10    0.0992      -1.72   -0.481   #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.227   0.00202 NA         NA         #> 2 C             0.698   0.00350 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"outcome-scale","dir":"Articles","previous_headings":"Model fitting in R > MAIC","what":"Outcome scale","title":"Binary data example","text":"explicitly specify outcome scale, default used fit data regression model. saw, case, default log-odds ratio corresponding \"logit\" link function binary data. However, can change scale may appropriate particular analysis. far implemented package, links corresponding relative treatment effect scales follows: full list possible transformed treatment effect scales : log-odds ratio, log-risk ratio, mean difference, risk difference, hazard ratio, hazard difference. binary data marginal treatment effect variance Log-risk ratio Treatment effect log(nB/NB)−log(nA/NA) \\log(n_B/N_B) - \\log(n_A/N_A)  variance 1nB−1NB+1nA−1NA \\frac{1}{n_B} - \\frac{1}{N_B} + \\frac{1}{n_A} - \\frac{1}{N_A} Risk difference Treatment effect nBNB−nANA \\frac{n_B}{N_B} - \\frac{n_A}{N_A}  variance nBNB(1−nBNB)+nANA(1−nANA) \\frac{n_B}{N_B} \\left( 1 - \\frac{n_B}{N_B} \\right) + \\frac{n_A}{N_A} \\left( 1 - \\frac{n_A}{N_A} \\right) change outcome scale, can pass scale argument outstandR() function. example, change scale risk difference, can use following code.","code":"outstandR_maic_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(formula = lin_form,                                      family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_maic_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.458    0.0870      -1.04      0.120 #> 2 AC           -1.14     0.0507      -1.59     -0.703 #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.225   0.00198 NA         NA         #> 2 C             0.695   0.00335 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"simulated-treatment-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Simulated treatment comparison","title":"Binary data example","text":"Simulated treatment comparison (STC) conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+βX(𝐱n−𝛉)+𝛃𝐄𝐌(βt+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌))(t≠C) g(\\mu_n) = \\beta_0 + \\beta_X (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) + \\boldsymbol{\\beta_{EM}} (\\beta_t + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) ) \\; \\mbox{}(t \\neq C) β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+Z+Z(X1−X1‾)+Z(X2−X2‾) y = X_3 + X_4 + Z + Z (X_1 - \\bar{X_1}) + Z (X_2 - \\bar{X_2}) However, outstandR() knows handle can simply pass (uncentred) formula . Change outcome scale last two approaches, perform G-computation firstly frequentist MLE Bayesian approach.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            -1.12   NA           NA        NA     #> 2 AC            -2.21   NA           NA        NA     #> 3 BC            -1.10    0.0992      -1.72     -0.481 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.153        NA NA         NA         #> 2 C             0.624        NA NA         NA outstandR_stc_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_stc_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.718   NA           NA        NA     #> 2 AC           -1.40    NA           NA        NA     #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.153        NA NA         NA         #> 2 C             0.624        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Binary data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝐗+(βz+𝐱𝐧𝐄𝐌𝛃𝐄𝐌)(t≠C) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_X} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_{EM}}) \\; \\mbox{}(t \\neq C) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0) Change outcome scale","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")))  outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.966    0.242       -1.93   -0.00274 #> 2 AC           -2.06     0.142       -2.80   -1.33    #> 3 BC           -1.10     0.0992      -1.72   -0.481   #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.224   0.00189 NA         NA         #> 2 C             0.687   0.00340 NA         NA outstandR_gcomp_ml_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_ml_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.463    0.0869      -1.04      0.115 #> 2 AC           -1.15     0.0505      -1.59     -0.708 #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.223   0.00205 NA         NA         #> 2 C             0.691   0.00348 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Binary data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment. , can change outcome scale.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.986    0.242       -1.95    -0.0218 #> 2 AC           -2.08     0.143       -2.82    -1.34   #> 3 BC           -1.10     0.0992      -1.72    -0.481  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.225   0.00199 NA         NA         #> 2 C             0.693   0.00340 NA         NA outstandR_gcomp_bayes_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_bayes_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.456    0.0848      -1.03      0.115 #> 2 AC           -1.14     0.0485      -1.57     -0.710 #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.225   0.00199 NA         NA         #> 2 C             0.693   0.00340 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Binary data example","text":"Marginalized treatment effect aggregate level data study obtained integrating covariate distribution BCBC study Δmarg=𝔼X∼fBC(X)[μT=1(X)−μT=0(X)]=∫[μT=1(X)−μT=0(X)]fBC(X)dX \\Delta^{\\text{marg}} = \\mathbb{E}_{X \\sim f_{\\text{BC}}(X)} \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] = \\int \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] f_{\\text{BC}}(X) \\; \\text{d}X aggregate level data likelihood Δ̂BC∼𝒩(Δmarg,SE2) \\hat{\\Delta}_{BC} \\sim \\mathcal{N}(\\Delta^{\\text{marg}}, SE^2) Change outcome scale .","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")))  outstandR_mim outstandR_mim #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.987    0.231       -1.93    -0.0452 #> 2 AC           -2.09     0.132       -2.80    -1.37   #> 3 BC           -1.10     0.0992      -1.72    -0.481  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA outstandR_mim_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_mim_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.456    0.0744     -0.991     0.0783 #> 2 AC           -1.14     0.0380     -1.52     -0.760  #> 3 BC           -0.686    0.0364     -1.06     -0.312  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ac-effect-in-bc-population","dir":"Articles","previous_headings":"Model fitting in R > Model comparison","what":"ACAC effect in BCBC population","title":"Binary data example","text":"true ACAC effect log scale BCBC (aggregate trial data) population βtAC+βEM(X‾1AC+X‾2AC)\\beta_t^{AC} + \\beta_{EM} (\\bar{X}^{AC}_1 + \\bar{X}_2^{AC}). Calculated naive approach just convert directly one population another, ignoring imbalance effect modifiers.","code":"d_AC_true <- b_trt + b_EM * (ald_trial$mean.X1 + ald_trial$mean.X2) d_AC_naive <-    ipd_trial |>    group_by(trt) |>    summarise(y_sum = sum(y), y_bar = mean(y), n = n()) |>    tidyr::pivot_wider(names_from = trt,                      values_from = c(y_sum, y_bar, n)) |>    mutate(d_AC =            log(y_bar_A/(1-y_bar_A)) - log(y_bar_C/(1-y_bar_C)),          var_AC =            1/(n_A-y_sum_A) + 1/y_sum_A + 1/(n_C-y_sum_C) + 1/y_sum_C)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ab-effect-in-bc-population","dir":"Articles","previous_headings":"Model fitting in R > Model comparison","what":"ABAB effect in BCBC population","title":"Binary data example","text":"indirect effect. true ABAB effect BCBC population βtAC−βtBC\\beta_t^{AC} - \\beta_t^{BC}. Following simulation study Remiro et al (2020) cancel true effect zero. naive comparison calculating ABAB effect BCBC population course, BCBC contrast calculated directly.","code":"d_BC <-   with(ald_trial, log(y.B.bar/(1-y.B.bar)) - log(y.C.bar/(1-y.C.bar)))  d_AB_naive <- d_AC_naive$d_AC - d_BC  var.d.BC <- with(ald_trial, 1/y.B.sum + 1/(N.B - y.B.sum) + 1/y.C.sum + 1/(N.C - y.C.sum))  var.d.AB.naive <- d_AC_naive$var_AC + var.d.BC"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"results","dir":"Articles","previous_headings":"","what":"Results","title":"Binary data example","text":"now combine outputs present plots tables. log-odds ratio table contrasts methods BCBC population given . can see different corresponds reasonably well one another. Next, let us look results log relative risk scale. First, true values calculated summary table ","code":"d_AB_true_lrr <- 0 d_AC_true_lrr <- log(plogis(d_A_true) / plogis(d_C_true)) d_AC_true_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"plots","dir":"Articles","previous_headings":"Results","what":"Plots","title":"Binary data example","text":"output can presented forest plots follows. horizontal bar represent different method facets group treatment comparison BCBC population. log-odds ratio log risk ratio plot given .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"simpler version Binary Data Example Simulated Data example. See document details exposition.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"general-problem","dir":"Articles","previous_headings":"","what":"General problem","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Consider one AB trial, company IPD, one AC trial, published aggregate data available. wish estimate comparison effects treatments B C appropriate scale target population P, denoted parameter dBC(P)d_{BC(P)}. make use bracketed subscripts denote specific population. Within AB population parameters μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)} μC(AB)\\mu_{C(AB)} representing expected outcome treatment (including parameters treatments studied AB trial, e.g. treatment C). AB trial provides estimators Y‾(AB)\\bar{Y}_{(AB)} Y‾B(AB)\\bar{Y}_{B(AB)} μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)}, respectively, summary outcomes. situation AC trial. suitable scale, example logit, risk difference, form estimators ΔAB(AB)\\Delta_{AB(AB)} ΔAC(AC)\\Delta_{AC(AC)} trial level (marginal) relative treatment effects. ΔAB(AB)=g(Y‾B(AB))−g(Y‾(AB)) \\Delta_{AB(AB)} = g(\\bar{Y}_{B{(AB)}}) - g(\\bar{Y}_{{(AB)}})","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Next, load data use analysis. data comes simulation study Remiro‐Azócar , Heath , Baio G (2020). consider binary outcomes using log-odds ratio measure effect. binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yny_n subject nn simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. general format data sets consist following.","code":"set.seed(555)  ipd_trial <- read.csv(here::here(\"raw-data\", \"AC_IPD.csv\"))  # AC patient-level data ald_trial <- read.csv(here::here(\"raw-data\", \"BC_ALD.csv\"))  # BC aggregate-level data"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"X*: patient measurements trt: treatment ID (integer) y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: proportion events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. Let us label treatment levels data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) head(ipd_trial) #>            X1        X2          X3          X4 trt y #> 1  0.43734111 0.6747901  0.93001035  0.09165363   A 0 #> 2  0.05643081 0.5987971  0.03557646  0.59954129   A 1 #> 3 -0.08048882 0.6843784  0.93147222 -0.11419716   A 0 #> 4 -0.38580926 0.5716644 -0.32252212  0.02551808   A 0 #> 5  1.00755116 0.8220826  0.92735892  0.84414221   A 1 #> 6  0.19443956 0.2031329  0.34990179  0.15633009   A 0 ald_trial #>     mean.X1   mean.X2   mean.X3   mean.X4     sd.X1     sd.X2     sd.X3 #> 1 0.5908996 0.6414179 0.5856529 0.6023671 0.3863145 0.4033615 0.4076097 #>      sd.X4 y.B.sum y.B.bar N.B y.C.sum y.C.bar N.C #> 1 0.395132     182   0.455 400     149   0.745 200"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. formula used model covariates prognostic variable y=X1+X2+X3+X4+(βt+βxX1+βxX2)t y = X_1 + X_2 + X_3 + X_4 + (\\beta_t + \\beta_x X_1 + \\beta_x X_2) t corresponds following R formula object passed argument strategy function. returned object class outstandR.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <- outstandR(ipd_trial, ald_trial,                             strategy = strategy_maic(formula = lin_form,                                                      family = binomial(link = \"logit\"))) outstandR_maic #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.101    0.173      -0.715      0.917 #> 2 AC           -1.15     0.137      -1.88      -0.427 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.434   0.00255 NA         NA         #> 2 C             0.704   0.00329 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD plugging-covariate mean values. last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <- outstandR(ipd_trial, ald_trial,                            strategy = strategy_stc(formula = lin_form,                                                    family = binomial(link = \"logit\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.176   NA           NA        NA     #> 2 AC           -1.43    NA           NA        NA     #> 3 BC           -1.25     0.0364      -1.63     -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.117        NA NA         NA         #> 2 C             0.356        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C.","code":"outstandR_gcomp_ml <- outstandR(ipd_trial, ald_trial,                                 strategy = strategy_gcomp_ml(formula = lin_form,                                                              family = binomial(link = \"logit\"))) outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.164    0.147      -0.586      0.915 #> 2 AC           -1.09     0.110      -1.74      -0.438 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.485   0.00235 NA         NA         #> 2 C             0.734   0.00251 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(formula = lin_form,                                            family = binomial(link = \"logit\"))) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 7.4e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.74 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.285 seconds (Warm-up) #> Chain 1:                0.327 seconds (Sampling) #> Chain 1:                0.612 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.6e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.301 seconds (Warm-up) #> Chain 2:                0.385 seconds (Sampling) #> Chain 2:                0.686 seconds (Total) #> Chain 2:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 3). #> Chain 3:  #> Chain 3: Gradient evaluation took 4.4e-05 seconds #> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.44 seconds. #> Chain 3: Adjust your expectations accordingly! #> Chain 3:  #> Chain 3:  #> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 3:  #> Chain 3:  Elapsed Time: 0.32 seconds (Warm-up) #> Chain 3:                0.328 seconds (Sampling) #> Chain 3:                0.648 seconds (Total) #> Chain 3:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 4). #> Chain 4:  #> Chain 4: Gradient evaluation took 1.9e-05 seconds #> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds. #> Chain 4: Adjust your expectations accordingly! #> Chain 4:  #> Chain 4:  #> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 4:  #> Chain 4:  Elapsed Time: 0.298 seconds (Warm-up) #> Chain 4:                0.262 seconds (Sampling) #> Chain 4:                0.56 seconds (Total) #> Chain 4: outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.151    0.141      -0.585      0.887 #> 2 AC           -1.10     0.105      -1.74      -0.467 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.485   0.00218 NA         NA         #> 2 C             0.736   0.00258 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Fit model .","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(formula = lin_form,                                     family = binomial(link = \"logit\"))) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 2.2e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.309 seconds (Warm-up) #> Chain 1:                0.336 seconds (Sampling) #> Chain 1:                0.645 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.9e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.309 seconds (Warm-up) #> Chain 2:                0.335 seconds (Sampling) #> Chain 2:                0.644 seconds (Total) #> Chain 2:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 3). #> Chain 3:  #> Chain 3: Gradient evaluation took 2.2e-05 seconds #> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds. #> Chain 3: Adjust your expectations accordingly! #> Chain 3:  #> Chain 3:  #> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 3:  #> Chain 3:  Elapsed Time: 0.323 seconds (Warm-up) #> Chain 3:                0.322 seconds (Sampling) #> Chain 3:                0.645 seconds (Total) #> Chain 3:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 4). #> Chain 4:  #> Chain 4: Gradient evaluation took 1.8e-05 seconds #> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds. #> Chain 4: Adjust your expectations accordingly! #> Chain 4:  #> Chain 4:  #> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 4:  #> Chain 4:  Elapsed Time: 0.322 seconds (Warm-up) #> Chain 4:                0.279 seconds (Sampling) #> Chain 4:                0.601 seconds (Total) #> Chain 4: outstandR_mim #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.153    0.131      -0.556      0.861 #> 2 AC           -1.10     0.0942     -1.70      -0.499 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Combine outputs log-odds ratio table contrasts methods.","code":"knitr::kable(   data.frame(   `MAIC` = unlist(outstandR_maic$contrasts),   `STC` = unlist(outstandR_stc$contrasts),   `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts),   `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts),   `MIM` = unlist(outstandR_mim$contrasts)) )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Binary data example","text":"vignette demonstrate use outstandR package fit range types models simulated binary data. Related vignettes provide equivalent analyses continuous count data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"analysis","dir":"Articles","previous_headings":"","what":"Analysis","title":"Binary data example","text":"First, let us load necessary packages.","code":"# install.packages(\"outstandR\", #  repos = c(\"https://statisticshealtheconomics.r-universe.dev\", \"https://cloud.r-project.org\")) # # install.packages(\"simcovariates\", #  repos = c(\"https://n8thangreen.r-universe.dev\", \"https://cloud.r-project.org\"))  library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"data","dir":"Articles","previous_headings":"Analysis","what":"Data","title":"Binary data example","text":"consider binary outcomes using log-odds ratio measure effect. example, binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yiy_i subject ii simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. simulation input parameters given . shall use gen_data() function available simcovariates package GitHub. treatment column return data binary takes values 0 1. include extra information treatment names. define lable two level factor 1 C 0 follows. Similarly, obtain aggregate data simulate IPD additional summarise step. set different mean values meanX_BC meanX_EM_BC otherwise use parameter values ACAC trial. general format data sets ‘long’ style consisting following.","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  covariate_defns_ipd <- list(   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  b_prognostic <- c(PF_cont_1 = b_X, PF_cont_2 = b_X)  b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)  num_normal_covs <- length(covariate_defns_ipd) cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs) diag(cor_matrix) <- 1  rownames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\") colnames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\")  ipd_trial <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ipd,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = binomial(\"logit\")) ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) covariate_defns_ald <- list(   PF_cont_1 = list(type = continuous(mean = meanX_BC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_BC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_BC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_BC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  BC.IPD <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ald,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = binomial(\"logit\"))  BC.IPD$trt <- factor(BC.IPD$trt, labels = c(\"C\", \"B\"))  # covariate summary statistics # assume same between treatments cov.X <-    BC.IPD %>%   as.data.frame() |>    dplyr::select(matches(\"^(PF|EM)\"), trt) |>    tidyr::pivot_longer(     cols = starts_with(\"PF\") | starts_with(\"EM\"),     names_to = \"variable\",     values_to = \"value\") |>   group_by(variable) %>%   summarise(     mean = mean(value),     sd = sd(value)   ) %>%   tidyr::pivot_longer(     cols = c(\"mean\", \"sd\"),     names_to = \"statistic\",     values_to = \"value\") %>%   ungroup() |>    mutate(trt = NA)  # outcome summary.y <-    BC.IPD |>    as.data.frame() |>    dplyr::select(y, trt) %>%   tidyr::pivot_longer(cols = \"y\",                names_to = \"variable\",                values_to = \"value\") %>%   group_by(variable, trt) %>%   summarise(     mean = mean(value),     sd = sd(value),     sum = sum(value)   ) %>%   tidyr::pivot_longer(     cols = c(\"mean\", \"sd\", \"sum\"),     names_to = \"statistic\",     values_to = \"value\") %>%   ungroup() #> `summarise()` has grouped output by 'variable'. You can override using the #> `.groups` argument.  # sample sizes summary.N <-    BC.IPD |>    group_by(trt) |>    count(name = \"N\") |>    tidyr::pivot_longer(     cols = \"N\",     names_to = \"statistic\",     values_to = \"value\") |>    mutate(variable = NA_character_) |>    dplyr::select(variable, statistic, value, trt)    ald_trial <- rbind.data.frame(cov.X, summary.y, summary.N)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Analysis > Data","what":"ipd_trial: Individual patient data","title":"Binary data example","text":"PF_*: Patient measurements prognostic factors EM_*: Patient measurements effect modifiers trt: Treatment label (factor) y: Indicator whether event observed (two level factor)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Analysis > Data","what":"ald_trial: Aggregate-level data","title":"Binary data example","text":"variable: Covariate name. case treatment arm sample size NA statistic: Summary statistic name mean, standard deviation sum value: Numerical value summary statistic trt: Treatment label. assume common covariate distribution treatment arms NA data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt takes either new treatment standard care / status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; event total, average sample size treatment B C.","code":"head(ipd_trial) #>   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt y     true_eta #> 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C 0  0.582883524 #> 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A 1 -1.476422106 #> 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A 0  0.005184912 #> 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C 1  0.520117172 #> 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A 1 -1.760974264 #> 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A 0 -2.139514435 ald_trial #> # A tibble: 16 × 4 #>    variable  statistic   value trt   #>    <chr>     <chr>       <dbl> <chr> #>  1 EM_cont_1 mean        0.616 NA    #>  2 EM_cont_1 sd          0.408 NA    #>  3 EM_cont_2 mean        0.635 NA    #>  4 EM_cont_2 sd          0.354 NA    #>  5 PF_cont_1 mean        0.666 NA    #>  6 PF_cont_1 sd          0.398 NA    #>  7 PF_cont_2 mean        0.663 NA    #>  8 PF_cont_2 sd          0.404 NA    #>  9 y         mean        0.597 C     #> 10 y         sd          0.494 C     #> 11 y         sum        43     C     #> 12 y         mean        0.297 B     #> 13 y         sd          0.459 B     #> 14 y         sum        38     B     #> 15 NA        N          72     C     #> 16 NA        N         128     B"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"regression-model","dir":"Articles","previous_headings":"Analysis > Data","what":"Regression model","title":"Binary data example","text":"true logistic outcome model use simulate data logit(pt)=β0+βX(X3+X4)+[βt+βEM(X1+X2)](t≠C) \\text{logit}(p_{t}) = \\beta_0 + \\beta_X (X_3 + X_4) + [\\beta_{t} + \\beta_{EM} (X_1 + X_2)] \\; \\text{}(t \\neq C) ()\\text{}() indicator function taking value 1 true 0 otherwise. , treatment CC right hand side becomes β0+βX(X3+X4)\\beta_0 + \\beta_X (X_3 + X_4) comparator treatments AA BB additional βt+βEM(X1+X2)\\beta_t + \\beta_{EM} (X_1 + X_2) component consisting effect modifier terms coefficient treatment parameter, βt\\beta_t (b_trt R code), .e. log odds-ratio (LOR) logit model. Finally, ptp_{t} probability experiencing event interest treatment tt.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Analysis","what":"Output statistics","title":"Binary data example","text":"obtain marginal treatment effect marginal variance. definition calculated depends type data outcome scale. current example binary data log-odds ratio marginal treatment effect log(nB/(NB−nB)nC/(NB−nB))=log(nBnC‾)−log(nCnB‾) \\log\\left( \\frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \\right) = \\log(n_B n_{\\bar{C}}) - \\log(n_C n_{\\bar{B}}) marginal variance 1nC+1nC‾+1nB+1nB‾ \\frac{1}{n_C} + \\frac{1}{n_{\\bar{C}}} + \\frac{1}{n_B} + \\frac{1}{n_{\\bar{B}}} nB,nCn_B, n_C number events arm C‾\\bar{C} compliment CC, e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c. outcome scales discussed .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Binary data example","text":"outstandR package written easy use essentially consists single function, outstandR(). can used run different types model, combined specific parameters call strategies. first two arguments outstandR() individual patient aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"model-formula","dir":"Articles","previous_headings":"Model fitting in R","what":"Model formula","title":"Binary data example","text":"take advantage -built R formula object define models. allow us easily pull components object consistently use . Defining EM_cont_1,EM_cont_2EM\\_cont\\_1, EM\\_cont\\_2 effect modifiers, PF_cont_1,PF_cont_2PF\\_cont\\_1, PF\\_cont\\_2 prognostic variables ZZ treatment indicator formula used model y=PF_cont_1+PF_cont_2+Z+Z×EM_cont_1+Z×EM_cont_2 y = PF\\_cont\\_1 + PF\\_cont\\_2 + Z + Z \\times EM\\_cont\\_1 + Z \\times EM\\_cont\\_2 Notice include link function interest appears linear regression. corresponds following R formula object pass argument strategy function. Note succinct formula additionally include X1,X2X_1, X_2 prognostic factors equivalent (may actually want). recover original formula can modified follows. note MAIC approach strictly use regression way methods considered directly comparable sense decided use consistent syntax across models using ‘formula’.","code":"lin_form <- as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt + trt:EM_cont_1 + trt:EM_cont_2\") y ~ PF_cont_1 + PF_cont_2 + trt*(EM_cont_1 + EM_cont_2) y ~ PF_cont_1 + PF_cont_2 + trt*(EM_cont_1 + EM_cont_2) - EM_cont_1 - EM_cont_2"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"matching-adjusted-indirect-comparison-maic","dir":"Articles","previous_headings":"Model fitting in R","what":"Matching-Adjusted Indirect Comparison (MAIC)","title":"Binary data example","text":"single call outstandR() sufficient run model. pass strategy argument strategy_maic() function arguments formula = lin_form defined family = binomial(link = \"logit\") binary data logistic link. Internally, using individual patient level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. returned object class outstandR. see list object 2 parts. first contains statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument. second element list contains absolute effect estimates. print method available outstandR objects human-readable output","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = binomial(link = \"logit\"))) str(outstandR_maic) #> List of 2 #>  $ contrasts:List of 3 #>   ..$ means    :List of 3 #>   .. ..$ AB: num 0.607 #>   .. ..$ AC: num -0.649 #>   .. ..$ BC: num -1.26 #>   ..$ variances:List of 3 #>   .. ..$ AB: num 0.233 #>   .. ..$ AC: num 0.137 #>   .. ..$ BC: num 0.0952 #>   ..$ CI       :List of 3 #>   .. ..$ AB: num [1:2] -0.338 1.552 #>   .. ..$ AC: num [1:2] -1.3757 0.0776 #>   .. ..$ BC: num [1:2] -1.861 -0.652 #>  $ absolute :List of 2 #>   ..$ means    :List of 2 #>   .. ..$ A: Named num 0.341 #>   .. .. ..- attr(*, \"names\")= chr \"mean_A\" #>   .. ..$ C: Named num 0.495 #>   .. .. ..- attr(*, \"names\")= chr \"mean_C\" #>   ..$ variances:List of 2 #>   .. ..$ A: Named num 0.00271 #>   .. .. ..- attr(*, \"names\")= chr \"mean_A\" #>   .. ..$ C: Named num 0.00518 #>   .. .. ..- attr(*, \"names\")= chr \"mean_C\" #>  - attr(*, \"CI\")= num 0.95 #>  - attr(*, \"ref_trt\")= chr \"C\" #>  - attr(*, \"scale\")= chr \"log_odds\" #>  - attr(*, \"model\")= chr \"binomial\" #>  - attr(*, \"class\")= chr [1:2] \"outstandR\" \"list\" outstandR_maic #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.607    0.233      -0.338     1.55   #> 2 AC           -0.649    0.137      -1.38      0.0776 #> 3 BC           -1.26     0.0952     -1.86     -0.652  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.341   0.00271 NA         NA         #> 2 C             0.495   0.00518 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"outcome-scale","dir":"Articles","previous_headings":"Model fitting in R > Matching-Adjusted Indirect Comparison (MAIC)","what":"Outcome scale","title":"Binary data example","text":"explicitly specify outcome scale, default used fit data regression model. saw, case, default log-odds ratio corresponding \"logit\" link function binary data. However, can change scale may appropriate particular analysis. far implemented package, links corresponding relative treatment effect scales follows: full list possible transformed treatment effect scales : log-odds ratio, log-risk ratio, mean difference, risk difference, hazard ratio, hazard difference. binary data marginal treatment effect variance Log-risk ratio Treatment effect log(nB/NB)−log(nA/NA) \\log(n_B/N_B) - \\log(n_A/N_A) variance 1nB−1NB+1nA−1NA \\frac{1}{n_B} - \\frac{1}{N_B} + \\frac{1}{n_A} - \\frac{1}{N_A} Risk difference Treatment effect nBNB−nANA \\frac{n_B}{N_B} - \\frac{n_A}{N_A} variance nBNB(1−nBNB)+nANA(1−nANA) \\frac{n_B}{N_B} \\left( 1 - \\frac{n_B}{N_B} \\right) + \\frac{n_A}{N_A} \\left( 1 - \\frac{n_A}{N_A} \\right) change outcome scale, can pass scale argument outstandR() function. example, change scale risk difference, can use following code.","code":"outstandR_maic_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(formula = lin_form,                                      family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_maic_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.307    0.0793     -0.244     0.859  #> 2 AC           -0.392    0.0514     -0.836     0.0527 #> 3 BC           -0.699    0.0279     -1.03     -0.372  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.339   0.00258 NA         NA         #> 2 C             0.501   0.00537 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"simulated-treatment-comparison-stc","dir":"Articles","previous_headings":"Model fitting in R","what":"Simulated treatment comparison (STC)","title":"Binary data example","text":"Simulated treatment comparison (STC) conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD anad ‘plugging-’ mean covariate values aggregate data study. can simply pass formula modified call strategy_stc(). Changing outcome scale LRR gives following approaches follow naturally simple ‘plug-’ version STC. perform G-computation firstly frequentist MLE Bayesian approach.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           0.0584   NA           NA        NA     #> 2 AC          -1.20     NA           NA        NA     #> 3 BC          -1.26      0.0952      -1.86     -0.652 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.137        NA NA         NA         #> 2 C             0.344        NA NA         NA outstandR_stc_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_stc_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.224   NA           NA        NA     #> 2 AC           -0.923   NA           NA        NA     #> 3 BC           -0.699    0.0279      -1.03     -0.372 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.137        NA NA         NA         #> 2 C             0.344        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Binary data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝐗+(βz+𝐱𝐧𝐄𝐌𝛃𝐄𝐌)(t≠C) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_X} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_{EM}}) \\; \\mbox{}(t \\neq C) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* performed previous approaches, call outstandR() change strategy strategy_gcomp_ml(), , let us change outcome scale LRR","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.602    0.232      -0.342     1.55   #> 2 AC           -0.654    0.137      -1.38      0.0714 #> 3 BC           -1.26     0.0952     -1.86     -0.652  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.411   0.00291 NA         NA         #> 2 C             0.570   0.00563 NA         NA outstandR_gcomp_ml_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_ml_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.377    0.0602     -0.104     0.858  #> 2 AC           -0.322    0.0323     -0.674     0.0307 #> 3 BC           -0.699    0.0279     -1.03     -0.372  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.409   0.00276 NA         NA         #> 2 C             0.563   0.00504 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Binary data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. strategy function plug-outstandR() call approach strategy_gcomp_bayes(), , can change outcome scale LRR.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.612    0.228      -0.325     1.55   #> 2 AC           -0.644    0.133      -1.36      0.0713 #> 3 BC           -1.26     0.0952     -1.86     -0.652  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.411   0.00288 NA         NA         #> 2 C             0.568   0.00521 NA         NA outstandR_gcomp_bayes_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_bayes_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.375    0.0607     -0.108     0.858  #> 2 AC           -0.324    0.0328     -0.679     0.0308 #> 3 BC           -0.699    0.0279     -1.03     -0.372  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.411   0.00288 NA         NA         #> 2 C             0.568   0.00521 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Binary data example","text":"final method obtain marginalized treatment effect aggregate level data study, obtained integrating covariate distribution aggregate level data BCBC study Δmarg=𝔼X∼fBC(X)[μT=1(X)−μT=0(X)]=∫[μT=1(X)−μT=0(X)]fBC(X)dX \\Delta^{\\text{marg}} = \\mathbb{E}_{X \\sim f_{\\text{BC}}(X)} \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] = \\int \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] f_{\\text{BC}}(X) \\; \\text{d}X aggregate level data likelihood Δ̂BC∼𝒩(Δmarg,SE2) \\hat{\\Delta}_{BC} \\sim \\mathcal{N}(\\Delta^{\\text{marg}}, SE^2) multiple imputation marginalisation strategy function strategy_mim(), Change outcome scale LRR,","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_mim #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.612    0.216      -0.299     1.52   #> 2 AC           -0.644    0.121      -1.33      0.0386 #> 3 BC           -1.26     0.0952     -1.86     -0.652  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA outstandR_mim_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_mim_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.375    0.0516    -0.0704     0.820  #> 2 AC           -0.324    0.0237    -0.626     -0.0227 #> 3 BC           -0.699    0.0279    -1.03      -0.372  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ac-effect-in-bc-population","dir":"Articles","previous_headings":"Model comparison","what":"ACAC effect in BCBC population","title":"Binary data example","text":"true ACAC effect log scale BCBC (aggregate trial data) population βtAC+βEM(X‾1AC+X‾2AC)\\beta_t^{AC} + \\beta_{EM} (\\bar{X}^{AC}_1 + \\bar{X}_2^{AC}). Calculated naive approach just convert directly one population another, ignoring imbalance effect modifiers.","code":"mean_X1 <- ald_trial$value[ald_trial$statistic == \"mean\" & ald_trial$variable == \"EM_cont_1\"] mean_X2 <- ald_trial$value[ald_trial$statistic == \"mean\" & ald_trial$variable == \"EM_cont_1\"]  d_AC_true <- b_trt + b_EM * (mean_X1 + mean_X2) d_AC_naive <-    ipd_trial |>    dplyr::group_by(trt) |>    dplyr::summarise(y_sum = sum(y), y_bar = mean(y), n = n()) |>    tidyr::pivot_wider(names_from = trt,                      values_from = c(y_sum, y_bar, n)) |>    dplyr::mutate(d_AC =                   log(y_bar_A/(1-y_bar_A)) - log(y_bar_C/(1-y_bar_C)),                 var_AC =                   1/(n_A-y_sum_A) + 1/y_sum_A + 1/(n_C-y_sum_C) + 1/y_sum_C)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ab-effect-in-bc-population","dir":"Articles","previous_headings":"Model comparison","what":"ABAB effect in BCBC population","title":"Binary data example","text":"indirect effect. true ABAB effect BCBC population βtAC−βtBC\\beta_t^{AC} - \\beta_t^{BC}. Following simulation study Remiro et al (2020) cancel true effect zero. naive comparison calculating ABAB effect BCBC population course, BCBC contrast calculated directly.","code":"# reshape to make extraction easier ald_out <- ald_trial |>    dplyr::filter(variable == \"y\" | is.na(variable)) |>    mutate(stat_trt = paste0(statistic, \"_\", trt)) |>    dplyr::select(stat_trt, value) |>    pivot_wider(names_from = stat_trt, values_from = value)  d_BC <-   with(ald_out, log(mean_B/(1-mean_B)) - log(mean_C/(1-mean_C)))  d_AB_naive <- d_AC_naive$d_AC - d_BC  var.d.BC <- with(ald_out, 1/sum_B + 1/(N_B - sum_B) + 1/sum_C + 1/(N_C - sum_C))  var.d.AB.naive <- d_AC_naive$var_AC + var.d.BC"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"results","dir":"Articles","previous_headings":"","what":"Results","title":"Binary data example","text":"now combine outputs present plots tables. log-odds ratio table contrasts methods BCBC population given . can see different corresponds reasonably well one another. Next, let us look results log relative risk scale. First, true values calculated summary table ","code":"d_AB_true_lrr <- 0 d_AC_true_lrr <- log(plogis(d_A_true) / plogis(d_C_true)) d_AC_true_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"plots","dir":"Articles","previous_headings":"Results","what":"Plots","title":"Binary data example","text":"output can presented forest plots follows. horizontal bar represent different method facets group treatment comparison BCBC population. log-odds ratio log risk ratio plot given .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Continuous data example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Continuous data example","text":"Next, load data use analysis. data comes simulation study Remiro‐Azócar , Heath , Baio G (2020). consider binary outcomes using log-odds ratio measure effect. binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yny_n subject nn simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. Use gen_data() function available simcovariates package. Similarly, aggregate data additional summarise step. general format data sets consist following.","code":"library(dplyr) #>  #> Attaching package: 'dplyr' #> The following objects are masked from 'package:stats': #>  #>     filter, lag #> The following objects are masked from 'package:base': #>  #>     intersect, setdiff, setequal, union library(MASS) #>  #> Attaching package: 'MASS' #> The following object is masked from 'package:dplyr': #>  #>     select  N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = gaussian(link = \"identity\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = gaussian(link = \"identity\"))  cov.X <- BC.IPD %>%   summarise(across(starts_with(\"X\"),                    list(mean = mean, sd = sd),                    .names = \"{fn}.{col}\"))  out.B <- dplyr::filter(BC.IPD, trt == 1) %>%   summarise(y.B.sum = sum(y),             y.B.bar = mean(y),             y.B.sd = sd(y),             N.B = n())  out.C <- dplyr::filter(BC.IPD, trt == 0) %>%   summarise(y.C.sum = sum(y),             y.C.bar = mean(y),             y.C.sd = sd(y),             N.C = n())  ald_trial <- cbind.data.frame(cov.X, out.B, out.C)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Continuous data example","text":"X*: patient measurements trt: treatment ID (integer) y: continuous outcome measure","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Continuous data example","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement mean.y: sd.y: Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"head(ipd_trial) #>           X1         X2         X3         X4 trt          y #> 1 0.42066874  1.0957407 0.37118099  1.3291540   A  0.8949999 #> 2 0.51227329  0.9079984 0.30560144 -0.1842358   A -1.7550940 #> 3 1.00347612  0.8136847 1.25054503  1.1986315   A -0.6521005 #> 4 0.05641685  0.5318140 0.54799796  0.6694090   A -0.6260983 #> 5 0.42997845  0.5274304 0.09140568  0.1222184   A -1.2882834 #> 6 0.06916082 -0.3125090 0.99150666 -0.1102693   A -3.0170689 ald_trial #>     mean.X1     sd.X1   mean.X2    sd.X2   mean.X3     sd.X3  mean.X4     sd.X4 #> 1 0.6081015 0.3865186 0.6462269 0.412924 0.5903258 0.3842429 0.635176 0.3831984 #>     y.B.sum   y.B.bar   y.B.sd N.B  y.C.sum   y.C.bar   y.C.sd N.C #> 1 -135.0634 -1.015514 1.159787 133 12.38076 0.1847875 1.019683  67"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Continuous data example","text":"implement MAIC, STC, G-computation methods obtain marginal variance, defined  marginal treatment effect, defined log-odds ratio,  C‾\\bar{C} compliment CC e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Continuous data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Continuous data example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2 corresponds following R formula object passed argument strategy function. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_maic #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.339    0.0533     -0.791      0.113 #> 2 AC           -1.54     0.0276     -1.87      -1.21  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -1.14     0.0112 NA         NA         #> 2 C             0.396    0.0179 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Continuous data example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1) β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2}) However, outstandR() knows handle can simply pass (uncentred) formula . last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.363   NA           NA        NA     #> 2 AC           -1.56    NA           NA        NA     #> 3 BC           -1.20     0.0256      -1.51     -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A           -1.47          NA NA         NA         #> 2 C            0.0930        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Continuous data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(formula = lin_form,                                          family = gaussian(link = \"identity\"))) outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.348    0.0596     -0.826      0.130 #> 2 AC           -1.55     0.0339     -1.91      -1.19  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -1.10     0.0113 NA         NA         #> 2 C             0.444    0.0241 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Continuous data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.335    0.0560     -0.799      0.129 #> 2 AC           -1.54     0.0304     -1.88      -1.19  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -1.10     0.0113 NA         NA         #> 2 C             0.433    0.0206 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Continuous data example","text":"ref equationhere equation ","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_mim #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.335    0.0538     -0.789      0.120 #> 2 AC           -1.53     0.0281     -1.86      -1.21  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Continuous data example","text":"Combine outputs relative effects table contrasts methods.","code":"knitr::kable(   data.frame(     `MAIC` = unlist(outstandR_maic$contrasts$means),     `STC` = unlist(outstandR_stc$contrasts$means),     `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts$means),     `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts$means),     `MIM` = unlist(outstandR_mim$contrasts$means))   |>      round(2))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Continuous data example","text":"vignette performing population adjustment methods continuous data, order compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. demonstrate apply MAIC, STC, G-computation ML, G-computation Bayesian inference multiple imputation marginalisation. document structure follow binary data example vignette referred details.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Continuous data example","text":"First, let us load necessary packages.","code":"# install.packages(\"outstandR\", #  repos = c(\"https://statisticshealtheconomics.r-universe.dev\", \"https://cloud.r-project.org\")) # # install.packages(\"simcovariates\", #  repos = c(\"https://n8thangreen.r-universe.dev\", \"https://cloud.r-project.org\"))  library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Continuous data example","text":"first simulate IPD ALD data. See binary data example vignette details implemented. difference example change family argument gen_data() gaussian(link = \"identity\"), corresponding continuous data case. gen_data() function available simcovariates package GitHub. Similarly, aggregate data additional summarise step (see binary data example vignette code). general format data sets ‘long’ style consisting following.","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  covariate_defns_ipd <- list(   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  b_prognostic <- c(PF_cont_1 = b_X, PF_cont_2 = b_X)  b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)  num_normal_covs <- length(covariate_defns_ipd) cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs) diag(cor_matrix) <- 1  rownames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\") colnames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\")  ipd_trial <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ipd,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = gaussian(\"identity\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\"))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Continuous data example","text":"PF_*: Patient measurements prognostic factors EM_*: Patient measurements effect modifiers trt: Treatment label (factor) y: Continuous numeric","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Continuous data example","text":"variable: Covariate name. case treatment arm sample size NA statistic: Summary statistic name mean, standard deviation sum value: Numerical value summary statistic trt: Treatment label. assume common covariate distribution treatment arms NA data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt takes either new treatment standard care / status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; total, average sample size treatment B C. following implement MAIC, STC, G-computation methods obtain marginal variance marginal treatment effect.","code":"head(ipd_trial) #>   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt          y     true_eta #> 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C  1.9634929  0.582883524 #> 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A  0.1985888 -1.476422106 #> 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A  1.1820915  0.005184912 #> 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C  0.3712188  0.520117172 #> 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A -1.9387976 -1.760974264 #> 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A -1.3363926 -2.139514435 ald_trial #> # A tibble: 16 × 4 #>    variable  statistic    value trt   #>    <chr>     <chr>        <dbl> <chr> #>  1 EM_cont_1 mean         0.618 NA    #>  2 EM_cont_1 sd           0.406 NA    #>  3 EM_cont_2 mean         0.649 NA    #>  4 EM_cont_2 sd           0.376 NA    #>  5 PF_cont_1 mean         0.662 NA    #>  6 PF_cont_1 sd           0.370 NA    #>  7 PF_cont_2 mean         0.623 NA    #>  8 PF_cont_2 sd           0.389 NA    #>  9 y         mean         0.437 C     #> 10 y         sd           1.13  C     #> 11 y         sum         28.0   C     #> 12 y         mean        -1.04  B     #> 13 y         sd           1.16  B     #> 14 y         sum       -142.    B     #> 15 NA        N           64     C     #> 16 NA        N          136     B"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Continuous data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided . formula used model, passed argument strategy function ","code":"lin_form <- as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Continuous data example","text":"mentioned , pass model specific strategy function main outstandR() function, case use strategy_maic(). returned object class outstandR.","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_maic #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: mean_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.199    0.0798     -0.354      0.753 #> 2 AC           -1.28     0.0497     -1.72      -0.845 #> 3 BC           -1.48     0.0301     -1.82      -1.14  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -1.14     0.0174 NA         NA         #> 2 C             0.139    0.0303 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"simulated-treatment-comparison-stc","dir":"Articles","previous_headings":"Model fitting in R","what":"Simulated Treatment Comparison (STC)","title":"Continuous data example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. Simply pass formula strategy_stc() strategy function.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: mean_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           NaN      NA           NA         NA    #> 2 AC           NaN      NA           NA         NA    #> 3 BC            -1.48    0.0301      -1.82      -1.14 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            NaN           NA NA         NA         #> 2 C             -1.57        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Continuous data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. Pass strategy_gcomp_ml() strategy function.","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = gaussian(link = \"identity\")))  outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: mean_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.314    0.0693     -0.202      0.830 #> 2 AC           -1.17     0.0392     -1.56      -0.779 #> 3 BC           -1.48     0.0301     -1.82      -1.14  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -0.889    0.0134 NA         NA         #> 2 C             0.278    0.0296 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Continuous data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Pass strategy_gcomp_bayes() strategy function.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: mean_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.311    0.0760     -0.229      0.852 #> 2 AC           -1.17     0.0459     -1.59      -0.750 #> 3 BC           -1.48     0.0301     -1.82      -1.14  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -0.888    0.0165 NA         NA         #> 2 C             0.282    0.0305 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Continuous data example","text":"Finally, strategy function pass outstandR() multiple imputation marginalisation strategy_mim(),","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_mim #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: mean_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.312    0.0724     -0.215      0.839 #> 2 AC           -1.17     0.0423     -1.57      -0.766 #> 3 BC           -1.48     0.0301     -1.82      -1.14  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Continuous data example","text":"Combine outputs relative effects table contrasts methods.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"analysis","dir":"Articles","previous_headings":"","what":"Analysis","title":"COPD Analysis","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"data","dir":"Articles","previous_headings":"Analysis","what":"Data","title":"COPD Analysis","text":"general format data sets consist following.","code":"set.seed(555)  AC.IPD <- read.csv(here::here(\"raw-data\", \"AC_IPD.csv\"))  # AC patient-level data BC.ALD <- read.csv(here::here(\"raw-data\", \"BC_ALD.csv\"))  # BC aggregate-level data"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"ac-ipd-individual-patient-data","dir":"Articles","previous_headings":"Analysis > Data","what":"AC.IPD: Individual patient data","title":"COPD Analysis","text":"X*: patient measurements trt: treatment ID y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"bc-ald-aggregate-level-data","dir":"Articles","previous_headings":"Analysis > Data","what":"BC.ALD: Aggregate-level data","title":"COPD Analysis","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: total number events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution.","code":"head(AC.IPD) #>            X1        X2          X3          X4 trt y #> 1  0.43734111 0.6747901  0.93001035  0.09165363   1 0 #> 2  0.05643081 0.5987971  0.03557646  0.59954129   1 1 #> 3 -0.08048882 0.6843784  0.93147222 -0.11419716   1 0 #> 4 -0.38580926 0.5716644 -0.32252212  0.02551808   1 0 #> 5  1.00755116 0.8220826  0.92735892  0.84414221   1 1 #> 6  0.19443956 0.2031329  0.34990179  0.15633009   1 0 BC.ALD #>     mean.X1   mean.X2   mean.X3   mean.X4     sd.X1     sd.X2     sd.X3 #> 1 0.5908996 0.6414179 0.5856529 0.6023671 0.3863145 0.4033615 0.4076097 #>      sd.X4 y.B.sum y.B.bar N.B y.C.sum y.C.bar N.C #> 1 0.395132     182   0.455 400     149   0.745 200"},{"path":[]},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"COPD Analysis","text":"formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2  corresponds following R formula object passed argument strategy function. returned object class outstandR.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <- outstandR(AC.IPD, BC.ALD, strategy = strategy_maic(formula = lin_form)) outstandR_maic"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"COPD Analysis","text":"g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1) y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2})  However, outstandR() knows handle can simply pass (uncentred) formula .","code":"outstandR_stc <- outstandR(AC.IPD, BC.ALD, strategy = strategy_stc(formula = lin_form)) outstandR_stc"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"COPD Analysis","text":"g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_ml(formula = lin_form)) outstandR_gcomp_ml"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"COPD Analysis","text":"p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^*","code":"outstandR_gcomp_bayes <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_bayes(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 7e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.7 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.174 seconds (Warm-up) #> Chain 1:                0.18 seconds (Sampling) #> Chain 1:                0.354 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 9e-06 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.175 seconds (Warm-up) #> Chain 2:                0.2 seconds (Sampling) #> Chain 2:                0.375 seconds (Total) #> Chain 2: outstandR_gcomp_bayes"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"COPD Analysis","text":"Combine outputs","code":"outstandR_mim <- outstandR(AC.IPD, BC.ALD, strategy = strategy_mim(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 1.6e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 1: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 1: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 1: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 1: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 1: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 1: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 1: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.093 seconds (Warm-up) #> Chain 1:                0.3 seconds (Sampling) #> Chain 1:                0.393 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.1e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 2: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 2: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 2: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 2: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 2: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 2: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 2: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.085 seconds (Warm-up) #> Chain 2:                0.288 seconds (Sampling) #> Chain 2:                0.373 seconds (Total) #> Chain 2: outstandR_mim knitr::kable(   data.frame(   `MAIC` = unlist(outstandR_maic$contrasts),   `STC` = unlist(outstandR_stc$contrasts),   `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts),   `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts),   `MIM` = unlist(outstandR_mim$contrasts)) )"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Count data example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Count data example","text":"First, use gen_data() function available simcovariates package. Similarly, aggregate data additional summarise step.","code":"library(dplyr) library(MASS) N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = poisson(link = \"log\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = poisson(link = \"log\"))  cov.X <- BC.IPD %>%   summarise(across(starts_with(\"X\"),                    list(mean = mean, sd = sd),                    .names = \"{fn}.{col}\"))  out.C <- dplyr::filter(BC.IPD, trt == 1) %>%   summarise(y.B.sum = sum(y),             y.B.bar = mean(y),             N.B = n())  out.B <- dplyr::filter(BC.IPD, trt == 0) %>%   summarise(y.C.sum = sum(y),             y.C.bar = mean(y),             N.C = n())  ald_trial <- cbind.data.frame(cov.X, out.C, out.B)  # By definition, the true log-OR relative effect in the AC population between AC is `r b_trt`. Between BC is `r b_trt` and between AB is `r b_trt - b_trt`. # A naive indirect comparison, ignoring the presence of effect modifiers, would calculate the C vs B effect in the AC population as # `b_trt - b_trt`."},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Count data example","text":"implement MAIC, STC, G-computation methods obtain marginal variance, defined  marginal treatment effect, defined log-odds ratio,  C‾\\bar{C} compliment CC e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Count data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Count data example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats(). formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2 corresponds following R formula object passed argument strategy function. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_maic"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Count data example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1) β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2}) However, outstandR() knows handle can simply pass (uncentred) formula . last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = poisson(link = \"log\")))  outstandR_stc"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Count data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = poisson(link = \"log\")))  outstandR_gcomp_ml"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Count data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_gcomp_bayes"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Count data example","text":"ref equationhere equation ","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_mim"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Count data example","text":"Combine outputs log-odds ratio table contrasts methods.","code":"knitr::kable(   data.frame(     `MAIC` = unlist(outstandR_maic$contrasts$means),     `STC` = unlist(outstandR_stc$contrasts$means),     `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts$means),     `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts$means),     `MIM` = unlist(outstandR_mim$contrasts$means)) ) |>    round(2)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Count data example","text":"vignette performing population adjustment methods count data, order compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. demonstrate apply MAIC, STC, G-computation ML, G-computation Bayesian inference multiple imputation marginalisation. document structure follow binary data example vignette referred details.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Count data example","text":"First, let us load necessary packages.","code":"# install.packages(\"outstandR\", #  repos = c(\"https://statisticshealtheconomics.r-universe.dev\", \"https://cloud.r-project.org\")) # # install.packages(\"simcovariates\", #  repos = c(\"https://n8thangreen.r-universe.dev\", \"https://cloud.r-project.org\"))  library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Count data example","text":"first simulate IPD ALD count data. See binary data example vignette details implemented. difference example change family argument gen_data() poisson(link = \"log\"), corresponding count data case. gen_data() function available simcovariates package GitHub. Similarly, aggregate data additional summarise step (see binary data example vignette code). general format data sets ‘long’ style consisting following.","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  covariate_defns_ipd <- list(   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  b_prognostic <- c(PF_cont_1 = b_X, PF_cont_2 = b_X)  b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)  num_normal_covs <- length(covariate_defns_ipd) cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs) diag(cor_matrix) <- 1  rownames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\") colnames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\")  ipd_trial <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ipd,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = poisson(\"log\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\"))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Count data example","text":"PF_*: Patient measurements prognostic factors EM_*: Patient measurements effect modifiers trt: Treatment label (factor) y: Counts","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Count data example","text":"variable: Covariate name. case treatment arm sample size NA statistic: Summary statistic name mean, standard deviation sum value: Numerical value summary statistic trt: Treatment label. assume common covariate distribution treatment arms NA data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt takes either new treatment standard care / status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; total, average sample size treatment B C. following implement MAIC, STC, G-computation methods obtain marginal variance marginal treatment effect.","code":"head(ipd_trial) #>   id   PF_cont_1   PF_cont_2  EM_cont_1   EM_cont_2 trt y     true_eta #> 1  1  0.75056436  0.95597583  0.3158969  1.19430733   C 4  0.582883524 #> 2  2  0.83246940  0.11789773  0.5094678  0.08180243   A 1 -1.476422106 #> 3  3  1.13401333  1.15036919  1.2342379  0.74771694   A 3  0.005184912 #> 4  4  0.78518298  0.83080451 -0.1625820  0.35223227   C 1  0.520117172 #> 5  5 -0.38547667  0.87070020  0.7213797 -0.03557032   A 1 -1.760974264 #> 6  6 -0.04851591 -0.03013213  0.6580067  0.05853054   A 0 -2.139514435 ald_trial #> # A tibble: 16 × 4 #>    variable  statistic   value trt   #>    <chr>     <chr>       <dbl> <chr> #>  1 EM_cont_1 mean        0.616 NA    #>  2 EM_cont_1 sd          0.408 NA    #>  3 EM_cont_2 mean        0.635 NA    #>  4 EM_cont_2 sd          0.354 NA    #>  5 PF_cont_1 mean        0.666 NA    #>  6 PF_cont_1 sd          0.398 NA    #>  7 PF_cont_2 mean        0.663 NA    #>  8 PF_cont_2 sd          0.404 NA    #>  9 y         mean        1.07  C     #> 10 y         sd          1.01  C     #> 11 y         sum        77     C     #> 12 y         mean        0.438 B     #> 13 y         sd          0.750 B     #> 14 y         sum        56     B     #> 15 NA        N          72     C     #> 16 NA        N         128     B"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Count data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided . formula used model, passed argument strategy function ","code":"lin_form <- as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Count data example","text":"mentioned , pass model specific strategy function main outstandR() function, case use strategy_maic(). returned object class outstandR.","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = poisson(link = \"log\"))) #> log rate used #>  #> log rate used outstandR_maic #> Object of class 'outstandR'  #> Model: poisson  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           0.0524    0.0801     -0.502      0.607 #> 2 AC          -0.841     0.0493     -1.28      -0.406 #> 3 BC          -0.894     0.0308     -1.24      -0.550 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.500   0.00577 NA         NA         #> 2 C             1.16    0.0292  NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"simulated-treatment-comparison-stc","dir":"Articles","previous_headings":"Model fitting in R","what":"Simulated Treatment Comparison (STC)","title":"Count data example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. Simply pass formula strategy_stc() strategy function.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = poisson(link = \"log\"))) #> log rate used #>  #> log rate used outstandR_stc #> Object of class 'outstandR'  #> Model: poisson  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB          NaN       NA           NA        NA     #> 2 AC          NaN       NA           NA        NA     #> 3 BC           -0.894    0.0308      -1.24     -0.550 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A           NaN            NA NA         NA         #> 2 C             0.330        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Count data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. Pass strategy_gcomp_ml() strategy function.","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: poisson  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           0.0169    0.0798     -0.537      0.571 #> 2 AC          -0.877     0.0490     -1.31      -0.443 #> 3 BC          -0.894     0.0308     -1.24      -0.550 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.621   0.00936 NA         NA         #> 2 C             1.50    0.0717  NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Count data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Pass strategy_gcomp_bayes() strategy function.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: poisson  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           0.0233    0.0851     -0.548      0.595 #> 2 AC          -0.871     0.0543     -1.33      -0.414 #> 3 BC          -0.894     0.0308     -1.24      -0.550 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.616    0.0102 NA         NA         #> 2 C             1.48     0.0678 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Count data example","text":"Finally, strategy function pass outstandR() multiple imputation marginalisation strategy_mim(),","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = poisson(link = \"log\"))) #> log rate used #>  #> log rate used outstandR_mim #> Object of class 'outstandR'  #> Model: poisson  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           0.0237    0.0825     -0.539      0.587 #> 2 AC          -0.870     0.0517     -1.32      -0.425 #> 3 BC          -0.894     0.0308     -1.24      -0.550 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Count data example","text":"Combine outputs relative effects table contrasts methods.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"User-defined target population","text":"See vignettes details.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"data","dir":"Articles","previous_headings":"Introduction","what":"Data","title":"User-defined target population","text":"","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = binomial(\"logit\")) ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = binomial(\"logit\"))  BC.IPD$trt <- factor(BC.IPD$trt, labels = c(\"C\", \"B\"))  # covariate summary statistics # assume same between treatments cov.X <-    BC.IPD %>%   as.data.frame() |>    dplyr::select(X1, X2, X3, X4, trt) %>%   pivot_longer(cols = starts_with(\"X\"), names_to = \"variable\", values_to = \"value\") %>%   group_by(variable) %>%   summarise(     mean = mean(value),     sd = sd(value)   ) %>%   pivot_longer(cols = c(\"mean\", \"sd\"), names_to = \"statistic\", values_to = \"value\") %>%   ungroup() |>    mutate(trt = NA)  # outcome summary.y <-    BC.IPD |>    as.data.frame() |>    dplyr::select(y, trt) %>%   pivot_longer(cols = \"y\", names_to = \"variable\", values_to = \"value\") %>%   group_by(variable, trt) %>%   summarise(     mean = mean(value),     sd = sd(value),     sum = sum(value)   ) %>%   pivot_longer(cols = c(\"mean\", \"sd\", \"sum\"),                names_to = \"statistic\", values_to = \"value\") %>%   ungroup()  # sample sizes summary.N <-    BC.IPD |>    group_by(trt) |>    count(name = \"N\") |>    pivot_longer(cols = \"N\", names_to = \"statistic\", values_to = \"value\") |>    mutate(variable = NA_character_) |>    dplyr::select(variable, statistic, value, trt)    ald_trial <- rbind.data.frame(cov.X, summary.y, summary.N) lin_form <- as.formula(\"y ~ X3 + X4 + trt + trt:X1 + trt:X2\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Introduction","what":"Parametric G-computation with maximum-likelihood estimation","title":"User-defined target population","text":", let us change outcome scale LRR","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_ml outstandR_gcomp_ml_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_ml_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Introduction","what":"Bayesian G-computation with MCMC","title":"User-defined target population","text":", can change outcome scale LRR.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_bayes outstandR_gcomp_bayes_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_bayes_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Introduction","what":"Multiple imputation marginalisation","title":"User-defined target population","text":"Change outcome scale LRR,","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_mim outstandR_mim_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_mim_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Nathan Green. Author, maintainer, copyright holder. Chengyang Gao. Author. Antonio Remiro-Azocar. Author.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Green N, Gao C, Remiro-Azocar (2026). outstandR: Model-Based Standardisation Indirect Treatment Comparison Limited Subject-Level Data. R package version 2.0.0, https://StatisticsHealthEconomics.github.io/outstandR/.","code":"@Manual{,   title = {outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data},   author = {Nathan Green and Chengyang Gao and Antonio Remiro-Azocar},   year = {2026},   note = {R package version 2.0.0},   url = {https://StatisticsHealthEconomics.github.io/outstandR/}, }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":null,"dir":"","previous_headings":"","what":"outstandR: Outcome Regression Standardisation","title":"outstandR: Outcome Regression Standardisation","text":"outstandR R package population-adjusted indirect treatment comparison (ITC). implements various methods adjust cross-trial differences effect modifiers individual patient data (IPD) available one trial aggregate-level data (ALD) available another.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"core-architecture","dir":"","previous_headings":"","what":"Core Architecture","title":"outstandR: Outcome Regression Standardisation","text":"package follows “Strategy” pattern users define adjustment method using strategy_* functions pass main outstandR() wrapper.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"key-methods","dir":"","previous_headings":"Core Architecture","what":"Key Methods","title":"outstandR: Outcome Regression Standardisation","text":"MAIC (Matching-Adjusted Indirect Comparison): Non-parametric likelihood reweighting. G-computation (ML & Bayesian): Model-based standardisation (STC deprecated favour G-computation). MIM (Multiple Imputation Marginalization): Parametric G-computation using multiple imputation.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"main-entry-points","dir":"","previous_headings":"Core Architecture","what":"Main Entry Points","title":"outstandR: Outcome Regression Standardisation","text":"outstandR(ipd_trial, ald_trial, strategy, ...): primary user-facing function. strategy_maic(formula, ...): Define MAIC strategy. strategy_gcomp_ml(formula, ...): Define Maximum Likelihood G-computation strategy. strategy_gcomp_bayes(formula, ...): Define Bayesian G-computation strategy. strategy_mim(formula, ...): Define Multiple Imputation Marginalization strategy.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"standard-commands","dir":"","previous_headings":"Development Workflows","what":"Standard Commands","title":"outstandR: Outcome Regression Standardisation","text":"Documenting: devtools::document() (updates NAMESPACE man/). Testing: devtools::test() testthat::test_local(). Checking: devtools::check() (standard R package quality check). Building Site: pkgdown::build_site() (updates documentation website docs/).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"project-structure","dir":"","previous_headings":"Development Workflows","what":"Project Structure","title":"outstandR: Outcome Regression Standardisation","text":"outstandR.R: Main wrapper. strategy_.R: Strategy class definitions logic. maic.R, gcomp_ml.R, mim.R: Method-specific implementations. tests/testthat/: Unit tests organized feature/method. vignettes/: Detailed usage examples methodology documentation. man/: Auto-generated documentation (edit manually). data/: Built-datasets examples testing.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"engineering-standards","dir":"","previous_headings":"","what":"Engineering Standards","title":"outstandR: Outcome Regression Standardisation","text":"Consistency: Follow standard R package conventions. Documentation: Use roxygen2 Markdown support (Roxygen: list(markdown = TRUE) DESCRIPTION). Testing: New features bug fixes MUST include testthat tests. S3 Classes: Strategies main output use S3 classes (outstandR, strategy, maic, etc.). User Feedback: Use cli glue informative console output. Dependencies: Prefer dplyr, tidyr, rlang data manipulation tidy evaluation.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"ipd-individual-patient-data","dir":"","previous_headings":"Data Formats","what":"IPD (Individual Patient Data)","title":"outstandR: Outcome Regression Standardisation","text":"data frame long format containing: - treatment column (e.g., trt). - outcome column (e.g., y). - Covariates used adjustment.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"ald-aggregate-level-data","dir":"","previous_headings":"Data Formats","what":"ALD (Aggregate-Level Data)","title":"outstandR: Outcome Regression Standardisation","text":"data frame specific columns: - variable: Covariate name. - statistic: “mean”, “sd”, “prop”, “sum”, “N”. - value: Numeric value. - trt: Treatment label (NA common across arms).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"outstandr-outcome-regression-standardisation","dir":"","previous_headings":"","what":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Indirect treatment comparison limited subject-level data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"overview","dir":"","previous_headings":"","what":"Overview","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"outstandR R package designed facilitate unified framework Population-Adjusted Indirect Comparison (PAIC) Health Technology Assessment (HTA). facilitates outcome regression standardisation using model-based approaches head--head clinical trials absent trial populations differ effect modifiers. streamlining workflow covariate simulation, model standardisation, contrast estimation, outstandR enables robust compatible evidence synthesis, particularly scenarios individual patient data (IPD) limited one trials compared.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"who-is-this-package-for","dir":"","previous_headings":"","what":"Who is this package for?","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"target audience outstandR includes statisticians health economists performing indirect treatment comparisons requiring cross-trial population adjustment. simplifies implementation model-based standardization two core steps: Covariate simulation (overcome limited subject-level data aggregate-level data studies). Indirect comparison across studies targeting compatible marginal treatment effects.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Install released version CRAN: install development version GitHub using R-universe: Alternatively, may wish download directly repo ","code":"install.packages(\"outstandR\") install.packages(\"outstandR\",    repos = c(\"https://statisticshealtheconomics.r-universe.dev\",              \"https://cloud.r-project.org\")) remotes::install_github(\"StatisticsHealthEconomics/outstandR\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"background","dir":"","previous_headings":"","what":"Background","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Population adjustment methods increasingly used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. outstandR package allows implementation range methods situation including following: Matching-Adjusted Indirect Comparison (MAIC) based weighting, sensitive poor covariate overlap extrapolate beyond observed covariate space. reweights individual patient-level data (IPD) match aggregate characteristics comparator trial, thereby aligning populations. Parametric G-computation maximum likelihood: method fits outcome model IPD using maximum likelihood estimation, uses model predict outcomes comparator population. allows extrapolation beyond observed covariate space requires correct specification outcome model avoid bias. Parametric G-computation Bayesian inference: Similar maximum likelihood version, approach fits outcome model within Bayesian framework. allows coherent propagation uncertainty prior distributions posterior inference, enabling probabilistic sensitivity analysis full uncertainty quantification. Multiple imputation marginalization method based parametric G-computation: Current outcome regression-based alternatives can extrapolate target conditional treatment effect incompatible indirect comparison. adjusting covariates, one must integrate average conditional estimate relevant population recover compatible marginal treatment effect. can easily applied outcome regression generalized linear model Cox model. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. method can accommodate Bayesian statistical framework, naturally integrates analysis probabilistic framework. Simulated Treatment Comparison (STC) [DEPRECATED]: previously common, standard STC can produce biased marginal estimates due aggregation bias non-collapsibility using non-linear link functions. Note: STC formally deprecated v1.0.1 favor robust G-computation approaches.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"general-problem","dir":"","previous_headings":"","what":"General problem","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Consider one trial, company IPD, comparing treatments C, herein call AC trial. Also, consider second trial comparing treatments B C, similarly called BC trial. trial published aggregate data available. wish estimate comparison effects treatments B appropriate scale target population P, denoted parameter dAB(P)d_{AB(P)}. make use bracketed subscripts denote specific population. Within BC population parameters μB(BC)\\mu_{B(BC)} μC(BC)\\mu_{C(BC)} representing expected outcome treatment (including parameters treatments studied BC trial, e.g. treatment ). BC trial provides estimators Y‾B(BC)\\bar Y_{B(BC)} Y‾C(BC)\\bar Y_{C(BC)} μB(BC)\\mu_{B(BC)}, μC(BC)\\mu_{C(BC)}, respectively, summary outcomes. situation AC trial. suitable scale, example log-odds ratio, risk difference, form estimators Δ̂BC(BC)\\hat{\\Delta}{BC(BC)} Δ̂AC(AC)\\hat{\\Delta}_{AC(AC)} trial level (marginal) relative treatment effects. shall assume always represented difference , example, risk ratio log scale. Δ̂AC(AC)=g(Y‾C(AC))−g(Y‾(AC)) \\hat{\\Delta}_{AC{(AC)}} = g(\\bar{Y}_{C{(AC)}}) - g(\\bar{Y}_{{(AC)}}) similarly Δ̂BC(BC)\\hat{\\Delta}_{BC(BC)}. assume difference effect modifiers trials, estimator relative treatment effect dAB(BC)d_{AB(BC)} Δ̂AB(BC)=Δ̂BC(BC)−Δ̂AC(BC). \\hat{\\Delta}_{AB(BC)} = \\hat{\\Delta}_{BC(BC)} - \\hat{\\Delta}_{AC(BC)}. However, distributions effect modifiers different trial populations, relative treatment effect estimated trial simply combined . purpose population-adjustment ITC include estimate Δ̂AC(BC)\\hat{\\Delta}_{AC(BC)}.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"references","dir":"","previous_headings":"","what":"References","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"R package contains code originally written papers: Remiro-Azócar, ., Heath, . & Baio, G. (2022) Parametric G-computation Compatible Indirect Treatment Comparisons Limited Individual Patient Data. Res Synth Methods;1–31. Remiro-Azócar, ., Heath, ., & Baio, G. (2023) Model-based standardization using multiple imputation. BMC Medical Research Methodology, 1–15. https://doi.org/10.1186/s12874-024-02157-x","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"contributing","dir":"","previous_headings":"","what":"Contributing","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"welcome contributions! Please submit contributions Pull Requests, following contributing guidelines. report issues /seek support, please file new ticket issue tracker. Please note project released Contributor Code Conduct. participating project agree abide terms. [!NOTE] package licensed GPLv3. information, see LICENSE.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"GNU General Public License","title":"GNU General Public License","text":"Version 3, 29 June 2007Copyright © 2007 Free Software Foundation, Inc. <http://fsf.org/> Everyone permitted copy distribute verbatim copies license document, changing allowed.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/LICENSE.html","id":"preamble","dir":"","previous_headings":"","what":"Preamble","title":"GNU General Public License","text":"GNU General Public License free, copyleft license software kinds works. licenses software practical works designed take away freedom share change works. contrast, GNU General Public License intended guarantee freedom share change versions program–make sure remains free software users. , Free Software Foundation, use GNU General Public License software; applies also work released way authors. can apply programs, . speak free software, referring freedom, price. 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This is free software, and you are welcome to redistribute it under certain conditions; type 'show c' for details."},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set for individual level patient data — AC_IPD","title":"Data set for individual level patient data — AC_IPD","text":"data set contains simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set for individual level patient data — AC_IPD","text":"data list including variables needed outstandR basic example. variables follows: X1 Numeric covariate X2 Numeric covariate X3 Numeric covariate X4 Numeric covariate trt Integer treatment identifier y Integer binary outcome","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Data set for individual level patient data — AC_IPD","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Data set for individual level patient data — AC_IPD","text":"Remiro‐Azócar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"data set contains simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"","code":"data(AC_IPD_binY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"id Numeric unique identifier PF_cont_1 Numeric prognostic factor continuous covariate PF_cont_2 Numeric prognostic factor continuous covariate EM_cont_1 Numeric effect modifier continuous covariate EM_cont_2 Numeric effect modifier continuous covariate trt Factor treatment identifier. Levels , C y Integer binary outcome true_eta Numeric linear predictor","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":null,"dir":"Reference","previous_headings":"","what":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"data set contains simulated patient covariate outcome values. Corresponds ALD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"","code":"data(AC_IPD_contY_mixedX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"y-x-x-x-trt-trt-x-x-x-","dir":"Reference","previous_headings":"","what":"y ~ X1 + X3 + X4 + trt + trt:(X2 + X3 + X4)","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"id Numeric unique identifier X1 Numeric prognostic factor continuous covariate X2 Numeric prognostic factor effect modifier binary covariate X3 Numeric prognostic factor effect modifier continuous covariate X4 Numeric effect modifier binary covariate trt Factor treatment identifier. Levels , C y Integer binary outcome true_eta Numeric linear predictor","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"data set contains simulated patient covariate outcome values. Corresponds ALD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"","code":"data(AC_IPD_countY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"id Numeric unique identifier PF_cont_1 Numeric prognostic factor continuous covariate PF_cont_2 Numeric prognostic factor continuous covariate EM_cont_1 Numeric effect modifier continuous covariate EM_cont_2 Numeric effect modifier continuous covariate trt Factor treatment identifier. Levels , C y Integer non-negative count outcome true_eta Numeric linear predictor","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate-level data mean and variance statistics — ALD_stats","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"Computes mean variance marginal treatment effects aggregate-level trial data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"","code":"ALD_stats(strategy, ald, treatments = list(\"B\", \"C\"), scale)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"strategy list containing strategy details, including family distribution. ald Aggregate-level trial data treatments Treatment labels list; default B, C (common; e.g. placebo) scale scaling parameter calculation.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"list containing: mean marginal treatment effect mean. var marginal treatment effect variance.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"","code":"if (FALSE) { # \\dontrun{ strategy <- list(family = list(family = \"binomial\"))  # basic version ald <- data.frame(trial = 1:5, n_B = c(10, 20, 15, 30, 25), n_C = c(12, 18, 20, 25, 22)) ALD_stats(strategy, ald, treatments = list(\"B\", \"C\"), scale = \"log\") } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set for aggregate level patient data in wide format — BC_ALD","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"data set contains summaries simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"data list including variables needed outstandR basic example. variables follows: mean.X1 Numeric value mean.X2 Numeric value mean.X3 Numeric value mean.X4 Numeric value sd.X1 Numeric standard deviation value sd.X2 Numeric standard deviation value sd.X3 Numeric standard deviation value sd.X4 Numeric standard deviation value y.B.sum Integer number patients event B treatment y.B.bar Numeric proportion patients B treatment N.B Integer Total number patients B treatment y.C.sum Integer number patients event C treatment y.C.bar Numeric proportion patients C treatment N.C Integer total number patients C treatment","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"Remiro‐Azócar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"data set contains summaries simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"","code":"data(BC_ALD_binY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"variable String covariate outcome name. EM_cont_1, EM_cont_2, PF_cont_1, PF_cont_2, y. statistic String summary statistic name. mean, sd, sum, N value Numeric value trt Treatment (arm) name. B, C","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"data set contains summaries simulated patient covariate outcome values. Corresponds IPD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"","code":"data(BC_ALD_contY_mixedX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"y-x-x-x-trt-trt-x-x-x-","dir":"Reference","previous_headings":"","what":"y ~ X1 + X3 + X4 + trt + trt:(X2 + X3 + X4)","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"variable String covariate outcome name. X1, X2, X3, X4, y. statistic String summary statistic name. mean, sd, prob, sum, N value Numeric value trt Treatment (arm) name. B, C","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"data set contains summaries simulated patient covariate outcome values. Corresponds IPD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"","code":"data(BC_ALD_countY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"variable String covariate outcome name. EM_cont_1, EM_cont_2, PF_cont_1, PF_cont_2, y. statistic String summary statistic name. mean, sd, sum, N value Numeric value trt Treatment (arm) name. B, C","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_long.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set for aggregate level patient data in long format — BC_ALD_long","title":"Data set for aggregate level patient data in long format — BC_ALD_long","text":"data set contains summaries simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_long.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set for aggregate level patient data in long format — BC_ALD_long","text":"data frame 4 variables: statistic character string trt factor value numeric value variable character string","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_long.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Data set for aggregate level patient data in long format — BC_ALD_long","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.html","id":null,"dir":"Reference","previous_headings":"","what":"Bias estimate — bias","title":"Bias estimate — bias","text":"Bias estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bias estimate — bias","text":"","code":"bias(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bias estimate — bias","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of bias estimate — bias.mcse","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"Monte Carlo SE bias estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"","code":"bias.mcse(theta.hat)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"theta.hat theta hat","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"\\(sqrt(1/(nsim*(nsim-1))*tmp)\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Average Treatment Effect — calculate_ate","title":"Calculate Average Treatment Effect — calculate_ate","text":"Computes average treatment effect (ATE) based specified effect scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Average Treatment Effect — calculate_ate","text":"","code":"calculate_ate(mean_comp, mean_ref, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Average Treatment Effect — calculate_ate","text":"mean_comp, mean_ref Mean outcome comparator reference / common effect character string specifying effect scale. Options : \"log_odds\" Log-odds difference. \"risk_difference\" Risk difference. \"delta_z\" Probit scale difference (z-scores). \"log_relative_risk_rare_events\" Log relative risk rare events. \"log_relative_risk\" Log relative risk.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Average Treatment Effect — calculate_ate","text":"Numeric computed average treatment effect specified scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate Average Treatment Effect — calculate_ate","text":"","code":"calculate_ate(mean_comp = 0.7, mean_ref = 0.5, effect = \"log_odds\") #> [1] 0.8472979 calculate_ate(mean_comp = 0.7, mean_ref = 0.5, effect = \"risk_difference\") #> [1] 0.2"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Wrapper — calculate_trial_mean","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"Calculate Trial Mean Wrapper","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"","code":"calculate_trial_mean(ald, tid, effect, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. family Family distribution","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"Calculate Trial Mean Binary Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"","code":"calculate_trial_mean_binary(ald, tid, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"Calculate Trial Mean Continuous Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"","code":"calculate_trial_mean_continuous(ald, tid, effect, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Count Data — calculate_trial_mean_count","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"Calculate Trial Mean Count Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"","code":"calculate_trial_mean_count(ald, tid, effect, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance — calculate_trial_variance","title":"Calculate trial variance — calculate_trial_variance","text":"Computes variance treatment effects trial based specified family distribution.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance — calculate_trial_variance","text":"","code":"calculate_trial_variance(ald, tid, effect, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance — calculate_trial_variance","text":"ald Aggregate-level data. Data frame. tid Treatment identifier used extract relevant columns ald. effect character string specifying effect scale (e.g., \"log_odds\", \"risk_difference\"). family character string specifying model family (e.g., \"binomial\", \"gaussian\").","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance — calculate_trial_variance","text":"Numeric computed variance treatment effects.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate trial variance — calculate_trial_variance","text":"","code":"ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))                    calculate_trial_variance(   ald, tid = \"B\", effect = \"log_odds\", family = \"binomial\") #> [1] 0.04"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance binary — calculate_trial_variance_binary","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"Calculate trial variance binary","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"","code":"calculate_trial_variance_binary(ald, tid, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"ald Aggregate level data tid Treatment ID effect Effect","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"Numeric value total variance.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance continuous — calculate_trial_variance_continuous","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"Calculate trial variance continuous","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"","code":"calculate_trial_variance_continuous(ald, tid, effect, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"Numeric value total variance.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance count — calculate_trial_variance_count","title":"Calculate trial variance count — calculate_trial_variance_count","text":"Calculate trial variance count","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance count — calculate_trial_variance_count","text":"","code":"calculate_trial_variance_count(ald, tid, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance count — calculate_trial_variance_count","text":"ald Aggregate level data. Data frame long format. tid Treatment ID. effect Effect name. String.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance count — calculate_trial_variance_count","text":"Numeric value total variance.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate-level data mean and variance statistics — calc_ALD_stats","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"Computes mean variance marginal treatment effects aggregate-level trial data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"","code":"calc_ALD_stats(strategy, analysis_params)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"strategy list containing strategy details, including family distribution. analysis_params list containing: ald Aggregate-level trial data ref_trt Treatment labels reference (common; e.g. placebo) ald_comp Treatment labels comparator scale scaling parameter calculation. \"log_odds\", \"risk_difference\", \"log_relative_risk\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"list containing: mean marginal treatment effect mean. var marginal treatment effect variance.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"","code":"strategy <- list(family = list(family = \"binomial\"))  # basic version  ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))  calc_ALD_stats(strategy = strategy,                list(ald = ald,                     ref_trt = \"C\",                     ald_comp = \"B\",                     scale = \"log_odds\")) #> $mean #> [1] -0.4054651 #>  #> $var #> [1] 0.08166667 #>"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":null,"dir":"Reference","previous_headings":"","what":"Bayesian G-computation using Stan — calc_gcomp_bayes","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"Calculate draws binary responses posterior predictive distribution Bayesian G-computation method using Hamiltonian Monte Carlo.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"","code":"calc_gcomp_bayes(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"strategy list specifying model strategy, including: outcome_model: linear regression formula object. family: family object specifying distribution link function (e.g., binomial). iter: Number iterations MCMC sampling. warmup: Number warmup iterations MCMC sampling. chains: Number MCMC chains. analysis_params List analysis parameters. Must contain ipd ald. ... Additional arguments passed rstanarm::stan_glm().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"list containing: means: list containing: Posterior means comparator treatment group. Posterior means reference treatment group. model: list containing fit object (stan_glm), rho, N, stan_args.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"","code":"strategy <- list(   outcome_model = y ~ trt:X1,   family = binomial(),   rho = NA,   N = 1000L,   marginal_distns = NA,   marginal_params = NA,   trt_var = \"trt\",   iter = 2000,   warmup = 500,   chains = 4)  ipd <- data.frame(    trt = sample(c(\"A\", \"C\"), size = 100, replace = TRUE),    X1 = rnorm(100, 1, 1),    y = sample(c(1,0), size = 100, prob = c(0.7, 0.3), replace = TRUE))  ald <- data.frame(   trt = c(NA, NA, \"B\", \"C\", \"B\", \"C\"),   variable = c(\"X1\", \"X1\", \"y\", \"y\", NA, NA),   statistic = c(\"mean\", \"sd\", \"sum\", \"sum\", \"N\", \"N\"),   value = c(0.5, 0.1, 10, 12, 20, 25))  res <-    calc_gcomp_bayes(     strategy,     analysis_params = list(       ipd = ipd, ald = ald,        ref_trt = \"C\",       ipd_comp = \"A\"))  str(res, max.level = 2, list.len = 3, vec.len = 2) #> List of 3 #>  $ means          :List of 2 #>   ..$ A: num [1:2000] 0.626 0.69 ... #>   ..$ C: num [1:2000] 0.61 0.667 ... #>  $ point_estimates:List of 2 #>   ..$ A: num 0.603 #>   ..$ C: num 0.586 #>  $ model          :List of 4 #>   ..$ fit      :List of 28 #>   .. ..- attr(*, \"class\")= chr [1:3] \"stanreg\" \"glm\" ... #>   ..$ rho      : logi NA #>   ..$ N        : int 1000 #>   .. [list output truncated]"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"Computes mean difference treatment effects using bootstrap resampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"","code":"calc_gcomp_ml(strategy, analysis_params)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"strategy list specifying model strategy, including: R: Number bootstrap replications. outcome_model: linear regression formula object outcome model. family: family object specifying distribution link function (e.g., binomial). N: Synthetic sample size g-computation. analysis_params List analysis parameters.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"list containing: means: list containing: : Bootstrap estimates comparator treatment group \"\". C: Bootstrap estimates reference treatment group \"C\". model: list containing fit object, rho, N.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"","code":"strategy <- list(   outcome_model = y ~ trt:X1,   family = binomial(),   rho = NA,   N = 1000L,   n_boot = 100L,   marginal_distns = NA,   marginal_params = NA,   trt_var = \"trt\")  ipd <- data.frame(trt = sample(c(\"A\", \"C\"), size = 100, replace = TRUE),                   X1 = rnorm(100, 1, 1),                   y = sample(c(1,0), size = 100, prob = c(0.7,0.3), replace = TRUE))  ald <- data.frame(trt = c(NA, NA, \"B\", \"C\", \"B\", \"C\"),                   variable = c(\"X1\", \"X1\", \"y\", \"y\", NA, NA),                   statistic = c(\"mean\", \"sd\", \"sum\", \"sum\", \"N\", \"N\"),                   value = c(0.5, 0.1, 10, 12, 20, 25))  calc_gcomp_ml(   strategy,   analysis_params =      list(ipd = ipd, ald = ald,           ref_trt = \"C\",           ipd_comp = \"A\")) #> $means #> $means$A #>   [1] 0.7524448 0.7208018 0.6857046 0.7773186 0.7379123 0.7953863 0.7416379 #>   [8] 0.7333357 0.6740201 0.7496222 0.7004516 0.7565848 0.7328825 0.7406903 #>  [15] 0.7488645 0.7340921 0.6933722 0.7124750 0.8259316 0.8126080 0.7030263 #>  [22] 0.7026071 0.7626186 0.7341363 0.7593515 0.7545032 0.8159394 0.7371818 #>  [29] 0.7284083 0.6787501 0.6071921 0.7056624 0.7314274 0.6486667 0.7948652 #>  [36] 0.8041567 0.6859274 0.7155094 0.7249215 0.7912577 0.6099682 0.6655606 #>  [43] 0.8584396 0.6814494 0.7191635 0.7445806 0.6603892 0.7538379 0.7519644 #>  [50] 0.7192660 0.7830961 0.8151415 0.6831753 0.7150227 0.8449769 0.7668341 #>  [57] 0.7483105 0.7879836 0.7614439 0.8144559 0.6243036 0.6539474 0.7320960 #>  [64] 0.7168957 0.7408405 0.7626611 0.7756132 0.7237764 0.7889745 0.7579104 #>  [71] 0.7375602 0.7413274 0.6781683 0.6714261 0.7565422 0.8332126 0.6637191 #>  [78] 0.5921426 0.7549736 0.7339375 0.7560676 0.7910103 0.7243667 0.7994549 #>  [85] 0.8220225 0.8462224 0.7428240 0.5864449 0.7003216 0.7453676 0.8061360 #>  [92] 0.8159053 0.6917901 0.6791657 0.7111803 0.7263968 0.7310195 0.7909051 #>  [99] 0.7227581 0.7323826 #>  #> $means$C #>   [1] 0.7309018 0.7420960 0.6819819 0.6978632 0.7191187 0.7537383 0.7023496 #>   [8] 0.7228270 0.6564365 0.7003893 0.6392001 0.6893771 0.6915394 0.7598735 #>  [15] 0.6611513 0.7114534 0.6330323 0.6893841 0.8136764 0.8007598 0.7033007 #>  [22] 0.7148683 0.7531519 0.7223997 0.7248275 0.7375199 0.7290035 0.7066567 #>  [29] 0.7381150 0.7441146 0.5489844 0.6454383 0.7261025 0.6269568 0.7808563 #>  [36] 0.7845551 0.6790214 0.7108215 0.7857677 0.7722908 0.5920379 0.6711567 #>  [43] 0.7735766 0.7082050 0.7105959 0.6968303 0.6837809 0.7379012 0.7804497 #>  [50] 0.7257683 0.7395591 0.7641128 0.5839501 0.7344368 0.7883609 0.7415819 #>  [57] 0.7914461 0.7409043 0.7648980 0.7197088 0.6058059 0.6712301 0.7169338 #>  [64] 0.6840646 0.7066697 0.6927932 0.7584608 0.7285138 0.7396870 0.7564756 #>  [71] 0.7302828 0.6995002 0.6820383 0.6638061 0.7293550 0.8527352 0.6752132 #>  [78] 0.6727563 0.7111311 0.6847701 0.7357006 0.7539906 0.7102805 0.7856127 #>  [85] 0.8156423 0.8199455 0.7346005 0.6136072 0.7113708 0.7010819 0.7942727 #>  [92] 0.7816347 0.6858805 0.6637144 0.7716140 0.7212641 0.7290398 0.7679028 #>  [99] 0.6818292 0.7198914 #>  #>  #> $point_estimates #> $point_estimates$A #>         1  #> 0.7321823  #>  #> $point_estimates$C #>         0  #> 0.7163028  #>  #>  #> $model #> $model$fit #>  #> Call:  glm(formula = outcome_model, family = family, data = ipd) #>  #> Coefficients: #> (Intercept)      trtA:X1      trtC:X1   #>     0.93459      0.14321     -0.01688   #>  #> Degrees of Freedom: 99 Total (i.e. Null);  97 Residual #> Null Deviance:\t    116.7  #> Residual Deviance: 116.3 \tAIC: 122.3 #>  #> $model$rho #> [1] NA #>  #> $model$N #> [1] 1000 #>  #> $model$n_boot #> [1] 100 #>  #>"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation using Stan — calc_gcomp_bayes","title":"G-computation using Stan — calc_gcomp_bayes","text":"Calculate draws binary responses posterior predictive distribution Bayesian G-computation method using Hamiltonian Monte Carlo.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation using Stan — calc_gcomp_bayes","text":"","code":"calc_gcomp_bayes(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation using Stan — calc_gcomp_bayes","text":"strategy list specifying model strategy, including: formula linear regression formula object. family family object specifying distribution link function (e.g., binomial). iter Number iterations MCMC sampling. warmup Number warmup iterations MCMC sampling. chains Number MCMC chains. ipd Individual-level patient data. Dataframe one row per patient outcome, treatment covariate columns. ald Aggregate-level data. Single row matrix summary statistics covariate treatment outcomes. format 'mean.' 'sd.' covariates 'y..sum', 'y..bar', 'y.*.sd' treatments B C. assume common distribution treatment arm.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation using Stan — calc_gcomp_bayes","text":"list \\(y^*_A\\) \\(y^*_C\\) posterior predictions: `0` Posterior means reference treatment group \"C\". `1` Posterior means comparator treatment group \"\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G-computation using Stan — calc_gcomp_bayes","text":"","code":"if (FALSE) { # \\dontrun{ strategy <- list(   formula = y ~ trt + age,   family = binomial(),   iter = 2000,   warmup = 500,   chains = 4 ) ipd <- data.frame(trt = c(\"A\", \"C\"),                   y = c(1, 0),                   age = c(30, 40)) ald <- data.frame() calc_gcomp_bayes(strategy, ipd, ald) } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate individual-level patient data statistics — calc_IPD_stats","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Computes mean variance statistics individual-level patient data using various approaches, including Matching-Adjusted Indirect Comparison (MAIC), Simulated Treatment Comparison (STC), G-computation via Maximum Likelihood Estimation (MLE) Bayesian inference.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"","code":"calc_IPD_stats(strategy, analysis_params, ...)  # Default S3 method calc_IPD_stats(...)  # S3 method for class 'stc' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'maic' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'gcomp_ml' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'gcomp_bayes' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'mim' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"strategy list corresponding different modelling approaches analysis_params list containing: ipd: Individual-level patient data (data frame) ald: Aggregate-level trial data (data frame) ref_trt: Treatment label reference arm (common; e.g., \"C\") ipd_comp: Treatment label comparator arm IPD (e.g., \"\") scale: Scaling parameter (\"log_odds\", \"risk_difference\", \"log_relative_risk\") ... Additional arguments var_method string specifying variance estimation method, either \"sample\" (default) \"sandwich\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"list containing: contrasts: list elements mean var. absolute: list elements mean var.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"simulated-treatment-comparison-statistics","dir":"Reference","previous_headings":"","what":"Simulated treatment comparison statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"IPD reference \"C\" comparator \"\" trial arms used fit regression model describing observed outcomes \\(y\\) terms relevant baseline characteristics \\(x\\) treatment variable \\(z\\).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"matching-adjusted-indirect-comparison-statistics","dir":"Reference","previous_headings":"","what":"Matching-adjusted indirect comparison statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Marginal IPD comparator treatment \"\" vs reference treatment \"C\" treatment effect estimates using bootstrapping sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"g-computation-maximum-likelihood-statistics","dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Compute non-parametric bootstrap default \\(R=1000\\) resamples.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"g-computation-bayesian-statistics","dir":"Reference","previous_headings":"","what":"G-computation Bayesian statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Using Stan, compute marginal relative effects IPD comparator \"\" vs reference \"C\" treatment arms MCMC sample transforming probability linear predictor scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"multiple-imputation-marginalisation","dir":"Reference","previous_headings":"","what":"Multiple imputation marginalisation","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Using Stan, compute marginal relative treatment effect IPD comparator \"\" vs reference \"C\" arms MCMC sample transforming probability linear predictor scale. Approximate using imputation combining estimates using pooling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"","code":"strategy <- strategy_maic(   formula = list(outcome_model = y ~ trt,  # default                   balance_model = ~ X1),   family = binomial()) #> Treatment is guessed as: trt  ipd <- data.frame(trt = sample(c(\"A\", \"C\"), size = 100, replace = TRUE),                   X1 = rnorm(100, 1, 1),                   y = sample(c(1,0), size = 100, prob = c(0.7,0.3), replace = TRUE))  ald <- data.frame(trt = c(NA, \"B\", \"C\", \"B\", \"C\"),                   variable = c(\"X1\", \"y\", \"y\", NA, NA),                   statistic = c(\"mean\", \"sum\", \"sum\", \"N\", \"N\"),                   value = c(0.5, 10, 12, 20, 25))  calc_IPD_stats(strategy,   analysis_params = list(ipd = ipd, ald = ald, scale = \"log_odds\")) #> $contrasts #> $contrasts$mean #> [1] 0.0404359 #>  #> $contrasts$var #> [1] 0.2441335 #>  #>  #> $absolute #> $absolute$mean #>         A         C  #> 0.5667870 0.5562863  #>  #> $absolute$var #>           A           C  #> 0.006112309 0.007795801  #>  #>  #> $method_name #> [1] \"MAIC\" #>  #> $model #> $model$weights #>   weights1   weights2   weights3   weights4   weights5   weights6   weights7  #>  0.5097557  0.9862214  0.1767722  1.0189126  0.4083001  0.3004525  0.5227465  #>   weights8   weights9  weights10  weights11  weights12  weights13  weights14  #>  0.2650783  0.5314778  0.8255845  0.4200238  1.9246909  1.6187657  0.4651878  #>  weights15  weights16  weights17  weights18  weights19  weights20  weights21  #>  0.4238390  0.4253863  2.4215912  2.1405183  2.2258621  1.3013718  1.3575855  #>  weights22  weights23  weights24  weights25  weights26  weights27  weights28  #>  0.2828358  1.1742708  1.9678484  0.4041438  0.4765942  1.0933591  0.3810760  #>  weights29  weights30  weights31  weights32  weights33  weights34  weights35  #>  0.5973394  1.4076416  0.8244193  0.3731263  0.7741472  0.9083386  0.1294497  #>  weights36  weights37  weights38  weights39  weights40  weights41  weights42  #>  0.5622625  0.5166102  1.6685593  0.2084445  0.4586885  0.9201768  0.3863122  #>  weights43  weights44  weights45  weights46  weights47  weights48  weights49  #>  0.5076362  0.5611625  0.4537915  0.3643097  0.3339151  0.3729876  1.1400251  #>  weights50  weights51  weights52  weights53  weights54  weights55  weights56  #>  0.8037654  0.7215501  1.6619502  0.1326304  0.6915303  1.1697328  1.9035924  #>  weights57  weights58  weights59  weights60  weights61  weights62  weights63  #>  1.1017251  0.3539011  1.4816379  0.5736033  1.3541201  0.7266439  1.5106265  #>  weights64  weights65  weights66  weights67  weights68  weights69  weights70  #>  0.4651451  0.3815356  0.9272789  0.6387655  0.2490713  0.4498635  0.8699813  #>  weights71  weights72  weights73  weights74  weights75  weights76  weights77  #>  0.4311347  0.6371576  0.5781595  1.2766576  0.8184790  1.6135860  1.6471549  #>  weights78  weights79  weights80  weights81  weights82  weights83  weights84  #>  0.8892978  0.2861711  0.8390482  1.1599676  0.7896686  0.6933948  1.1559473  #>  weights85  weights86  weights87  weights88  weights89  weights90  weights91  #>  0.8915050  1.0140840  1.2954799  0.6523693  0.4526894  0.7622167  1.0480156  #>  weights92  weights93  weights94  weights95  weights96  weights97  weights98  #>  0.5038243  0.1916380  0.1984988  0.1956611  2.0358831  1.1200094  0.5659745  #>  weights99 weights100  #>  0.6973233  0.8650603  #>  #> $model$ESS #>      ESS  #> 71.57563  #>  #>"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate MAIC — calc_maic","title":"Calculate MAIC — calc_maic","text":"Calculate MAIC","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate MAIC — calc_maic","text":"","code":"calc_maic(strategy, analysis_params)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate MAIC — calc_maic","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters. Must contain ipd (individual patient data) ald (aggregated lead data).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate MAIC — calc_maic","text":"list containing: means: list containing: : Bootstrap estimates comparator treatment group \"\". C: Bootstrap estimates reference treatment group \"C\". model: list containing model diagnostics derived original data: weights: Vector calculated weights patients ipd. ESS: Effective Sample Size.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiple imputation marginalization (MIM) — calc_mim","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"Multiple imputation marginalization (MIM)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"","code":"calc_mim(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters. Must contain ipd ald. ... Additional argument pass Stan model","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"list containing: means: list containing named vectors posterior means (one per synthesis n_imp): Comparator means. Reference means. model: list containing: fit: first-stage rstanarm::stan_glm() object. hats.v: Vector variance point estimates synthesis. n_imp: Number posterior prediction draws (syntheses). rho, N, stan_args: Strategy model parameters.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate simulated treatment comparison statistics — calc_stc","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"Calculate simulated treatment comparison statistics","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"","code":"calc_stc(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters. Must contain ipd (individual patient data). ... Additional arguments.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"list containing: means: list containing: : Mean comparator treatment group \"\". C: Mean reference treatment group \"C\". model: fitted stats::glm() object.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":null,"dir":"Reference","previous_headings":"","what":"Check balance formula — check_balance_formula","title":"Check balance formula — check_balance_formula","text":"Check balance formula","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check balance formula — check_balance_formula","text":"","code":"check_balance_formula(formula, trt_var = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check balance formula — check_balance_formula","text":"formula Formula balance model trt_var Treatment variable (used warn mistakenly included)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check balance formula — check_balance_formula","text":"return value, called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":null,"dir":"Reference","previous_headings":"","what":"Check outcome formula — check_formula","title":"Check outcome formula — check_formula","text":"Check outcome formula","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check outcome formula — check_formula","text":"","code":"check_formula(formula, trt_var = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check outcome formula — check_formula","text":"formula Formula outcome model trt_var Treatment variable","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check outcome formula — check_formula","text":"return value, called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula_base.html","id":null,"dir":"Reference","previous_headings":"","what":"Base formula validator — check_formula_base","title":"Base formula validator — check_formula_base","text":"Base formula validator","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula_base.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Base formula validator — check_formula_base","text":"","code":"check_formula_base(   formula,   trt_var = NULL,   must_have_response = TRUE,   must_have_trt = TRUE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":null,"dir":"Reference","previous_headings":"","what":"Continuity Correction — continuity_correction","title":"Continuity Correction — continuity_correction","text":"Continuity Correction","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Continuity Correction — continuity_correction","text":"","code":"continuity_correction(ald, correction = 0.5, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Continuity Correction — continuity_correction","text":"ald Aggregate level data. Data frame long format. correction Continuity correction numeric size. Default 0.5. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Continuity Correction — continuity_correction","text":"Corrected aggregate level data frame.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute covariance matrix — cor2cov","title":"Compute covariance matrix — cor2cov","text":"Compute covariance matrix","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute covariance matrix — cor2cov","text":"","code":"cor2cov(cormat, S)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute covariance matrix — cor2cov","text":"cormat correlation matrix S vector standard deviations covariance matrix","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute covariance matrix — cor2cov","text":"Required input mvrnorm.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":null,"dir":"Reference","previous_headings":"","what":"Coverage estimate — coverage","title":"Coverage estimate — coverage","text":"Coverage estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Coverage estimate — coverage","text":"","code":"coverage(low, upp, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Coverage estimate — coverage","text":"low Low upp Upper theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Coverage estimate — coverage","text":"\\(sum(in_range)/nsim\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of coverage estimate — coverage.mcse","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"Monte Carlo SE coverage estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"","code":"coverage.mcse(coverage, nsim)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"coverage Coverage nsim Number simulations","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"\\(sqrt((coverage*(1 - coverage))/nsim)\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":null,"dir":"Reference","previous_headings":"","what":"Empirical standard error — empse","title":"Empirical standard error — empse","text":"Empirical standard error","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Empirical standard error — empse","text":"","code":"empse(theta.hat)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Empirical standard error — empse","text":"theta.hat Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Empirical standard error — empse","text":"\\(sqrt(tmp/(nsim-1))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"EmpSE MCSE — empse.mcse","title":"EmpSE MCSE — empse.mcse","text":"EmpSE MCSE","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"EmpSE MCSE — empse.mcse","text":"","code":"empse.mcse(empse, nsim)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"EmpSE MCSE — empse.mcse","text":"empse EMPSE nsim Number simulations","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"EmpSE MCSE — empse.mcse","text":"\\(empse/(sqrt(2*(nsim-1)))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"Computes robust (sandwich) variance estimator treatment effect.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"","code":"estimate_var_sandwich(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters (ipd, ald, etc.) ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"Numeric variance estimate treatment contrast","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/find_conversion_path.html","id":null,"dir":"Reference","previous_headings":"","what":"recursive function to find conversion path — find_conversion_path","title":"recursive function to find conversion path — find_conversion_path","text":"recursive function find conversion path","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/find_conversion_path.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"recursive function to find conversion path — find_conversion_path","text":"","code":"find_conversion_path(from, to, visited = c())"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/find_conversion_path.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"recursive function to find conversion path — find_conversion_path","text":"","code":"find_conversion_path(\"log_odds\", \"relative_risk\") #> Error in find_conversion_path(\"log_odds\", \"relative_risk\"): could not find function \"find_conversion_path\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"use bootstrapping function (e.g., boot::boot()). bootstrap sample data, calculates relative treatment effect (e.g., log odds ratio, log relative risk, risk difference) using G-computation maximum likelihood.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"","code":"gcomp_ml.boot(   data,   indices,   R,   outcome_model = NULL,   family,   trt_var,   ref_trt = NA,   comp_trt = NA,   rho = NA,   N = 1000,   marginal_distns = NA,   marginal_params = NA,   ald )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"data data frame containing original individual participant data (IPD). indices vector indices supplied bootstrapping function, used resample data. family 'family' object specifying distribution link function (e.g., 'binomial'). See stats::family() details. rho named square matrix specifying correlation covariates synthetic data generation. Defaults NA, assuming independence. N Synthetic sample size G-computation marginal_distns, marginal_params Marginal distributions parameters ald data frame aggregate-level data providing covariate distributions.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"single numeric value representing relative treatment effect","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"Marginal vs C log-odds ratio (mean difference expected log-odds) estimated transforming probability linear predictor scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"","code":"gcomp_ml_log_odds_ratio(formula, ipd, ald)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"formula Linear regression formula object ipd Individual-level data ald Aggregate-level data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"Difference log-odds","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"\\(\\log(\\hat{\\mu}_A/(1 - \\hat{\\mu}_A)) - \\log(\\hat{\\mu}_C/(1 - \\hat{\\mu}_C))\\)","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"G-computation maximum likelihood mean outcomes arm","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"","code":"gcomp_ml_means(   outcome_model,   family,   ipd,   ald,   trt_var,   rho = NA,   N = 1000,   ref_trt,   comp_trt,   marginal_distns = NA,   marginal_params = NA )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"family 'family' object specifying distribution link function (e.g., 'binomial'). See stats::family() details. ipd Individual-level patient data. Dataframe one row per patient outcome, treatment covariate columns. ald Aggregate-level data. Long format summary statistics covariate treatment outcomes. assume common distribution treatment arm. rho named square matrix covariate correlations; default NA. N Synthetic sample size g-computation marginal_distns, marginal_params Marginal distributions parameters","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"list containing: stats: Named vector marginal mean probabilities model: fitted glm object","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation using Stan — gcomp_bayes","title":"G-computation using Stan — gcomp_bayes","text":"Calculate draws binary responses posterior predictive distribution Bayesian G-computation method using Hamiltonian Monte Carlo.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation using Stan — gcomp_bayes","text":"","code":"gcomp_bayes(formula = NULL, ipd, ald)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation using Stan — gcomp_bayes","text":"formula Linear regression formula object ipd Individual-level data ald Aggregate-level data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation using Stan — gcomp_bayes","text":"list \\(y^*_A\\) \\(y^*_C\\) posterior predictions","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"Generate simulated datasets IPD covariates binary outcome trial","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"","code":"gen_data(   N,   b_trt,   b_X,   b_EM,   b_0,   meanX_EM,   sdX_EM,   meanX,   sdX,   corX,   allocation,   family = binomial(\"logit\") )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"N Total number patients b_trt b coefficient active treatment vs. common comparator b_X b coefficients prognostic variable X b_EM b coefficients effect modifiers b_0 Intercept coefficient meanX Mean normally-distributed covariate X sdX Standard deviation covariate X corX Covariate correlation coefficient X allocation Allocation active treatment proportion total; 0 1 event_rate Event rate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"Data frame X, trt y","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"","code":"if (FALSE) { # \\dontrun{ x <- gen_data(  N = 100,  b_trt = log(0.17),  b_X = -log(0.5),  b_EM = -log(0.67),  b_0 = -0.62,  meanX = 0.6,  sdX = 0.4,  event_rate = 0.35,   corX = 0.2,  allocation = 2/3)   head(x) } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":null,"dir":"Reference","previous_headings":"","what":"Retrieve list of allowed variance methods — get_allowed_var_methods","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"Retrieve list allowed variance methods","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"","code":"get_allowed_var_methods(strategy)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"strategy Strategy object","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"Character vector allowed methods. First element default.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":null,"dir":"Reference","previous_headings":"","what":"Get study comparator treatment names — get_comparator","title":"Get study comparator treatment names — get_comparator","text":"Get study comparator treatment names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get study comparator treatment names — get_comparator","text":"","code":"get_comparator(dat, ref_trt, trt_var = \"trt\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get study comparator treatment names — get_comparator","text":"dat Data frame. ref_trt Reference treatment. String. trt_var Treatment variable. String default \"trt\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get study comparator treatment names — get_comparator","text":"Comparator string names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get covariate names — get_covariate_names","title":"Get covariate names — get_covariate_names","text":"Get covariate names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get covariate names — get_covariate_names","text":"","code":"get_covariate_names(formula)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get covariate names — get_covariate_names","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get covariate names — get_covariate_names","text":"Covariate names character vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":null,"dir":"Reference","previous_headings":"","what":"Get effect modifiers — get_effect_modifiers","title":"Get effect modifiers — get_effect_modifiers","text":"Get effect modifiers","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get effect modifiers — get_effect_modifiers","text":"","code":"get_effect_modifiers(formula)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get effect modifiers — get_effect_modifiers","text":"formula Linear regression formula string","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get effect modifiers — get_effect_modifiers","text":"Effect modifiers names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get effect modifiers — get_eff_mod_names","title":"Get effect modifiers — get_eff_mod_names","text":"Get effect modifiers","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get effect modifiers — get_eff_mod_names","text":"","code":"get_eff_mod_names(formula, trt_var = \"trt\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get effect modifiers — get_eff_mod_names","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax. trt_var Treatment variable name; Default 'trt'.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get effect modifiers — get_eff_mod_names","text":"Effect modifiers strings names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get mean names — get_mean_names","title":"Get mean names — get_mean_names","text":"Get mean names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get mean names — get_mean_names","text":"","code":"get_mean_names(ald, keep_nms)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get mean names — get_mean_names","text":"ald Aggregate-level data. Single row matrix summary statistics covariate treatment outcomes. format 'mean.' 'sd.' covariates 'y..sum', 'y..bar', 'y.*.sd' treatments B C. assume common distribution treatment arm. keep_nms Variable names character vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get mean names — get_mean_names","text":"Mean names vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":null,"dir":"Reference","previous_headings":"","what":"Get reference treatment — get_ref_trt","title":"Get reference treatment — get_ref_trt","text":"Get reference treatment","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get reference treatment — get_ref_trt","text":"","code":"get_ref_trt(ref_trt, trt, ipd_trial, ald_trial)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get reference treatment — get_ref_trt","text":"ref_trt Reference treatment trt Treatment ipd_trial dataframe IPD ald_trial dataframe ALD","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get reference treatment — get_ref_trt","text":"String reference treatment name.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_robust_vcov.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov","title":"Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov","text":"Calculates (X'WX)^-1 (X' W^2 r^2 X) (X'WX)^-1","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_robust_vcov.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov","text":"","code":"get_robust_vcov(fit)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get standard deviation names — get_sd_names","title":"Get standard deviation names — get_sd_names","text":"Get standard deviation names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get standard deviation names — get_sd_names","text":"","code":"get_sd_names(ald, keep_nms)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get standard deviation names — get_sd_names","text":"ald Aggregate-level data. Single row matrix summary statistics covariate treatment outcomes. format 'mean.' 'sd.' covariates 'y..sum', 'y..bar', 'y.*.sd' treatments B C. assume common distribution treatment arm. keep_nms Variable names character vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get standard deviation names — get_sd_names","text":"Standard deviation names vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":null,"dir":"Reference","previous_headings":"","what":"Get treatment effect scale corresponding to a link function — get_treatment_effect","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"Maps given link function corresponding treatment effect scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"","code":"get_treatment_effect(link)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"link character string specifying link function. Options : \"logit\" Log-odds scale. \"identity\" Risk difference. \"probit\" Probit scale. \"cloglog\" Log relative risk rare events. \"log\" Log relative risk.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"character string representing treatment effect scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"","code":"get_treatment_effect(link = \"logit\") #> [1] \"log_odds\"  get_treatment_effect(link = \"identity\") #> [1] \"mean_difference\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":null,"dir":"Reference","previous_headings":"","what":"Get treatment name — get_treatment_name","title":"Get treatment name — get_treatment_name","text":"Get treatment name","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get treatment name — get_treatment_name","text":"","code":"get_treatment_name(formula, trt_var = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get treatment name — get_treatment_name","text":"formula Formula trt_var Treatment variable","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get treatment name — get_treatment_name","text":"Treatment name string.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine and validate variance method for a strategy — get_var_method","title":"Determine and validate variance method for a strategy — get_var_method","text":"Determine validate variance method strategy","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine and validate variance method for a strategy — get_var_method","text":"","code":"get_var_method(strategy, user_method = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine and validate variance method for a strategy — get_var_method","text":"strategy Strategy object user_method User supplied method (string) NULL","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Determine and validate variance method for a strategy — get_var_method","text":"String name variance method use","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":null,"dir":"Reference","previous_headings":"","what":"Guess treatment name — guess_treatment_name","title":"Guess treatment name — guess_treatment_name","text":"variable appear interactions? pick first LHS interaction term. Finally, interactions pick last main effect term.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Guess treatment name — guess_treatment_name","text":"","code":"guess_treatment_name(formula)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Guess treatment name — guess_treatment_name","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Guess treatment name — guess_treatment_name","text":"Treatment name string.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — hat_Delta_stats","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"main, top-level wrapper hat_Delta_stats(). Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"","code":"hat_Delta_stats(AC.IPD, BC.ALD, strategy, CI = 0.95, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"AC.IPD Individual-level patient data. Suppose studies C. BC.ALD Aggregate-level data. Suppose studies B C. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml()  strategy_gcomp_bayes() CI Confidence interval; 0,1 ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"List length 3 statistics mimR class object. Containing statistics pair treatments. mean contrasts, variances confidence intervals, respectively.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1--31. ISSN 1759-2879, doi:10.1002/jrsm.1565 , 2108.12208.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"","code":"data(AC_IPD)  # AC patient-level data data(BC_ALD)  # BC aggregate-level data  # matching-adjusted indirect comparison hat_Delta_stats_maic <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_maic())  # simulated treatment comparison hat_Delta_stats_stc <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_stc())  # G-computation with maximum likelihood # hat_Delta_stats_gcomp_ml <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_gcomp_ml())  # G-computation with Bayesian inference hat_Delta_stats_gcomp_bayes <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_gcomp_bayes()) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.6e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.36 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.481 seconds (Warm-up) #> Chain 1:                0.592 seconds (Sampling) #> Chain 1:                1.073 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.7e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.514 seconds (Warm-up) #> Chain 2:                0.521 seconds (Sampling) #> Chain 2:                1.035 seconds (Total) #> Chain 2:"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate individual-level patient data statistics — IPD_stats","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Computes mean variance statistics individual-level patient data using various approaches, including Matching-Adjusted Indirect Comparison (MAIC), Simulated Treatment Comparison (STC), G-computation via Maximum Likelihood Estimation (MLE) Bayesian inference.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate individual-level patient data statistics — IPD_stats","text":"","code":"IPD_stats(strategy, ipd, ald, scale, ...)  # Default S3 method IPD_stats(...)  # S3 method for class 'mim' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'stc' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'maic' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'gcomp_ml' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'gcomp_bayes' IPD_stats(strategy, ipd, ald, scale, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate individual-level patient data statistics — IPD_stats","text":"strategy list corresponding different approaches ipd Individual-level data ald Aggregate-level data scale scaling parameter effect calculation. ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate individual-level patient data statistics — IPD_stats","text":"list containing: mean Estimated mean treatment effect. var Estimated variance treatment effect.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"multiple-imputation-marginalisation","dir":"Reference","previous_headings":"","what":"Multiple imputation marginalisation","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Using Stan, compute marginal relative treatment effect vs C MCMC sample transforming probability linear predictor scale. Approximate using imputation combining estimates using Rubin's rules, contrast IPD_stats.gcomp_bayes().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"simulated-treatment-comparison-statistics","dir":"Reference","previous_headings":"","what":"Simulated treatment comparison statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"IPD AC trial used fit regression model describing observed outcomes \\(y\\) terms relevant baseline characteristics \\(x\\) treatment variable \\(z\\).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"matching-adjusted-indirect-comparison-statistics","dir":"Reference","previous_headings":"","what":"Matching-adjusted indirect comparison statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Marginal vs C treatment effect estimates using bootstrapping sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"g-computation-maximum-likelihood-statistics","dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Compute non-parametric bootstrap default \\(R=1000\\) resamples.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"g-computation-bayesian-statistics","dir":"Reference","previous_headings":"","what":"G-computation Bayesian statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Using Stan, compute marginal log-odds ratio vs C MCMC sample transforming probability linear predictor scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate individual-level patient data statistics — IPD_stats","text":"","code":"if (FALSE) { # \\dontrun{ strategy <- strategy_maic() ipd <- data.frame(id = 1:100, treatment = sample(c(\"A\", \"C\"), 100, replace = TRUE), outcome = rnorm(100)) ald <- data.frame(treatment = c(\"A\", \"C\"), mean = c(0.2, 0.1), var = c(0.05, 0.03)) IPD_stats(strategy, ipd, ald, scale = \"log\") } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":null,"dir":"Reference","previous_headings":"","what":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"Creates method computing IPD mean variance statistics based supplied function.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"","code":"IPD_stat_factory(ipd_fun)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"ipd_fun function computes mean variance statistics individual-level patient data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"function computes mean variance statistics given strategy.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":null,"dir":"Reference","previous_headings":"","what":"Mean absolute error estimate — mae","title":"Mean absolute error estimate — mae","text":"Mean absolute error estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mean absolute error estimate — mae","text":"","code":"mae(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mean absolute error estimate — mae","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mean absolute error estimate — mae","text":"\\(sum(abs(theta.hat - theta))/nsim\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":null,"dir":"Reference","previous_headings":"","what":"MAIC bootstrap sample — maic.boot","title":"MAIC bootstrap sample — maic.boot","text":"Matching-adjusted indirect comparison bootstrap sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"MAIC bootstrap sample — maic.boot","text":"","code":"maic.boot(   data,   indices,   balance_matrix,   outcome_x_matrix,   outcome_y,   ald_targets,   scaling_factors,   trt_var,   family,   hat_w = NULL,   ipd = NULL,   outcome_model = NULL,   balance_model = NULL,   ald = NULL,   moments = 1,   int = FALSE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"MAIC bootstrap sample — maic.boot","text":"data Individual-level patient data (data frame). indices Vector indices, length original, define bootstrap sample. balance_matrix Pre-computed balance matrix. outcome_x_matrix Pre-computed outcome design matrix. outcome_y Pre-computed outcome vector. ald_targets Vector ALD targets. scaling_factors Vector scaling factors. trt_var Treatment variable name. family 'family' object specifying distribution link function. hat_w MAIC weights; default NULL calls maic_weights(). ipd Backwards compatibility IPD data (optional). outcome_model Backwards compatibility outcome model formula (optional). balance_model Backwards compatibility balance model formula (optional). ald Backwards compatibility ALD data (optional). moments Backwards compatibility moments (default 1). int Backwards compatibility interactions flag (default FALSE).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"MAIC bootstrap sample — maic.boot","text":"Vector fitted probabilities treatments C","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate MAIC weights — maic_weights","title":"Estimate MAIC weights — maic_weights","text":"Matching-adjusted indirect comparison weights. Method taken (Signorovitch et al. 2010) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate MAIC weights — maic_weights","text":"","code":"maic_weights(X_EM)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate MAIC weights — maic_weights","text":"X_EM Centred \\(S=1\\) effect modifiers IPD covariates; matrix data frame","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate MAIC weights — maic_weights","text":"Estimated weights individual; vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Estimate MAIC weights — maic_weights","text":"Signorovitch JE, Wu EQ, Yu AP, Gerrits CM, Kantor E, Bao Y, Gupta SR, Mulani PM (2010). “Comparative effectiveness without head--head trials: method matching-adjusted indirect comparisons applied psoriasis treatment adalimumab etanercept.” Pharmacoeconomics, 28(10), 935–945. ISSN 11707690. doi:10.2165/11538370-000000000-00000 . https://pubmed.ncbi.nlm.nih.gov/20831302/.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":null,"dir":"Reference","previous_headings":"","what":"Marginal treatment effect from reported event counts — marginal_treatment_effect","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"Computes relative treatment effect aggregate-level data using event counts.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"","code":"marginal_treatment_effect(ald, ref_trt = NA, comp_trt = NA, scale, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"ald Aggregate-level data ref_trt Treatment labels reference (common; e.g. placebo) comp_trt Treatment labels comparator scale scaling parameter calculation. family character string specifying family distribution (e.g., \"binomial\").","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"Numeric relative treatment effect.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"","code":"ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))                    marginal_treatment_effect(ald, ref_trt = \"C\", comp_trt = \"B\",                           scale = \"log_odds\", family = \"binomial\") #> [1] -0.4054651"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":null,"dir":"Reference","previous_headings":"","what":"Marginal effect variance using the delta method — marginal_variance","title":"Marginal effect variance using the delta method — marginal_variance","text":"Computes total variance marginal treatment effects using delta method.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Marginal effect variance using the delta method — marginal_variance","text":"","code":"marginal_variance(ald, ref_trt = NA, comp_trt = NA, scale, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Marginal effect variance using the delta method — marginal_variance","text":"ald Aggregate-level data ref_trt Treatment labels reference (common; e.g. placebo) comp_trt Treatment labels comparator scale scaling parameter calculation. family character string specifying family distribution (e.g., \"binomial\").","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Marginal effect variance using the delta method — marginal_variance","text":"Numeric total variance marginal treatment effects.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Marginal effect variance using the delta method — marginal_variance","text":"","code":"ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))                    marginal_variance(ald, ref_trt = \"C\", comp_trt = \"B\",                   scale = \"log_odds\", family = \"binomial\") #> [1] 0.08166667"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of any continuous performance metric — mcse.estimate","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"Monte Carlo SE continuous performance metric","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"","code":"mcse.estimate(pm)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"pm pm","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"\\(sqrt(sum((pm - pm_mean)^2)/(nsim*(nsim-1)))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mim.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiple imputation marginalization (MIM) — mim","title":"Multiple imputation marginalization (MIM) — mim","text":"Multiple imputation marginalization (MIM)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mim.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiple imputation marginalization (MIM) — mim","text":"","code":"mim(formula, ipd, ald, M = 1000, n.chains = 2, warmup = 1000, iters = 4000)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mim.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiple imputation marginalization (MIM) — mim","text":"ipd Individual-level data ald Aggregate-level data M Number syntheses used analysis stage (high low Monte Carlo error)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — mimR","title":"Calculate the difference between treatments using all evidence — mimR","text":"main, top-level wrapper {mimR}. Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — mimR","text":"","code":"mimR(AC.IPD, BC.ALD, strategy, CI = 0.95, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — mimR","text":"AC.IPD Individual-level patient data. Suppose studies C. BC.ALD Aggregate-level data. Suppose studies B C. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml()  strategy_gcomp_bayes() CI Confidence interval; 0,1 ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — mimR","text":"List length 3 statistics mimR class object. Containing statistics pair treatments. mean contrasts, variances confidence intervals, respectively.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — mimR","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1--31. ISSN 1759-2879, doi:10.1002/jrsm.1565 , 2108.12208.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — mimR","text":"","code":"data(AC_IPD)  # AC patient-level data data(BC_ALD)  # BC aggregate-level data  lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\")  # matching-adjusted indirect comparison mimR_maic <- mimR(AC_IPD, BC_ALD, strategy = strategy_maic(formula = lin_form))  # simulated treatment comparison mimR_stc <- mimR(AC_IPD, BC_ALD, strategy = strategy_stc(lin_form))  # G-computation with maximum likelihood # mimR_gcomp_ml <- mimR(AC_IPD, BC_ALD, strategy = strategy_gcomp_ml(lin_form))  # G-computation with Bayesian inference mimR_gcomp_bayes <- mimR(AC_IPD, BC_ALD, strategy = strategy_gcomp_bayes(lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.6e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.36 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.497 seconds (Warm-up) #> Chain 1:                0.516 seconds (Sampling) #> Chain 1:                1.013 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.6e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.505 seconds (Warm-up) #> Chain 2:                0.564 seconds (Sampling) #> Chain 2:                1.069 seconds (Total) #> Chain 2:"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — outstandR","title":"Calculate the difference between treatments using all evidence — outstandR","text":"main, top-level wrapper {outstandR}. Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"outstandR(AC.IPD, BC.ALD, strategy, CI = 0.95, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — outstandR","text":"AC.IPD Individual-level patient data. Suppose studies C. BC.ALD Aggregate-level data. Suppose studies B C. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml()  strategy_gcomp_bayes() CI Confidence interval; 0,1 ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — outstandR","text":"List length 3 statistics outstandR class object. Containing statistics pair treatments. mean contrasts, variances confidence intervals, respectively.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — outstandR","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1--31. ISSN 1759-2879, doi:10.1002/jrsm.1565 , 2108.12208.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"data(AC_IPD)  # AC patient-level data data(BC_ALD)  # BC aggregate-level data  lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\")  # matching-adjusted indirect comparison outstandR_maic <- outstandR(AC_IPD, BC_ALD, strategy = strategy_maic(formula = lin_form))  # simulated treatment comparison outstandR_stc <- outstandR(AC_IPD, BC_ALD, strategy = strategy_stc(lin_form))  # G-computation with maximum likelihood # outstandR_gcomp_ml <- outstandR(AC_IPD, BC_ALD, strategy = strategy_gcomp_ml(lin_form))  # G-computation with Bayesian inference outstandR_gcomp_bayes <- outstandR(AC_IPD, BC_ALD, strategy = strategy_gcomp_bayes(lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 7.1e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.71 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.71 seconds (Warm-up) #> Chain 1:                0.733 seconds (Sampling) #> Chain 1:                1.443 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 2.2e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.73 seconds (Warm-up) #> Chain 2:                0.817 seconds (Sampling) #> Chain 2:                1.547 seconds (Total) #> Chain 2:"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":null,"dir":"Reference","previous_headings":"","what":"Mean squared error estimate — mse","title":"Mean squared error estimate — mse","text":"Mean squared error estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mean squared error estimate — mse","text":"","code":"mse(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mean squared error estimate — mse","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mean squared error estimate — mse","text":"\\(sum((theta.hat - theta)^2)/nsim\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of MSE estimate — mse.mcse","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"Monte Carlo SE MSE estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"","code":"mse.mcse(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"\\(sqrt(sum((tmp - mse.est)^2)/(nsim*(nsim-1)))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/num_grad.html","id":null,"dir":"Reference","previous_headings":"","what":"Numerical Gradient — num_grad","title":"Numerical Gradient — num_grad","text":"Numerical Gradient","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/num_grad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Numerical Gradient — num_grad","text":"","code":"num_grad(func, x, h = 1e-05)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-class.html","id":null,"dir":"Reference","previous_headings":"","what":"outstandR class — outstandR-class","title":"outstandR class — outstandR-class","text":"outstandR class contains results running model function outstandR().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-class.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"outstandR class — outstandR-class","text":"Objects class outstandR following contrasts list containing statistics relative treatment effects: means: Estimated relative effects (e.g., log-odds ratios, risk differences). variances: Variance-covariance matrix relative effects. contrast_ci: Confidence intervals relative effects. absolute list containing statistics absolute treatment outcomes: means: Estimated absolute outcomes (e.g., probabilities, mean response). variances: Variance-covariance matrix absolute outcomes. ci: Confidence intervals absolute outcomes. CI confidence level used (e.g., 0.95). ref_trt name reference treatment. scale scale outcome (e.g., \"log odds\", \"probability\"). model list containing details underlying statistical model. Contents vary strategy: family: error distribution link function. fit: underlying model object (e.g., STC, G-Comp ML, Bayesian G-Comp). weights, ESS: (MAIC ) estimated weights Effective Sample Size. stan_args: (Bayesian G-Comp, MIM) Arguments passed Stan. rho: (G-Comp ML, MIM, Bayesian G-Comp) Correlation coefficient. N: (G-Comp ML, MIM, Bayesian G-Comp) Number iterations. nu, hats.v, M: (MIM ) Imputation parameters matrices.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-package.html","id":null,"dir":"Reference","previous_headings":"","what":"outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package","title":"outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package","text":"problem indirect treatment comparison limited subject-level data, package provides tools model-based standardisation several different computation approaches. See Remiro‐Azócar , Heath , Baio G (2022) “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data”, Res. Synth. Methods, 1–31. ISSN 1759-2879, doi:10.1002/jrsm.1565 .","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package","text":"Maintainer: Nathan Green n.green@ucl.ac.uk (ORCID) (ROR) [copyright holder] Authors: Nathan Green n.green@ucl.ac.uk (ORCID) (ROR) [copyright holder] Chengyang Gao chengyang.gao.15@ucl.ac.uk Antonio Remiro-Azocar antonio.remiro-azocar@bayer.com (ORCID)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — outstandR","title":"Calculate the difference between treatments using all evidence — outstandR","text":"main, top-level wrapper {outstandR}. Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"outstandR(   ipd_trial,   ald_trial,   strategy,   ref_trt = NA,   CI = 0.95,   scale = NULL,   var_method = NULL,   seed = NULL,   verbose = TRUE,   ... )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — outstandR","text":"ipd_trial Individual-level patient data. example, suppose studies C. long format must contain treatment column outcome column consistent formula object. labels treatment used internally must common treatment aggregate-level data trial. ald_trial Aggregate-level data. example, suppose studies B C. column names variable: Covariate name. case treatment arm sample size NA, statistic: Summary statistic name \"mean\", standard deviation \"sd\", probability \"prop\", \"sum\", value: Numerical value summary statistic, trt: Treatment label. assume common covariate distribution treatment arms NA. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml() strategy_gcomp_bayes(). ref_trt Reference / common / anchoring treatment name. CI Confidence interval level; 0,1 default 0.95. scale Relative treatment effect scale. NULL, scale automatically determined model. Choose \"log-odds\", \"log_relative_risk\", \"risk_difference\", \"delta_z\", \"mean_difference\", \"rate_difference\" depending data type. var_method Variance estimation method. seed Random seed. verbose Logical. TRUE, prints progress messages warnings. ... Additional arguments. Currently, can pass named arguments rstanarm::stan_glm() via strategy_gcomp_bayes().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — outstandR","text":"List length 11 statistics outstandR class object. Containing statistics pair treatments. mean, variances confidence intervals, contrasts absolute values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — outstandR","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1–31. ISSN 1759-2879. doi:10.1002/jrsm.1565 . 2108.12208.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"data(AC_IPD_binY_contX)  # A vs C individual patient-level data data(BC_ALD_binY_contX)  # B vs C aggregate-level data  # linear formula lin_form <- as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt*EM_cont_1 + trt*EM_cont_2\")                                  # sampling values of additional arguments picked for speed # select appropriate to specific analysis  # matching-adjusted indirect comparison outstandR_maic <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_maic(formula = lin_form, n_boot = 100)) #> Note: Using legacy 'formula' argument. #> --> Analysis Model: y ~ PF_cont_1 + PF_cont_2 + trt * EM_cont_1 + trt * EM_cont_2 #> --> Inferred Balance Model: ~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2 #>     (Balancing on means of these covariates by default) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: maic #>  #> ── MAIC Execution ── #>  #> ℹ Calculating weights using method of moments... #> ℹ Starting Bootstrap with 100 replicates.  # simulated treatment comparison outstandR_stc <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_stc(lin_form)) #> Warning: `strategy_stc()` was deprecated in outstandR 1.X.X. #> ℹ Please use `strategy_gcomp_ml()` instead. #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: stc  # \\donttest{ # G-computation with maximum likelihood outstandR_gcomp_ml <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_gcomp_ml(lin_form, n_boot = 100, N =100)) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: gcomp_ml #>  #> ── G-Computation (ML) Execution ── #>  #> ℹ Fitting initial model... #> ℹ Starting Bootstrap: 100 replicates. #> ℹ Simulating pseudo-pop (N=100) per replicate.  # G-computation with Bayesian inference outstandR_gcomp_bayes <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_gcomp_bayes(lin_form),   chains = 1, iter = 1000, warmup = 20) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: gcomp_bayes #>  #> ── G-Computation (Bayesian) Execution ── #>  #> ℹ Compiling/Sampling Stan model... #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 5.2e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: WARNING: There aren't enough warmup iterations to fit the #> Chain 1:          three stages of adaptation as currently configured. #> Chain 1:          Reducing each adaptation stage to 15%/75%/10% of #> Chain 1:          the given number of warmup iterations: #> Chain 1:            init_buffer = 3 #> Chain 1:            adapt_window = 15 #> Chain 1:            term_buffer = 2 #> Chain 1:  #> Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup) #> Chain 1: Iteration:  21 / 1000 [  2%]  (Sampling) #> Chain 1: Iteration: 520 / 1000 [ 52%]  (Sampling) #> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.001 seconds (Warm-up) #> Chain 1:                0.074 seconds (Sampling) #> Chain 1:                0.075 seconds (Total) #> Chain 1:   # Multiple imputation marginalization outstandR_mim <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_mim(lin_form,                           N = 100), # size of pseudo-population   chains = 1, iter = 1000, warmup = 20) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: mim #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.2e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.32 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: WARNING: There aren't enough warmup iterations to fit the #> Chain 1:          three stages of adaptation as currently configured. #> Chain 1:          Reducing each adaptation stage to 15%/75%/10% of #> Chain 1:          the given number of warmup iterations: #> Chain 1:            init_buffer = 3 #> Chain 1:            adapt_window = 15 #> Chain 1:            term_buffer = 2 #> Chain 1:  #> Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup) #> Chain 1: Iteration:  21 / 1000 [  2%]  (Sampling) #> Chain 1: Iteration: 120 / 1000 [ 12%]  (Sampling) #> Chain 1: Iteration: 220 / 1000 [ 22%]  (Sampling) #> Chain 1: Iteration: 320 / 1000 [ 32%]  (Sampling) #> Chain 1: Iteration: 420 / 1000 [ 42%]  (Sampling) #> Chain 1: Iteration: 520 / 1000 [ 52%]  (Sampling) #> Chain 1: Iteration: 620 / 1000 [ 62%]  (Sampling) #> Chain 1: Iteration: 720 / 1000 [ 72%]  (Sampling) #> Chain 1: Iteration: 820 / 1000 [ 82%]  (Sampling) #> Chain 1: Iteration: 920 / 1000 [ 92%]  (Sampling) #> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0 seconds (Warm-up) #> Chain 1:                0.075 seconds (Sampling) #> Chain 1:                0.075 seconds (Total) #> Chain 1:  #> Warning: There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See #> https://mc-stan.org/misc/warnings.html#bfmi-low #> Warning: Examine the pairs() plot to diagnose sampling problems # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Default Plot Method for outstandR Objects — plot.outstandR","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"Default Plot Method outstandR Objects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"","code":"# S3 method for class 'outstandR' plot(x, ..., type = c(\"both\", \"contrasts\", \"absolute\"), labels = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"x object class 'outstandR' list 'outstandR' objects. ... Additional 'outstandR' objects comparison. type Character, one \"\" (default), \"contrasts\", \"absolute\". labels Optional character vector names models.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"ggplot2::ggplot() object representing forest plot results.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prepare_covariate_distns.html","id":null,"dir":"Reference","previous_headings":"","what":"Prepare Covariate Distributions — prepare_covariate_distns","title":"Prepare Covariate Distributions — prepare_covariate_distns","text":"Resolves missing distributions parameters looking ALD. Allows partial specification (e.g., user specifies one variable, function auto-detects rest).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prepare_covariate_distns.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prepare Covariate Distributions — prepare_covariate_distns","text":"","code":"prepare_covariate_distns(   formula,   ald,   trt_var,   marginal_distns,   marginal_params,   verbose = FALSE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":null,"dir":"Reference","previous_headings":"","what":"Prepare Aggregate Level Data — prep_ald","title":"Prepare Aggregate Level Data — prep_ald","text":"Prepare Aggregate Level Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prepare Aggregate Level Data — prep_ald","text":"","code":"prep_ald(form, data, trt_var = \"trt\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prepare Aggregate Level Data — prep_ald","text":"form Formula data dataframe aggregate level data trt_var Treatment variable name","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prepare Aggregate Level Data — prep_ald","text":"data frame filtered ALD variables formula.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":null,"dir":"Reference","previous_headings":"","what":"Prepare Individual Patient Data — prep_ipd","title":"Prepare Individual Patient Data — prep_ipd","text":"Cleaning subsetting input dataset contain variables actually needed statistical models.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prepare Individual Patient Data — prep_ipd","text":"","code":"prep_ipd(form, data)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prepare Individual Patient Data — prep_ipd","text":"form Formula data Individual patient data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prepare Individual Patient Data — prep_ipd","text":"Model frame","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Print a Summary of a outstandR Object — print.outstandR","title":"Print a Summary of a outstandR Object — print.outstandR","text":"method function print() objects class \"outstandR\" created call outstandR()","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print a Summary of a outstandR Object — print.outstandR","text":"","code":"# S3 method for class 'outstandR' print(x, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print a Summary of a outstandR Object — print.outstandR","text":"x Objects class \"outstandR\" ... Additional arguments passed methods","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print a Summary of a outstandR Object — print.outstandR","text":"return value, called side effects","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute performance metrics for a given method — process_metrics","title":"Compute performance metrics for a given method — process_metrics","text":"Compute performance metrics given method","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute performance metrics for a given method — process_metrics","text":"","code":"process_metrics(means, variances, truth)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute performance metrics for a given method — process_metrics","text":"means Mean variances Variances truth Truth","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute performance metrics for a given method — process_metrics","text":"Named list","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":null,"dir":"Reference","previous_headings":"","what":"Objective function to minimize for standard method of moments MAIC — Q","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"Objective function minimize standard method moments MAIC","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"","code":"Q(beta, X)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"beta Beta coefficient find X Covariate value matrix, centred","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"Numeric value","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert aggregate data from wide to long format — reshape_ald_to_long","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"Convert aggregate data wide long format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"","code":"reshape_ald_to_long(df)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"df dataframe ALD","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"Data frame long format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert aggregate data from long to wide format — reshape_ald_to_wide","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"Convert aggregate data long wide format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"","code":"reshape_ald_to_wide(df)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"df Dataframe ALD","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"Data frame wide format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"","code":"df <-    data.frame(     variable = c(\"age\", \"age\", \"y\", \"y\", \"y\", \"y\", \"y\", \"y\", \"y\", \"y\"),     statistic = c(\"mean\", \"sd\", \"sum\", \"bar\", \"sd\", \"N\", \"sum\", \"bar\", \"sd\", \"N\"),     trt = c(NA, NA, \"B\", \"B\", \"B\", \"B\", \"C\", \"C\", \"C\", \"C\"),     value = c(1,1,1,1,1,1,1,1,1,1))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate and arrange result statistics — result_stats","title":"Calculate and arrange result statistics — result_stats","text":"Combining output aggregate level data studies BC adjusted individual level data studies AC single object.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate and arrange result statistics — result_stats","text":"","code":"result_stats(ipd_stats, ald_stats, CI = 0.95)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate and arrange result statistics — result_stats","text":"ipd_stats, ald_stats Trial data IPD ALD CI Confidence interval level, .e. 1-alpha; default 0.95","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate and arrange result statistics — result_stats","text":"List ITC output: contrasts: list relative effects containing: means variances CI absolute: list absolute effects containing: means variances CI","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"Generates synthetic cohort using normal copula based aggregate-level data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"","code":"simulate_ALD_pseudo_pop(   formula,   ipd = NULL,   ald = NULL,   trt_var,   rho = NA,   N = 1000,   marginal_distns = NA,   marginal_params = NA,   seed = NULL,   verbose = FALSE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax. ipd Individual-level patient data. Dataframe one row per patient outcome, treatment covariate columns. ald Aggregate-level data. Long format summary statistics covariate treatment outcomes. assume common distribution treatment arm. rho named square matrix covariate correlations single value; default NA takes IPD. N Sample size synthetic cohort. Default 1000. marginal_distns Marginal distributions names; vector default NA. Available distributions given stats::Distributions. See copula::Mvdc() details marginal_params Marginal distributions parameters; named list lists, default NA. See copula::Mvdc() details. seed Random seed verbose Default FALSE","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"data frame representing synthetic pseudo-population. contains N rows (one simulated individual) columns every covariate specified marginal_distns formula.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"","code":"if (FALSE) { # \\dontrun{  ## Example 1: Simulating data with explicitly defined marginals and ## a provided correlation matrix (rho)  my_formula <- y ~ x1 + x2*trt + trt  # Define marginal distributions (Normal for age, Lognormal for BMI) dists <- c(x1 = \"norm\", x2 = \"norm\")  # Define parameters matching the chosen distributions params <- list(   x1 = list(mean = 60, sd = 8),   x2 = list(mean = 3, sd = 0.1) )  # Define a 2x2 correlation matrix corr_mat <- matrix(c(1, 0.25,                      0.25, 1), nrow = 2,                    dimnames = list(c(\"x1\", \"x2\"),                                    c(\"x1\", \"x2\")))  # Generate the synthetic cohort sim_cohort_marginals_rho <- simulate_ALD_pseudo_pop(   formula = my_formula,   ald = mock_ald,   trt_var = \"trt\",   rho = corr_mat,   N = 100,   marginal_distns = dists,   marginal_params = params )  head(sim_cohort_marginals_rho)  ## Example 2: Estimating the correlation matrix (rho) from provided IPD  # Create some mock Individual Patient Data (IPD) mock_ipd <- data.frame(   x1 = rnorm(200, 60, 8),   x2 = rlnorm(200, 3.3, 0.1) )  mock_ald <- data.frame(   variable = c(\"x1\", \"x1\", \"x2\", \"x2\"),   statistic = c(\"mean\", \"sd\", \"mean\", \"sd\"),   value = c(1000, 500, 0.7, 0.1),   trt = NA )  # Generate the synthetic cohort using IPD for the correlation structure sim_cohort <- simulate_ALD_pseudo_pop(   formula = my_formula,   ipd = mock_ipd,   ald = mock_ald,   trt_var = \"trt\",   rho = NA,   N = 100 )  head(sim_cohort)  # Generate the synthetic cohort using IPD for the correlation structure # with marginals sim_cohort_marginals <- simulate_ALD_pseudo_pop(   formula = my_formula,   ipd = mock_ipd,   ald = mock_ald,   trt_var = \"trt\",   N = 100,   marginal_distns = dists,   marginal_params = params )  head(sim_cohort_marginals) } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy-class.html","id":null,"dir":"Reference","previous_headings":"","what":"Strategy class and subclasses — strategy-class","title":"Strategy class and subclasses — strategy-class","text":"strategy class virtual class defines statistical approach population adjustment indirect treatment comparisons objects constructors validate hyperparameters encapsulate modelling settings execution outstandR()","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy-class.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Strategy class and subclasses — strategy-class","text":"Objects class strategy common structure carry different subclasses trigger specific S3 method dispatch General fields Shared strategies: formula: linear regression formula outcome model family: base R family object specifying distribution link trt_var: name treatment variable. maic subclass Additional fields Matching-Adjusted Indirect Comparison: n_boot: Number bootstrap resamples variance estimation. stc subclass Additional fields Simulated Treatment Comparison: N: Synthetic sample size target population. gcomp_ml subclass Additional fields Maximum Likelihood G-computation: rho: Named square matrix covariate correlations. marginal_distns: Names marginal distributions covariates. marginal_params: Parameters marginal distributions. N: Synthetic sample size pseudo-population. n_boot: Number bootstrap resamples. gcomp_bayes subclass Additional fields Bayesian G-computation: rho, marginal_distns, marginal_params, N: gcomp_ml. ...: Additional arguments passed Stan engine via rstanarm::stan_glm(). mim subclass Additional fields Multiple Imputation Marginalization: rho: Correlation matrix. N: Number iterations/simulated individuals.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":null,"dir":"Reference","previous_headings":"","what":"New strategy objects — strategy_maic","title":"New strategy objects — strategy_maic","text":"Create type strategy class modelling approach.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"New strategy objects — strategy_maic","text":"","code":"strategy_maic(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   n_boot = 1000L,   moments = 1,   int = FALSE,   verbatim = TRUE )  strategy_stc(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL )  strategy_gcomp_ml(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   rho = NA,   marginal_distns = NA,   marginal_params = NA,   n_boot = 1000L,   N = 1000L )  strategy_gcomp_bayes(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   rho = NA,   marginal_distns = NA,   marginal_params = NA,   N = 1000L )  strategy_mim(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   rho = NA,   marginal_distns = NA,   marginal_params = NA,   N = 1000L )  new_strategy(strategy, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"New strategy objects — strategy_maic","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax. family 'family' object specifying distribution link function (e.g., 'binomial'). See stats::family() details. trt_var Treatment variable name; string n_boot number resamples used non-parametric bootstrap; integer moments Integer. number moments covariates balance. Setting moments = 2 includes original variables squared terms, effectively balances means variances. Default 1. int Logical. TRUE, includes two-way interactions covariates balancing model effectively balance covariances. Default FALSE verbatim Logical. Output console running. rho named square matrix covariate correlations; default NA marginal_distns Marginal distributions names; vector default NA. Available distributions given stats::Distributions. See copula::Mvdc() details marginal_params Marginal distributions parameters; list lists, default NA. See copula::Mvdc() details N Synthetic sample size g-computation strategy Class name strategy_maic, strategy_stc, strategy_gcomp_ml, strategy_gcomp_bayes, strategy_mim ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"New strategy objects — strategy_maic","text":"maic class object stc class object gcomp_ml class object gcomp_bayes class object mim class object Strategy list object","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"New strategy objects — strategy_maic","text":"current implementations focus binary, continuous, count outcomes, support survival data (using survival package) active development scheduled future version.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"matching-adjusted-indirect-comparison-maic-","dir":"Reference","previous_headings":"","what":"Matching-adjusted indirect comparison (MAIC)","title":"New strategy objects — strategy_maic","text":"MAIC form non-parametric likelihood reweighting method allows propensity score logistic regression model estimated without IPD AC population. mean outcomes \\(\\mu_{t(AC)}\\) treatment \\(t = ,B\\) AC target population estimated taking weighted average outcomes \\(Y\\) \\(N\\) individuals arm \\(t\\) AB population. Used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. $$ \\hat{Y}_{} = \\frac{\\sum_{=1}^{N} Y_{(AB)} w_{}}{\\sum_{=1}^{N} w_{}} $$ weight \\(w_{}\\) assigned \\(\\)-th individual receiving treatment \\(t\\) equal odds enrolled AC trial vs AB trial.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"simulated-treatment-comparison-stc-","dir":"Reference","previous_headings":"","what":"Simulated treatment comparison (STC)","title":"New strategy objects — strategy_maic","text":"strategy_stc() deprecated outstandR version 1.X.X. recommend using G-computation (strategy_gcomp_ml()) robust alternative type analysis. Outcome regression-based method targets conditional treatment effect. STC modification covariate adjustment method. outcome model fitted using IPD AB trial. example, $$ g(\\mu_{t(AB)}(X)) = \\beta_0 + \\beta_1^T X + (\\beta_B + \\beta_2^T X^{EM}) (t=B) $$ \\(\\beta_0\\) intercept term, \\(\\beta_1\\) vector coefficients prognostic variables, \\(\\beta_B\\) relative effect treatment B compared \\(X=0\\), \\(\\beta_2\\) vector coefficients effect modifiers \\(X^{EM}\\) subvector full covariate vector \\(X\\)), \\(\\mu_{t(AB)}(X)\\) expected outcome individual assigned treatment \\(t\\) covariate values \\(X\\) transformed onto chosen linear predictor scale link function \\(g(\\cdot)\\).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"g-computation-maximum-likelihood","dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood","title":"New strategy objects — strategy_maic","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. example, regression model observed outcome \\(y\\) covariates \\(x\\) treatment \\(z\\) fitted AC IPD: $$ g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\mbox{}(z_n=1) $$ context G-computation, regression model called “Q-model\". fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates \\(x*\\) predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: $$ \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) dx^* $$ estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: $$ \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0) $$","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"g-computation-bayesian","dir":"Reference","previous_headings":"","what":"G-computation Bayesian","title":"New strategy objects — strategy_maic","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size \\(N*\\) predicted outcomes \\(y*z\\) set intervention \\(z* \\\\{0, 1\\}\\) posterior predictive distribution specific treatment. defined \\(p(y*_{z*} | \\mathcal{D}_{AC}) = \\int_{\\beta} p(y*_{z*} | \\beta) p(\\beta | \\mathcal{D}_{AC}) d\\beta\\) \\(p(\\beta | \\mathcal{D}_{AC})\\) posterior distribution outcome regression coefficients \\(\\beta\\), encode predictor-outcome relationships observed AC trial IPD. given : $$ p(y*_{z*} \\mid \\mathcal{D}_{AC}) = \\int_{x*} p(y* \\mid z*, x*, \\mathcal{D}_{AC}) p(x* \\mid \\mathcal{D}_{AC}) dx* $$ $$ = \\int_{x*} \\int_{\\beta} p(y* \\mid z*, x*, \\beta) p(x* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta dx* $$ practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"multiple-imputation-marginalization-mim-","dir":"Reference","previous_headings":"","what":"Multiple imputation marginalization (MIM)","title":"New strategy objects — strategy_maic","text":"MIM targets marginal treatment effect using parametric G-computation within multiple imputation framework. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. particularly useful ensuring compatibility indirect comparisons adjusting effect modifiers.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary method for outstandR — summary.outstandR","title":"Summary method for outstandR — summary.outstandR","text":"Summary method outstandR","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary method for outstandR — summary.outstandR","text":"","code":"# S3 method for class 'outstandR' summary(object, CI = NA, ...)  # S3 method for class 'summary.outstandR' print(x, digits = 3, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary method for outstandR — summary.outstandR","text":"object outstandR() output object. CI Confidence interval level. ... Additional arguments. x object used select method. digits Minimal number significant digits, see print.default.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary method for outstandR — summary.outstandR","text":"List class summary.outstandR Original argument, mainly called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":null,"dir":"Reference","previous_headings":"","what":"Trial treatment effect with aggregate data — trial_treatment_effect","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"Calculate $$\\log(\\sum y_k (N_k - \\sum y_k))$$.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"","code":"trial_treatment_effect(ald, tid)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"ald Aggregate-level data tid Treatment label","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"Value","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":null,"dir":"Reference","previous_headings":"","what":"Trial variance with aggregate data — trial_variance","title":"Trial variance with aggregate data — trial_variance","text":"Calculate $$1/(\\sum y_k) + 1/(N_k - \\sum y_k)$$.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Trial variance with aggregate data — trial_variance","text":"","code":"trial_variance(ald, tid)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Trial variance with aggregate data — trial_variance","text":"ald Aggregate-level data tid Treatment label","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Trial variance with aggregate data — trial_variance","text":"Value","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":null,"dir":"Reference","previous_headings":"","what":"Input data validator — validate_outstandr","title":"Input data validator — validate_outstandr","text":"Input data validator","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Input data validator — validate_outstandr","text":"","code":"validate_outstandr(ipd_trial, ald_trial, strategy, CI, scale)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Input data validator — validate_outstandr","text":"ipd_trial Individual patient data ald_trial Aggregate level data strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. CI Confidence interval scale Outcome scale","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Input data validator — validate_outstandr","text":"return value, called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":null,"dir":"Reference","previous_headings":"","what":"Variability ratio — var.ratio","title":"Variability ratio — var.ratio","text":"Variability ratio","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Variability ratio — var.ratio","text":"","code":"var.ratio(theta.hat, std.err)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Variability ratio — var.ratio","text":"theta.hat Theta hat std.err Standard error","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Variability ratio — var.ratio","text":"Ratio","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Variability ratio MCSE — var.ratio.mcse","title":"Variability ratio MCSE — var.ratio.mcse","text":"Approximation ratio variance based independence avg. se emp.se see wolter2007outstandR","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Variability ratio MCSE — var.ratio.mcse","text":"","code":"var.ratio.mcse(avg.se, emp.se, var.avg.se, var.emp.se)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Variability ratio MCSE — var.ratio.mcse","text":"avg.se Average SE emp.se Emp SE var.avg.se Variance average SE var.emp.se Variance Emp SE","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Variability ratio MCSE — var.ratio.mcse","text":"wolter2007outstandR","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":null,"dir":"Reference","previous_headings":"","what":"Variance estimate by pooling — var_by_pooling","title":"Variance estimate by pooling — var_by_pooling","text":"Use combining rules estimate.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Variance estimate by pooling — var_by_pooling","text":"","code":"var_by_pooling(n_imp, bar.v, b)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Variance estimate by pooling — var_by_pooling","text":"n_imp Number syntheses used analysis stage (high low Monte Carlo error) bar.v \"within\" variance (average variance point estimates) b \"\" variance (sample variance point estimates)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Variance estimate by pooling — var_by_pooling","text":"Numeric value variance estimate using pooling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":null,"dir":"Reference","previous_headings":"","what":"Wald-type interval estimates — wald_type_interval","title":"Wald-type interval estimates — wald_type_interval","text":"Constructed using t-distribution nu degrees freedom.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Wald-type interval estimates — wald_type_interval","text":"","code":"wald_type_interval(n_imp, bar.v, b)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Wald-type interval estimates — wald_type_interval","text":"n_imp Number syntheses used analysis stage (high low Monte Carlo error) bar.v \"within\" variance (average variance point estimates) b \"\" variance (sample variance point estimates)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Wald-type interval estimates — wald_type_interval","text":"Numeric value Wald-type interval estimates.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"new-features-2-0-0","dir":"Changelog","previous_headings":"","what":"New features","title":"outstandR 2.0.0","text":"Explicit Model Specifications: package architecture fundamentally updated explicitly separate outcome prediction population weighting. formula argument across strategy_*() functions now accepts list containing outcome_model balance_model. conceptual split makes statistical intent methods like MAIC much clearer (.e., defining exactly covariates balance vs. regress ) future-proofs package upcoming doubly-robust methods require models simultaneously. support new architecture, strategy_maic() introduces intelligent defaults missing formula components: traditional single formula passed (legacy support), automatically infers balance_model stripping response treatment variables. balance_model omitted list, acts delayed function defaulting linear sum covariates found aggregate-level data (ALD). outcome_model omitted, gracefully defaults y ~ trt. outstandR() gains new verbose argument (defaulting TRUE), allowing users silence console output simulations repetitive tasks. also introduces proactive warnings computationally expensive operations (e.g., high n_boot MAIC, large N×RN \\times R ML G-computation) prevent users thinking session hung. MAIC weight estimation can now balance covariate variances covariances, reducing residual confounding mismatched distributions. Added moments argument strategy definition functions calc_maic(). Setting moments = 2 automatically expands balancing formula include squared terms. Added int argument strategy definition functions calc_maic(). Setting int = TRUE automatically expands balancing formula include two-way interactions covariates. Automatic variance target calculation moments = 2, maic.boot() function now automatically calculates required aggregate target squared terms (E[X2]E[X^2]) internally using base variable’s mean sd provided ALD.","code":"# New recommended approach  strategy_maic(   formula = list(     outcome_model = y ~ trt,      balance_model = ~ age + sex   ) )  # Legacy approach (still supported)  strategy_maic(formula = y ~ trt + age + sex)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"minor-improvements-and-fixes-2-0-0","dir":"Changelog","previous_headings":"","what":"Minor improvements and fixes","title":"outstandR 2.0.0","text":"Fixed critical bug strategy_mim() strategy_gcomp_bayes() covariate uncertainty fully propagated due incorrect looping predicted samples. Significantly improved performance MAIC method refactoring maic.boot() pre-calculate balance outcome matrices, reducing redundant computations bootstrap iterations. guess_treatment_name() (used hood strategies trt_var NULL) now smarter. correctly identifies treatment variable checking duplicated variables interaction terms, falling back last main effect term. check_balance_formula() added provide strict validation balance models. ensures formula one-sided (response variable) throws informative warning treatment variable mistakenly included. check_formula() now explicitly intercepts Surv objects outcome models. throws clear, informative error stating survival data support officially scheduled later version. Improved reproducibility side-effect management switching withr::local_seed() local random seed handling. Updated print.outstandR() method handle delayed balance model functions, providing clearer output auto-generated models. Standardized strategy naming: strategy_gcomp_stan() now strategy_gcomp_bayes() accurately reflect underlying statistical approach.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"deprecated-and-defunct-2-0-0","dir":"Changelog","previous_headings":"","what":"Deprecated and defunct","title":"outstandR 2.0.0","text":"strategy_stc() now deprecated removed future release. Simulated Treatment Comparison (STC) phased favor G-computation approaches (e.g., strategy_gcomp_ml()), offer better statistical properties population adjustment.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"outstandr-100","dir":"Changelog","previous_headings":"","what":"outstandR 1.0.0","title":"outstandR 1.0.0","text":"outstandR 1.0.0 marks major milestone, transforming original code Remiro-Azocar study generalized, user-friendly R package.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"breaking-changes--major-updates-1-0-0","dir":"Changelog","previous_headings":"","what":"Breaking changes & major updates","title":"outstandR 1.0.0","text":"aggregate-level data (ALD) input redesigned use standard long format, replacing legacy format used original study. Treatment labels covariate names longer hard-coded. outstandR now dynamically extracts treatment arms (e.g., rather “”, “B”, “C”) general covariates directly input data (5119596). Covariate generation functions separated moved standalone package, simcovariates.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"expanded-modelling-capabilities-1-0-0","dir":"Changelog","previous_headings":"","what":"Expanded modelling capabilities","title":"outstandR 1.0.0","text":"family argument outstandR() expanded support binary (binomial), continuous (gaussian), count data (poisson). Input data can now contain combination binary continuous covariates, specifically upgraded MAIC (4fb1e21). simulate_ALD_pseudo_pop() now accepts user-provided marginal arguments target distribution. can defined optionally via marginal_distns marginal_params strategy_gcomp_ml() strategy_gcomp_bayes(). Users can now explicitly select outcome scale (e.g., log-odds, risk difference, relative risk) using new scale argument outstandR(). Added support optional correlation structures ALD simulations (d48d0ab).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"output--documentation-improvements-1-0-0","dir":"Changelog","previous_headings":"","what":"Output & documentation improvements","title":"outstandR 1.0.0","text":"main outstandR() function now returns absolute values addition treatment contrasts (2f1fbd7). Added dedicated print() method outstandR objects cleanly display analysis results (983cb2f). Comprehensive, separate vignettes demonstrating workflows binary, continuous, count outcome data (fc10a68). complete package documentation website built using pkgdown now available via GitHub Pages (4df16f2).","code":""}]
+[{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-1-create-the-strategy-constructor","dir":"Articles","previous_headings":"","what":"Step 1: Create the Strategy Constructor","title":"Adding a New Strategy to `outstandR`","text":"File: R/strategy_.R First, create user-facing constructor function validates user inputs instantiates strategy object. convention, function named strategy_<method_name>(). must call internal new_strategy() function, passing class name validated arguments.","code":"#' @rdname strategy #'  #' @section Custom Method: #' Describe the statistical theory behind the new method here. #'  #' @param trt_var Treatment variable name #' @param my_custom_arg Description of your custom argument #'  #' @return `custom_method` class object #' @export strategy_custom_method <- function(formula = NULL,                                    family = gaussian(link = \"identity\"),                                    trt_var = NULL,                                    my_custom_arg = 100) {      # 1. Validate inputs using built-in helpers   check_formula(formula, trt_var)   check_family(family)      if (my_custom_arg <= 0) {     stop(\"my_custom_arg must be greater than 0.\")   }      # 2. Bundle arguments   args <- list(formula = formula,                family = family,                trt_var = get_treatment_name(formula, trt_var),                my_custom_arg = my_custom_arg)      # 3. Create object   do.call(new_strategy, c(strategy = \"custom_method\", args)) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-2-document-the-class-fields","dir":"Articles","previous_headings":"","what":"Step 2: Document the Class Fields","title":"Adding a New Strategy to `outstandR`","text":"File: R/strategy-class.R Update strategy-class documentation inform users internal fields new subclass carries. Add new \\item block details section:","code":"#'   \\item{custom_method subclass}{Additional fields for the Custom Method: #'     \\itemize{ #'       \\item `my_custom_arg`: Describes what this internal field does. #'     } #'   }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-3-write-the-core-calculation-function","dir":"Articles","previous_headings":"","what":"Step 3: Write the Core Calculation Function","title":"Adding a New Strategy to `outstandR`","text":"File: Create new file (e.g., R/custom_method.R) add existing calculation files. Write function actually performs maths. receive two arguments: strategy (object created Step 1) analysis_params (list containing pre-processed ipd, ald, treatment labels, etc.). Crucial Requirement: function MUST return list containing exactly two elements: means model. means$: Estimates comparator treatment group (can scalar, vector bootstrap/MCMC draws). means$C: Estimates reference treatment group (can scalar, vector bootstrap/MCMC draws). model: list underlying models diagnostics (e.g., weights, glm fit objects) want returned user.","code":"#' Calculate Custom Method #' @keywords internal calc_custom_method <- function(strategy, analysis_params) {      # Extract data and parameters   ipd <- analysis_params$ipd   ald <- analysis_params$ald   formula <- strategy$formula   custom_val <- strategy$my_custom_arg      # ... [PERFORM YOUR STATISTICAL MODELLING HERE] ...   # e.g., fit a model, run bootstraps, calculate weights      # Construct the strict return object   list(     means = list(       A = estimated_means_for_A,        C = estimated_means_for_C     ),     model = list(       fit = my_fitted_model,       custom_val = custom_val     )   ) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-4-register-the-s3-dispatch-method","dir":"Articles","previous_headings":"","what":"Step 4: Register the S3 Dispatch Method","title":"Adding a New Strategy to `outstandR`","text":"File: R/calc_IPD_stats.R plug core function outstandR’s top-level execution, must register S3 method calc_IPD_stats. outstandR handles relative treatment effect transformations (ATE) variance estimation automatically, simply pass core function IPD_stat_factory().","code":"#' @rdname calc_IPD_stats #' @section Custom Method statistics: #' Description of how the custom method calculates statistics. #' @export calc_IPD_stats.custom_method <- IPD_stat_factory(calc_custom_method)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-5-add-a-print-method","dir":"Articles","previous_headings":"","what":"Step 5: Add a Print Method","title":"Adding a New Strategy to `outstandR`","text":"File: R/print-strategies.R Finally, create nice console printout user types name instantiated strategy. Extend generic print.strategy using NextMethod() print common fields, print specific parameters.","code":"#' @export #' @method print custom_method print.custom_method <- function(x, ...) {   # Print the standard strategy info (formula, family)   NextMethod()       # Print custom subclass info   cat(pillar::style_subtle(\"  Parameters:\"), \"\\n\")   cat(\"    Custom Argument:     \", x$my_custom_arg, \"\\n\")      invisible(x) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"optional-step-6-passing-random-seeds","dir":"Articles","previous_headings":"","what":"(Optional) Step 6: Passing Random Seeds","title":"Adding a New Strategy to `outstandR`","text":"new method utilizes random number generator (e.g., MCMC sampling, pseudo-population simulation), might need catch top-level seed argument. File: R/outstandR.R Create add_seed S3 method strategy: section can append vignette developer guide. provides copy-pasteable utility script future contributors can use automate boilerplate setup new strategy.","code":"#' @export add_seed.custom_method <- function(strategy, fn_args, seed) {   if (!is.null(seed)) {     fn_args$seed <- seed   }   return(fn_args) }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"step-7-automating-boilerplate-with-a-scaffolding-script-optional","dir":"Articles","previous_headings":"","what":"Step 7: Automating Boilerplate with a Scaffolding Script (Optional)","title":"Adding a New Strategy to `outstandR`","text":"contributors find adding new strategies frequently, can automate creation boilerplate files using usethis package. recommend saving following helper function script file (e.g., scripts/scaffold_strategy.R). script automatically create necessary calculation file open registry files edit.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"how-to-use-it","dir":"Articles","previous_headings":"Step 7: Automating Boilerplate with a Scaffolding Script (Optional)","what":"How to Use It","title":"Adding a New Strategy to `outstandR`","text":"ready build new method, simply source script run function name new method: instantly set workspace, leaving focus solely statistical implementation rather package wiring! section can add Markdown document (perhaps end, right scaffolding script) outlines best practices writing robust, user-friendly strategy outstandR.","code":"# Load the helper function source(\"scripts/scaffold_strategy.R\")  # Scaffold a new method called \"gcomp_rf\" (e.g., Random Forest G-computation) scaffold_strategy(\"gcomp_rf\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"best-practices-for-writing-a-good-strategy","dir":"Articles","previous_headings":"","what":"Best Practices for Writing a Good Strategy","title":"Adding a New Strategy to `outstandR`","text":"contributing new statistical approach outstandR, following guidelines ensures method robust, user-friendly, maintainable.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"fail-fast-and-validate-early","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"1. Fail Fast and Validate Early","title":"Adding a New Strategy to `outstandR`","text":"Catch user errors constructor function (strategy_custom_method()) heavy computation begins. Use package’s built-check_formula() check_family() helpers. method requires specific types data (e.g., binary outcomes), enforce immediately:","code":"if (family$family != \"binomial\") {   cli::cli_abort(\"Custom Method currently only supports binary outcomes (`family = binomial()`).\") }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"return-a-rich-model-object","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"2. Return a Rich model Object","title":"Adding a New Strategy to `outstandR`","text":"core calculation function must return list means model. means strictly structured, model element free-form list. Use give user much diagnostic power possible. Good things include: raw fitted model objects (e.g., glm stanfit), calculated weights, convergence status flags, effective sample sizes (ESS). allows users extract model final outstandR object check diagnostics .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"handle-convergence-issues-gracefully","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"3. Handle Convergence Issues Gracefully","title":"Adding a New Strategy to `outstandR`","text":"Many population adjustment methods rely optimization iterative fitting (like GLMs MAIC). internal model fails converge, function shouldn’t crash entire R session—especially bootstrap loop. Wrap volatile model fitting tryCatch(). fit fails, return NA means pass warning user.","code":"fit <- tryCatch({   glm(formula, data = ipd, family = family) }, warning = function(w) {   # Handle warnings (e.g., probabilities numerically 0 or 1)   glm(formula, data = ipd, family = family) }, error = function(e) {   NULL # Return NULL on hard failure })  if (is.null(fit)) return(list(means = list(A = NA, C = NA), model = list(converged = FALSE)))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"respect-the-verbose-flag","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"4. Respect the verbose Flag","title":"Adding a New Strategy to `outstandR`","text":"outstandR provides global verbose argument users can silence console output heavy simulations. Extract verbose <- isTRUE(analysis_params$verbose) top calculation function. Use cli package print progress updates warn users computationally expensive steps, verbose true.","code":"if (verbose) {   cli::cli_h2(\"Custom Method Execution\")   cli::cli_alert_info(\"Optimizing weights. This may take a moment...\") }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/adding-a-new-strategy.html","id":"write-unit-tests-for-your-method","dir":"Articles","previous_headings":"Best Practices for Writing a Good Strategy","what":"5. Write Unit Tests for Your Method","title":"Adding a New Strategy to `outstandR`","text":"Whenever add new strategy, add corresponding test file tests/testthat/ (e.g., test-custom_method.R). Test strategy constructor throws errors bad inputs. Use package’s built-dummy data (AC_IPD_binY_contX, etc.) run fast, low-iteration version method ensure output list matches required list(means = ..., model = ...) structure.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Basic Example","text":"Population adjustment methods matching-adjusted indirect comparison (MAIC) increasingly used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. MAIC based propensity score weighting, sensitive poor covariate overlap extrapolate beyond observed covariate space. Current outcome regression-based alternatives can extrapolate target conditional treatment effect incompatible indirect comparison. adjusting covariates, one must integrate average conditional estimate relevant population recover compatible marginal treatment effect. propose marginalization method based parametric G-computation can easily applied outcome regression generalized linear model Cox model. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. method can accommodate Bayesian statistical framework, naturally integrates analysis probabilistic framework. simulation study provides proof--principle benchmarks method’s performance MAIC conventional outcome regression. Parametric G-computation achieves precise accurate estimates MAIC, particularly covariate overlap poor, yields unbiased marginal treatment effect estimates failures assumptions. Furthermore, marginalized regression-adjusted estimates provide greater precision accuracy conditional estimates produced conventional outcome regression.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"general-problem","dir":"Articles","previous_headings":"","what":"General problem","title":"Basic Example","text":"Consider one AB trial, company IPD, one AC trial, published aggregate data available. wish estimate comparison effects treatments B C appropriate scale target population P, denoted parameter dBC(P)d_{BC(P)}. make use bracketed subscripts denote specific population. Within AB population parameters μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)} μC(AB)\\mu_{C(AB)} representing expected outcome treatment (including parameters treatments studied AB trial, e.g. treatment C). AB trial provides estimators Y‾(AB)\\bar{Y}_{(AB)} Y‾B(AB)\\bar{Y}_{B(AB)} μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)}, respectively, summary outcomes. situation AC trial. suitable scale, example logit, risk difference, form estimators ΔAB(AB)\\Delta_{AB(AB)} ΔAC(AC)\\Delta_{AC(AC)} trial level (marginal) relative treatment effects. ΔAB(AB)=g(Y‾B(AB))−g(Y‾(AB)) \\Delta_{AB(AB)} = g(\\bar{Y}_{B{(AB)}}) - g(\\bar{Y}_{{(AB)}})","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Basic Example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Basic Example","text":"Next, load data use analysis. data comes simulation study Remiro‐Azócar , Heath , Baio G (2020). consider binary outcomes using log-odds ratio measure effect. binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yny_n subject nn simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. general format data sets consist following.","code":"set.seed(555)  AC.IPD <- read.csv(here::here(\"raw-data\", \"AC_IPD.csv\"))  # AC patient-level data BC.ALD <- read.csv(here::here(\"raw-data\", \"BC_ALD.csv\"))  # BC aggregate-level data"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"ac-ipd-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"AC.IPD: Individual patient data","title":"Basic Example","text":"X*: patient measurements trt: treatment ID y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"bc-ald-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"BC.ALD: Aggregate-level data","title":"Basic Example","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: total number events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"head(AC.IPD) #>            X1        X2          X3          X4 trt y #> 1  0.43734111 0.6747901  0.93001035  0.09165363   1 0 #> 2  0.05643081 0.5987971  0.03557646  0.59954129   1 1 #> 3 -0.08048882 0.6843784  0.93147222 -0.11419716   1 0 #> 4 -0.38580926 0.5716644 -0.32252212  0.02551808   1 0 #> 5  1.00755116 0.8220826  0.92735892  0.84414221   1 1 #> 6  0.19443956 0.2031329  0.34990179  0.15633009   1 0 BC.ALD #>     mean.X1   mean.X2   mean.X3   mean.X4     sd.X1     sd.X2     sd.X3 #> 1 0.5908996 0.6414179 0.5856529 0.6023671 0.3863145 0.4033615 0.4076097 #>      sd.X4 y.B.sum y.B.bar N.B y.C.sum y.C.bar N.C #> 1 0.395132     182   0.455 400     149   0.745 200"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Basic Example","text":"implement MAIC, STC, G-computation methods obtain marginal variance, defined 1nC+1nC‾+1nB+1nB‾ \\frac{1}{n_C} + \\frac{1}{n_{\\bar{C}}} + \\frac{1}{n_B} + \\frac{1}{n_{\\bar{B}}} marginal treatment effect, defined log(nB/(NB−nB)nC/(NB−nB))=log(nBnC‾)−log(nCnB‾) \\log\\left( \\frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \\right) = \\log(n_B n_{\\bar{C}}) - \\log(n_C n_{\\bar{B}})  C‾\\bar{C} compliment CC e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Basic Example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Basic Example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2  corresponds following R formula object passed argument strategy function. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <- outstandR(AC.IPD, BC.ALD, strategy = strategy_maic(formula = lin_form)) outstandR_maic #> $contrasts #> $contrasts$AB #> [1] 0.5008915 #>  #> $contrasts$AC #> [1] -1.151838 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #>           [,1] #> [1,] 0.1732497 #>  #> $variances$AC #>           [,1] #> [1,] 0.1368488 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.3149097  1.3166927 #>  #> $CI$AC #> [1] -1.8768893 -0.4267873 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Basic Example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1)  β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2})  However, outstandR() knows handle can simply pass (uncentred) formula . last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <- outstandR(AC.IPD, BC.ALD, strategy = strategy_stc(formula = lin_form)) outstandR_stc #> $contrasts #> $contrasts$AB #>     trt  #> 0.22425  #>  #> $contrasts$AC #>      trt  #> -1.42848  #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #> [1] 0.1690646 #>  #> $variances$AC #> [1] 0.1326637 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.5816375  1.0301375 #>  #> $CI$AC #> [1] -2.1423580 -0.7146016 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Basic Example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_ml(formula = lin_form)) outstandR_gcomp_ml #> $contrasts #> $contrasts$AB #> [1] 0.5645192 #>  #> $contrasts$AC #> [1] -1.088211 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #>           [,1] #> [1,] 0.1425196 #>  #> $variances$AC #>           [,1] #> [1,] 0.1061187 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.1754018  1.3044402 #>  #> $CI$AC #> [1] -1.7266857 -0.4497354 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Basic Example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment.","code":"outstandR_gcomp_bayes <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_bayes(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.8e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.38 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.522 seconds (Warm-up) #> Chain 1:                0.499 seconds (Sampling) #> Chain 1:                1.021 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.8e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.508 seconds (Warm-up) #> Chain 2:                0.534 seconds (Sampling) #> Chain 2:                1.042 seconds (Total) #> Chain 2: outstandR_gcomp_bayes #> $contrasts #> $contrasts$AB #> [1] 0.5614387 #>  #> $contrasts$AC #> [1] -1.091291 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #> [1] 0.137929 #>  #> $variances$AC #> [1] 0.1015281 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.1664684  1.2893457 #>  #> $CI$AC #> [1] -1.7158038 -0.4667785 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Basic_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Basic Example","text":"ref equationhere equation Combine outputs","code":"outstandR_mim <- outstandR(AC.IPD, BC.ALD, strategy = strategy_mim(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 2.3e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 1: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 1: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 1: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 1: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 1: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 1: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 1: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.254 seconds (Warm-up) #> Chain 1:                0.751 seconds (Sampling) #> Chain 1:                1.005 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.8e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 2: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 2: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 2: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 2: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 2: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 2: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 2: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.262 seconds (Warm-up) #> Chain 2:                0.768 seconds (Sampling) #> Chain 2:                1.03 seconds (Total) #> Chain 2: outstandR_mim #> $contrasts #> $contrasts$AB #> [1] 0.5811889 #>  #> $contrasts$AC #> [1] -1.071541 #>  #> $contrasts$BC #> [1] -1.65273 #>  #>  #> $variances #> $variances$AB #> [1] 0.1330941 #>  #> $variances$AC #> [1] 0.09669322 #>  #> $variances$BC #> [1] 0.03640091 #>  #>  #> $CI #> $CI$AB #> [1] -0.1338465  1.2962243 #>  #> $CI$AC #> [1] -1.6810021 -0.4620796 #>  #> $CI$BC #> [1] -2.026672 -1.278788 #>  #>  #> attr(,\"CI\") #> [1] 0.95 #> attr(,\"class\") #> [1] \"outstandR\" \"list\" knitr::kable(   data.frame(   `MAIC` = unlist(outstandR_maic$contrasts),   `STC` = unlist(outstandR_stc$contrasts),   `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts),   `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts),   `MIM` = unlist(outstandR_mim$contrasts)) )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Binary data example","text":"Population adjustment methods matching-adjusted indirect comparison (MAIC) increasingly used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. MAIC based propensity score weighting, sensitive poor covariate overlap extrapolate beyond observed covariate space. Current outcome regression-based alternatives can extrapolate target conditional treatment effect incompatible indirect comparison. adjusting covariates, one must integrate average conditional estimate relevant population recover compatible marginal treatment effect. propose marginalization method based parametric G-computation can easily applied outcome regression generalized linear model Cox model. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. method can accommodate Bayesian statistical framework, naturally integrates analysis probabilistic framework. simulation study provides proof--principle benchmarks method’s performance MAIC conventional outcome regression. Parametric G-computation achieves precise accurate estimates MAIC, particularly covariate overlap poor, yields unbiased marginal treatment effect estimates failures assumptions. Furthermore, marginalized regression-adjusted estimates provide greater precision accuracy conditional estimates produced conventional outcome regression.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"general-problem","dir":"Articles","previous_headings":"","what":"General problem","title":"Binary data example","text":"Consider one trial, company IPD, comparing treatments C, herein call AC trial. Also, consider second trial comparing treatments B C, similarly called BC trial. trial published aggregate data available. wish estimate comparison effects treatments B appropriate scale target population P, denoted parameter dAB(P)d_{AB(P)}. make use bracketed subscripts denote specific population. Within BC population parameters μB(BC)\\mu_{B(BC)} μC(BC)\\mu_{C(BC)} representing expected outcome treatment (including parameters treatments studied BC trial, e.g. treatment ). BC trial provides estimators Y‾B(BC)\\bar{Y}_{B(BC)} Y‾C(BC)\\bar{Y}_{C(BC)} μB(BC)\\mu_{B(BC)}, μC(BC)\\mu_{C(BC)}, respectively, summary outcomes. situation AC trial. suitable scale, example log-odds ratio, risk difference, form estimators ΔBC(BC)\\Delta_{BC(BC)} ΔAC(AC)\\Delta_{AC(AC)} trial level (marginal) relative treatment effects. shall assume always represented difference , example, risk ratio log scale. ΔAB(BC)=g(Y‾B(BC))−g(Y‾(BC)) \\Delta_{AB(BC)} = g(\\bar{Y}_{B{(BC)}}) - g(\\bar{Y}_{{(BC)}})","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Binary data example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Binary data example","text":"consider binary outcomes using log-odds ratio measure effect. example, binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yiy_i subject ii simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. IPD simulation input parameters given . shall use gen_data() function available simcovariates package. treatment column return data binary takes values 0 1. include extra information treatment names. define lable two level factor 1 C 0 follows. Similarly, obtain aggregate data simulate IPD additional summarise step. set different mean values meanX_BC meanX_EM_BC otherwise use parameter values ACAC case. general format data sets consist following.","code":"library(dplyr) library(MASS)  N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = binomial(\"logit\")) ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = binomial(\"logit\"))  cov.X <- BC.IPD %>%   summarise(across(starts_with(\"X\"),                    list(mean = mean, sd = sd),                    .names = \"{fn}.{col}\"))  out.B <- dplyr::filter(BC.IPD, trt == 1) %>%   summarise(y.B.sum = sum(y),             y.B.bar = mean(y),             y.B.sd = sd(y),             N.B = n())  out.C <- dplyr::filter(BC.IPD, trt == 0) %>%   summarise(y.C.sum = sum(y),             y.C.bar = mean(y),             y.C.sd = sd(y),             N.C = n())  ald_trial <- cbind.data.frame(cov.X, out.C, out.B)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Binary data example","text":"X*: patient measurements trt: treatment ID (integer) y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Binary data example","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: proportion events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt 1 corresponds new treatment , 0 standard care status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"head(ipd_trial) #>           X1         X2         X3         X4 trt y #> 1 0.42066874  1.0957407 0.37118099  1.3291540   A 1 #> 2 0.51227329  0.9079984 0.30560144 -0.1842358   A 0 #> 3 1.00347612  0.8136847 1.25054503  1.1986315   A 0 #> 4 0.05641685  0.5318140 0.54799796  0.6694090   A 0 #> 5 0.42997845  0.5274304 0.09140568  0.1222184   A 0 #> 6 0.06916082 -0.3125090 0.99150666 -0.1102693   A 0 ald_trial #>    mean.X1     sd.X1  mean.X2     sd.X2   mean.X3     sd.X3  mean.X4     sd.X4 #> 1 0.568822 0.3972807 0.623277 0.3850408 0.5787528 0.3906499 0.565223 0.3789089 #>   y.C.sum   y.C.bar    y.C.sd N.C y.B.sum   y.B.bar    y.B.sd N.B #> 1      34 0.5074627 0.5037175  67      34 0.2556391 0.4378691 133"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"regression-model","dir":"Articles","previous_headings":"Example analysis > Data","what":"Regression model","title":"Binary data example","text":"true logistic outcome model use simulate data logit(pt)=β0+βX(X3+X4)+[βt+βEM(X1+X2)](t≠C) \\text{logit}(p_{t}) = \\beta_0 + \\beta_X (X_3 + X_4) + [\\beta_{t} + \\beta_{EM} (X_1 + X_2)] \\; \\text{}(t \\neq C) , treatment CC right hand side becomes β0+βX(X3+X4)\\beta_0 + \\beta_X (X_3 + X_4) comparator treatments AA BB additional βt+βEM(X1+X2)\\beta_t + \\beta_{EM} (X_1 + X_2) component consisting effect modifier terms coefficient treatment parameter log odds-ratio (LOR), βt\\beta_t (b_trt R code). ptp_{t} probability experiencing event interest treatment tt.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Binary data example","text":"implement MAIC, STC, G-computation methods obtain marginal treatment effect marginal variance. definition calculated depends type data outcome scale. current example binary data log-odds ratio marginal treatment effect log(nB/(NB−nB)nC/(NB−nB))=log(nBnC‾)−log(nCnB‾) \\log\\left( \\frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \\right) = \\log(n_B n_{\\bar{C}}) - \\log(n_C n_{\\bar{B}}) marginal variance 1nC+1nC‾+1nB+1nB‾ \\frac{1}{n_C} + \\frac{1}{n_{\\bar{C}}} + \\frac{1}{n_B} + \\frac{1}{n_{\\bar{B}}}  nB,nCn_B, n_C number events arm C‾\\bar{C} compliment CC, e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c. scales discussed .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Binary data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"model-formula","dir":"Articles","previous_headings":"Model fitting in R","what":"Model formula","title":"Binary data example","text":"Defining X1,X2X_1, X_2 effect modifiers, X3,X4X_3, X_4 prognostic variables ZZ treatment indicator formula used model y=X3+X4+Z+ZX1+ZX2 y = X_3 + X_4 + Z + Z X_1 + Z X_2 corresponds following R formula object passed argument strategy function. Note succinct formula also include X1,X2X_1, X_2 prognostic factors equivalent, modified follows.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt + trt:X1 + trt:X2\") y ~ X3 + X4 + trt*(X1 + X2) y ~ X3 + X4 + trt*(X1 + X2) - X1 - X2"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Binary data example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument. print method available outstandR objects human-readable output","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = binomial(link = \"logit\"))) str(outstandR_maic) #> List of 2 #>  $ contrasts:List of 3 #>   ..$ means    :List of 3 #>   .. ..$ AB: num -1 #>   .. ..$ AC: num -2.1 #>   .. ..$ BC: num -1.1 #>   ..$ variances:List of 3 #>   .. ..$ AB: num 0.259 #>   .. ..$ AC: num 0.16 #>   .. ..$ BC: num 0.0992 #>   ..$ CI       :List of 3 #>   .. ..$ AB: num [1:2] -1.99888 -0.00345 #>   .. ..$ AC: num [1:2] -2.88 -1.32 #>   .. ..$ BC: num [1:2] -1.716 -0.481 #>  $ absolute :List of 2 #>   ..$ means    :List of 2 #>   .. ..$ A: Named num 0.227 #>   .. .. ..- attr(*, \"names\")= chr \"mean_A\" #>   .. ..$ C: Named num 0.698 #>   .. .. ..- attr(*, \"names\")= chr \"mean_C\" #>   ..$ variances:List of 2 #>   .. ..$ A: Named num 0.00202 #>   .. .. ..- attr(*, \"names\")= chr \"mean_A\" #>   .. ..$ C: Named num 0.0035 #>   .. .. ..- attr(*, \"names\")= chr \"mean_C\" #>  - attr(*, \"CI\")= num 0.95 #>  - attr(*, \"ref_trt\")= chr \"C\" #>  - attr(*, \"scale\")= chr \"log_odds\" #>  - attr(*, \"model\")= chr \"binomial\" #>  - attr(*, \"class\")= chr [1:2] \"outstandR\" \"list\" outstandR_maic #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            -1.00    0.259       -2.00   -0.00345 #> 2 AC            -2.10    0.160       -2.88   -1.32    #> 3 BC            -1.10    0.0992      -1.72   -0.481   #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.227   0.00202 NA         NA         #> 2 C             0.698   0.00350 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"outcome-scale","dir":"Articles","previous_headings":"Model fitting in R > MAIC","what":"Outcome scale","title":"Binary data example","text":"explicitly specify outcome scale, default used fit data regression model. saw, case, default log-odds ratio corresponding \"logit\" link function binary data. However, can change scale may appropriate particular analysis. far implemented package, links corresponding relative treatment effect scales follows: full list possible transformed treatment effect scales : log-odds ratio, log-risk ratio, mean difference, risk difference, hazard ratio, hazard difference. binary data marginal treatment effect variance Log-risk ratio Treatment effect log(nB/NB)−log(nA/NA) \\log(n_B/N_B) - \\log(n_A/N_A)  variance 1nB−1NB+1nA−1NA \\frac{1}{n_B} - \\frac{1}{N_B} + \\frac{1}{n_A} - \\frac{1}{N_A} Risk difference Treatment effect nBNB−nANA \\frac{n_B}{N_B} - \\frac{n_A}{N_A}  variance nBNB(1−nBNB)+nANA(1−nANA) \\frac{n_B}{N_B} \\left( 1 - \\frac{n_B}{N_B} \\right) + \\frac{n_A}{N_A} \\left( 1 - \\frac{n_A}{N_A} \\right) change outcome scale, can pass scale argument outstandR() function. example, change scale risk difference, can use following code.","code":"outstandR_maic_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(formula = lin_form,                                      family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_maic_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.458    0.0870      -1.04      0.120 #> 2 AC           -1.14     0.0507      -1.59     -0.703 #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.225   0.00198 NA         NA         #> 2 C             0.695   0.00335 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"simulated-treatment-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Simulated treatment comparison","title":"Binary data example","text":"Simulated treatment comparison (STC) conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+βX(𝐱n−𝛉)+𝛃𝐄𝐌(βt+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌))(t≠C) g(\\mu_n) = \\beta_0 + \\beta_X (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) + \\boldsymbol{\\beta_{EM}} (\\beta_t + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) ) \\; \\mbox{}(t \\neq C) β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+Z+Z(X1−X1‾)+Z(X2−X2‾) y = X_3 + X_4 + Z + Z (X_1 - \\bar{X_1}) + Z (X_2 - \\bar{X_2}) However, outstandR() knows handle can simply pass (uncentred) formula . Change outcome scale last two approaches, perform G-computation firstly frequentist MLE Bayesian approach.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            -1.12   NA           NA        NA     #> 2 AC            -2.21   NA           NA        NA     #> 3 BC            -1.10    0.0992      -1.72     -0.481 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.153        NA NA         NA         #> 2 C             0.624        NA NA         NA outstandR_stc_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_stc_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.718   NA           NA        NA     #> 2 AC           -1.40    NA           NA        NA     #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.153        NA NA         NA         #> 2 C             0.624        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Binary data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝐗+(βz+𝐱𝐧𝐄𝐌𝛃𝐄𝐌)(t≠C) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_X} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_{EM}}) \\; \\mbox{}(t \\neq C) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0) Change outcome scale","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")))  outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.966    0.242       -1.93   -0.00274 #> 2 AC           -2.06     0.142       -2.80   -1.33    #> 3 BC           -1.10     0.0992      -1.72   -0.481   #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.224   0.00189 NA         NA         #> 2 C             0.687   0.00340 NA         NA outstandR_gcomp_ml_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_ml_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.463    0.0869      -1.04      0.115 #> 2 AC           -1.15     0.0505      -1.59     -0.708 #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.223   0.00205 NA         NA         #> 2 C             0.691   0.00348 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Binary data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment. , can change outcome scale.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.986    0.242       -1.95    -0.0218 #> 2 AC           -2.08     0.143       -2.82    -1.34   #> 3 BC           -1.10     0.0992      -1.72    -0.481  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.225   0.00199 NA         NA         #> 2 C             0.693   0.00340 NA         NA outstandR_gcomp_bayes_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_bayes_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.456    0.0848      -1.03      0.115 #> 2 AC           -1.14     0.0485      -1.57     -0.710 #> 3 BC           -0.686    0.0364      -1.06     -0.312 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.225   0.00199 NA         NA         #> 2 C             0.693   0.00340 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Binary data example","text":"Marginalized treatment effect aggregate level data study obtained integrating covariate distribution BCBC study Δmarg=𝔼X∼fBC(X)[μT=1(X)−μT=0(X)]=∫[μT=1(X)−μT=0(X)]fBC(X)dX \\Delta^{\\text{marg}} = \\mathbb{E}_{X \\sim f_{\\text{BC}}(X)} \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] = \\int \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] f_{\\text{BC}}(X) \\; \\text{d}X aggregate level data likelihood Δ̂BC∼𝒩(Δmarg,SE2) \\hat{\\Delta}_{BC} \\sim \\mathcal{N}(\\Delta^{\\text{marg}}, SE^2) Change outcome scale .","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")))  outstandR_mim outstandR_mim #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.987    0.231       -1.93    -0.0452 #> 2 AC           -2.09     0.132       -2.80    -1.37   #> 3 BC           -1.10     0.0992      -1.72    -0.481  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA outstandR_mim_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_mim_lrr #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_relative_risk  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.456    0.0744     -0.991     0.0783 #> 2 AC           -1.14     0.0380     -1.52     -0.760  #> 3 BC           -0.686    0.0364     -1.06     -0.312  #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ac-effect-in-bc-population","dir":"Articles","previous_headings":"Model fitting in R > Model comparison","what":"ACAC effect in BCBC population","title":"Binary data example","text":"true ACAC effect log scale BCBC (aggregate trial data) population βtAC+βEM(X‾1AC+X‾2AC)\\beta_t^{AC} + \\beta_{EM} (\\bar{X}^{AC}_1 + \\bar{X}_2^{AC}). Calculated naive approach just convert directly one population another, ignoring imbalance effect modifiers.","code":"d_AC_true <- b_trt + b_EM * (ald_trial$mean.X1 + ald_trial$mean.X2) d_AC_naive <-    ipd_trial |>    group_by(trt) |>    summarise(y_sum = sum(y), y_bar = mean(y), n = n()) |>    tidyr::pivot_wider(names_from = trt,                      values_from = c(y_sum, y_bar, n)) |>    mutate(d_AC =            log(y_bar_A/(1-y_bar_A)) - log(y_bar_C/(1-y_bar_C)),          var_AC =            1/(n_A-y_sum_A) + 1/y_sum_A + 1/(n_C-y_sum_C) + 1/y_sum_C)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"ab-effect-in-bc-population","dir":"Articles","previous_headings":"Model fitting in R > Model comparison","what":"ABAB effect in BCBC population","title":"Binary data example","text":"indirect effect. true ABAB effect BCBC population βtAC−βtBC\\beta_t^{AC} - \\beta_t^{BC}. Following simulation study Remiro et al (2020) cancel true effect zero. naive comparison calculating ABAB effect BCBC population course, BCBC contrast calculated directly.","code":"d_BC <-   with(ald_trial, log(y.B.bar/(1-y.B.bar)) - log(y.C.bar/(1-y.C.bar)))  d_AB_naive <- d_AC_naive$d_AC - d_BC  var.d.BC <- with(ald_trial, 1/y.B.sum + 1/(N.B - y.B.sum) + 1/y.C.sum + 1/(N.C - y.C.sum))  var.d.AB.naive <- d_AC_naive$var_AC + var.d.BC"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"results","dir":"Articles","previous_headings":"","what":"Results","title":"Binary data example","text":"now combine outputs present plots tables. log-odds ratio table contrasts methods BCBC population given . can see different corresponds reasonably well one another. Next, let us look results log relative risk scale. First, true values calculated summary table ","code":"d_AB_true_lrr <- 0 d_AC_true_lrr <- log(plogis(d_A_true) / plogis(d_C_true)) d_AC_true_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_example.html","id":"plots","dir":"Articles","previous_headings":"Results","what":"Plots","title":"Binary data example","text":"output can presented forest plots follows. horizontal bar represent different method facets group treatment comparison BCBC population. log-odds ratio log risk ratio plot given .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"simpler version Binary Data Example Simulated Data example. See document details exposition.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"general-problem","dir":"Articles","previous_headings":"","what":"General problem","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Consider one AB trial, company IPD, one AC trial, published aggregate data available. wish estimate comparison effects treatments B C appropriate scale target population P, denoted parameter dBC(P)d_{BC(P)}. make use bracketed subscripts denote specific population. Within AB population parameters μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)} μC(AB)\\mu_{C(AB)} representing expected outcome treatment (including parameters treatments studied AB trial, e.g. treatment C). AB trial provides estimators Y‾(AB)\\bar{Y}_{(AB)} Y‾B(AB)\\bar{Y}_{B(AB)} μA(AB)\\mu_{( AB)}, μB(AB)\\mu_{B(AB)}, respectively, summary outcomes. situation AC trial. suitable scale, example logit, risk difference, form estimators ΔAB(AB)\\Delta_{AB(AB)} ΔAC(AC)\\Delta_{AC(AC)} trial level (marginal) relative treatment effects. ΔAB(AB)=g(Y‾B(AB))−g(Y‾(AB)) \\Delta_{AB(AB)} = g(\\bar{Y}_{B{(AB)}}) - g(\\bar{Y}_{{(AB)}})","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Next, load data use analysis. data comes simulation study Remiro‐Azócar , Heath , Baio G (2020). consider binary outcomes using log-odds ratio measure effect. binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yny_n subject nn simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. general format data sets consist following.","code":"set.seed(555)  ipd_trial <- read.csv(here::here(\"raw-data\", \"AC_IPD.csv\"))  # AC patient-level data ald_trial <- read.csv(here::here(\"raw-data\", \"BC_ALD.csv\"))  # BC aggregate-level data"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"X*: patient measurements trt: treatment ID (integer) y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: proportion events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. Let us label treatment levels data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) head(ipd_trial) #>            X1        X2          X3          X4 trt y #> 1  0.43734111 0.6747901  0.93001035  0.09165363   A 0 #> 2  0.05643081 0.5987971  0.03557646  0.59954129   A 1 #> 3 -0.08048882 0.6843784  0.93147222 -0.11419716   A 0 #> 4 -0.38580926 0.5716644 -0.32252212  0.02551808   A 0 #> 5  1.00755116 0.8220826  0.92735892  0.84414221   A 1 #> 6  0.19443956 0.2031329  0.34990179  0.15633009   A 0 ald_trial #>     mean.X1   mean.X2   mean.X3   mean.X4     sd.X1     sd.X2     sd.X3 #> 1 0.5908996 0.6414179 0.5856529 0.6023671 0.3863145 0.4033615 0.4076097 #>      sd.X4 y.B.sum y.B.bar N.B y.C.sum y.C.bar N.C #> 1 0.395132     182   0.455 400     149   0.745 200"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. formula used model covariates prognostic variable y=X1+X2+X3+X4+(βt+βxX1+βxX2)t y = X_1 + X_2 + X_3 + X_4 + (\\beta_t + \\beta_x X_1 + \\beta_x X_2) t corresponds following R formula object passed argument strategy function. returned object class outstandR.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <- outstandR(ipd_trial, ald_trial,                             strategy = strategy_maic(formula = lin_form,                                                      family = binomial(link = \"logit\"))) outstandR_maic #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.101    0.173      -0.715      0.917 #> 2 AC           -1.15     0.137      -1.88      -0.427 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.434   0.00255 NA         NA         #> 2 C             0.704   0.00329 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD plugging-covariate mean values. last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <- outstandR(ipd_trial, ald_trial,                            strategy = strategy_stc(formula = lin_form,                                                    family = binomial(link = \"logit\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.176   NA           NA        NA     #> 2 AC           -1.43    NA           NA        NA     #> 3 BC           -1.25     0.0364      -1.63     -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.117        NA NA         NA         #> 2 C             0.356        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C.","code":"outstandR_gcomp_ml <- outstandR(ipd_trial, ald_trial,                                 strategy = strategy_gcomp_ml(formula = lin_form,                                                              family = binomial(link = \"logit\"))) outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.164    0.147      -0.586      0.915 #> 2 AC           -1.09     0.110      -1.74      -0.438 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.485   0.00235 NA         NA         #> 2 C             0.734   0.00251 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(formula = lin_form,                                            family = binomial(link = \"logit\"))) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 7.4e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.74 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.285 seconds (Warm-up) #> Chain 1:                0.327 seconds (Sampling) #> Chain 1:                0.612 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.6e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.301 seconds (Warm-up) #> Chain 2:                0.385 seconds (Sampling) #> Chain 2:                0.686 seconds (Total) #> Chain 2:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 3). #> Chain 3:  #> Chain 3: Gradient evaluation took 4.4e-05 seconds #> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.44 seconds. #> Chain 3: Adjust your expectations accordingly! #> Chain 3:  #> Chain 3:  #> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 3:  #> Chain 3:  Elapsed Time: 0.32 seconds (Warm-up) #> Chain 3:                0.328 seconds (Sampling) #> Chain 3:                0.648 seconds (Total) #> Chain 3:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 4). #> Chain 4:  #> Chain 4: Gradient evaluation took 1.9e-05 seconds #> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds. #> Chain 4: Adjust your expectations accordingly! #> Chain 4:  #> Chain 4:  #> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 4:  #> Chain 4:  Elapsed Time: 0.298 seconds (Warm-up) #> Chain 4:                0.262 seconds (Sampling) #> Chain 4:                0.56 seconds (Total) #> Chain 4: outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.151    0.141      -0.585      0.887 #> 2 AC           -1.10     0.105      -1.74      -0.467 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A             0.485   0.00218 NA         NA         #> 2 C             0.736   0.00258 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Fit model .","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(formula = lin_form,                                     family = binomial(link = \"logit\"))) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 2.2e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.309 seconds (Warm-up) #> Chain 1:                0.336 seconds (Sampling) #> Chain 1:                0.645 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.9e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.309 seconds (Warm-up) #> Chain 2:                0.335 seconds (Sampling) #> Chain 2:                0.644 seconds (Total) #> Chain 2:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 3). #> Chain 3:  #> Chain 3: Gradient evaluation took 2.2e-05 seconds #> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds. #> Chain 3: Adjust your expectations accordingly! #> Chain 3:  #> Chain 3:  #> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 3:  #> Chain 3:  Elapsed Time: 0.323 seconds (Warm-up) #> Chain 3:                0.322 seconds (Sampling) #> Chain 3:                0.645 seconds (Total) #> Chain 3:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 4). #> Chain 4:  #> Chain 4: Gradient evaluation took 1.8e-05 seconds #> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds. #> Chain 4: Adjust your expectations accordingly! #> Chain 4:  #> Chain 4:  #> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup) #> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup) #> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup) #> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup) #> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup) #> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup) #> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling) #> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling) #> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling) #> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling) #> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling) #> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling) #> Chain 4:  #> Chain 4:  Elapsed Time: 0.322 seconds (Warm-up) #> Chain 4:                0.279 seconds (Sampling) #> Chain 4:                0.601 seconds (Total) #> Chain 4: outstandR_mim #> Object of class 'outstandR'  #> Model: binomial  #> Scale: log_odds  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB            0.153    0.131      -0.556      0.861 #> 2 AC           -1.10     0.0942     -1.70      -0.499 #> 3 BC           -1.25     0.0364     -1.63      -0.879 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_data_Remiro-Azocar.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Binary data example using data from Remiro-Azocar et al. (2020)","text":"Combine outputs log-odds ratio table contrasts methods.","code":"knitr::kable(   data.frame(   `MAIC` = unlist(outstandR_maic$contrasts),   `STC` = unlist(outstandR_stc$contrasts),   `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts),   `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts),   `MIM` = unlist(outstandR_mim$contrasts)) )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Binary data example","text":"vignette demonstrate use outstandR package fit range types models simulated binary data. Related vignettes provide equivalent analyses continuous count data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"analysis","dir":"Articles","previous_headings":"","what":"Analysis","title":"Binary data example","text":"First, let us load necessary packages.","code":"# install.packages(\"outstandR\", #  repos = c(\"https://statisticshealtheconomics.r-universe.dev\", \"https://cloud.r-project.org\")) # # install.packages(\"simcovariates\", #  repos = c(\"https://n8thangreen.r-universe.dev\", \"https://cloud.r-project.org\"))  library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)  # from GitHub"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"data","dir":"Articles","previous_headings":"Analysis","what":"Data","title":"Binary data example","text":"consider binary outcomes using log-odds ratio measure effect. example, binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yiy_i subject ii simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. simulation input parameters given . Translating R code. shall use gen_data() function available simcovariates package GitHub. , need define list covariates distribution type relationship outcome role either prognostic, effect_modifier . treatment column return data binary takes values 0 1. include extra information treatment names. define lable two level factor 1 C 0 follows. Similarly, obtain aggregate data simulate IPD additional summarise step. set different mean values meanX_BC meanX_EM_BC otherwise use parameter values ACAC trial. First, simulate underlying IPD similarly AC trial. Next, aggregate data. summarise() covariates, sample sizes outcomes separately bind results together. general format data sets ‘long’ style consisting following.","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_PF <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value covariate_defns_ipd <- list(   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)  b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)  num_normal_covs <- length(covariate_defns_ipd) cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs) diag(cor_matrix) <- 1  rownames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\") colnames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\")  ipd_trial <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ipd,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = binomial(\"logit\")) ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) covariate_defns_ald <- list(   PF_cont_1 = list(type = continuous(mean = meanX_BC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_BC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_BC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_BC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  BC.IPD <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ald,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = binomial(\"logit\"))  BC.IPD$trt <- factor(BC.IPD$trt, labels = c(\"C\", \"B\")) # covariate summary statistics # assume same between treatments cov.X <-    BC.IPD %>%   as.data.frame() |>    dplyr::select(matches(\"^(PF|EM)\"), trt) |>    tidyr::pivot_longer(     cols = starts_with(\"PF\") | starts_with(\"EM\"),     names_to = \"variable\",     values_to = \"value\") |>   group_by(variable) %>%   summarise(     mean = mean(value),     sd = sd(value)   ) %>%   tidyr::pivot_longer(     cols = c(\"mean\", \"sd\"),     names_to = \"statistic\",     values_to = \"value\") %>%   ungroup() |>    mutate(trt = NA)  # outcome summary.y <-    BC.IPD |>    as.data.frame() |>    dplyr::select(y, trt) %>%   tidyr::pivot_longer(cols = \"y\",                names_to = \"variable\",                values_to = \"value\") %>%   group_by(variable, trt) %>%   summarise(     mean = mean(value),     sd = sd(value),     sum = sum(value)   ) %>%   tidyr::pivot_longer(     cols = c(\"mean\", \"sd\", \"sum\"),     names_to = \"statistic\",     values_to = \"value\") %>%   ungroup()  # sample sizes summary.N <-    BC.IPD |>    group_by(trt) |>    count(name = \"N\") |>    tidyr::pivot_longer(     cols = \"N\",     names_to = \"statistic\",     values_to = \"value\") |>    mutate(variable = NA_character_) |>    dplyr::select(variable, statistic, value, trt)    ald_trial <- rbind.data.frame(cov.X, summary.y, summary.N)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Analysis > Data","what":"ipd_trial: Individual patient data","title":"Binary data example","text":"PF_*: Patient measurements prognostic factors EM_*: Patient measurements effect modifiers trt: Treatment label (factor) y: Indicator whether event observed (two level factor)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Analysis > Data","what":"ald_trial: Aggregate-level data","title":"Binary data example","text":"variable: Covariate name. case treatment arm sample size NA statistic: Summary statistic name mean, standard deviation sum value: Numerical value summary statistic trt: Treatment label. assume common covariate distribution treatment arms NA final data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt takes either new treatment standard care / status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; event total, average sample size treatment B C.","code":"head(ipd_trial) ald_trial"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"regression-model","dir":"Articles","previous_headings":"Analysis > Data","what":"Regression model","title":"Binary data example","text":"true logistic outcome model use simulate data logit(pt)=β0+βPF(X3+X4)+[βt+βEM(X1+X2)](t≠C) \\text{logit}(p_{t}) = \\beta_0 + \\beta_{PF} (X_3 + X_4) + [\\beta_{t} + \\beta_{EM} (X_1 + X_2)] \\; \\text{}(t \\neq C) ()\\text{}() indicator function taking value 1 true 0 otherwise. , treatment CC right hand side becomes β0+βPF(X3+X4)\\beta_0 + \\beta_{PF} (X_3 + X_4) comparator treatments AA BB additional βt+βEM(X1+X2)\\beta_t + \\beta_{EM} (X_1 + X_2) component consisting effect modifier terms coefficient treatment parameter, βt\\beta_t (b_trt R code), .e. log odds-ratio (LOR) logit model. Finally, ptp_{t} probability experiencing event interest treatment tt.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Analysis","what":"Output statistics","title":"Binary data example","text":"obtain marginal treatment effect marginal variance. definition calculated depends type data outcome scale. current example binary data log-odds ratio marginal treatment effect log⁡(nB/(NB−nB)nC/(NB−nB))=log⁡(nBnC‾)−log⁡(nCnB‾) \\log\\left( \\frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \\right) = \\log(n_B n_{\\bar{C}}) - \\log(n_C n_{\\bar{B}}) marginal variance 1nC+1nC‾+1nB+1nB‾ \\frac{1}{n_C} + \\frac{1}{n_{\\bar{C}}} + \\frac{1}{n_B} + \\frac{1}{n_{\\bar{B}}} nB,nCn_B, n_C number events arm C‾\\bar{C} compliment CC, e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c. outcome scales discussed .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Binary data example","text":"outstandR package written easy use essentially consists single function, outstandR(). can used run different types model, combined specific parameters call strategies. first two arguments outstandR() individual patient aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"model-formula","dir":"Articles","previous_headings":"Model fitting in R","what":"Model formula","title":"Binary data example","text":"take advantage -built R formula object define models. allow us easily pull components object consistently use . Defining EM_cont_1,EM_cont_2EM\\_cont\\_1, EM\\_cont\\_2 effect modifiers, PF_cont_1,PF_cont_2PF\\_cont\\_1, PF\\_cont\\_2 prognostic variables ZZ treatment indicator formula used model y=PF_cont_1+PF_cont_2+Z+Z×EM_cont_1+Z×EM_cont_2 y = PF\\_cont\\_1 + PF\\_cont\\_2 + Z + Z \\times EM\\_cont\\_1 + Z \\times EM\\_cont\\_2 Notice include link function interest appears linear regression. corresponds following R formula object pass argument strategy function. Note succinct formula additionally include X1,X2X_1, X_2 prognostic factors equivalent (may actually want). recover original formula can modified follows. note MAIC approach strictly use regression way methods considered directly comparable sense decided use consistent syntax across models using ‘formula’.","code":"lin_form <- list(   outcome_model = as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2\"),   balance_model = as.formula(\"~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2\") ) y ~ PF_cont_1 + PF_cont_2 + trt*(EM_cont_1 + EM_cont_2) y ~ PF_cont_1 + PF_cont_2 + trt*(EM_cont_1 + EM_cont_2) - EM_cont_1 - EM_cont_2"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"matching-adjusted-indirect-comparison-maic","dir":"Articles","previous_headings":"Model fitting in R","what":"Matching-Adjusted Indirect Comparison (MAIC)","title":"Binary data example","text":"single call outstandR() sufficient run model. pass strategy argument strategy_maic() function arguments formula = lin_form defined family = binomial(link = \"logit\") binary data logistic link. Internally, using individual patient level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. returned object class outstandR. see list object 2 parts. first contains statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument. second element list contains absolute effect estimates. print method available outstandR objects human-readable output","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = binomial(link = \"logit\"))) str(outstandR_maic) outstandR_maic"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"outcome-scale","dir":"Articles","previous_headings":"Model fitting in R > Matching-Adjusted Indirect Comparison (MAIC)","what":"Outcome scale","title":"Binary data example","text":"explicitly specify outcome scale, default used fit data regression model. saw, case, default log-odds ratio corresponding \"logit\" link function binary data. However, can change scale may appropriate particular analysis. far implemented package, links corresponding relative treatment effect scales follows: full list possible transformed treatment effect scales : log-odds ratio, log-risk ratio, mean difference, risk difference, hazard ratio, hazard difference. binary data marginal treatment effect variance Log-risk ratio Treatment effect log⁡(nB/NB)−log⁡(nA/NA) \\log(n_B/N_B) - \\log(n_A/N_A) variance 1nB−1NB+1nA−1NA \\frac{1}{n_B} - \\frac{1}{N_B} + \\frac{1}{n_A} - \\frac{1}{N_A} Risk difference Treatment effect nBNB−nANA \\frac{n_B}{N_B} - \\frac{n_A}{N_A} variance nBNB(1−nBNB)+nANA(1−nANA) \\frac{n_B}{N_B} \\left( 1 - \\frac{n_B}{N_B} \\right) + \\frac{n_A}{N_A} \\left( 1 - \\frac{n_A}{N_A} \\right) change outcome scale, can pass scale argument outstandR() function. example, change scale risk difference, can use following code.","code":"outstandR_maic_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(formula = lin_form,                                      family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_maic_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Binary data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝐏𝐅+(βz+𝐱𝐧𝐄𝐌𝛃𝐄𝐌)(t≠C) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_{PF}} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_{EM}}) \\; \\mbox{}(t \\neq C) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* performed previous approaches, call outstandR() change strategy strategy_gcomp_ml(), , let us change outcome scale LRR","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_ml outstandR_gcomp_ml_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_ml_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Binary data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. strategy function plug-outstandR() call approach strategy_gcomp_bayes(), , can change outcome scale LRR.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_bayes outstandR_gcomp_bayes_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_bayes_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Binary data example","text":"final method obtain marginalized treatment effect aggregate level data study, obtained integrating covariate distribution aggregate level data BCBC study Δmarg=𝔼X∼fBC(X)[μT=1(X)−μT=0(X)]=∫[μT=1(X)−μT=0(X)]fBC(X)dX \\Delta^{\\text{marg}} = \\mathbb{E}_{X \\sim f_{\\text{BC}}(X)} \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] = \\int \\left[ \\mu_{T=1}(X) - \\mu_{T=0}(X) \\right] f_{\\text{BC}}(X) \\; \\text{d}X aggregate level data likelihood Δ̂BC∼𝒩(Δmarg,SE2) \\hat{\\Delta}_{BC} \\sim \\mathcal{N}(\\Delta^{\\text{marg}}, SE^2) multiple imputation marginalisation strategy function strategy_mim(), Change outcome scale LRR,","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_mim outstandR_mim_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_mim_lrr"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ac-effect-in-bc-population","dir":"Articles","previous_headings":"Model comparison","what":"ACAC effect in BCBC population","title":"Binary data example","text":"true ACAC effect log scale BCBC (aggregate trial data) population βtAC+βEM(X‾1AC+X‾2AC)\\beta_t^{AC} + \\beta_{EM} (\\bar{X}^{AC}_1 + \\bar{X}_2^{AC}). Calculated naive approach just convert directly one population another, ignoring imbalance effect modifiers.","code":"mean_X1 <- ald_trial$value[ald_trial$statistic == \"mean\" & ald_trial$variable == \"EM_cont_1\"] mean_X2 <- ald_trial$value[ald_trial$statistic == \"mean\" & ald_trial$variable == \"EM_cont_1\"]  d_AC_true <- b_trt + b_EM * (mean_X1 + mean_X2) d_AC_naive <-    ipd_trial |>    dplyr::group_by(trt) |>    dplyr::summarise(y_sum = sum(y), y_bar = mean(y), n = n()) |>    tidyr::pivot_wider(names_from = trt,                      values_from = c(y_sum, y_bar, n)) |>    dplyr::mutate(d_AC =                   log(y_bar_A/(1-y_bar_A)) - log(y_bar_C/(1-y_bar_C)),                 var_AC =                   1/(n_A-y_sum_A) + 1/y_sum_A + 1/(n_C-y_sum_C) + 1/y_sum_C)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"ab-effect-in-bc-population","dir":"Articles","previous_headings":"Model comparison","what":"ABAB effect in BCBC population","title":"Binary data example","text":"indirect effect. true ABAB effect BCBC population βtAC−βtBC\\beta_t^{AC} - \\beta_t^{BC}. Following simulation study Remiro et al (2020) cancel true effect zero. naive comparison calculating ABAB effect BCBC population Alternatively, can compute using outstandR’s built-calc_bucher_naive() function: course, BCBC contrast calculated directly.","code":"# reshape to make extraction easier ald_out <- ald_trial |>    dplyr::filter(variable == \"y\" | is.na(variable)) |>    mutate(stat_trt = paste0(statistic, \"_\", trt)) |>    dplyr::select(stat_trt, value) |>    pivot_wider(names_from = stat_trt, values_from = value)  d_BC <-   with(ald_out, log(mean_B/(1-mean_B)) - log(mean_C/(1-mean_C)))  d_AB_naive <- d_AC_naive$d_AC - d_BC  var.d.BC <- with(ald_out, 1/sum_B + 1/(N_B - sum_B) + 1/sum_C + 1/(N_C - sum_C))  var.d.AB.naive <- d_AC_naive$var_AC + var.d.BC naive_results <- calc_bucher_naive(ipd_trial, ald_trial, outcome_model = lin_form, family = binomial(link = \"logit\")) naive_results"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"results","dir":"Articles","previous_headings":"","what":"Results","title":"Binary data example","text":"now combine outputs present plots tables. log-odds ratio table contrasts methods BCBC population given . can see different corresponds reasonably well one another. Next, let us look results log relative risk scale. First, true values calculated summary table ","code":"d_AB_true_lrr <- 0 d_AC_true_lrr <- log(plogis(d_A_true) / plogis(d_C_true)) d_AC_true_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Binary_outcome_example.html","id":"plots","dir":"Articles","previous_headings":"Results","what":"Plots","title":"Binary data example","text":"output can presented forest plots follows. horizontal bar represent different method facets group treatment comparison BCBC population. log-odds ratio log risk ratio plot given .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Continuous data example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Continuous data example","text":"Next, load data use analysis. data comes simulation study Remiro‐Azócar , Heath , Baio G (2020). consider binary outcomes using log-odds ratio measure effect. binary outcome may response treatment occurrence adverse event. trials AC BC, outcome yny_n subject nn simulated Bernoulli distribution probabilities success generated logistic regression. BC trial, individual-level covariates outcomes aggregated obtain summaries. continuous covariates summarized means standard deviations, available analyst published study table baseline characteristics RCT publication. binary outcomes summarized overall event table. Typically, published study provides aggregate information analyst. Use gen_data() function available simcovariates package. Similarly, aggregate data additional summarise step. general format data sets consist following.","code":"library(dplyr) #>  #> Attaching package: 'dplyr' #> The following objects are masked from 'package:stats': #>  #>     filter, lag #> The following objects are masked from 'package:base': #>  #>     intersect, setdiff, setequal, union library(MASS) #>  #> Attaching package: 'MASS' #> The following object is masked from 'package:dplyr': #>  #>     select  N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = gaussian(link = \"identity\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = gaussian(link = \"identity\"))  cov.X <- BC.IPD %>%   summarise(across(starts_with(\"X\"),                    list(mean = mean, sd = sd),                    .names = \"{fn}.{col}\"))  out.B <- dplyr::filter(BC.IPD, trt == 1) %>%   summarise(y.B.sum = sum(y),             y.B.bar = mean(y),             y.B.sd = sd(y),             N.B = n())  out.C <- dplyr::filter(BC.IPD, trt == 0) %>%   summarise(y.C.sum = sum(y),             y.C.bar = mean(y),             y.C.sd = sd(y),             N.C = n())  ald_trial <- cbind.data.frame(cov.X, out.B, out.C)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Continuous data example","text":"X*: patient measurements trt: treatment ID (integer) y: continuous outcome measure","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Continuous data example","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement mean.y: sd.y: Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. case, 4 covariate mean standard deviation values; event total, average sample size treatment B, C.","code":"head(ipd_trial) #>           X1         X2         X3         X4 trt          y #> 1 0.42066874  1.0957407 0.37118099  1.3291540   A  0.8949999 #> 2 0.51227329  0.9079984 0.30560144 -0.1842358   A -1.7550940 #> 3 1.00347612  0.8136847 1.25054503  1.1986315   A -0.6521005 #> 4 0.05641685  0.5318140 0.54799796  0.6694090   A -0.6260983 #> 5 0.42997845  0.5274304 0.09140568  0.1222184   A -1.2882834 #> 6 0.06916082 -0.3125090 0.99150666 -0.1102693   A -3.0170689 ald_trial #>     mean.X1     sd.X1   mean.X2    sd.X2   mean.X3     sd.X3  mean.X4     sd.X4 #> 1 0.6081015 0.3865186 0.6462269 0.412924 0.5903258 0.3842429 0.635176 0.3831984 #>     y.B.sum   y.B.bar   y.B.sd N.B  y.C.sum   y.C.bar   y.C.sd N.C #> 1 -135.0634 -1.015514 1.159787 133 12.38076 0.1847875 1.019683  67"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Continuous data example","text":"implement MAIC, STC, G-computation methods obtain marginal variance, defined  marginal treatment effect, defined log-odds ratio,  C‾\\bar{C} compliment CC e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Continuous data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Continuous data example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats. formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2 corresponds following R formula object passed argument strategy function. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_maic #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.339    0.0533     -0.791      0.113 #> 2 AC           -1.54     0.0276     -1.87      -1.21  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -1.14     0.0112 NA         NA         #> 2 C             0.396    0.0179 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Continuous data example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1) β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2}) However, outstandR() knows handle can simply pass (uncentred) formula . last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_stc #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.363   NA           NA        NA     #> 2 AC           -1.56    NA           NA        NA     #> 3 BC           -1.20     0.0256      -1.51     -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A           -1.47          NA NA         NA         #> 2 C            0.0930        NA NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Continuous data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(formula = lin_form,                                          family = gaussian(link = \"identity\"))) outstandR_gcomp_ml #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.348    0.0596     -0.826      0.130 #> 2 AC           -1.55     0.0339     -1.91      -1.19  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -1.10     0.0113 NA         NA         #> 2 C             0.444    0.0241 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Continuous data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_gcomp_bayes #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.335    0.0560     -0.799      0.129 #> 2 AC           -1.54     0.0304     -1.88      -1.19  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl> <lgl>      <lgl>      #> 1 A            -1.10     0.0113 NA         NA         #> 2 C             0.433    0.0206 NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Continuous data example","text":"ref equationhere equation ","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_mim #> Object of class 'outstandR'  #> Model: gaussian  #> Scale: risk_difference  #> Common treatment: C  #> Individual patient data study: AC  #> Aggregate level data study: BC  #> Confidence interval level: 0.95  #>  #> Contrasts: #>  #> # A tibble: 3 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>         <dbl>     <dbl>      <dbl>      <dbl> #> 1 AB           -0.335    0.0538     -0.789      0.120 #> 2 AC           -1.53     0.0281     -1.86      -1.21  #> 3 BC           -1.20     0.0256     -1.51      -0.887 #>  #> Absolute: #>  #> # A tibble: 2 × 5 #>   Treatments Estimate Std.Error lower.0.95 upper.0.95 #>   <chr>      <lgl>    <lgl>     <lgl>      <lgl>      #> 1 A          NA       NA        NA         NA         #> 2 C          NA       NA        NA         NA"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_data_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Continuous data example","text":"Combine outputs relative effects table contrasts methods.","code":"knitr::kable(   data.frame(     `MAIC` = unlist(outstandR_maic$contrasts$means),     `STC` = unlist(outstandR_stc$contrasts$means),     `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts$means),     `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts$means),     `MIM` = unlist(outstandR_mim$contrasts$means))   |>      round(2))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Continuous data example","text":"vignette performing population adjustment methods continuous data, order compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. demonstrate apply MAIC, G-computation ML, G-computation Bayesian inference multiple imputation marginalisation. document structure follow binary data example vignette referred details.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Continuous data example","text":"First, let us load necessary packages.","code":"# install.packages(\"outstandR\", #  repos = c(\"https://statisticshealtheconomics.r-universe.dev\", \"https://cloud.r-project.org\")) # # install.packages(\"simcovariates\", #  repos = c(\"https://n8thangreen.r-universe.dev\", \"https://cloud.r-project.org\"))  library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Continuous data example","text":"first simulate IPD ALD data. See binary data example vignette details implemented. difference example change family argument gen_data() gaussian(link = \"identity\"), corresponding continuous data case. gen_data() function available simcovariates package GitHub. Similarly, aggregate data additional summarise step (see binary data example vignette code). general format data sets ‘long’ style consisting following.","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_PF <- -log(0.5)      # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value covariate_defns_ipd <- list(   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)  b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)  num_normal_covs <- length(covariate_defns_ipd) cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs) diag(cor_matrix) <- 1  rownames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\") colnames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\")  ipd_trial <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ipd,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = gaussian(\"identity\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\"))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Continuous data example","text":"PF_*: Patient measurements prognostic factors EM_*: Patient measurements effect modifiers trt: Treatment label (factor) y: Continuous numeric","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Continuous data example","text":"variable: Covariate name. case treatment arm sample size NA statistic: Summary statistic name mean, standard deviation sum value: Numerical value summary statistic trt: Treatment label. assume common covariate distribution treatment arms NA data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt takes either new treatment standard care / status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; total, average sample size treatment B C. following implement MAIC G-computation methods obtain marginal variance marginal treatment effect.","code":"head(ipd_trial) ald_trial"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Continuous data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided . formula used model, passed argument strategy function ","code":"lin_form <- list(   outcome_model = as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2\"),   balance_model = as.formula(\"~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2\") )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Continuous data example","text":"mentioned , pass model specific strategy function main outstandR() function, case use strategy_maic(). returned object class outstandR.","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_maic"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Continuous data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Pass strategy_gcomp_bayes() strategy function.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_gcomp_bayes"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Continuous data example","text":"Finally, strategy function pass outstandR() multiple imputation marginalisation strategy_mim(),","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = gaussian(link = \"identity\"))) outstandR_mim"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Continuous_outcome_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Continuous data example","text":"Combine outputs relative effects table contrasts methods.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"analysis","dir":"Articles","previous_headings":"","what":"Analysis","title":"COPD Analysis","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"data","dir":"Articles","previous_headings":"Analysis","what":"Data","title":"COPD Analysis","text":"general format data sets consist following.","code":"set.seed(555)  AC.IPD <- read.csv(here::here(\"raw-data\", \"AC_IPD.csv\"))  # AC patient-level data BC.ALD <- read.csv(here::here(\"raw-data\", \"BC_ALD.csv\"))  # BC aggregate-level data"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"ac-ipd-individual-patient-data","dir":"Articles","previous_headings":"Analysis > Data","what":"AC.IPD: Individual patient data","title":"COPD Analysis","text":"X*: patient measurements trt: treatment ID y: (logical) indicator whether event observed","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"bc-ald-aggregate-level-data","dir":"Articles","previous_headings":"Analysis > Data","what":"BC.ALD: Aggregate-level data","title":"COPD Analysis","text":"mean.X*: mean patient measurement sd.X*: standard deviation patient measurement y.*.sum: total number events y.*.bar: total number events N.*: total number individuals Note wildcard * usually integer 1 trial identifier B, C. data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution.","code":"head(AC.IPD) #>            X1        X2          X3          X4 trt y #> 1  0.43734111 0.6747901  0.93001035  0.09165363   1 0 #> 2  0.05643081 0.5987971  0.03557646  0.59954129   1 1 #> 3 -0.08048882 0.6843784  0.93147222 -0.11419716   1 0 #> 4 -0.38580926 0.5716644 -0.32252212  0.02551808   1 0 #> 5  1.00755116 0.8220826  0.92735892  0.84414221   1 1 #> 6  0.19443956 0.2031329  0.34990179  0.15633009   1 0 BC.ALD #>     mean.X1   mean.X2   mean.X3   mean.X4     sd.X1     sd.X2     sd.X3 #> 1 0.5908996 0.6414179 0.5856529 0.6023671 0.3863145 0.4033615 0.4076097 #>      sd.X4 y.B.sum y.B.bar N.B y.C.sum y.C.bar N.C #> 1 0.395132     182   0.455 400     149   0.745 200"},{"path":[]},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"COPD Analysis","text":"formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2  corresponds following R formula object passed argument strategy function. returned object class outstandR.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <- outstandR(AC.IPD, BC.ALD, strategy = strategy_maic(formula = lin_form)) outstandR_maic"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"COPD Analysis","text":"g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1) y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2})  However, outstandR() knows handle can simply pass (uncentred) formula .","code":"outstandR_stc <- outstandR(AC.IPD, BC.ALD, strategy = strategy_stc(formula = lin_form)) outstandR_stc"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"COPD Analysis","text":"g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_ml(formula = lin_form)) outstandR_gcomp_ml"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"COPD Analysis","text":"p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^*","code":"outstandR_gcomp_bayes <- outstandR(AC.IPD, BC.ALD, strategy = strategy_gcomp_bayes(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 7e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.7 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.174 seconds (Warm-up) #> Chain 1:                0.18 seconds (Sampling) #> Chain 1:                0.354 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 9e-06 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.175 seconds (Warm-up) #> Chain 2:                0.2 seconds (Sampling) #> Chain 2:                0.375 seconds (Total) #> Chain 2: outstandR_gcomp_bayes"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/copd_analysis.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"COPD Analysis","text":"Combine outputs","code":"outstandR_mim <- outstandR(AC.IPD, BC.ALD, strategy = strategy_mim(formula = lin_form)) #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 1.6e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 1: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 1: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 1: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 1: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 1: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 1: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 1: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.093 seconds (Warm-up) #> Chain 1:                0.3 seconds (Sampling) #> Chain 1:                0.393 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.1e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1001 / 4000 [ 25%]  (Sampling) #> Chain 2: Iteration: 1400 / 4000 [ 35%]  (Sampling) #> Chain 2: Iteration: 1800 / 4000 [ 45%]  (Sampling) #> Chain 2: Iteration: 2200 / 4000 [ 55%]  (Sampling) #> Chain 2: Iteration: 2600 / 4000 [ 65%]  (Sampling) #> Chain 2: Iteration: 3000 / 4000 [ 75%]  (Sampling) #> Chain 2: Iteration: 3400 / 4000 [ 85%]  (Sampling) #> Chain 2: Iteration: 3800 / 4000 [ 95%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.085 seconds (Warm-up) #> Chain 2:                0.288 seconds (Sampling) #> Chain 2:                0.373 seconds (Total) #> Chain 2: outstandR_mim knitr::kable(   data.frame(   `MAIC` = unlist(outstandR_maic$contrasts),   `STC` = unlist(outstandR_stc$contrasts),   `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts),   `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts),   `MIM` = unlist(outstandR_mim$contrasts)) )"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Count data example","text":"First, let us load necessary packages.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Count data example","text":"First, use gen_data() function available simcovariates package. Similarly, aggregate data additional summarise step.","code":"library(dplyr) library(MASS) N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = poisson(link = \"log\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = poisson(link = \"log\"))  cov.X <- BC.IPD %>%   summarise(across(starts_with(\"X\"),                    list(mean = mean, sd = sd),                    .names = \"{fn}.{col}\"))  out.C <- dplyr::filter(BC.IPD, trt == 1) %>%   summarise(y.B.sum = sum(y),             y.B.bar = mean(y),             N.B = n())  out.B <- dplyr::filter(BC.IPD, trt == 0) %>%   summarise(y.C.sum = sum(y),             y.C.bar = mean(y),             N.C = n())  ald_trial <- cbind.data.frame(cov.X, out.C, out.B)  # By definition, the true log-OR relative effect in the AC population between AC is `r b_trt`. Between BC is `r b_trt` and between AB is `r b_trt - b_trt`. # A naive indirect comparison, ignoring the presence of effect modifiers, would calculate the C vs B effect in the AC population as # `b_trt - b_trt`."},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"output-statistics","dir":"Articles","previous_headings":"Example analysis","what":"Output statistics","title":"Count data example","text":"implement MAIC, STC, G-computation methods obtain marginal variance, defined  marginal treatment effect, defined log-odds ratio,  C‾\\bar{C} compliment CC e.g. nC‾=NC−ncn_{\\bar{C}} = N_C - n_c.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Count data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Count data example","text":"Using individual level data AC firstly perform non-parametric bootstrap maic.boot function R = 1000 replicates. function fits treatment coefficient marginal effect vs C. returned value object class boot {boot} package. calculate bootstrap mean variance wrapper function maic_boot_stats(). formula used model y=X3+X4+βtX1+βtX2 y = X_3 + X_4 + \\beta_t X_1 + \\beta_t X_2 corresponds following R formula object passed argument strategy function. returned object class outstandR. see list object 3 parts, containing statistics pair treatments. mean contrasts, variances confidence intervals (CI), respectively. default CI 95% can altered outstandR CI argument.","code":"lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\") outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_maic"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"stc","dir":"Articles","previous_headings":"Model fitting in R","what":"STC","title":"Count data example","text":"STC conventional outcome regression method. involves fitting regression model outcome treatment covariates IPD. IPD effect modifiers centred mean BC values. g(μn)=β0+(𝐱n−𝛉)β1+(βz+(𝐱𝐧𝐄𝐌−𝛉𝐄𝐌)𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + (\\boldsymbol{x}_n - \\boldsymbol{\\theta}) \\beta_1 + (\\beta_z + (\\boldsymbol{x_n^{EM}} - \\boldsymbol{\\theta^{EM}}) \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n=1) β0\\beta_0 intercept, β1\\beta_1 covariate coefficients, βz\\beta_z β2\\beta_2 effect modifier coefficients, znz_n indicator variables effect alternative treatment. g(⋅)g(\\cdot) link function e.g. log\\log. already mentioned, running STC analysis almost identical previous analysis now use strategy_stc() strategy function instead formula centered covariates. y=X3+X4+βt(X1−X1‾)+βt(X2−X2‾) y = X_3 + X_4 + \\beta_t(X_1 - \\bar{X_1}) + \\beta_t(X_2 - \\bar{X_2}) However, outstandR() knows handle can simply pass (uncentred) formula . last two approaches, perform G-computation firstly frequentist MLE approach Bayesian approach.","code":"outstandR_stc <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_stc(               formula = lin_form,               family = poisson(link = \"log\")))  outstandR_stc"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Count data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. First, regression model observed outcome yy covariates xx treatment zz fitted AC IPD: g(μn)=β0+𝐱n𝛃𝟏+(βz+𝐱𝐧𝐄𝐌𝛃𝟐)(zn=1) g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\; \\mbox{}(z_n = 1) context G-computation, regression model often called “Q-model.” fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates x*x* predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: μ̂0=∫x*g−1(β̂0+x*β̂1)p(x*)dx* \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) \\; \\text{d}x^* estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: Δ̂10(2)=g(μ̂1)−g(μ̂0) \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0)","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = poisson(link = \"log\")))  outstandR_gcomp_ml"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Count data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*∈{0,1}z^* \\\\{0, 1\\} posterior predictive distribution specific treatment. defined p(yz**∣𝒟AC)=∫βp(yz**∣β)p(β∣𝒟AC)dβp(y^*_{z^*} \\mid \\mathcal{D}_{AC}) = \\int_{\\beta} p(y^*_{z^*} \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta p(β∣𝒟AC)p(\\beta \\mid \\mathcal{D}_{AC}) posterior distribution outcome regression coefficients β\\beta, encode predictor-outcome relationships observed AC trial IPD. given : p(yz**∣𝒟AC)=∫x*p(y*∣z*,x*,𝒟AC)p(x*∣𝒟AC)dx* p(y^*_{^z*} \\mid \\mathcal{D}_{AC}) = \\int_{x^*} p(y^* \\mid z^*, x^*, \\mathcal{D}_{AC}) p(x^* \\mid \\mathcal{D}_{AC})\\; \\text{d}x^* =∫x*∫βp(y*∣z*,x*,β)p(x*∣β)p(β∣𝒟AC)dβdx* = \\int_{x^*} \\int_{\\beta} p(y^* \\mid z^*, x^*, \\beta) p(x^* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC})\\; d\\beta \\; \\text{d}x^* practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling. average, variance interval estimates marginal treatment effect can derived empirically draws posterior density. can draw vector size N*N^* predicted outcomes yz*y^*_z set intervention z*z^* posterior predictive distribution specific treatment.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_gcomp_bayes"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Count data example","text":"ref equationhere equation ","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_mim"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_data_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Count data example","text":"Combine outputs log-odds ratio table contrasts methods.","code":"knitr::kable(   data.frame(     `MAIC` = unlist(outstandR_maic$contrasts$means),     `STC` = unlist(outstandR_stc$contrasts$means),     `Gcomp ML` = unlist(outstandR_gcomp_ml$contrasts$means),     `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$contrasts$means),     `MIM` = unlist(outstandR_mim$contrasts$means)) ) |>    round(2)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Count data example","text":"vignette performing population adjustment methods count data, order compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. demonstrate apply MAIC, G-computation ML, G-computation Bayesian inference multiple imputation marginalisation. document structure follow binary data example vignette referred details.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"example-analysis","dir":"Articles","previous_headings":"","what":"Example analysis","title":"Count data example","text":"First, let us load necessary packages.","code":"# install.packages(\"outstandR\", #  repos = c(\"https://statisticshealtheconomics.r-universe.dev\", \"https://cloud.r-project.org\")) # # install.packages(\"simcovariates\", #  repos = c(\"https://n8thangreen.r-universe.dev\", \"https://cloud.r-project.org\"))  library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"data","dir":"Articles","previous_headings":"Example analysis","what":"Data","title":"Count data example","text":"first simulate IPD ALD count data. See binary data example vignette details implemented. difference example change family argument gen_data() poisson(link = \"log\"), corresponding count data case. gen_data() function available simcovariates package GitHub. Similarly, aggregate data additional summarise step (see binary data example vignette code). general format data sets ‘long’ style consisting following.","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_PF <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value covariate_defns_ipd <- list(   PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),                     role = \"prognostic\"),   PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),                     role = \"prognostic\"),   EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),                     role = \"effect_modifier\"),   EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),                     role = \"effect_modifier\") )  b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)  b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)  num_normal_covs <- length(covariate_defns_ipd) cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs) diag(cor_matrix) <- 1  rownames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\") colnames(cor_matrix) <- c(\"PF_cont_1\", \"PF_cont_2\", \"EM_cont_1\", \"EM_cont_2\")  ipd_trial <- simcovariates::gen_data(   N = N,   b_0 = b_0,   b_trt = b_trt,   covariate_defns = covariate_defns_ipd,   b_prognostic = b_prognostic,   b_effect_modifier = b_effect_modifier,   cor_matrix = cor_matrix,   trt_assignment = list(prob_trt1 = allocation),   family = poisson(\"log\"))  ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\"))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"ipd_trial-individual-patient-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ipd_trial: Individual patient data","title":"Count data example","text":"PF_*: Patient measurements prognostic factors EM_*: Patient measurements effect modifiers trt: Treatment label (factor) y: Counts","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"ald_trial-aggregate-level-data","dir":"Articles","previous_headings":"Example analysis > Data","what":"ald_trial: Aggregate-level data","title":"Count data example","text":"variable: Covariate name. case treatment arm sample size NA statistic: Summary statistic name mean, standard deviation sum value: Numerical value summary statistic trt: Treatment label. assume common covariate distribution treatment arms NA data look like following. 4 correlated continuous covariates generated per subject, simulated multivariate normal distribution. Treatment trt takes either new treatment standard care / status quo C. ITC ‘anchored’ via C, common treatment. case, 4 covariate mean standard deviation values; total, average sample size treatment B C. following implement MAIC G-computation methods obtain marginal variance marginal treatment effect.","code":"head(ipd_trial) ald_trial"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"model-fitting-in-r","dir":"Articles","previous_headings":"","what":"Model fitting in R","title":"Count data example","text":"outstandR package written easy use essential consists single function, outstandR(). can used run different types model, call strategies. first two arguments outstandR() individual aggregate-level data, respectively. strategy argument outstandR takes functions called strategy_*(), wildcard * replaced name particular method required, e.g. strategy_maic() MAIC. specific example provided . formula used model, passed argument strategy function ","code":"lin_form <- list(   outcome_model = as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2\"),   balance_model = as.formula(\"~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2\") )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"maic","dir":"Articles","previous_headings":"Model fitting in R","what":"MAIC","title":"Count data example","text":"mentioned , pass model specific strategy function main outstandR() function, case use strategy_maic(). returned object class outstandR.","code":"outstandR_maic <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_maic(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_maic"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Model fitting in R","what":"Parametric G-computation with maximum-likelihood estimation","title":"Count data example","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. Pass strategy_gcomp_ml() strategy function.","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_gcomp_ml"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Model fitting in R","what":"Bayesian G-computation with MCMC","title":"Count data example","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Pass strategy_gcomp_bayes() strategy function.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_gcomp_bayes"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Model fitting in R","what":"Multiple imputation marginalisation","title":"Count data example","text":"Finally, strategy function pass outstandR() multiple imputation marginalisation strategy_mim(),","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = poisson(link = \"log\"))) outstandR_mim"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/Count_outcome_example.html","id":"model-comparison","dir":"Articles","previous_headings":"Model fitting in R","what":"Model comparison","title":"Count data example","text":"Combine outputs relative effects table contrasts methods.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"User-defined target population","text":"See vignettes details.","code":"library(boot)      # non-parametric bootstrap in MAIC and ML G-computation library(copula)    # simulating BC covariates from Gaussian copula library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation library(tidyr) library(dplyr) library(MASS) library(outstandR) library(simcovariates)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"data","dir":"Articles","previous_headings":"Introduction","what":"Data","title":"User-defined target population","text":"","code":"N <- 200 allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1) b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator b_X <- -log(0.5)       # conditional effect of each prognostic variable b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC) sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate corX <- 0.2            # covariate correlation coefficient   b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value  ipd_trial <- gen_data(N, b_trt, b_X, b_EM, b_0,                       meanX_AC, sdX,                        meanX_EM_AC, sdX_EM,                        corX, allocation,                       family = binomial(\"logit\")) ipd_trial$trt <- factor(ipd_trial$trt, labels = c(\"C\", \"A\")) BC.IPD <- gen_data(N, b_trt, b_X, b_EM, b_0,                    meanX_BC, sdX,                     meanX_EM_BC, sdX_EM,                     corX, allocation,                    family = binomial(\"logit\"))  BC.IPD$trt <- factor(BC.IPD$trt, labels = c(\"C\", \"B\"))  # covariate summary statistics # assume same between treatments cov.X <-    BC.IPD %>%   as.data.frame() |>    dplyr::select(X1, X2, X3, X4, trt) %>%   pivot_longer(cols = starts_with(\"X\"), names_to = \"variable\", values_to = \"value\") %>%   group_by(variable) %>%   summarise(     mean = mean(value),     sd = sd(value)   ) %>%   pivot_longer(cols = c(\"mean\", \"sd\"), names_to = \"statistic\", values_to = \"value\") %>%   ungroup() |>    mutate(trt = NA)  # outcome summary.y <-    BC.IPD |>    as.data.frame() |>    dplyr::select(y, trt) %>%   pivot_longer(cols = \"y\", names_to = \"variable\", values_to = \"value\") %>%   group_by(variable, trt) %>%   summarise(     mean = mean(value),     sd = sd(value),     sum = sum(value)   ) %>%   pivot_longer(cols = c(\"mean\", \"sd\", \"sum\"),                names_to = \"statistic\", values_to = \"value\") %>%   ungroup()  # sample sizes summary.N <-    BC.IPD |>    group_by(trt) |>    count(name = \"N\") |>    pivot_longer(cols = \"N\", names_to = \"statistic\", values_to = \"value\") |>    mutate(variable = NA_character_) |>    dplyr::select(variable, statistic, value, trt)    ald_trial <- rbind.data.frame(cov.X, summary.y, summary.N) lin_form <- as.formula(\"y ~ X3 + X4 + trt + trt:X1 + trt:X2\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"parametric-g-computation-with-maximum-likelihood-estimation","dir":"Articles","previous_headings":"Introduction","what":"Parametric G-computation with maximum-likelihood estimation","title":"User-defined target population","text":", let us change outcome scale LRR","code":"outstandR_gcomp_ml <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_ml outstandR_gcomp_ml_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_ml(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_ml_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"bayesian-g-computation-with-mcmc","dir":"Articles","previous_headings":"Introduction","what":"Bayesian G-computation with MCMC","title":"User-defined target population","text":", can change outcome scale LRR.","code":"outstandR_gcomp_bayes <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_gcomp_bayes outstandR_gcomp_bayes_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_gcomp_bayes(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_gcomp_bayes_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/articles/user-defined-target-pop.html","id":"multiple-imputation-marginalisation","dir":"Articles","previous_headings":"Introduction","what":"Multiple imputation marginalisation","title":"User-defined target population","text":"Change outcome scale LRR,","code":"outstandR_mim <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\"))) outstandR_mim outstandR_mim_lrr <-   outstandR(ipd_trial, ald_trial,             strategy = strategy_mim(               formula = lin_form,               family = binomial(link = \"logit\")),             scale = \"log_relative_risk\") outstandR_mim_lrr"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Nathan Green. Author, maintainer, copyright holder. Chengyang Gao. Author. Antonio Remiro-Azocar. Author.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Green N, Gao C, Remiro-Azocar (2026). outstandR: Model-Based Standardisation Indirect Treatment Comparison Limited Subject-Level Data. R package version 2.0.0, https://StatisticsHealthEconomics.github.io/outstandR/.","code":"@Manual{,   title = {outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data},   author = {Nathan Green and Chengyang Gao and Antonio Remiro-Azocar},   year = {2026},   note = {R package version 2.0.0},   url = {https://StatisticsHealthEconomics.github.io/outstandR/}, }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":null,"dir":"","previous_headings":"","what":"outstandR: Outcome Regression Standardisation","title":"outstandR: Outcome Regression Standardisation","text":"outstandR R package population-adjusted indirect treatment comparison (ITC). implements various methods adjust cross-trial differences effect modifiers individual patient data (IPD) available one trial aggregate-level data (ALD) available another.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"core-architecture","dir":"","previous_headings":"","what":"Core Architecture","title":"outstandR: Outcome Regression Standardisation","text":"package follows “Strategy” pattern users define adjustment method using strategy_* functions pass main outstandR() wrapper.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"key-methods","dir":"","previous_headings":"Core Architecture","what":"Key Methods","title":"outstandR: Outcome Regression Standardisation","text":"MAIC (Matching-Adjusted Indirect Comparison): Non-parametric likelihood reweighting. G-computation (ML & Bayesian): Model-based standardisation (STC deprecated favour G-computation). MIM (Multiple Imputation Marginalization): Parametric G-computation using multiple imputation.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"main-entry-points","dir":"","previous_headings":"Core Architecture","what":"Main Entry Points","title":"outstandR: Outcome Regression Standardisation","text":"outstandR(ipd_trial, ald_trial, strategy, ...): primary user-facing function. strategy_maic(formula, ...): Define MAIC strategy. strategy_gcomp_ml(formula, ...): Define Maximum Likelihood G-computation strategy. strategy_gcomp_bayes(formula, ...): Define Bayesian G-computation strategy. strategy_mim(formula, ...): Define Multiple Imputation Marginalization strategy.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"standard-commands","dir":"","previous_headings":"Development Workflows","what":"Standard Commands","title":"outstandR: Outcome Regression Standardisation","text":"Documenting: devtools::document() (updates NAMESPACE man/). Testing: devtools::test() testthat::test_local(). Checking: devtools::check() (standard R package quality check). Building Site: pkgdown::build_site() (updates documentation website docs/).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"project-structure","dir":"","previous_headings":"Development Workflows","what":"Project Structure","title":"outstandR: Outcome Regression Standardisation","text":"outstandR.R: Main wrapper. strategy_.R: Strategy class definitions logic. maic.R, gcomp_ml.R, mim.R: Method-specific implementations. tests/testthat/: Unit tests organized feature/method. vignettes/: Detailed usage examples methodology documentation. man/: Auto-generated documentation (edit manually). data/: Built-datasets examples testing.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"engineering-standards","dir":"","previous_headings":"","what":"Engineering Standards","title":"outstandR: Outcome Regression Standardisation","text":"Consistency: Follow standard R package conventions. Documentation: Use roxygen2 Markdown support (Roxygen: list(markdown = TRUE) DESCRIPTION). Testing: New features bug fixes MUST include testthat tests. S3 Classes: Strategies main output use S3 classes (outstandR, strategy, maic, etc.). User Feedback: Use cli glue informative console output. Dependencies: Prefer dplyr, tidyr, rlang data manipulation tidy evaluation.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"ipd-individual-patient-data","dir":"","previous_headings":"Data Formats","what":"IPD (Individual Patient Data)","title":"outstandR: Outcome Regression Standardisation","text":"data frame long format containing: - treatment column (e.g., trt). - outcome column (e.g., y). - Covariates used adjustment.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/GEMINI.html","id":"ald-aggregate-level-data","dir":"","previous_headings":"Data Formats","what":"ALD (Aggregate-Level Data)","title":"outstandR: Outcome Regression Standardisation","text":"data frame specific columns: - variable: Covariate name. - statistic: “mean”, “sd”, “prop”, “sum”, “N”. - value: Numeric value. - trt: Treatment label (NA common across arms).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"outstandr-outcome-regression-standardisation","dir":"","previous_headings":"","what":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Indirect treatment comparison limited subject-level data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"overview","dir":"","previous_headings":"","what":"Overview","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"outstandR R package designed facilitate unified framework Population-Adjusted Indirect Comparison (PAIC) Health Technology Assessment (HTA). facilitates outcome regression standardisation using model-based approaches head--head clinical trials absent trial populations differ effect modifiers. streamlining workflow covariate simulation, model standardisation, contrast estimation, outstandR enables robust compatible evidence synthesis, particularly scenarios individual patient data (IPD) limited one trials compared.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"who-is-this-package-for","dir":"","previous_headings":"","what":"Who is this package for?","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"target audience outstandR includes statisticians health economists performing indirect treatment comparisons requiring cross-trial population adjustment. simplifies implementation model-based standardization two core steps: Covariate simulation (overcome limited subject-level data aggregate-level data studies). Indirect comparison across studies targeting compatible marginal treatment effects.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Install released version CRAN: install development version GitHub using R-universe: Alternatively, may wish download directly repo ","code":"install.packages(\"outstandR\") install.packages(\"outstandR\",    repos = c(\"https://statisticshealtheconomics.r-universe.dev\",              \"https://cloud.r-project.org\")) remotes::install_github(\"StatisticsHealthEconomics/outstandR\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"background","dir":"","previous_headings":"","what":"Background","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Population adjustment methods increasingly used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. outstandR package allows implementation range methods situation including following: Matching-Adjusted Indirect Comparison (MAIC) based weighting, sensitive poor covariate overlap extrapolate beyond observed covariate space. reweights individual patient-level data (IPD) match aggregate characteristics comparator trial, thereby aligning populations. Parametric G-computation maximum likelihood: method fits outcome model IPD using maximum likelihood estimation, uses model predict outcomes comparator population. allows extrapolation beyond observed covariate space requires correct specification outcome model avoid bias. Parametric G-computation Bayesian inference: Similar maximum likelihood version, approach fits outcome model within Bayesian framework. allows coherent propagation uncertainty prior distributions posterior inference, enabling probabilistic sensitivity analysis full uncertainty quantification. Multiple imputation marginalization method based parametric G-computation: Current outcome regression-based alternatives can extrapolate target conditional treatment effect incompatible indirect comparison. adjusting covariates, one must integrate average conditional estimate relevant population recover compatible marginal treatment effect. can easily applied outcome regression generalized linear model Cox model. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. method can accommodate Bayesian statistical framework, naturally integrates analysis probabilistic framework. Simulated Treatment Comparison (STC) [DEPRECATED]: previously common, standard STC can produce biased marginal estimates due aggregation bias non-collapsibility using non-linear link functions. Note: STC formally deprecated v2.0.0 favour robust G-computation approaches.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"general-problem","dir":"","previous_headings":"","what":"General problem","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"Consider one trial, company IPD, comparing treatments C, herein call AC trial. Also, consider second trial comparing treatments B C, similarly called BC trial. trial published aggregate data available. wish estimate comparison effects treatments B appropriate scale target population P, denoted parameter dAB(P)d_{AB(P)}. make use bracketed subscripts denote specific population. Within BC population parameters μB(BC)\\mu_{B(BC)} μC(BC)\\mu_{C(BC)} representing expected outcome treatment (including parameters treatments studied BC trial, e.g. treatment ). BC trial provides estimators Y‾B(BC)\\bar Y_{B(BC)} Y‾C(BC)\\bar Y_{C(BC)} μB(BC)\\mu_{B(BC)}, μC(BC)\\mu_{C(BC)}, respectively, summary outcomes. situation AC trial. suitable scale, example log-odds ratio, risk difference, form estimators Δ̂BC(BC)\\hat{\\Delta}{BC(BC)} Δ̂AC(AC)\\hat{\\Delta}_{AC(AC)} trial level (marginal) relative treatment effects. shall assume always represented difference , example, risk ratio log scale. Δ̂AC(AC)=g(Y‾C(AC))−g(Y‾(AC)) \\hat{\\Delta}_{AC{(AC)}} = g(\\bar{Y}_{C{(AC)}}) - g(\\bar{Y}_{{(AC)}}) similarly Δ̂BC(BC)\\hat{\\Delta}_{BC(BC)}. assume difference effect modifiers trials, estimator relative treatment effect dAB(BC)d_{AB(BC)} Δ̂AB(BC)=Δ̂BC(BC)−Δ̂AC(BC). \\hat{\\Delta}_{AB(BC)} = \\hat{\\Delta}_{BC(BC)} - \\hat{\\Delta}_{AC(BC)}. However, distributions effect modifiers different trial populations, relative treatment effect estimated trial simply combined . purpose population-adjustment ITC include estimate Δ̂AC(BC)\\hat{\\Delta}_{AC(BC)}.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"references","dir":"","previous_headings":"","what":"References","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"R package contains code originally written papers: Remiro-Azócar, ., Heath, . & Baio, G. (2022) Parametric G-computation Compatible Indirect Treatment Comparisons Limited Individual Patient Data. Res Synth Methods;1–31. Remiro-Azócar, ., Heath, ., & Baio, G. (2023) Model-based standardization using multiple imputation. BMC Medical Research Methodology, 1–15. https://doi.org/10.1186/s12874-024-02157-x","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/index.html","id":"contributing","dir":"","previous_headings":"","what":"Contributing","title":"Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data","text":"welcome contributions! Please submit contributions Pull Requests, following contributing guidelines. report issues /seek support, please file new ticket issue tracker. Please note project released Contributor Code Conduct. participating project agree abide terms. [!NOTE] package licensed GPLv3. information, see LICENSE.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"GNU General Public License","title":"GNU General Public License","text":"Version 3, 29 June 2007Copyright © 2007 Free Software Foundation, Inc. <http://fsf.org/> Everyone permitted copy distribute verbatim copies license document, changing allowed.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/LICENSE.html","id":"preamble","dir":"","previous_headings":"","what":"Preamble","title":"GNU General Public License","text":"GNU General Public License free, copyleft license software kinds works. licenses software practical works designed take away freedom share change works. contrast, GNU General Public License intended guarantee freedom share change versions program–make sure remains free software users. , Free Software Foundation, use GNU General Public License software; applies also work released way authors. can apply programs, . speak free software, referring freedom, price. 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Interpretation of Sections 15 and 16","title":"GNU General Public License","text":"disclaimer warranty limitation liability provided given local legal effect according terms, reviewing courts shall apply local law closely approximates absolute waiver civil liability connection Program, unless warranty assumption liability accompanies copy Program return fee. END TERMS CONDITIONS","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/LICENSE.html","id":"how-to-apply-these-terms-to-your-new-programs","dir":"","previous_headings":"","what":"How to Apply These Terms to Your New Programs","title":"GNU General Public License","text":"develop new program, want greatest possible use public, best way achieve make free software everyone can redistribute change terms. , attach following notices program. safest attach start source file effectively state exclusion warranty; file least “copyright” line pointer full notice found. Also add information contact electronic paper mail. program terminal interaction, make output short notice like starts interactive mode: hypothetical commands show w show c show appropriate parts General Public License. course, program’s commands might different; GUI interface, use “box”. also get employer (work programmer) school, , sign “copyright disclaimer” program, necessary. information , apply follow GNU GPL, see <http://www.gnu.org/licenses/>. GNU General Public License permit incorporating program proprietary programs. program subroutine library, may consider useful permit linking proprietary applications library. want , use GNU Lesser General Public License instead License. first, please read <http://www.gnu.org/philosophy/--lgpl.html>.","code":"<one line to give the program's name and a brief idea of what it does.> Copyright (C) <year>  <name of author>  This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.  This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.  You should have received a copy of the GNU General Public License along with this program.  If not, see <http://www.gnu.org/licenses/>. <program>  Copyright (C) <year>  <name of author> This program comes with ABSOLUTELY NO WARRANTY; for details type 'show w'. This is free software, and you are welcome to redistribute it under certain conditions; type 'show c' for details."},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set for individual level patient data — AC_IPD","title":"Data set for individual level patient data — AC_IPD","text":"data set contains simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set for individual level patient data — AC_IPD","text":"data list including variables needed outstandR basic example. variables follows: X1 Numeric covariate X2 Numeric covariate X3 Numeric covariate X4 Numeric covariate trt Integer treatment identifier y Integer binary outcome","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Data set for individual level patient data — AC_IPD","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Data set for individual level patient data — AC_IPD","text":"Remiro‐Azócar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"data set contains simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"","code":"data(AC_IPD_binY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"id Numeric unique identifier PF_cont_1 Numeric prognostic factor continuous covariate PF_cont_2 Numeric prognostic factor continuous covariate EM_cont_1 Numeric effect modifier continuous covariate EM_cont_2 Numeric effect modifier continuous covariate trt Factor treatment identifier. Levels , C y Integer binary outcome true_eta Numeric linear predictor","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_binY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Individual-level patient data for binary outcome, continuous covariates — AC_IPD_binY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":null,"dir":"Reference","previous_headings":"","what":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"data set contains simulated patient covariate outcome values. Corresponds ALD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"","code":"data(AC_IPD_contY_mixedX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"y-x-x-x-trt-trt-x-x-x-","dir":"Reference","previous_headings":"","what":"y ~ X1 + X3 + X4 + trt + trt:(X2 + X3 + X4)","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"id Numeric unique identifier X1 Numeric prognostic factor continuous covariate X2 Numeric prognostic factor effect modifier binary covariate X3 Numeric prognostic factor effect modifier continuous covariate X4 Numeric effect modifier binary covariate trt Factor treatment identifier. Levels , C y Integer binary outcome true_eta Numeric linear predictor","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_contY_mixedX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Individual-level patient data for continuous outcome, mixed covariates — AC_IPD_contY_mixedX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"data set contains simulated patient covariate outcome values. Corresponds ALD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"","code":"data(AC_IPD_countY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"id Numeric unique identifier PF_cont_1 Numeric prognostic factor continuous covariate PF_cont_2 Numeric prognostic factor continuous covariate EM_cont_1 Numeric effect modifier continuous covariate EM_cont_2 Numeric effect modifier continuous covariate trt Factor treatment identifier. Levels , C y Integer non-negative count outcome true_eta Numeric linear predictor","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/AC_IPD_countY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Individual-level patient data for count outcome, continuous covariates — AC_IPD_countY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate-level data mean and variance statistics — ALD_stats","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"Computes mean variance marginal treatment effects aggregate-level trial data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"","code":"ALD_stats(strategy, ald, treatments = list(\"B\", \"C\"), scale)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"strategy list containing strategy details, including family distribution. ald Aggregate-level trial data treatments Treatment labels list; default B, C (common; e.g. placebo) scale scaling parameter calculation.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"list containing: mean marginal treatment effect mean. var marginal treatment effect variance.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ALD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate-level data mean and variance statistics — ALD_stats","text":"","code":"if (FALSE) { # \\dontrun{ strategy <- list(family = list(family = \"binomial\"))  # basic version ald <- data.frame(trial = 1:5, n_B = c(10, 20, 15, 30, 25), n_C = c(12, 18, 20, 25, 22)) ALD_stats(strategy, ald, treatments = list(\"B\", \"C\"), scale = \"log\") } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set for aggregate level patient data in wide format — BC_ALD","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"data set contains summaries simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"data list including variables needed outstandR basic example. variables follows: mean.X1 Numeric value mean.X2 Numeric value mean.X3 Numeric value mean.X4 Numeric value sd.X1 Numeric standard deviation value sd.X2 Numeric standard deviation value sd.X3 Numeric standard deviation value sd.X4 Numeric standard deviation value y.B.sum Integer number patients event B treatment y.B.bar Numeric proportion patients B treatment N.B Integer Total number patients B treatment y.C.sum Integer number patients event C treatment y.C.bar Numeric proportion patients C treatment N.C Integer total number patients C treatment","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Data set for aggregate level patient data in wide format — BC_ALD","text":"Remiro‐Azócar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"data set contains summaries simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"","code":"data(BC_ALD_binY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"variable String covariate outcome name. EM_cont_1, EM_cont_2, PF_cont_1, PF_cont_2, y. statistic String summary statistic name. mean, sd, sum, N value Numeric value trt Treatment (arm) name. B, C","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_binY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Aggregate level patient data for binary outcome, continuous covariates — BC_ALD_binY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"data set contains summaries simulated patient covariate outcome values. Corresponds IPD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"","code":"data(BC_ALD_contY_mixedX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"y-x-x-x-trt-trt-x-x-x-","dir":"Reference","previous_headings":"","what":"y ~ X1 + X3 + X4 + trt + trt:(X2 + X3 + X4)","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"variable String covariate outcome name. X1, X2, X3, X4, y. statistic String summary statistic name. mean, sd, prob, sum, N value Numeric value trt Treatment (arm) name. B, C","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_contY_mixedX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Aggregate level patient data for continuous outcome, mixed covariates — BC_ALD_contY_mixedX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"data set contains summaries simulated patient covariate outcome values. Corresponds IPD data set.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"","code":"data(BC_ALD_countY_contX)"},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"y-pf-cont-pf-cont-trt-trt-em-cont-em-cont-","dir":"Reference","previous_headings":"","what":"y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"variable String covariate outcome name. EM_cont_1, EM_cont_2, PF_cont_1, PF_cont_2, y. statistic String summary statistic name. mean, sd, sum, N value Numeric value trt Treatment (arm) name. B, C","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_countY_contX.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Aggregate level patient data for count outcome, continuous covariates — BC_ALD_countY_contX","text":"Remiro‐Azocar , Heath , Baio G (2022)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_long.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set for aggregate level patient data in long format — BC_ALD_long","title":"Data set for aggregate level patient data in long format — BC_ALD_long","text":"data set contains summaries simulated patient covariate outcome values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_long.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set for aggregate level patient data in long format — BC_ALD_long","text":"data frame 4 variables: statistic character string trt factor value numeric value variable character string","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/BC_ALD_long.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Data set for aggregate level patient data in long format — BC_ALD_long","text":"Simulated data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.html","id":null,"dir":"Reference","previous_headings":"","what":"Bias estimate — bias","title":"Bias estimate — bias","text":"Bias estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bias estimate — bias","text":"","code":"bias(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bias estimate — bias","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of bias estimate — bias.mcse","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"Monte Carlo SE bias estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"","code":"bias.mcse(theta.hat)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"theta.hat theta hat","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/bias.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of bias estimate — bias.mcse","text":"\\(sqrt(1/(nsim*(nsim-1))*tmp)\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Average Treatment Effect — calculate_ate","title":"Calculate Average Treatment Effect — calculate_ate","text":"Computes average treatment effect (ATE) based specified effect scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Average Treatment Effect — calculate_ate","text":"","code":"calculate_ate(mean_comp, mean_ref, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Average Treatment Effect — calculate_ate","text":"mean_comp, mean_ref Mean outcome comparator reference / common effect character string specifying effect scale. Options : \"log_odds\" Log-odds difference. \"risk_difference\" Risk difference. \"delta_z\" Probit scale difference (z-scores). \"log_relative_risk_rare_events\" Log relative risk rare events. \"log_relative_risk\" Log relative risk.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Average Treatment Effect — calculate_ate","text":"Numeric computed average treatment effect specified scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_ate.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate Average Treatment Effect — calculate_ate","text":"","code":"calculate_ate(mean_comp = 0.7, mean_ref = 0.5, effect = \"log_odds\") #> [1] 0.8472979 calculate_ate(mean_comp = 0.7, mean_ref = 0.5, effect = \"risk_difference\") #> [1] 0.2"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Wrapper — calculate_trial_mean","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"Calculate Trial Mean Wrapper","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"","code":"calculate_trial_mean(ald, tid, effect, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. family Family distribution","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Wrapper — calculate_trial_mean","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"Calculate Trial Mean Binary Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"","code":"calculate_trial_mean_binary(ald, tid, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_binary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Binary Data — calculate_trial_mean_binary","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"Calculate Trial Mean Continuous Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"","code":"calculate_trial_mean_continuous(ald, tid, effect, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_continuous.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Continuous Data — calculate_trial_mean_continuous","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Trial Mean Count Data — calculate_trial_mean_count","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"Calculate Trial Mean Count Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"","code":"calculate_trial_mean_count(ald, tid, effect, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_mean_count.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Trial Mean Count Data — calculate_trial_mean_count","text":"Numeric mean value.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance — calculate_trial_variance","title":"Calculate trial variance — calculate_trial_variance","text":"Computes variance treatment effects trial based specified family distribution.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance — calculate_trial_variance","text":"","code":"calculate_trial_variance(ald, tid, effect, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance — calculate_trial_variance","text":"ald Aggregate-level data. Data frame. tid Treatment identifier used extract relevant columns ald. effect character string specifying effect scale (e.g., \"log_odds\", \"risk_difference\"). family character string specifying model family (e.g., \"binomial\", \"gaussian\").","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance — calculate_trial_variance","text":"Numeric computed variance treatment effects.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate trial variance — calculate_trial_variance","text":"","code":"ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))                    calculate_trial_variance(   ald, tid = \"B\", effect = \"log_odds\", family = \"binomial\") #> [1] 0.04"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance binary — calculate_trial_variance_binary","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"Calculate trial variance binary","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"","code":"calculate_trial_variance_binary(ald, tid, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"ald Aggregate level data tid Treatment ID effect Effect","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_binary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance binary — calculate_trial_variance_binary","text":"Numeric value total variance.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance continuous — calculate_trial_variance_continuous","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"Calculate trial variance continuous","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"","code":"calculate_trial_variance_continuous(ald, tid, effect, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"ald Aggregate level data. Data frame long format. tid Treatment ID effect Effect name. String. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance continuous — calculate_trial_variance_continuous","text":"Numeric value total variance.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate trial variance count — calculate_trial_variance_count","title":"Calculate trial variance count — calculate_trial_variance_count","text":"Calculate trial variance count","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate trial variance count — calculate_trial_variance_count","text":"","code":"calculate_trial_variance_count(ald, tid, effect)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate trial variance count — calculate_trial_variance_count","text":"ald Aggregate level data. Data frame long format. tid Treatment ID. effect Effect name. String.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate trial variance count — calculate_trial_variance_count","text":"Numeric value total variance.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate-level data mean and variance statistics — calc_ALD_stats","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"Computes mean variance marginal treatment effects aggregate-level trial data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"","code":"calc_ALD_stats(strategy, analysis_params)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"strategy list containing strategy details, including family distribution. analysis_params list containing: ald Aggregate-level trial data ref_trt Treatment labels reference (common; e.g. placebo) ald_comp Treatment labels comparator scale scaling parameter calculation. \"log_odds\", \"risk_difference\", \"log_relative_risk\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"list containing: mean marginal treatment effect mean. var marginal treatment effect variance.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate-level data mean and variance statistics — calc_ALD_stats","text":"","code":"strategy <- list(family = list(family = \"binomial\"))  # basic version  ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))  calc_ALD_stats(strategy = strategy,                list(ald = ald,                     ref_trt = \"C\",                     ald_comp = \"B\",                     scale = \"log_odds\")) #> $mean #> [1] -0.4054651 #>  #> $var #> [1] 0.08166667 #>"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate Naive (Unadjusted) Bucher Indirect Comparison — calc_bucher_naive","title":"Calculate Naive (Unadjusted) Bucher Indirect Comparison — calc_bucher_naive","text":"Calculates unadjusted indirect comparison two active treatments via common comparator using standard Bucher method. Estimates calculated link scale (e.g., log-odds) back-transformed requested scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate Naive (Unadjusted) Bucher Indirect Comparison — calc_bucher_naive","text":"","code":"calc_bucher_naive(   ipd_trial,   ald_trial,   outcome_model,   family,   ref_trt = \"C\",   scale = NULL )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate Naive (Unadjusted) Bucher Indirect Comparison — calc_bucher_naive","text":"ipd_trial Data frame containing Individual Patient Data. ald_trial Data frame containing Aggregate Level Data. outcome_model Formula specifying outcome model (used identify variables). family family object (e.g., binomial(link=\"logit\")). ref_trt Character string identifying common comparator treatment. scale Character string specifying desired output scale (e.g., \"risk_difference\").","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate Naive (Unadjusted) Bucher Indirect Comparison — calc_bucher_naive","text":"list containing naive point estimate, variance, standard error.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":null,"dir":"Reference","previous_headings":"","what":"Bayesian G-computation using Stan — calc_gcomp_bayes","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"Calculate draws binary responses posterior predictive distribution Bayesian G-computation method using Hamiltonian Monte Carlo.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"","code":"calc_gcomp_bayes(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"strategy list specifying model strategy, including: outcome_model: linear regression formula object. family: family object specifying distribution link function (e.g., binomial). iter: Number iterations MCMC sampling. warmup: Number warmup iterations MCMC sampling. chains: Number MCMC chains. analysis_params List analysis parameters. Must contain ipd ald. ... Additional arguments passed rstanarm::stan_glm().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"list containing: means: list containing: Posterior means comparator treatment group. Posterior means reference treatment group. model: list containing fit object (stan_glm), rho, N, stan_args.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bayesian G-computation using Stan — calc_gcomp_bayes","text":"","code":"strategy <- list(   outcome_model = y ~ trt:X1,   family = binomial(),   rho = NA,   N = 1000L,   marginal_distns = NA,   marginal_params = NA,   trt_var = \"trt\",   iter = 2000,   warmup = 500,   chains = 4)  ipd <- data.frame(    trt = sample(c(\"A\", \"C\"), size = 100, replace = TRUE),    X1 = rnorm(100, 1, 1),    y = sample(c(1,0), size = 100, prob = c(0.7, 0.3), replace = TRUE))  ald <- data.frame(   trt = c(NA, NA, \"B\", \"C\", \"B\", \"C\"),   variable = c(\"X1\", \"X1\", \"y\", \"y\", NA, NA),   statistic = c(\"mean\", \"sd\", \"sum\", \"sum\", \"N\", \"N\"),   value = c(0.5, 0.1, 10, 12, 20, 25))  res <-    calc_gcomp_bayes(     strategy,     analysis_params = list(       ipd = ipd, ald = ald,        ref_trt = \"C\",       ipd_comp = \"A\"))  str(res, max.level = 2, list.len = 3, vec.len = 2) #> List of 3 #>  $ means          :List of 2 #>   ..$ A: num [1:2000] 0.626 0.69 ... #>   ..$ C: num [1:2000] 0.61 0.667 ... #>  $ point_estimates:List of 2 #>   ..$ A: num 0.603 #>   ..$ C: num 0.586 #>  $ model          :List of 4 #>   ..$ fit      :List of 28 #>   .. ..- attr(*, \"class\")= chr [1:3] \"stanreg\" \"glm\" ... #>   ..$ rho      : logi NA #>   ..$ N        : int 1000 #>   .. [list output truncated]"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"Computes mean difference treatment effects using bootstrap resampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"","code":"calc_gcomp_ml(strategy, analysis_params)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"strategy list specifying model strategy, including: R: Number bootstrap replications. outcome_model: linear regression formula object outcome model. family: family object specifying distribution link function (e.g., binomial). N: Synthetic sample size g-computation. analysis_params List analysis parameters.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"list containing: means: list containing: : Bootstrap estimates comparator treatment group \"\". C: Bootstrap estimates reference treatment group \"C\". model: list containing fit object, rho, N.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G-computation Maximum Likelihood Bootstrap — calc_gcomp_ml","text":"","code":"strategy <- list(   outcome_model = y ~ trt:X1,   family = binomial(),   rho = NA,   N = 1000L,   n_boot = 100L,   marginal_distns = NA,   marginal_params = NA,   trt_var = \"trt\")  ipd <- data.frame(trt = sample(c(\"A\", \"C\"), size = 100, replace = TRUE),                   X1 = rnorm(100, 1, 1),                   y = sample(c(1,0), size = 100, prob = c(0.7,0.3), replace = TRUE))  ald <- data.frame(trt = c(NA, NA, \"B\", \"C\", \"B\", \"C\"),                   variable = c(\"X1\", \"X1\", \"y\", \"y\", NA, NA),                   statistic = c(\"mean\", \"sd\", \"sum\", \"sum\", \"N\", \"N\"),                   value = c(0.5, 0.1, 10, 12, 20, 25))  calc_gcomp_ml(   strategy,   analysis_params =      list(ipd = ipd, ald = ald,           ref_trt = \"C\",           ipd_comp = \"A\")) #> $means #> $means$A #>   [1] 0.7524448 0.7208018 0.6857046 0.7773186 0.7379123 0.7953863 0.7416379 #>   [8] 0.7333357 0.6740201 0.7496222 0.7004516 0.7565848 0.7328825 0.7406903 #>  [15] 0.7488645 0.7340921 0.6933722 0.7124750 0.8259316 0.8126080 0.7030263 #>  [22] 0.7026071 0.7626186 0.7341363 0.7593515 0.7545032 0.8159394 0.7371818 #>  [29] 0.7284083 0.6787501 0.6071921 0.7056624 0.7314274 0.6486667 0.7948652 #>  [36] 0.8041567 0.6859274 0.7155094 0.7249215 0.7912577 0.6099682 0.6655606 #>  [43] 0.8584396 0.6814494 0.7191635 0.7445806 0.6603892 0.7538379 0.7519644 #>  [50] 0.7192660 0.7830961 0.8151415 0.6831753 0.7150227 0.8449769 0.7668341 #>  [57] 0.7483105 0.7879836 0.7614439 0.8144559 0.6243036 0.6539474 0.7320960 #>  [64] 0.7168957 0.7408405 0.7626611 0.7756132 0.7237764 0.7889745 0.7579104 #>  [71] 0.7375602 0.7413274 0.6781683 0.6714261 0.7565422 0.8332126 0.6637191 #>  [78] 0.5921426 0.7549736 0.7339375 0.7560676 0.7910103 0.7243667 0.7994549 #>  [85] 0.8220225 0.8462224 0.7428240 0.5864449 0.7003216 0.7453676 0.8061360 #>  [92] 0.8159053 0.6917901 0.6791657 0.7111803 0.7263968 0.7310195 0.7909051 #>  [99] 0.7227581 0.7323826 #>  #> $means$C #>   [1] 0.7309018 0.7420960 0.6819819 0.6978632 0.7191187 0.7537383 0.7023496 #>   [8] 0.7228270 0.6564365 0.7003893 0.6392001 0.6893771 0.6915394 0.7598735 #>  [15] 0.6611513 0.7114534 0.6330323 0.6893841 0.8136764 0.8007598 0.7033007 #>  [22] 0.7148683 0.7531519 0.7223997 0.7248275 0.7375199 0.7290035 0.7066567 #>  [29] 0.7381150 0.7441146 0.5489844 0.6454383 0.7261025 0.6269568 0.7808563 #>  [36] 0.7845551 0.6790214 0.7108215 0.7857677 0.7722908 0.5920379 0.6711567 #>  [43] 0.7735766 0.7082050 0.7105959 0.6968303 0.6837809 0.7379012 0.7804497 #>  [50] 0.7257683 0.7395591 0.7641128 0.5839501 0.7344368 0.7883609 0.7415819 #>  [57] 0.7914461 0.7409043 0.7648980 0.7197088 0.6058059 0.6712301 0.7169338 #>  [64] 0.6840646 0.7066697 0.6927932 0.7584608 0.7285138 0.7396870 0.7564756 #>  [71] 0.7302828 0.6995002 0.6820383 0.6638061 0.7293550 0.8527352 0.6752132 #>  [78] 0.6727563 0.7111311 0.6847701 0.7357006 0.7539906 0.7102805 0.7856127 #>  [85] 0.8156423 0.8199455 0.7346005 0.6136072 0.7113708 0.7010819 0.7942727 #>  [92] 0.7816347 0.6858805 0.6637144 0.7716140 0.7212641 0.7290398 0.7679028 #>  [99] 0.6818292 0.7198914 #>  #>  #> $point_estimates #> $point_estimates$A #>         1  #> 0.7321823  #>  #> $point_estimates$C #>         0  #> 0.7163028  #>  #>  #> $model #> $model$fit #>  #> Call:  glm(formula = outcome_model, family = family, data = ipd) #>  #> Coefficients: #> (Intercept)      trtA:X1      trtC:X1   #>     0.93459      0.14321     -0.01688   #>  #> Degrees of Freedom: 99 Total (i.e. Null);  97 Residual #> Null Deviance:\t    116.7  #> Residual Deviance: 116.3 \tAIC: 122.3 #>  #> $model$rho #> [1] NA #>  #> $model$N #> [1] 1000 #>  #> $model$n_boot #> [1] 100 #>  #>"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation using Stan — calc_gcomp_bayes","title":"G-computation using Stan — calc_gcomp_bayes","text":"Calculate draws binary responses posterior predictive distribution Bayesian G-computation method using Hamiltonian Monte Carlo.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation using Stan — calc_gcomp_bayes","text":"","code":"calc_gcomp_bayes(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation using Stan — calc_gcomp_bayes","text":"strategy list specifying model strategy, including: formula linear regression formula object. family family object specifying distribution link function (e.g., binomial). iter Number iterations MCMC sampling. warmup Number warmup iterations MCMC sampling. chains Number MCMC chains. ipd Individual-level patient data. Dataframe one row per patient outcome, treatment covariate columns. ald Aggregate-level data. Single row matrix summary statistics covariate treatment outcomes. format 'mean.' 'sd.' covariates 'y..sum', 'y..bar', 'y.*.sd' treatments B C. assume common distribution treatment arm.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation using Stan — calc_gcomp_bayes","text":"list \\(y^*_A\\) \\(y^*_C\\) posterior predictions: `0` Posterior means reference treatment group \"C\". `1` Posterior means comparator treatment group \"\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G-computation using Stan — calc_gcomp_bayes","text":"","code":"if (FALSE) { # \\dontrun{ strategy <- list(   formula = y ~ trt + age,   family = binomial(),   iter = 2000,   warmup = 500,   chains = 4 ) ipd <- data.frame(trt = c(\"A\", \"C\"),                   y = c(1, 0),                   age = c(30, 40)) ald <- data.frame() calc_gcomp_bayes(strategy, ipd, ald) } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate individual-level patient data statistics — calc_IPD_stats","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Computes mean variance statistics individual-level patient data using various approaches, including Matching-Adjusted Indirect Comparison (MAIC), Simulated Treatment Comparison (STC), G-computation via Maximum Likelihood Estimation (MLE) Bayesian inference.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"","code":"calc_IPD_stats(strategy, analysis_params, ...)  # Default S3 method calc_IPD_stats(...)  # S3 method for class 'stc' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'maic' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'gcomp_ml' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'gcomp_bayes' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)  # S3 method for class 'mim' calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"strategy list corresponding different modelling approaches analysis_params list containing: ipd: Individual-level patient data (data frame) ald: Aggregate-level trial data (data frame) ref_trt: Treatment label reference arm (common; e.g., \"C\") ipd_comp: Treatment label comparator arm IPD (e.g., \"\") scale: Scaling parameter (\"log_odds\", \"risk_difference\", \"log_relative_risk\") ... Additional arguments var_method string specifying variance estimation method, either \"sample\" (default) \"sandwich\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"list containing: contrasts: list elements mean var. absolute: list elements mean var.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"simulated-treatment-comparison-statistics","dir":"Reference","previous_headings":"","what":"Simulated treatment comparison statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"IPD reference \"C\" comparator \"\" trial arms used fit regression model describing observed outcomes \\(y\\) terms relevant baseline characteristics \\(x\\) treatment variable \\(z\\).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"matching-adjusted-indirect-comparison-statistics","dir":"Reference","previous_headings":"","what":"Matching-adjusted indirect comparison statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Marginal IPD comparator treatment \"\" vs reference treatment \"C\" treatment effect estimates using bootstrapping sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"g-computation-maximum-likelihood-statistics","dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Compute non-parametric bootstrap default \\(R=1000\\) resamples.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"g-computation-bayesian-statistics","dir":"Reference","previous_headings":"","what":"G-computation Bayesian statistics","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Using Stan, compute marginal relative effects IPD comparator \"\" vs reference \"C\" treatment arms MCMC sample transforming probability linear predictor scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"multiple-imputation-marginalisation","dir":"Reference","previous_headings":"","what":"Multiple imputation marginalisation","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"Using Stan, compute marginal relative treatment effect IPD comparator \"\" vs reference \"C\" arms MCMC sample transforming probability linear predictor scale. Approximate using imputation combining estimates using pooling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_IPD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate individual-level patient data statistics — calc_IPD_stats","text":"","code":"strategy <- strategy_maic(   formula = list(outcome_model = y ~ trt,  # default                   balance_model = ~ X1),   family = binomial()) #> Treatment is guessed as: trt  ipd <- data.frame(trt = sample(c(\"A\", \"C\"), size = 100, replace = TRUE),                   X1 = rnorm(100, 1, 1),                   y = sample(c(1,0), size = 100, prob = c(0.7,0.3), replace = TRUE))  ald <- data.frame(trt = c(NA, \"B\", \"C\", \"B\", \"C\"),                   variable = c(\"X1\", \"y\", \"y\", NA, NA),                   statistic = c(\"mean\", \"sum\", \"sum\", \"N\", \"N\"),                   value = c(0.5, 10, 12, 20, 25))  calc_IPD_stats(strategy,   analysis_params = list(ipd = ipd, ald = ald, scale = \"log_odds\")) #> $contrasts #> $contrasts$mean #> [1] 0.0404359 #>  #> $contrasts$var #> [1] 0.2441335 #>  #>  #> $absolute #> $absolute$mean #>         A         C  #> 0.5667870 0.5562863  #>  #> $absolute$var #>           A           C  #> 0.006112309 0.007795801  #>  #>  #> $method_name #> [1] \"MAIC\" #>  #> $model #> $model$weights #>   weights1   weights2   weights3   weights4   weights5   weights6   weights7  #>  0.5097557  0.9862214  0.1767722  1.0189126  0.4083001  0.3004525  0.5227465  #>   weights8   weights9  weights10  weights11  weights12  weights13  weights14  #>  0.2650783  0.5314778  0.8255845  0.4200238  1.9246909  1.6187657  0.4651878  #>  weights15  weights16  weights17  weights18  weights19  weights20  weights21  #>  0.4238390  0.4253863  2.4215912  2.1405183  2.2258621  1.3013718  1.3575855  #>  weights22  weights23  weights24  weights25  weights26  weights27  weights28  #>  0.2828358  1.1742708  1.9678484  0.4041438  0.4765942  1.0933591  0.3810760  #>  weights29  weights30  weights31  weights32  weights33  weights34  weights35  #>  0.5973394  1.4076416  0.8244193  0.3731263  0.7741472  0.9083386  0.1294497  #>  weights36  weights37  weights38  weights39  weights40  weights41  weights42  #>  0.5622625  0.5166102  1.6685593  0.2084445  0.4586885  0.9201768  0.3863122  #>  weights43  weights44  weights45  weights46  weights47  weights48  weights49  #>  0.5076362  0.5611625  0.4537915  0.3643097  0.3339151  0.3729876  1.1400251  #>  weights50  weights51  weights52  weights53  weights54  weights55  weights56  #>  0.8037654  0.7215501  1.6619502  0.1326304  0.6915303  1.1697328  1.9035924  #>  weights57  weights58  weights59  weights60  weights61  weights62  weights63  #>  1.1017251  0.3539011  1.4816379  0.5736033  1.3541201  0.7266439  1.5106265  #>  weights64  weights65  weights66  weights67  weights68  weights69  weights70  #>  0.4651451  0.3815356  0.9272789  0.6387655  0.2490713  0.4498635  0.8699813  #>  weights71  weights72  weights73  weights74  weights75  weights76  weights77  #>  0.4311347  0.6371576  0.5781595  1.2766576  0.8184790  1.6135860  1.6471549  #>  weights78  weights79  weights80  weights81  weights82  weights83  weights84  #>  0.8892978  0.2861711  0.8390482  1.1599676  0.7896686  0.6933948  1.1559473  #>  weights85  weights86  weights87  weights88  weights89  weights90  weights91  #>  0.8915050  1.0140840  1.2954799  0.6523693  0.4526894  0.7622167  1.0480156  #>  weights92  weights93  weights94  weights95  weights96  weights97  weights98  #>  0.5038243  0.1916380  0.1984988  0.1956611  2.0358831  1.1200094  0.5659745  #>  weights99 weights100  #>  0.6973233  0.8650603  #>  #> $model$ESS #>      ESS  #> 71.57563  #>  #>"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate MAIC — calc_maic","title":"Calculate MAIC — calc_maic","text":"Calculate MAIC","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate MAIC — calc_maic","text":"","code":"calc_maic(strategy, analysis_params)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate MAIC — calc_maic","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters. Must contain ipd (individual patient data) ald (aggregated lead data).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_maic.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate MAIC — calc_maic","text":"list containing: means: list containing: : Bootstrap estimates comparator treatment group \"\". C: Bootstrap estimates reference treatment group \"C\". model: list containing model diagnostics derived original data: weights: Vector calculated weights patients ipd. ESS: Effective Sample Size.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiple imputation marginalization (MIM) — calc_mim","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"Multiple imputation marginalization (MIM)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"","code":"calc_mim(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters. Must contain ipd ald. ... Additional argument pass Stan model","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_mim.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Multiple imputation marginalization (MIM) — calc_mim","text":"list containing: means: list containing named vectors posterior means (one per synthesis n_imp): Comparator means. Reference means. model: list containing: fit: first-stage rstanarm::stan_glm() object. hats.v: Vector variance point estimates synthesis. n_imp: Number posterior prediction draws (syntheses). rho, N, stan_args: Strategy model parameters.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate simulated treatment comparison statistics — calc_stc","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"Calculate simulated treatment comparison statistics","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"","code":"calc_stc(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters. Must contain ipd (individual patient data). ... Additional arguments.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_stc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate simulated treatment comparison statistics — calc_stc","text":"list containing: means: list containing: : Mean comparator treatment group \"\". C: Mean reference treatment group \"C\". model: fitted stats::glm() object.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":null,"dir":"Reference","previous_headings":"","what":"Check balance formula — check_balance_formula","title":"Check balance formula — check_balance_formula","text":"Check balance formula","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check balance formula — check_balance_formula","text":"","code":"check_balance_formula(formula, trt_var = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check balance formula — check_balance_formula","text":"formula Formula balance model trt_var Treatment variable (used warn mistakenly included)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_balance_formula.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check balance formula — check_balance_formula","text":"return value, called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":null,"dir":"Reference","previous_headings":"","what":"Check outcome formula — check_formula","title":"Check outcome formula — check_formula","text":"Check outcome formula","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check outcome formula — check_formula","text":"","code":"check_formula(formula, trt_var = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check outcome formula — check_formula","text":"formula Formula outcome model trt_var Treatment variable","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check outcome formula — check_formula","text":"return value, called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula_base.html","id":null,"dir":"Reference","previous_headings":"","what":"Base formula validator — check_formula_base","title":"Base formula validator — check_formula_base","text":"Base formula validator","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/check_formula_base.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Base formula validator — check_formula_base","text":"","code":"check_formula_base(   formula,   trt_var = NULL,   must_have_response = TRUE,   must_have_trt = TRUE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":null,"dir":"Reference","previous_headings":"","what":"Continuity Correction — continuity_correction","title":"Continuity Correction — continuity_correction","text":"Continuity Correction","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Continuity Correction — continuity_correction","text":"","code":"continuity_correction(ald, correction = 0.5, verbatim = FALSE)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Continuity Correction — continuity_correction","text":"ald Aggregate level data. Data frame long format. correction Continuity correction numeric size. Default 0.5. verbatim Print messages, logical","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/continuity_correction.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Continuity Correction — continuity_correction","text":"Corrected aggregate level data frame.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute covariance matrix — cor2cov","title":"Compute covariance matrix — cor2cov","text":"Compute covariance matrix","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute covariance matrix — cor2cov","text":"","code":"cor2cov(cormat, S)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute covariance matrix — cor2cov","text":"cormat correlation matrix S vector standard deviations covariance matrix","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/cor2cov.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute covariance matrix — cor2cov","text":"Required input mvrnorm.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":null,"dir":"Reference","previous_headings":"","what":"Coverage estimate — coverage","title":"Coverage estimate — coverage","text":"Coverage estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Coverage estimate — coverage","text":"","code":"coverage(low, upp, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Coverage estimate — coverage","text":"low Low upp Upper theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Coverage estimate — coverage","text":"\\(sum(in_range)/nsim\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of coverage estimate — coverage.mcse","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"Monte Carlo SE coverage estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"","code":"coverage.mcse(coverage, nsim)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"coverage Coverage nsim Number simulations","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/coverage.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of coverage estimate — coverage.mcse","text":"\\(sqrt((coverage*(1 - coverage))/nsim)\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":null,"dir":"Reference","previous_headings":"","what":"Empirical standard error — empse","title":"Empirical standard error — empse","text":"Empirical standard error","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Empirical standard error — empse","text":"","code":"empse(theta.hat)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Empirical standard error — empse","text":"theta.hat Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Empirical standard error — empse","text":"\\(sqrt(tmp/(nsim-1))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"EmpSE MCSE — empse.mcse","title":"EmpSE MCSE — empse.mcse","text":"EmpSE MCSE","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"EmpSE MCSE — empse.mcse","text":"","code":"empse.mcse(empse, nsim)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"EmpSE MCSE — empse.mcse","text":"empse EMPSE nsim Number simulations","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/empse.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"EmpSE MCSE — empse.mcse","text":"\\(empse/(sqrt(2*(nsim-1)))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"Computes robust (sandwich) variance estimator treatment effect.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"","code":"estimate_var_sandwich(strategy, analysis_params, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. analysis_params List analysis parameters (ipd, ald, etc.) ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/estimate_var_sandwich.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate Variance Sandwich Estimator — estimate_var_sandwich","text":"Numeric variance estimate treatment contrast","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/find_conversion_path.html","id":null,"dir":"Reference","previous_headings":"","what":"recursive function to find conversion path — find_conversion_path","title":"recursive function to find conversion path — find_conversion_path","text":"recursive function find conversion path","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/find_conversion_path.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"recursive function to find conversion path — find_conversion_path","text":"","code":"find_conversion_path(from, to, visited = c())"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/find_conversion_path.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"recursive function to find conversion path — find_conversion_path","text":"","code":"find_conversion_path(\"log_odds\", \"relative_risk\") #> Error in find_conversion_path(\"log_odds\", \"relative_risk\"): could not find function \"find_conversion_path\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"use bootstrapping function (e.g., boot::boot()). bootstrap sample data, calculates relative treatment effect (e.g., log odds ratio, log relative risk, risk difference) using G-computation maximum likelihood.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"","code":"gcomp_ml.boot(   data,   indices,   R,   outcome_model = NULL,   family,   trt_var,   ref_trt = NA,   comp_trt = NA,   rho = NA,   N = 1000,   marginal_distns = NA,   marginal_params = NA,   ald )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"data data frame containing original individual participant data (IPD). indices vector indices supplied bootstrapping function, used resample data. family 'family' object specifying distribution link function (e.g., 'binomial'). See stats::family() details. rho named square matrix specifying correlation covariates synthetic data generation. Defaults NA, assuming independence. N Synthetic sample size G-computation marginal_distns, marginal_params Marginal distributions parameters ald data frame aggregate-level data providing covariate distributions.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml.boot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bootstrap for G-computation via Maximum Likelihood — gcomp_ml.boot","text":"single numeric value representing relative treatment effect","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"Marginal vs C log-odds ratio (mean difference expected log-odds) estimated transforming probability linear predictor scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"","code":"gcomp_ml_log_odds_ratio(formula, ipd, ald)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"formula Linear regression formula object ipd Individual-level data ald Aggregate-level data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"Difference log-odds","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_log_odds_ratio.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"G-computation Maximum Likelihood Log-Odds Ratio — gcomp_ml_log_odds_ratio","text":"\\(\\log(\\hat{\\mu}_A/(1 - \\hat{\\mu}_A)) - \\log(\\hat{\\mu}_C/(1 - \\hat{\\mu}_C))\\)","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"G-computation maximum likelihood mean outcomes arm","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"","code":"gcomp_ml_means(   outcome_model,   family,   ipd,   ald,   trt_var,   rho = NA,   N = 1000,   ref_trt,   comp_trt,   marginal_distns = NA,   marginal_params = NA )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"family 'family' object specifying distribution link function (e.g., 'binomial'). See stats::family() details. ipd Individual-level patient data. Dataframe one row per patient outcome, treatment covariate columns. ald Aggregate-level data. Long format summary statistics covariate treatment outcomes. assume common distribution treatment arm. rho named square matrix covariate correlations; default NA. N Synthetic sample size g-computation marginal_distns, marginal_params Marginal distributions parameters","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_ml_means.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation maximum likelihood mean outcomes by arm — gcomp_ml_means","text":"list containing: stats: Named vector marginal mean probabilities model: fitted glm object","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":null,"dir":"Reference","previous_headings":"","what":"G-computation using Stan — gcomp_bayes","title":"G-computation using Stan — gcomp_bayes","text":"Calculate draws binary responses posterior predictive distribution Bayesian G-computation method using Hamiltonian Monte Carlo.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G-computation using Stan — gcomp_bayes","text":"","code":"gcomp_bayes(formula = NULL, ipd, ald)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G-computation using Stan — gcomp_bayes","text":"formula Linear regression formula object ipd Individual-level data ald Aggregate-level data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gcomp_stan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G-computation using Stan — gcomp_bayes","text":"list \\(y^*_A\\) \\(y^*_C\\) posterior predictions","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"Generate simulated datasets IPD covariates binary outcome trial","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"","code":"gen_data(   N,   b_trt,   b_X,   b_EM,   b_0,   meanX_EM,   sdX_EM,   meanX,   sdX,   corX,   allocation,   family = binomial(\"logit\") )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"N Total number patients b_trt b coefficient active treatment vs. common comparator b_X b coefficients prognostic variable X b_EM b coefficients effect modifiers b_0 Intercept coefficient meanX Mean normally-distributed covariate X sdX Standard deviation covariate X corX Covariate correlation coefficient X allocation Allocation active treatment proportion total; 0 1 event_rate Event rate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"Data frame X, trt y","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/gen_data.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate simulated datasets of IPD covariates and binary outcome for a trial — gen_data","text":"","code":"if (FALSE) { # \\dontrun{ x <- gen_data(  N = 100,  b_trt = log(0.17),  b_X = -log(0.5),  b_EM = -log(0.67),  b_0 = -0.62,  meanX = 0.6,  sdX = 0.4,  event_rate = 0.35,   corX = 0.2,  allocation = 2/3)   head(x) } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":null,"dir":"Reference","previous_headings":"","what":"Retrieve list of allowed variance methods — get_allowed_var_methods","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"Retrieve list allowed variance methods","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"","code":"get_allowed_var_methods(strategy)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"strategy Strategy object","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_allowed_var_methods.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Retrieve list of allowed variance methods — get_allowed_var_methods","text":"Character vector allowed methods. First element default.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":null,"dir":"Reference","previous_headings":"","what":"Get study comparator treatment names — get_comparator","title":"Get study comparator treatment names — get_comparator","text":"Get study comparator treatment names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get study comparator treatment names — get_comparator","text":"","code":"get_comparator(dat, ref_trt, trt_var = \"trt\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get study comparator treatment names — get_comparator","text":"dat Data frame. ref_trt Reference treatment. String. trt_var Treatment variable. String default \"trt\".","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_comparator.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get study comparator treatment names — get_comparator","text":"Comparator string names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get covariate names — get_covariate_names","title":"Get covariate names — get_covariate_names","text":"Get covariate names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get covariate names — get_covariate_names","text":"","code":"get_covariate_names(formula)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get covariate names — get_covariate_names","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_covariate_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get covariate names — get_covariate_names","text":"Covariate names character vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":null,"dir":"Reference","previous_headings":"","what":"Get effect modifiers — get_effect_modifiers","title":"Get effect modifiers — get_effect_modifiers","text":"Get effect modifiers","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get effect modifiers — get_effect_modifiers","text":"","code":"get_effect_modifiers(formula)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get effect modifiers — get_effect_modifiers","text":"formula Linear regression formula string","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_effect_modifiers.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get effect modifiers — get_effect_modifiers","text":"Effect modifiers names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get effect modifiers — get_eff_mod_names","title":"Get effect modifiers — get_eff_mod_names","text":"Get effect modifiers","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get effect modifiers — get_eff_mod_names","text":"","code":"get_eff_mod_names(formula, trt_var = \"trt\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get effect modifiers — get_eff_mod_names","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax. trt_var Treatment variable name; Default 'trt'.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_eff_mod_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get effect modifiers — get_eff_mod_names","text":"Effect modifiers strings names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get mean names — get_mean_names","title":"Get mean names — get_mean_names","text":"Get mean names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get mean names — get_mean_names","text":"","code":"get_mean_names(ald, keep_nms)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get mean names — get_mean_names","text":"ald Aggregate-level data. Single row matrix summary statistics covariate treatment outcomes. format 'mean.' 'sd.' covariates 'y..sum', 'y..bar', 'y.*.sd' treatments B C. assume common distribution treatment arm. keep_nms Variable names character vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_mean_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get mean names — get_mean_names","text":"Mean names vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":null,"dir":"Reference","previous_headings":"","what":"Get reference treatment — get_ref_trt","title":"Get reference treatment — get_ref_trt","text":"Get reference treatment","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get reference treatment — get_ref_trt","text":"","code":"get_ref_trt(ref_trt, trt, ipd_trial, ald_trial)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get reference treatment — get_ref_trt","text":"ref_trt Reference treatment trt Treatment ipd_trial dataframe IPD ald_trial dataframe ALD","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_ref_trt.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get reference treatment — get_ref_trt","text":"String reference treatment name.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_robust_vcov.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov","title":"Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov","text":"Calculates (X'WX)^-1 (X' W^2 r^2 X) (X'WX)^-1","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_robust_vcov.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Robust Covariance Matrix (HC0-style) — get_robust_vcov","text":"","code":"get_robust_vcov(fit)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":null,"dir":"Reference","previous_headings":"","what":"Get standard deviation names — get_sd_names","title":"Get standard deviation names — get_sd_names","text":"Get standard deviation names","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get standard deviation names — get_sd_names","text":"","code":"get_sd_names(ald, keep_nms)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get standard deviation names — get_sd_names","text":"ald Aggregate-level data. Single row matrix summary statistics covariate treatment outcomes. format 'mean.' 'sd.' covariates 'y..sum', 'y..bar', 'y.*.sd' treatments B C. assume common distribution treatment arm. keep_nms Variable names character vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_sd_names.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get standard deviation names — get_sd_names","text":"Standard deviation names vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":null,"dir":"Reference","previous_headings":"","what":"Get treatment effect scale corresponding to a link function — get_treatment_effect","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"Maps given link function corresponding treatment effect scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"","code":"get_treatment_effect(link)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"link character string specifying link function. Options : \"logit\" Log-odds scale. \"identity\" Risk difference. \"probit\" Probit scale. \"cloglog\" Log relative risk rare events. \"log\" Log relative risk.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"character string representing treatment effect scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_effect.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get treatment effect scale corresponding to a link function — get_treatment_effect","text":"","code":"get_treatment_effect(link = \"logit\") #> [1] \"log_odds\"  get_treatment_effect(link = \"identity\") #> [1] \"mean_difference\""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":null,"dir":"Reference","previous_headings":"","what":"Get treatment name — get_treatment_name","title":"Get treatment name — get_treatment_name","text":"Get treatment name","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get treatment name — get_treatment_name","text":"","code":"get_treatment_name(formula, trt_var = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get treatment name — get_treatment_name","text":"formula Formula trt_var Treatment variable","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_treatment_name.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get treatment name — get_treatment_name","text":"Treatment name string.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine and validate variance method for a strategy — get_var_method","title":"Determine and validate variance method for a strategy — get_var_method","text":"Determine validate variance method strategy","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine and validate variance method for a strategy — get_var_method","text":"","code":"get_var_method(strategy, user_method = NULL)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine and validate variance method for a strategy — get_var_method","text":"strategy Strategy object user_method User supplied method (string) NULL","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/get_var_method.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Determine and validate variance method for a strategy — get_var_method","text":"String name variance method use","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":null,"dir":"Reference","previous_headings":"","what":"Guess treatment name — guess_treatment_name","title":"Guess treatment name — guess_treatment_name","text":"variable appear interactions? pick first LHS interaction term. Finally, interactions pick last main effect term.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Guess treatment name — guess_treatment_name","text":"","code":"guess_treatment_name(formula)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Guess treatment name — guess_treatment_name","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/guess_treatment_name.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Guess treatment name — guess_treatment_name","text":"Treatment name string.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — hat_Delta_stats","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"main, top-level wrapper hat_Delta_stats(). Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"","code":"hat_Delta_stats(AC.IPD, BC.ALD, strategy, CI = 0.95, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"AC.IPD Individual-level patient data. Suppose studies C. BC.ALD Aggregate-level data. Suppose studies B C. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml()  strategy_gcomp_bayes() CI Confidence interval; 0,1 ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"List length 3 statistics mimR class object. Containing statistics pair treatments. mean contrasts, variances confidence intervals, respectively.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1--31. ISSN 1759-2879, doi:10.1002/jrsm.1565 , 2108.12208.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/hat_Delta_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — hat_Delta_stats","text":"","code":"data(AC_IPD)  # AC patient-level data data(BC_ALD)  # BC aggregate-level data  # matching-adjusted indirect comparison hat_Delta_stats_maic <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_maic())  # simulated treatment comparison hat_Delta_stats_stc <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_stc())  # G-computation with maximum likelihood # hat_Delta_stats_gcomp_ml <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_gcomp_ml())  # G-computation with Bayesian inference hat_Delta_stats_gcomp_bayes <- hat_Delta_stats(AC_IPD, BC_ALD, strategy = strategy_gcomp_bayes()) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.6e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.36 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.481 seconds (Warm-up) #> Chain 1:                0.592 seconds (Sampling) #> Chain 1:                1.073 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.7e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.514 seconds (Warm-up) #> Chain 2:                0.521 seconds (Sampling) #> Chain 2:                1.035 seconds (Total) #> Chain 2:"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate individual-level patient data statistics — IPD_stats","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Computes mean variance statistics individual-level patient data using various approaches, including Matching-Adjusted Indirect Comparison (MAIC), Simulated Treatment Comparison (STC), G-computation via Maximum Likelihood Estimation (MLE) Bayesian inference.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate individual-level patient data statistics — IPD_stats","text":"","code":"IPD_stats(strategy, ipd, ald, scale, ...)  # Default S3 method IPD_stats(...)  # S3 method for class 'mim' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'stc' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'maic' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'gcomp_ml' IPD_stats(strategy, ipd, ald, scale, ...)  # S3 method for class 'gcomp_bayes' IPD_stats(strategy, ipd, ald, scale, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate individual-level patient data statistics — IPD_stats","text":"strategy list corresponding different approaches ipd Individual-level data ald Aggregate-level data scale scaling parameter effect calculation. ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate individual-level patient data statistics — IPD_stats","text":"list containing: mean Estimated mean treatment effect. var Estimated variance treatment effect.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"multiple-imputation-marginalisation","dir":"Reference","previous_headings":"","what":"Multiple imputation marginalisation","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Using Stan, compute marginal relative treatment effect vs C MCMC sample transforming probability linear predictor scale. Approximate using imputation combining estimates using Rubin's rules, contrast IPD_stats.gcomp_bayes().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"simulated-treatment-comparison-statistics","dir":"Reference","previous_headings":"","what":"Simulated treatment comparison statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"IPD AC trial used fit regression model describing observed outcomes \\(y\\) terms relevant baseline characteristics \\(x\\) treatment variable \\(z\\).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"matching-adjusted-indirect-comparison-statistics","dir":"Reference","previous_headings":"","what":"Matching-adjusted indirect comparison statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Marginal vs C treatment effect estimates using bootstrapping sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"g-computation-maximum-likelihood-statistics","dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Compute non-parametric bootstrap default \\(R=1000\\) resamples.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"g-computation-bayesian-statistics","dir":"Reference","previous_headings":"","what":"G-computation Bayesian statistics","title":"Calculate individual-level patient data statistics — IPD_stats","text":"Using Stan, compute marginal log-odds ratio vs C MCMC sample transforming probability linear predictor scale.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate individual-level patient data statistics — IPD_stats","text":"","code":"if (FALSE) { # \\dontrun{ strategy <- strategy_maic() ipd <- data.frame(id = 1:100, treatment = sample(c(\"A\", \"C\"), 100, replace = TRUE), outcome = rnorm(100)) ald <- data.frame(treatment = c(\"A\", \"C\"), mean = c(0.2, 0.1), var = c(0.05, 0.03)) IPD_stats(strategy, ipd, ald, scale = \"log\") } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":null,"dir":"Reference","previous_headings":"","what":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"Creates method computing IPD mean variance statistics based supplied function.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"","code":"IPD_stat_factory(ipd_fun)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"ipd_fun function computes mean variance statistics individual-level patient data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/IPD_stat_factory.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Factory function for creating calc_IPD_stats methods — IPD_stat_factory","text":"function computes mean variance statistics given strategy.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":null,"dir":"Reference","previous_headings":"","what":"Mean absolute error estimate — mae","title":"Mean absolute error estimate — mae","text":"Mean absolute error estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mean absolute error estimate — mae","text":"","code":"mae(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mean absolute error estimate — mae","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mae.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mean absolute error estimate — mae","text":"\\(sum(abs(theta.hat - theta))/nsim\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":null,"dir":"Reference","previous_headings":"","what":"MAIC bootstrap sample — maic.boot","title":"MAIC bootstrap sample — maic.boot","text":"Matching-adjusted indirect comparison bootstrap sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"MAIC bootstrap sample — maic.boot","text":"","code":"maic.boot(   data,   indices,   balance_matrix,   outcome_x_matrix,   outcome_y,   ald_targets,   scaling_factors,   trt_var,   family,   hat_w = NULL,   ipd = NULL,   outcome_model = NULL,   balance_model = NULL,   ald = NULL,   moments = 1,   int = FALSE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"MAIC bootstrap sample — maic.boot","text":"data Individual-level patient data (data frame). indices Vector indices, length original, define bootstrap sample. balance_matrix Pre-computed balance matrix. outcome_x_matrix Pre-computed outcome design matrix. outcome_y Pre-computed outcome vector. ald_targets Vector ALD targets. scaling_factors Vector scaling factors. trt_var Treatment variable name. family 'family' object specifying distribution link function. hat_w MAIC weights; default NULL calls maic_weights(). ipd Backwards compatibility IPD data (optional). outcome_model Backwards compatibility outcome model formula (optional). balance_model Backwards compatibility balance model formula (optional). ald Backwards compatibility ALD data (optional). moments Backwards compatibility moments (default 1). int Backwards compatibility interactions flag (default FALSE).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic.boot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"MAIC bootstrap sample — maic.boot","text":"Vector fitted probabilities treatments C","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate MAIC weights — maic_weights","title":"Estimate MAIC weights — maic_weights","text":"Matching-adjusted indirect comparison weights. Method taken (Signorovitch et al. 2010) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate MAIC weights — maic_weights","text":"","code":"maic_weights(X_EM)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate MAIC weights — maic_weights","text":"X_EM Centred \\(S=1\\) effect modifiers IPD covariates; matrix data frame","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate MAIC weights — maic_weights","text":"Estimated weights individual; vector","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/maic_weights.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Estimate MAIC weights — maic_weights","text":"Signorovitch JE, Wu EQ, Yu AP, Gerrits CM, Kantor E, Bao Y, Gupta SR, Mulani PM (2010). “Comparative effectiveness without head--head trials: method matching-adjusted indirect comparisons applied psoriasis treatment adalimumab etanercept.” Pharmacoeconomics, 28(10), 935–945. ISSN 11707690, doi:10.2165/11538370-000000000-00000 , https://pubmed.ncbi.nlm.nih.gov/20831302/.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":null,"dir":"Reference","previous_headings":"","what":"Marginal treatment effect from reported event counts — marginal_treatment_effect","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"Computes relative treatment effect aggregate-level data using event counts.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"","code":"marginal_treatment_effect(ald, ref_trt = NA, comp_trt = NA, scale, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"ald Aggregate-level data ref_trt Treatment labels reference (common; e.g. placebo) comp_trt Treatment labels comparator scale scaling parameter calculation. family character string specifying family distribution (e.g., \"binomial\").","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"Numeric relative treatment effect.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_treatment_effect.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Marginal treatment effect from reported event counts — marginal_treatment_effect","text":"","code":"ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))                    marginal_treatment_effect(ald, ref_trt = \"C\", comp_trt = \"B\",                           scale = \"log_odds\", family = \"binomial\") #> [1] -0.4054651"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":null,"dir":"Reference","previous_headings":"","what":"Marginal effect variance using the delta method — marginal_variance","title":"Marginal effect variance using the delta method — marginal_variance","text":"Computes total variance marginal treatment effects using delta method.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Marginal effect variance using the delta method — marginal_variance","text":"","code":"marginal_variance(ald, ref_trt = NA, comp_trt = NA, scale, family)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Marginal effect variance using the delta method — marginal_variance","text":"ald Aggregate-level data ref_trt Treatment labels reference (common; e.g. placebo) comp_trt Treatment labels comparator scale scaling parameter calculation. family character string specifying family distribution (e.g., \"binomial\").","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Marginal effect variance using the delta method — marginal_variance","text":"Numeric total variance marginal treatment effects.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/marginal_variance.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Marginal effect variance using the delta method — marginal_variance","text":"","code":"ald <- data.frame(trt = c(\"B\",\"C\",\"B\",\"C\"),                   variable = c(NA, NA, \"y\", \"y\"),                   statistic = c(\"N\", \"N\", \"sum\", \"sum\"),                   value = c(100, 100, 50, 60))                    marginal_variance(ald, ref_trt = \"C\", comp_trt = \"B\",                   scale = \"log_odds\", family = \"binomial\") #> [1] 0.08166667"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of any continuous performance metric — mcse.estimate","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"Monte Carlo SE continuous performance metric","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"","code":"mcse.estimate(pm)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"pm pm","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mcse.estimate.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of any continuous performance metric — mcse.estimate","text":"\\(sqrt(sum((pm - pm_mean)^2)/(nsim*(nsim-1)))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mim.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiple imputation marginalization (MIM) — mim","title":"Multiple imputation marginalization (MIM) — mim","text":"Multiple imputation marginalization (MIM)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mim.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiple imputation marginalization (MIM) — mim","text":"","code":"mim(formula, ipd, ald, M = 1000, n.chains = 2, warmup = 1000, iters = 4000)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mim.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiple imputation marginalization (MIM) — mim","text":"ipd Individual-level data ald Aggregate-level data M Number syntheses used analysis stage (high low Monte Carlo error)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — mimR","title":"Calculate the difference between treatments using all evidence — mimR","text":"main, top-level wrapper {mimR}. Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — mimR","text":"","code":"mimR(AC.IPD, BC.ALD, strategy, CI = 0.95, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — mimR","text":"AC.IPD Individual-level patient data. Suppose studies C. BC.ALD Aggregate-level data. Suppose studies B C. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml()  strategy_gcomp_bayes() CI Confidence interval; 0,1 ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — mimR","text":"List length 3 statistics mimR class object. Containing statistics pair treatments. mean contrasts, variances confidence intervals, respectively.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — mimR","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1--31. ISSN 1759-2879, doi:10.1002/jrsm.1565 , 2108.12208.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mimR.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — mimR","text":"","code":"data(AC_IPD)  # AC patient-level data data(BC_ALD)  # BC aggregate-level data  lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\")  # matching-adjusted indirect comparison mimR_maic <- mimR(AC_IPD, BC_ALD, strategy = strategy_maic(formula = lin_form))  # simulated treatment comparison mimR_stc <- mimR(AC_IPD, BC_ALD, strategy = strategy_stc(lin_form))  # G-computation with maximum likelihood # mimR_gcomp_ml <- mimR(AC_IPD, BC_ALD, strategy = strategy_gcomp_ml(lin_form))  # G-computation with Bayesian inference mimR_gcomp_bayes <- mimR(AC_IPD, BC_ALD, strategy = strategy_gcomp_bayes(lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.6e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.36 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.497 seconds (Warm-up) #> Chain 1:                0.516 seconds (Sampling) #> Chain 1:                1.013 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 1.6e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.505 seconds (Warm-up) #> Chain 2:                0.564 seconds (Sampling) #> Chain 2:                1.069 seconds (Total) #> Chain 2:"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — outstandR","title":"Calculate the difference between treatments using all evidence — outstandR","text":"main, top-level wrapper {outstandR}. Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"outstandR(AC.IPD, BC.ALD, strategy, CI = 0.95, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — outstandR","text":"AC.IPD Individual-level patient data. Suppose studies C. BC.ALD Aggregate-level data. Suppose studies B C. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml()  strategy_gcomp_bayes() CI Confidence interval; 0,1 ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — outstandR","text":"List length 3 statistics outstandR class object. Containing statistics pair treatments. mean contrasts, variances confidence intervals, respectively.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — outstandR","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1--31. ISSN 1759-2879, doi:10.1002/jrsm.1565 , 2108.12208.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/ModStanR.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"data(AC_IPD)  # AC patient-level data data(BC_ALD)  # BC aggregate-level data  lin_form <- as.formula(\"y ~ X3 + X4 + trt*X1 + trt*X2\")  # matching-adjusted indirect comparison outstandR_maic <- outstandR(AC_IPD, BC_ALD, strategy = strategy_maic(formula = lin_form))  # simulated treatment comparison outstandR_stc <- outstandR(AC_IPD, BC_ALD, strategy = strategy_stc(lin_form))  # G-computation with maximum likelihood # outstandR_gcomp_ml <- outstandR(AC_IPD, BC_ALD, strategy = strategy_gcomp_ml(lin_form))  # G-computation with Bayesian inference outstandR_gcomp_bayes <- outstandR(AC_IPD, BC_ALD, strategy = strategy_gcomp_bayes(lin_form)) #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 7.1e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.71 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 1: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 1: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 1: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 1: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 1: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 1: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 1: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 1: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.71 seconds (Warm-up) #> Chain 1:                0.733 seconds (Sampling) #> Chain 1:                1.443 seconds (Total) #> Chain 1:  #>  #> SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2). #> Chain 2:  #> Chain 2: Gradient evaluation took 2.2e-05 seconds #> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds. #> Chain 2: Adjust your expectations accordingly! #> Chain 2:  #> Chain 2:  #> Chain 2: Iteration:    1 / 4000 [  0%]  (Warmup) #> Chain 2: Iteration:  400 / 4000 [ 10%]  (Warmup) #> Chain 2: Iteration:  800 / 4000 [ 20%]  (Warmup) #> Chain 2: Iteration: 1200 / 4000 [ 30%]  (Warmup) #> Chain 2: Iteration: 1600 / 4000 [ 40%]  (Warmup) #> Chain 2: Iteration: 2000 / 4000 [ 50%]  (Warmup) #> Chain 2: Iteration: 2001 / 4000 [ 50%]  (Sampling) #> Chain 2: Iteration: 2400 / 4000 [ 60%]  (Sampling) #> Chain 2: Iteration: 2800 / 4000 [ 70%]  (Sampling) #> Chain 2: Iteration: 3200 / 4000 [ 80%]  (Sampling) #> Chain 2: Iteration: 3600 / 4000 [ 90%]  (Sampling) #> Chain 2: Iteration: 4000 / 4000 [100%]  (Sampling) #> Chain 2:  #> Chain 2:  Elapsed Time: 0.73 seconds (Warm-up) #> Chain 2:                0.817 seconds (Sampling) #> Chain 2:                1.547 seconds (Total) #> Chain 2:"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":null,"dir":"Reference","previous_headings":"","what":"Mean squared error estimate — mse","title":"Mean squared error estimate — mse","text":"Mean squared error estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mean squared error estimate — mse","text":"","code":"mse(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mean squared error estimate — mse","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mean squared error estimate — mse","text":"\\(sum((theta.hat - theta)^2)/nsim\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Monte Carlo SE of MSE estimate — mse.mcse","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"Monte Carlo SE MSE estimate","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"","code":"mse.mcse(theta.hat, theta)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"theta.hat Theta hat theta Theta","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/mse.mcse.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Monte Carlo SE of MSE estimate — mse.mcse","text":"\\(sqrt(sum((tmp - mse.est)^2)/(nsim*(nsim-1)))\\)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/num_grad.html","id":null,"dir":"Reference","previous_headings":"","what":"Numerical Gradient — num_grad","title":"Numerical Gradient — num_grad","text":"Numerical Gradient","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/num_grad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Numerical Gradient — num_grad","text":"","code":"num_grad(func, x, h = 1e-05)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-class.html","id":null,"dir":"Reference","previous_headings":"","what":"outstandR class — outstandR-class","title":"outstandR class — outstandR-class","text":"outstandR class contains results running model function outstandR().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-class.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"outstandR class — outstandR-class","text":"Objects class outstandR following contrasts list containing statistics relative treatment effects: means: Estimated relative effects (e.g., log-odds ratios, risk differences). variances: Variance-covariance matrix relative effects. contrast_ci: Confidence intervals relative effects. absolute list containing statistics absolute treatment outcomes: means: Estimated absolute outcomes (e.g., probabilities, mean response). variances: Variance-covariance matrix absolute outcomes. ci: Confidence intervals absolute outcomes. CI confidence level used (e.g., 0.95). ref_trt name reference treatment. scale scale outcome (e.g., \"log odds\", \"probability\"). model list containing details underlying statistical model. Contents vary strategy: family: error distribution link function. fit: underlying model object (e.g., STC, G-Comp ML, Bayesian G-Comp). weights, ESS: (MAIC ) estimated weights Effective Sample Size. stan_args: (Bayesian G-Comp, MIM) Arguments passed Stan. rho: (G-Comp ML, MIM, Bayesian G-Comp) Correlation coefficient. N: (G-Comp ML, MIM, Bayesian G-Comp) Number iterations. nu, hats.v, M: (MIM ) Imputation parameters matrices.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-package.html","id":null,"dir":"Reference","previous_headings":"","what":"outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package","title":"outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package","text":"problem indirect treatment comparison limited subject-level data, package provides tools model-based standardisation several different computation approaches. See Remiro‐Azócar , Heath , Baio G (2022) “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data”, Res. Synth. Methods, 1–31. ISSN 1759-2879, doi:10.1002/jrsm.1565 .","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data — outstandR-package","text":"Maintainer: Nathan Green n.green@ucl.ac.uk (ORCID) (ROR) [copyright holder] Authors: Chengyang Gao chengyang.gao.15@ucl.ac.uk Antonio Remiro-Azocar antonio.remiro-azocar@bayer.com (ORCID)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the difference between treatments using all evidence — outstandR","title":"Calculate the difference between treatments using all evidence — outstandR","text":"main, top-level wrapper {outstandR}. Methods taken (Remiro‐Azócar et al. 2022) .","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"outstandR(   ipd_trial,   ald_trial,   strategy,   ref_trt = NA,   CI = 0.95,   scale = NULL,   var_method = NULL,   seed = NULL,   verbose = TRUE,   ... )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the difference between treatments using all evidence — outstandR","text":"ipd_trial Individual-level patient data. example, suppose studies C. long format must contain treatment column outcome column consistent formula object. labels treatment used internally must common treatment aggregate-level data trial. ald_trial Aggregate-level data. example, suppose studies B C. column names variable: Covariate name. case treatment arm sample size NA, statistic: Summary statistic name \"mean\", standard deviation \"sd\", probability \"prop\", \"sum\", value: Numerical value summary statistic, trt: Treatment label. assume common covariate distribution treatment arms NA. strategy Computation strategy function. can strategy_maic(), strategy_stc(), strategy_gcomp_ml() strategy_gcomp_bayes(). ref_trt Reference / common / anchoring treatment name. CI Confidence interval level; 0,1 default 0.95. scale Relative treatment effect scale. NULL, scale automatically determined model. Choose \"log-odds\", \"log_relative_risk\", \"risk_difference\", \"delta_z\", \"mean_difference\", \"rate_difference\" depending data type. var_method Variance estimation method. seed Random seed. verbose Logical. TRUE, prints progress messages warnings. ... Additional arguments. Currently, can pass named arguments rstanarm::stan_glm() via strategy_gcomp_bayes().","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the difference between treatments using all evidence — outstandR","text":"List length 11 statistics outstandR class object. Containing statistics pair treatments. mean, variances confidence intervals, contrasts absolute values.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the difference between treatments using all evidence — outstandR","text":"Remiro‐Azócar , Heath , Baio G (2022). “Parametric G‐computation compatible indirect treatment comparisons limited individual patient data.” Res. Synth. Methods, 1–31. ISSN 1759-2879, doi:10.1002/jrsm.1565 , 2108.12208.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/outstandR.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the difference between treatments using all evidence — outstandR","text":"","code":"data(AC_IPD_binY_contX)  # A vs C individual patient-level data data(BC_ALD_binY_contX)  # B vs C aggregate-level data  # linear formula lin_form <- as.formula(\"y ~ PF_cont_1 + PF_cont_2 + trt*EM_cont_1 + trt*EM_cont_2\")                                  # sampling values of additional arguments picked for speed # select appropriate to specific analysis  # matching-adjusted indirect comparison outstandR_maic <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_maic(formula = lin_form, n_boot = 100)) #> Note: Using legacy 'formula' argument. #> --> Analysis Model: y ~ PF_cont_1 + PF_cont_2 + trt * EM_cont_1 + trt * EM_cont_2 #> --> Inferred Balance Model: ~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2 #>     (Balancing on means of these covariates by default) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: maic #>  #> ── MAIC Execution ── #>  #> ℹ Calculating weights using method of moments... #> ℹ Starting Bootstrap with 100 replicates.  # simulated treatment comparison outstandR_stc <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_stc(lin_form)) #> Warning: `strategy_stc()` was deprecated in outstandR 1.X.X. #> ℹ Please use `strategy_gcomp_ml()` instead. #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: stc  # \\donttest{ # G-computation with maximum likelihood outstandR_gcomp_ml <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_gcomp_ml(lin_form, n_boot = 100, N =100)) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: gcomp_ml #>  #> ── G-Computation (ML) Execution ── #>  #> ℹ Fitting initial model... #> ℹ Starting Bootstrap: 100 replicates. #> ℹ Simulating pseudo-pop (N=100) per replicate.  # G-computation with Bayesian inference outstandR_gcomp_bayes <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_gcomp_bayes(lin_form),   chains = 1, iter = 1000, warmup = 20) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: gcomp_bayes #>  #> ── G-Computation (Bayesian) Execution ── #>  #> ℹ Compiling/Sampling Stan model... #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 3.7e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.37 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: WARNING: There aren't enough warmup iterations to fit the #> Chain 1:          three stages of adaptation as currently configured. #> Chain 1:          Reducing each adaptation stage to 15%/75%/10% of #> Chain 1:          the given number of warmup iterations: #> Chain 1:            init_buffer = 3 #> Chain 1:            adapt_window = 15 #> Chain 1:            term_buffer = 2 #> Chain 1:  #> Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup) #> Chain 1: Iteration:  21 / 1000 [  2%]  (Sampling) #> Chain 1: Iteration: 520 / 1000 [ 52%]  (Sampling) #> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0.002 seconds (Warm-up) #> Chain 1:                0.103 seconds (Sampling) #> Chain 1:                0.105 seconds (Total) #> Chain 1:   # Multiple imputation marginalization outstandR_mim <- outstandR(   AC_IPD_binY_contX, BC_ALD_binY_contX,   strategy = strategy_mim(lin_form,                           N = 100), # size of pseudo-population   chains = 1, iter = 1000, warmup = 20) #>  #> ── Starting outstandR Analysis ───────────────────────────────────────────────── #> ℹ Strategy: mim #>  #> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1). #> Chain 1:  #> Chain 1: Gradient evaluation took 2.2e-05 seconds #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds. #> Chain 1: Adjust your expectations accordingly! #> Chain 1:  #> Chain 1:  #> Chain 1: WARNING: There aren't enough warmup iterations to fit the #> Chain 1:          three stages of adaptation as currently configured. #> Chain 1:          Reducing each adaptation stage to 15%/75%/10% of #> Chain 1:          the given number of warmup iterations: #> Chain 1:            init_buffer = 3 #> Chain 1:            adapt_window = 15 #> Chain 1:            term_buffer = 2 #> Chain 1:  #> Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup) #> Chain 1: Iteration:  21 / 1000 [  2%]  (Sampling) #> Chain 1: Iteration: 120 / 1000 [ 12%]  (Sampling) #> Chain 1: Iteration: 220 / 1000 [ 22%]  (Sampling) #> Chain 1: Iteration: 320 / 1000 [ 32%]  (Sampling) #> Chain 1: Iteration: 420 / 1000 [ 42%]  (Sampling) #> Chain 1: Iteration: 520 / 1000 [ 52%]  (Sampling) #> Chain 1: Iteration: 620 / 1000 [ 62%]  (Sampling) #> Chain 1: Iteration: 720 / 1000 [ 72%]  (Sampling) #> Chain 1: Iteration: 820 / 1000 [ 82%]  (Sampling) #> Chain 1: Iteration: 920 / 1000 [ 92%]  (Sampling) #> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling) #> Chain 1:  #> Chain 1:  Elapsed Time: 0 seconds (Warm-up) #> Chain 1:                0.107 seconds (Sampling) #> Chain 1:                0.107 seconds (Total) #> Chain 1:  #> Warning: There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See #> https://mc-stan.org/misc/warnings.html#bfmi-low #> Warning: Examine the pairs() plot to diagnose sampling problems # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Default Plot Method for outstandR Objects — plot.outstandR","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"Default Plot Method outstandR Objects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"","code":"# S3 method for class 'outstandR' plot(   x,   ...,   type = c(\"both\", \"contrasts\", \"absolute\"),   labels = NULL,   include_naive = TRUE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"x object class 'outstandR' list 'outstandR' objects. ... Additional 'outstandR' objects comparison. type Character, one \"\" (default), \"contrasts\", \"absolute\". labels Optional character vector names models. include_naive Logical. naive (unadjusted) estimates included plot? Default TRUE.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/plot.outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Default Plot Method for outstandR Objects — plot.outstandR","text":"ggplot2::ggplot() object representing forest plot results.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prepare_covariate_distns.html","id":null,"dir":"Reference","previous_headings":"","what":"Prepare Covariate Distributions — prepare_covariate_distns","title":"Prepare Covariate Distributions — prepare_covariate_distns","text":"Resolves missing distributions parameters looking ALD. Allows partial specification (e.g., user specifies one variable, function auto-detects rest).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prepare_covariate_distns.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prepare Covariate Distributions — prepare_covariate_distns","text":"","code":"prepare_covariate_distns(   formula,   ald,   trt_var,   marginal_distns,   marginal_params,   verbose = FALSE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":null,"dir":"Reference","previous_headings":"","what":"Prepare Aggregate Level Data — prep_ald","title":"Prepare Aggregate Level Data — prep_ald","text":"Prepare Aggregate Level Data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prepare Aggregate Level Data — prep_ald","text":"","code":"prep_ald(form, data, trt_var = \"trt\")"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prepare Aggregate Level Data — prep_ald","text":"form Formula data dataframe aggregate level data trt_var Treatment variable name","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ald.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prepare Aggregate Level Data — prep_ald","text":"data frame filtered ALD variables formula.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":null,"dir":"Reference","previous_headings":"","what":"Prepare Individual Patient Data — prep_ipd","title":"Prepare Individual Patient Data — prep_ipd","text":"Cleaning subsetting input dataset contain variables actually needed statistical models.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prepare Individual Patient Data — prep_ipd","text":"","code":"prep_ipd(form, data)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prepare Individual Patient Data — prep_ipd","text":"form Formula data Individual patient data","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/prep_ipd.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prepare Individual Patient Data — prep_ipd","text":"Model frame","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Print a Summary of a outstandR Object — print.outstandR","title":"Print a Summary of a outstandR Object — print.outstandR","text":"method function print() objects class \"outstandR\" created call outstandR()","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print a Summary of a outstandR Object — print.outstandR","text":"","code":"# S3 method for class 'outstandR' print(x, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print a Summary of a outstandR Object — print.outstandR","text":"x Objects class \"outstandR\" ... Additional arguments passed methods","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/print.outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print a Summary of a outstandR Object — print.outstandR","text":"return value, called side effects","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute performance metrics for a given method — process_metrics","title":"Compute performance metrics for a given method — process_metrics","text":"Compute performance metrics given method","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute performance metrics for a given method — process_metrics","text":"","code":"process_metrics(means, variances, truth)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute performance metrics for a given method — process_metrics","text":"means Mean variances Variances truth Truth","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/process_metrics.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute performance metrics for a given method — process_metrics","text":"Named list","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":null,"dir":"Reference","previous_headings":"","what":"Objective function to minimize for standard method of moments MAIC — Q","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"Objective function minimize standard method moments MAIC","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"","code":"Q(beta, X)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"beta Beta coefficient find X Covariate value matrix, centred","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/Q.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Objective function to minimize for standard method of moments MAIC — Q","text":"Numeric value","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert aggregate data from wide to long format — reshape_ald_to_long","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"Convert aggregate data wide long format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"","code":"reshape_ald_to_long(df)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"df dataframe ALD","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_long.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert aggregate data from wide to long format — reshape_ald_to_long","text":"Data frame long format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert aggregate data from long to wide format — reshape_ald_to_wide","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"Convert aggregate data long wide format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"","code":"reshape_ald_to_wide(df)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"df Dataframe ALD","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"Data frame wide format","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/reshape_ald_to_wide.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert aggregate data from long to wide format — reshape_ald_to_wide","text":"","code":"df <-    data.frame(     variable = c(\"age\", \"age\", \"y\", \"y\", \"y\", \"y\", \"y\", \"y\", \"y\", \"y\"),     statistic = c(\"mean\", \"sd\", \"sum\", \"bar\", \"sd\", \"N\", \"sum\", \"bar\", \"sd\", \"N\"),     trt = c(NA, NA, \"B\", \"B\", \"B\", \"B\", \"C\", \"C\", \"C\", \"C\"),     value = c(1,1,1,1,1,1,1,1,1,1))"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate and arrange result statistics — result_stats","title":"Calculate and arrange result statistics — result_stats","text":"Combining output aggregate level data studies BC adjusted individual level data studies AC single object.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate and arrange result statistics — result_stats","text":"","code":"result_stats(ipd_stats, ald_stats, CI = 0.95)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate and arrange result statistics — result_stats","text":"ipd_stats, ald_stats Trial data IPD ALD CI Confidence interval level, .e. 1-alpha; default 0.95","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/result_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate and arrange result statistics — result_stats","text":"List ITC output: contrasts: list relative effects containing: means variances CI absolute: list absolute effects containing: means variances CI","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"Generates synthetic cohort using normal copula based aggregate-level data.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"","code":"simulate_ALD_pseudo_pop(   formula,   ipd = NULL,   ald = NULL,   trt_var,   rho = NA,   N = 1000,   marginal_distns = NA,   marginal_params = NA,   seed = NULL,   verbose = FALSE )"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax. ipd Individual-level patient data. Dataframe one row per patient outcome, treatment covariate columns. ald Aggregate-level data. Long format summary statistics covariate treatment outcomes. assume common distribution treatment arm. rho named square matrix covariate correlations single value; default NA takes IPD. N Sample size synthetic cohort. Default 1000. marginal_distns Marginal distributions names; vector default NA. Available distributions given stats::Distributions. See copula::Mvdc() details marginal_params Marginal distributions parameters; named list lists, default NA. See copula::Mvdc() details. seed Random seed verbose Default FALSE","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"data frame representing synthetic pseudo-population. contains N rows (one simulated individual) columns every covariate specified marginal_distns formula.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/simulate_ALD_pseudo_pop.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate Aggregate-Level Data Pseudo-Population — simulate_ALD_pseudo_pop","text":"","code":"if (FALSE) { # \\dontrun{  ## Example 1: Simulating data with explicitly defined marginals and ## a provided correlation matrix (rho)  my_formula <- y ~ x1 + x2*trt + trt  # Define marginal distributions (Normal for age, Lognormal for BMI) dists <- c(x1 = \"norm\", x2 = \"norm\")  # Define parameters matching the chosen distributions params <- list(   x1 = list(mean = 60, sd = 8),   x2 = list(mean = 3, sd = 0.1) )  # Define a 2x2 correlation matrix corr_mat <- matrix(c(1, 0.25,                      0.25, 1), nrow = 2,                    dimnames = list(c(\"x1\", \"x2\"),                                    c(\"x1\", \"x2\")))  # Generate the synthetic cohort sim_cohort_marginals_rho <- simulate_ALD_pseudo_pop(   formula = my_formula,   ald = mock_ald,   trt_var = \"trt\",   rho = corr_mat,   N = 100,   marginal_distns = dists,   marginal_params = params )  head(sim_cohort_marginals_rho)  ## Example 2: Estimating the correlation matrix (rho) from provided IPD  # Create some mock Individual Patient Data (IPD) mock_ipd <- data.frame(   x1 = rnorm(200, 60, 8),   x2 = rlnorm(200, 3.3, 0.1) )  mock_ald <- data.frame(   variable = c(\"x1\", \"x1\", \"x2\", \"x2\"),   statistic = c(\"mean\", \"sd\", \"mean\", \"sd\"),   value = c(1000, 500, 0.7, 0.1),   trt = NA )  # Generate the synthetic cohort using IPD for the correlation structure sim_cohort <- simulate_ALD_pseudo_pop(   formula = my_formula,   ipd = mock_ipd,   ald = mock_ald,   trt_var = \"trt\",   rho = NA,   N = 100 )  head(sim_cohort)  # Generate the synthetic cohort using IPD for the correlation structure # with marginals sim_cohort_marginals <- simulate_ALD_pseudo_pop(   formula = my_formula,   ipd = mock_ipd,   ald = mock_ald,   trt_var = \"trt\",   N = 100,   marginal_distns = dists,   marginal_params = params )  head(sim_cohort_marginals) } # }"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy-class.html","id":null,"dir":"Reference","previous_headings":"","what":"Strategy class and subclasses — strategy-class","title":"Strategy class and subclasses — strategy-class","text":"strategy class virtual class defines statistical approach population adjustment indirect treatment comparisons objects constructors validate hyperparameters encapsulate modelling settings execution outstandR()","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy-class.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Strategy class and subclasses — strategy-class","text":"Objects class strategy common structure carry different subclasses trigger specific S3 method dispatch General fields Shared strategies: formula: linear regression formula outcome model family: base R family object specifying distribution link trt_var: name treatment variable. maic subclass Additional fields Matching-Adjusted Indirect Comparison: n_boot: Number bootstrap resamples variance estimation. stc subclass Additional fields Simulated Treatment Comparison: N: Synthetic sample size target population. gcomp_ml subclass Additional fields Maximum Likelihood G-computation: rho: Named square matrix covariate correlations. marginal_distns: Names marginal distributions covariates. marginal_params: Parameters marginal distributions. N: Synthetic sample size pseudo-population. n_boot: Number bootstrap resamples. gcomp_bayes subclass Additional fields Bayesian G-computation: rho, marginal_distns, marginal_params, N: gcomp_ml. ...: Additional arguments passed Stan engine via rstanarm::stan_glm(). mim subclass Additional fields Multiple Imputation Marginalization: rho: Correlation matrix. N: Number iterations/simulated individuals.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":null,"dir":"Reference","previous_headings":"","what":"New strategy objects — strategy_maic","title":"New strategy objects — strategy_maic","text":"Create type strategy class modelling approach.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"New strategy objects — strategy_maic","text":"","code":"strategy_maic(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   n_boot = 1000L,   moments = 1,   int = FALSE,   verbatim = TRUE )  strategy_stc(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL )  strategy_gcomp_ml(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   rho = NA,   marginal_distns = NA,   marginal_params = NA,   n_boot = 1000L,   N = 1000L )  strategy_gcomp_bayes(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   rho = NA,   marginal_distns = NA,   marginal_params = NA,   N = 1000L )  strategy_mim(   formula = NULL,   family = gaussian(link = \"identity\"),   trt_var = NULL,   rho = NA,   marginal_distns = NA,   marginal_params = NA,   N = 1000L )  new_strategy(strategy, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"New strategy objects — strategy_maic","text":"formula Linear regression formula object. Prognostic factors (PF) main effects effect modifiers (EM) interactions treatment variable, e.g., y ~ X1 + trt + trt:X2. covariates PF EM use * syntax. family 'family' object specifying distribution link function (e.g., 'binomial'). See stats::family() details. trt_var Treatment variable name; string n_boot number resamples used non-parametric bootstrap; integer moments Integer. number moments covariates balance. Setting moments = 2 includes original variables squared terms, effectively balances means variances. Default 1. int Logical. TRUE, includes two-way interactions covariates balancing model effectively balance covariances. Default FALSE verbatim Logical. Output console running. rho named square matrix covariate correlations; default NA marginal_distns Marginal distributions names; vector default NA. Available distributions given stats::Distributions. See copula::Mvdc() details marginal_params Marginal distributions parameters; list lists, default NA. See copula::Mvdc() details N Synthetic sample size g-computation strategy Class name strategy_maic, strategy_stc, strategy_gcomp_ml, strategy_gcomp_bayes, strategy_mim ... Additional arguments","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"New strategy objects — strategy_maic","text":"maic class object stc class object gcomp_ml class object gcomp_bayes class object mim class object Strategy list object","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"New strategy objects — strategy_maic","text":"current implementations focus binary, continuous, count outcomes, support survival data (using survival package) active development scheduled future version.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"matching-adjusted-indirect-comparison-maic-","dir":"Reference","previous_headings":"","what":"Matching-adjusted indirect comparison (MAIC)","title":"New strategy objects — strategy_maic","text":"MAIC form non-parametric likelihood reweighting method allows propensity score logistic regression model estimated without IPD AC population. mean outcomes \\(\\mu_{t(AC)}\\) treatment \\(t = ,B\\) AC target population estimated taking weighted average outcomes \\(Y\\) \\(N\\) individuals arm \\(t\\) AB population. Used compare marginal treatment effects cross-trial differences effect modifiers limited patient-level data. $$ \\hat{Y}_{} = \\frac{\\sum_{=1}^{N} Y_{(AB)} w_{}}{\\sum_{=1}^{N} w_{}} $$ weight \\(w_{}\\) assigned \\(\\)-th individual receiving treatment \\(t\\) equal odds enrolled AC trial vs AB trial.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"simulated-treatment-comparison-stc-","dir":"Reference","previous_headings":"","what":"Simulated treatment comparison (STC)","title":"New strategy objects — strategy_maic","text":"strategy_stc() deprecated outstandR version 1.X.X. recommend using G-computation (strategy_gcomp_ml()) robust alternative type analysis. Outcome regression-based method targets conditional treatment effect. STC modification covariate adjustment method. outcome model fitted using IPD AB trial. example, $$ g(\\mu_{t(AB)}(X)) = \\beta_0 + \\beta_1^T X + (\\beta_B + \\beta_2^T X^{EM}) (t=B) $$ \\(\\beta_0\\) intercept term, \\(\\beta_1\\) vector coefficients prognostic variables, \\(\\beta_B\\) relative effect treatment B compared \\(X=0\\), \\(\\beta_2\\) vector coefficients effect modifiers \\(X^{EM}\\) subvector full covariate vector \\(X\\)), \\(\\mu_{t(AB)}(X)\\) expected outcome individual assigned treatment \\(t\\) covariate values \\(X\\) transformed onto chosen linear predictor scale link function \\(g(\\cdot)\\).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"g-computation-maximum-likelihood","dir":"Reference","previous_headings":"","what":"G-computation maximum likelihood","title":"New strategy objects — strategy_maic","text":"G-computation marginalizes conditional estimates separating regression modelling estimation marginal treatment effect versus C. example, regression model observed outcome \\(y\\) covariates \\(x\\) treatment \\(z\\) fitted AC IPD: $$ g(\\mu_n) = \\beta_0 + \\boldsymbol{x}_n \\boldsymbol{\\beta_1} + (\\beta_z + \\boldsymbol{x_n^{EM}} \\boldsymbol{\\beta_2}) \\mbox{}(z_n=1) $$ context G-computation, regression model called “Q-model\". fitted Q-model, regression coefficients treated nuisance parameters. parameters applied simulated covariates \\(x*\\) predict hypothetical outcomes subject possible treatments. Namely, pair predicted outcomes, also called potential outcomes, C, generated subject. plugging treatment C regression fit every simulated observation, predict marginal outcome mean hypothetical scenario units treatment C: $$ \\hat{\\mu}_0 = \\int_{x^*} g^{-1} (\\hat{\\beta}_0 + x^* \\hat{\\beta}_1 ) p(x^*) dx^* $$ estimate marginal population-average treatment effect versus C linear predictor scale, one back-transforms scale average predictions, taken subjects natural outcome scale, calculates difference average linear predictions: $$ \\hat{\\Delta}^{(2)}_{10} = g(\\hat{\\mu}_1) - g(\\hat{\\mu}_0) $$","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"g-computation-bayesian","dir":"Reference","previous_headings":"","what":"G-computation Bayesian","title":"New strategy objects — strategy_maic","text":"difference Bayesian G-computation maximum-likelihood counterpart estimated distribution predicted outcomes. Bayesian approach also marginalizes, integrates standardizes joint posterior distribution conditional nuisance parameters outcome regression, well joint covariate distribution. Draw vector size \\(N*\\) predicted outcomes \\(y*z\\) set intervention \\(z* \\\\{0, 1\\}\\) posterior predictive distribution specific treatment. defined \\(p(y*_{z*} | \\mathcal{D}_{AC}) = \\int_{\\beta} p(y*_{z*} | \\beta) p(\\beta | \\mathcal{D}_{AC}) d\\beta\\) \\(p(\\beta | \\mathcal{D}_{AC})\\) posterior distribution outcome regression coefficients \\(\\beta\\), encode predictor-outcome relationships observed AC trial IPD. given : $$ p(y*_{z*} \\mid \\mathcal{D}_{AC}) = \\int_{x*} p(y* \\mid z*, x*, \\mathcal{D}_{AC}) p(x* \\mid \\mathcal{D}_{AC}) dx* $$ $$ = \\int_{x*} \\int_{\\beta} p(y* \\mid z*, x*, \\beta) p(x* \\mid \\beta) p(\\beta \\mid \\mathcal{D}_{AC}) d\\beta dx* $$ practice, integrals can approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/strategy.html","id":"multiple-imputation-marginalization-mim-","dir":"Reference","previous_headings":"","what":"Multiple imputation marginalization (MIM)","title":"New strategy objects — strategy_maic","text":"MIM targets marginal treatment effect using parametric G-computation within multiple imputation framework. approach views covariate adjustment regression nuisance model separates estimation evaluation marginal treatment effect interest. particularly useful ensuring compatibility indirect comparisons adjusting effect modifiers.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary method for outstandR — summary.outstandR","title":"Summary method for outstandR — summary.outstandR","text":"Summary method outstandR","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary method for outstandR — summary.outstandR","text":"","code":"# S3 method for class 'outstandR' summary(object, CI = NA, ...)  # S3 method for class 'summary.outstandR' print(x, digits = 3, ...)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary method for outstandR — summary.outstandR","text":"object outstandR() output object. CI Confidence interval level. ... Additional arguments. x object used select method. digits Minimal number significant digits, see print.default.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/summary.outstandR.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary method for outstandR — summary.outstandR","text":"List class summary.outstandR Original argument, mainly called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":null,"dir":"Reference","previous_headings":"","what":"Trial treatment effect with aggregate data — trial_treatment_effect","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"Calculate $$\\log(\\sum y_k (N_k - \\sum y_k))$$.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"","code":"trial_treatment_effect(ald, tid)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"ald Aggregate-level data tid Treatment label","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_treatment_effect.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Trial treatment effect with aggregate data — trial_treatment_effect","text":"Value","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":null,"dir":"Reference","previous_headings":"","what":"Trial variance with aggregate data — trial_variance","title":"Trial variance with aggregate data — trial_variance","text":"Calculate $$1/(\\sum y_k) + 1/(N_k - \\sum y_k)$$.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Trial variance with aggregate data — trial_variance","text":"","code":"trial_variance(ald, tid)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Trial variance with aggregate data — trial_variance","text":"ald Aggregate-level data tid Treatment label","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/trial_variance.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Trial variance with aggregate data — trial_variance","text":"Value","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":null,"dir":"Reference","previous_headings":"","what":"Input data validator — validate_outstandr","title":"Input data validator — validate_outstandr","text":"Input data validator","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Input data validator — validate_outstandr","text":"","code":"validate_outstandr(ipd_trial, ald_trial, strategy, CI, scale)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Input data validator — validate_outstandr","text":"ipd_trial Individual patient data ald_trial Aggregate level data strategy object class strategy created functions strategy_maic(), strategy_stc(), strategy_mim(). Contains modelling details like formula family. CI Confidence interval scale Outcome scale","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/validate_outstandr.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Input data validator — validate_outstandr","text":"return value, called side effects","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":null,"dir":"Reference","previous_headings":"","what":"Variability ratio — var.ratio","title":"Variability ratio — var.ratio","text":"Variability ratio","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Variability ratio — var.ratio","text":"","code":"var.ratio(theta.hat, std.err)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Variability ratio — var.ratio","text":"theta.hat Theta hat std.err Standard error","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Variability ratio — var.ratio","text":"Ratio","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":null,"dir":"Reference","previous_headings":"","what":"Variability ratio MCSE — var.ratio.mcse","title":"Variability ratio MCSE — var.ratio.mcse","text":"Approximation ratio variance based independence avg. se emp.se see wolter2007outstandR","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Variability ratio MCSE — var.ratio.mcse","text":"","code":"var.ratio.mcse(avg.se, emp.se, var.avg.se, var.emp.se)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Variability ratio MCSE — var.ratio.mcse","text":"avg.se Average SE emp.se Emp SE var.avg.se Variance average SE var.emp.se Variance Emp SE","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var.ratio.mcse.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Variability ratio MCSE — var.ratio.mcse","text":"wolter2007outstandR","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":null,"dir":"Reference","previous_headings":"","what":"Variance estimate by pooling — var_by_pooling","title":"Variance estimate by pooling — var_by_pooling","text":"Use combining rules estimate.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Variance estimate by pooling — var_by_pooling","text":"","code":"var_by_pooling(n_imp, bar.v, b)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Variance estimate by pooling — var_by_pooling","text":"n_imp Number syntheses used analysis stage (high low Monte Carlo error) bar.v \"within\" variance (average variance point estimates) b \"\" variance (sample variance point estimates)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/var_by_pooling.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Variance estimate by pooling — var_by_pooling","text":"Numeric value variance estimate using pooling.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":null,"dir":"Reference","previous_headings":"","what":"Wald-type interval estimates — wald_type_interval","title":"Wald-type interval estimates — wald_type_interval","text":"Constructed using t-distribution nu degrees freedom.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Wald-type interval estimates — wald_type_interval","text":"","code":"wald_type_interval(n_imp, bar.v, b)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Wald-type interval estimates — wald_type_interval","text":"n_imp Number syntheses used analysis stage (high low Monte Carlo error) bar.v \"within\" variance (average variance point estimates) b \"\" variance (sample variance point estimates)","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/reference/wald_type_interval.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Wald-type interval estimates — wald_type_interval","text":"Numeric value Wald-type interval estimates.","code":""},{"path":[]},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"new-features-2-0-0","dir":"Changelog","previous_headings":"","what":"New features","title":"outstandR 2.0.0","text":"Explicit Model Specifications: package architecture fundamentally updated explicitly separate outcome prediction population weighting. formula argument across strategy_*() functions now accepts list containing outcome_model balance_model. conceptual split makes statistical intent methods like MAIC much clearer (.e., defining exactly covariates balance vs. regress ) future-proofs package upcoming doubly-robust methods require models simultaneously. support new architecture, strategy_maic() introduces intelligent defaults missing formula components: traditional single formula passed (legacy support), automatically infers balance_model stripping response treatment variables. balance_model omitted list, acts delayed function defaulting linear sum covariates found aggregate-level data (ALD). outcome_model omitted, gracefully defaults y ~ trt. outstandR() gains new verbose argument (defaulting TRUE), allowing users silence console output simulations repetitive tasks. also introduces proactive warnings computationally expensive operations (e.g., high n_boot MAIC, large N×RN \\times R ML G-computation) prevent users thinking session hung. MAIC weight estimation can now balance covariate variances covariances, reducing residual confounding mismatched distributions. Added moments argument strategy definition functions calc_maic(). Setting moments = 2 automatically expands balancing formula include squared terms. Added int argument strategy definition functions calc_maic(). Setting int = TRUE automatically expands balancing formula include two-way interactions covariates. Automatic variance target calculation moments = 2, maic.boot() function now automatically calculates required aggregate target squared terms (E[X2]E[X^2]) internally using base variable’s mean sd provided ALD.","code":"# New recommended approach  strategy_maic(   formula = list(     outcome_model = y ~ trt,      balance_model = ~ age + sex   ) )  # Legacy approach (still supported)  strategy_maic(formula = y ~ trt + age + sex)"},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"minor-improvements-and-fixes-2-0-0","dir":"Changelog","previous_headings":"","what":"Minor improvements and fixes","title":"outstandR 2.0.0","text":"Fixed critical bug strategy_mim() strategy_gcomp_bayes() covariate uncertainty fully propagated due incorrect looping predicted samples. Significantly improved performance MAIC method refactoring maic.boot() pre-calculate balance outcome matrices, reducing redundant computations bootstrap iterations. guess_treatment_name() (used hood strategies trt_var NULL) now smarter. correctly identifies treatment variable checking duplicated variables interaction terms, falling back last main effect term. check_balance_formula() added provide strict validation balance models. ensures formula one-sided (response variable) throws informative warning treatment variable mistakenly included. check_formula() now explicitly intercepts Surv objects outcome models. throws clear, informative error stating survival data support officially scheduled later version. Improved reproducibility side-effect management switching withr::local_seed() local random seed handling. Updated print.outstandR() method handle delayed balance model functions, providing clearer output auto-generated models. Standardized strategy naming: strategy_gcomp_stan() now strategy_gcomp_bayes() accurately reflect underlying statistical approach.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"deprecated-and-defunct-2-0-0","dir":"Changelog","previous_headings":"","what":"Deprecated and defunct","title":"outstandR 2.0.0","text":"strategy_stc() now deprecated removed future release. Simulated Treatment Comparison (STC) phased favor G-computation approaches (e.g., strategy_gcomp_ml()), offer better statistical properties population adjustment.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"outstandr-100","dir":"Changelog","previous_headings":"","what":"outstandR 1.0.0","title":"outstandR 1.0.0","text":"outstandR 1.0.0 marks major milestone, transforming original code Remiro-Azocar study generalized, user-friendly R package.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"breaking-changes--major-updates-1-0-0","dir":"Changelog","previous_headings":"","what":"Breaking changes & major updates","title":"outstandR 1.0.0","text":"aggregate-level data (ALD) input redesigned use standard long format, replacing legacy format used original study. Treatment labels covariate names longer hard-coded. outstandR now dynamically extracts treatment arms (e.g., rather “”, “B”, “C”) general covariates directly input data (5119596). Covariate generation functions separated moved standalone package, simcovariates.","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"expanded-modelling-capabilities-1-0-0","dir":"Changelog","previous_headings":"","what":"Expanded modelling capabilities","title":"outstandR 1.0.0","text":"family argument outstandR() expanded support binary (binomial), continuous (gaussian), count data (poisson). Input data can now contain combination binary continuous covariates, specifically upgraded MAIC (4fb1e21). simulate_ALD_pseudo_pop() now accepts user-provided marginal arguments target distribution. can defined optionally via marginal_distns marginal_params strategy_gcomp_ml() strategy_gcomp_bayes(). Users can now explicitly select outcome scale (e.g., log-odds, risk difference, relative risk) using new scale argument outstandR(). Added support optional correlation structures ALD simulations (d48d0ab).","code":""},{"path":"https://StatisticsHealthEconomics.github.io/outstandR/news/index.html","id":"output--documentation-improvements-1-0-0","dir":"Changelog","previous_headings":"","what":"Output & documentation improvements","title":"outstandR 1.0.0","text":"main outstandR() function now returns absolute values addition treatment contrasts (2f1fbd7). Added dedicated print() method outstandR objects cleanly display analysis results (983cb2f). Comprehensive, separate vignettes demonstrating workflows binary, continuous, count outcome data (fc10a68). complete package documentation website built using pkgdown now available via GitHub Pages (4df16f2).","code":""}]
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index c6bf26d..2747eac 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -41,6 +41,7 @@
 <url><loc>https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_continuous.html</loc></url>
 <url><loc>https://StatisticsHealthEconomics.github.io/outstandR/reference/calculate_trial_variance_count.html</loc></url>
 <url><loc>https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_ALD_stats.html</loc></url>
+<url><loc>https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_bucher_naive.html</loc></url>
 <url><loc>https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_bayes.html</loc></url>
 <url><loc>https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_ml.html</loc></url>
 <url><loc>https://StatisticsHealthEconomics.github.io/outstandR/reference/calc_gcomp_stan.html</loc></url>
diff --git a/inst/jss-section.html b/inst/jss-section.html
index be32d29..428f834 100644
--- a/inst/jss-section.html
+++ b/inst/jss-section.html
@@ -277,10 +277,13 @@ <h4 class="anchored" data-anchor-id="running-outstandr">Running outstandR()</h4>
 <div class="cell-output cell-output-stderr">
 <pre><code>ℹ Starting Bootstrap with 1000 replicates.</code></pre>
 </div>
+<div class="cell-output cell-output-stderr">
+<pre><code>Treatment is guessed as: trt</code></pre>
+</div>
 </div>
 <p>As detailed in Section X, the <code>outstandR()</code> function returns a list object. To help with interpreting the results, <code>outstandR</code> includes a convenience <code>print</code> method.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb22"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>Object of class 'outstandR' 
 ITC algorithm: MAIC 
@@ -388,8 +391,8 @@ <h4 class="anchored" data-anchor-id="running-outstandr">Running outstandR()</h4>
 </div>
 <p>Forest plots of the results across all adjustment strategies for the binary outcome are given in Figure X by calling the following.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb47"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(outstandR_maic, outstandR_stc, outstandR_gcomp_ml, </span>
-<span id="cb47-2"><a href="#cb47-2" aria-hidden="true" tabindex="-1"></a>     outstandR_gcomp_bayes, outstandR_mim)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb48"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(outstandR_maic, outstandR_stc, outstandR_gcomp_ml, </span>
+<span id="cb48-2"><a href="#cb48-2" aria-hidden="true" tabindex="-1"></a>     outstandR_gcomp_bayes, outstandR_mim)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output-display">
 <div>
 <figure class="figure">
@@ -407,9 +410,9 @@ <h3 class="anchored" data-anchor-id="continuous-outcome-data">Continuous outcome
 <p>Analogous to the first example with binary outcomes and continuous covariates, we now extend this for the case of continuous outcomes and a mixture of binary and continuous covariates. The same steps are followed.</p>
 <p>First, read in the data.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb48"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a><span class="co"># A vs C individual-level data</span></span>
-<span id="cb48-2"><a href="#cb48-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(AC_IPD_contY_mixedX)</span>
-<span id="cb48-3"><a href="#cb48-3" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(AC_IPD_contY_mixedX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb49"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a><span class="co"># A vs C individual-level data</span></span>
+<span id="cb49-2"><a href="#cb49-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(AC_IPD_contY_mixedX)</span>
+<span id="cb49-3"><a href="#cb49-3" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(AC_IPD_contY_mixedX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>  id        X1 X2        X3 X4 trt          y   true_eta
 1  1 0.3066158  0 1.0794085  0   A -2.3321553 -0.9789591
@@ -419,9 +422,9 @@ <h3 class="anchored" data-anchor-id="continuous-outcome-data">Continuous outcome
 5  5 0.5672248  0 0.5305725  0   A -3.3441703 -1.3985394
 6  6 0.4897103  1 0.1289250  1   A -1.2286456 -0.3974177</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb50"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb50-1"><a href="#cb50-1" aria-hidden="true" tabindex="-1"></a><span class="co"># B vs C aggregate-level data</span></span>
-<span id="cb50-2"><a href="#cb50-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(BC_ALD_contY_mixedX)</span>
-<span id="cb50-3"><a href="#cb50-3" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(BC_ALD_contY_mixedX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb51"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb51-1"><a href="#cb51-1" aria-hidden="true" tabindex="-1"></a><span class="co"># B vs C aggregate-level data</span></span>
+<span id="cb51-2"><a href="#cb51-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(BC_ALD_contY_mixedX)</span>
+<span id="cb51-3"><a href="#cb51-3" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(BC_ALD_contY_mixedX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code># A tibble: 14 × 4
    variable statistic   value trt  
@@ -449,11 +452,11 @@ <h3 class="anchored" data-anchor-id="continuous-outcome-data">Continuous outcome
 \]</span></p>
 <p>This corresponds to the <code>R</code> formula given by</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb52"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a>lin_form_mixedX <span class="ot">&lt;-</span> <span class="fu">as.formula</span>(<span class="st">"y ~ X1 + X2 + X3 + trt + trt:(X1 + X2 + X4)"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb53"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>lin_form_mixedX <span class="ot">&lt;-</span> <span class="fu">as.formula</span>(<span class="st">"y ~ X1 + X2 + X3 + trt + trt:(X1 + X2 + X4)"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>The balance formula includes the effect modifiers and is given by</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb53"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>bal_form_mixedX <span class="ot">&lt;-</span> <span class="fu">as.formula</span>(<span class="st">"~ X1 + X2 + X4"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb54"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a>bal_form_mixedX <span class="ot">&lt;-</span> <span class="fu">as.formula</span>(<span class="st">"~ X1 + X2 + X4"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <section id="relative-treatment-effect" class="level4">
 <h4 class="anchored" data-anchor-id="relative-treatment-effect">Relative treatment effect</h4>
@@ -471,16 +474,16 @@ <h4 class="anchored" data-anchor-id="relative-treatment-effect">Relative treatme
 <h4 class="anchored" data-anchor-id="running-outstandr-1">Running outstandR()</h4>
 <p>A difference from the previous binary outcome data example is the <code>family = gaussian(link = "identity")</code> argument indicating a Normal linear regression. The full call to <code>outstandR()</code> is:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb54"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a>outstandR_maic <span class="ot">&lt;-</span> </span>
-<span id="cb54-2"><a href="#cb54-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
-<span id="cb54-3"><a href="#cb54-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_contY_mixedX, </span>
-<span id="cb54-4"><a href="#cb54-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_contY_mixedX,</span>
-<span id="cb54-5"><a href="#cb54-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(</span>
-<span id="cb54-6"><a href="#cb54-6" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> <span class="fu">formula</span>(<span class="st">"y ~ trt"</span>),</span>
-<span id="cb54-7"><a href="#cb54-7" aria-hidden="true" tabindex="-1"></a>                     <span class="at">balance_model =</span> bal_form_mixedX),</span>
-<span id="cb54-8"><a href="#cb54-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">gaussian</span>(<span class="at">link =</span> <span class="st">"identity"</span>)),</span>
-<span id="cb54-9"><a href="#cb54-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span></span>
-<span id="cb54-10"><a href="#cb54-10" aria-hidden="true" tabindex="-1"></a>  )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb55"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a>outstandR_maic <span class="ot">&lt;-</span> </span>
+<span id="cb55-2"><a href="#cb55-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
+<span id="cb55-3"><a href="#cb55-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_contY_mixedX, </span>
+<span id="cb55-4"><a href="#cb55-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_contY_mixedX,</span>
+<span id="cb55-5"><a href="#cb55-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(</span>
+<span id="cb55-6"><a href="#cb55-6" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> <span class="fu">formula</span>(<span class="st">"y ~ trt"</span>),</span>
+<span id="cb55-7"><a href="#cb55-7" aria-hidden="true" tabindex="-1"></a>                     <span class="at">balance_model =</span> bal_form_mixedX),</span>
+<span id="cb55-8"><a href="#cb55-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">gaussian</span>(<span class="at">link =</span> <span class="st">"identity"</span>)),</span>
+<span id="cb55-9"><a href="#cb55-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span></span>
+<span id="cb55-10"><a href="#cb55-10" aria-hidden="true" tabindex="-1"></a>  )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code>Treatment is guessed as: trt</code></pre>
 </div>
@@ -508,13 +511,17 @@ <h4 class="anchored" data-anchor-id="running-outstandr-1">Running outstandR()</h
 <div class="cell-output cell-output-stderr">
 <pre><code>ℹ Starting Bootstrap with 1000 replicates.</code></pre>
 </div>
+<div class="cell-output cell-output-stderr">
+<pre><code>Treatment is guessed as: trt</code></pre>
+</div>
 </div>
 <p>Again, if we interrogate the output we see the same list format. The differences from the first example are the model and scale components correspond to the continuous input data used. That is, the default output contrast is the mean difference.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb64"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb64-1"><a href="#cb64-1" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(outstandR_maic, <span class="at">max.level =</span> <span class="dv">1</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb66"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb66-1"><a href="#cb66-1" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(outstandR_maic, <span class="at">max.level =</span> <span class="dv">1</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>List of 13
+<pre><code>List of 14
  $ results      :List of 2
+ $ naive        :List of 3
  $ call         : language outstandR(ipd_trial = AC_IPD_contY_mixedX, ald_trial = BC_ALD_contY_mixedX,      strategy = strategy_maic(formula| __truncated__ ...
  $ outcome_model:Class 'formula'  language y ~ trt
   .. ..- attr(*, ".Environment")=&lt;environment: R_GlobalEnv&gt; 
@@ -532,7 +539,7 @@ <h4 class="anchored" data-anchor-id="running-outstandr-1">Running outstandR()</h
  $ model        :List of 3
  - attr(*, "class")= chr [1:2] "outstandR" "list"</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb66"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb66-1"><a href="#cb66-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb68"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb68-1"><a href="#cb68-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>Object of class 'outstandR' 
 ITC algorithm: MAIC 
@@ -635,8 +642,8 @@ <h4 class="anchored" data-anchor-id="running-outstandr-1">Running outstandR()</h
 </div>
 </div>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb91"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb91-1"><a href="#cb91-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(outstandR_maic, outstandR_stc, outstandR_gcomp_ml, </span>
-<span id="cb91-2"><a href="#cb91-2" aria-hidden="true" tabindex="-1"></a>     outstandR_gcomp_bayes, outstandR_mim)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb93"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb93-1"><a href="#cb93-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(outstandR_maic, outstandR_stc, outstandR_gcomp_ml, </span>
+<span id="cb93-2"><a href="#cb93-2" aria-hidden="true" tabindex="-1"></a>     outstandR_gcomp_bayes, outstandR_mim)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output-display">
 <div>
 <figure class="figure">
@@ -652,9 +659,9 @@ <h4 class="anchored" data-anchor-id="running-outstandr-1">Running outstandR()</h
 <h3 class="anchored" data-anchor-id="count-outcome-data">Count outcome data</h3>
 <p>First, read in and view the two data sets.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb92"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb92-1"><a href="#cb92-1" aria-hidden="true" tabindex="-1"></a><span class="co"># A vs C individual-level data</span></span>
-<span id="cb92-2"><a href="#cb92-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(AC_IPD_countY_contX)</span>
-<span id="cb92-3"><a href="#cb92-3" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(AC_IPD_countY_contX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb94"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb94-1"><a href="#cb94-1" aria-hidden="true" tabindex="-1"></a><span class="co"># A vs C individual-level data</span></span>
+<span id="cb94-2"><a href="#cb94-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(AC_IPD_countY_contX)</span>
+<span id="cb94-3"><a href="#cb94-3" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(AC_IPD_countY_contX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>  id   PF_cont_1 PF_cont_2 EM_cont_1   EM_cont_2 trt y    true_eta
 1  1 -0.03120828 0.2000877 0.7946610  0.59843299   A 0 -1.69699568
@@ -664,9 +671,9 @@ <h3 class="anchored" data-anchor-id="count-outcome-data">Count outcome data</h3>
 5  5  0.49349123 0.9075975 0.6009318 -0.02910612   A 1 -1.17179280
 6  6  0.48906050 0.2393630 0.4741692  0.45545576   C 1 -0.09509531</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb94"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb94-1"><a href="#cb94-1" aria-hidden="true" tabindex="-1"></a><span class="co"># B vs C aggregate-level data</span></span>
-<span id="cb94-2"><a href="#cb94-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(BC_ALD_countY_contX)</span>
-<span id="cb94-3"><a href="#cb94-3" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(BC_ALD_countY_contX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb96"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb96-1"><a href="#cb96-1" aria-hidden="true" tabindex="-1"></a><span class="co"># B vs C aggregate-level data</span></span>
+<span id="cb96-2"><a href="#cb96-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(BC_ALD_countY_contX)</span>
+<span id="cb96-3"><a href="#cb96-3" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(BC_ALD_countY_contX)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code># A tibble: 16 × 4
    variable  statistic   value trt  
@@ -709,15 +716,15 @@ <h4 class="anchored" data-anchor-id="relative-treatment-effects-1">Relative trea
 <h4 class="anchored" data-anchor-id="running-outstandr-2">Running outstandR()</h4>
 <p>A difference from the previous outcome data examples is the <code>family = poisson(link = "log")</code> argument indicating a log linear regression. The full call to <code>outstandR()</code> is</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb96"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb96-1"><a href="#cb96-1" aria-hidden="true" tabindex="-1"></a>outstandR_maic <span class="ot">&lt;-</span> </span>
-<span id="cb96-2"><a href="#cb96-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
-<span id="cb96-3"><a href="#cb96-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_countY_contX,</span>
-<span id="cb96-4"><a href="#cb96-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_countY_contX,</span>
-<span id="cb96-5"><a href="#cb96-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(</span>
-<span id="cb96-6"><a href="#cb96-6" aria-hidden="true" tabindex="-1"></a>               <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> <span class="fu">formula</span>(<span class="st">"y ~ trt"</span>),</span>
-<span id="cb96-7"><a href="#cb96-7" aria-hidden="true" tabindex="-1"></a>                              <span class="at">balance_model =</span> bal_form_contX),</span>
-<span id="cb96-8"><a href="#cb96-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">poisson</span>(<span class="at">link =</span> <span class="st">"log"</span>)),</span>
-<span id="cb96-9"><a href="#cb96-9" aria-hidden="true" tabindex="-1"></a>             <span class="at">seed =</span> <span class="dv">12345</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb98"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb98-1"><a href="#cb98-1" aria-hidden="true" tabindex="-1"></a>outstandR_maic <span class="ot">&lt;-</span> </span>
+<span id="cb98-2"><a href="#cb98-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
+<span id="cb98-3"><a href="#cb98-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_countY_contX,</span>
+<span id="cb98-4"><a href="#cb98-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_countY_contX,</span>
+<span id="cb98-5"><a href="#cb98-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(</span>
+<span id="cb98-6"><a href="#cb98-6" aria-hidden="true" tabindex="-1"></a>               <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> <span class="fu">formula</span>(<span class="st">"y ~ trt"</span>),</span>
+<span id="cb98-7"><a href="#cb98-7" aria-hidden="true" tabindex="-1"></a>                              <span class="at">balance_model =</span> bal_form_contX),</span>
+<span id="cb98-8"><a href="#cb98-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">poisson</span>(<span class="at">link =</span> <span class="st">"log"</span>)),</span>
+<span id="cb98-9"><a href="#cb98-9" aria-hidden="true" tabindex="-1"></a>             <span class="at">seed =</span> <span class="dv">12345</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code>Treatment is guessed as: trt</code></pre>
 </div>
@@ -745,10 +752,13 @@ <h4 class="anchored" data-anchor-id="running-outstandr-2">Running outstandR()</h
 <div class="cell-output cell-output-stderr">
 <pre><code>ℹ Starting Bootstrap with 1000 replicates.</code></pre>
 </div>
+<div class="cell-output cell-output-stderr">
+<pre><code>Treatment is guessed as: trt</code></pre>
+</div>
 </div>
 <p>The differences from the first example are that the model and scale attributes correspond to the input data used. That is, the default output contrast is the mean difference.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb106"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb106-1"><a href="#cb106-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb109"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb109-1"><a href="#cb109-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>Object of class 'outstandR' 
 ITC algorithm: MAIC 
@@ -851,8 +861,8 @@ <h4 class="anchored" data-anchor-id="running-outstandr-2">Running outstandR()</h
 </div>
 </div>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb131"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb131-1"><a href="#cb131-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(outstandR_maic, outstandR_stc, outstandR_gcomp_ml, </span>
-<span id="cb131-2"><a href="#cb131-2" aria-hidden="true" tabindex="-1"></a>     outstandR_gcomp_bayes, outstandR_mim)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb134"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb134-1"><a href="#cb134-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(outstandR_maic, outstandR_stc, outstandR_gcomp_ml, </span>
+<span id="cb134-2"><a href="#cb134-2" aria-hidden="true" tabindex="-1"></a>     outstandR_gcomp_bayes, outstandR_mim)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output-display">
 <div>
 <figure class="figure">
@@ -944,18 +954,18 @@ <h2 class="anchored" data-anchor-id="user-specified-outcome-scales">User-specifi
 <p>For log-odds and log-relative risk on continuous data, the <code>R</code> code implies a transformation of the mean before calculating the variance. For “log_odds”, it uses <span class="math inline">\(\frac{\pi^2}{3 N_t}\)</span>, which is the variance of a logit-transformed mean when the underlying data are assumed to be normal and mapped to (0,1) scale, and then transformed to logit (often used for proportions derived from continuous data or for scores that can be thought of as probabilities).</p>
 <p>For example, to obtain a risk difference instead of the default log-odds ratio for the binary outcome analysis (previously shown in Section 4), we specify <code>scale = "risk_difference"</code>.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb132"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb132-1"><a href="#cb132-1" aria-hidden="true" tabindex="-1"></a>outstandR_maic_rd <span class="ot">&lt;-</span> </span>
-<span id="cb132-2"><a href="#cb132-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
-<span id="cb132-3"><a href="#cb132-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_binY_contX, </span>
-<span id="cb132-4"><a href="#cb132-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_binY_contX,</span>
-<span id="cb132-5"><a href="#cb132-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(</span>
-<span id="cb132-6"><a href="#cb132-6" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> <span class="fu">formula</span>(<span class="st">"y ~ trt"</span>),</span>
-<span id="cb132-7"><a href="#cb132-7" aria-hidden="true" tabindex="-1"></a>                     <span class="at">balance_model =</span> bal_form_contX),</span>
-<span id="cb132-8"><a href="#cb132-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">"logit"</span>)</span>
-<span id="cb132-9"><a href="#cb132-9" aria-hidden="true" tabindex="-1"></a>    ),</span>
-<span id="cb132-10"><a href="#cb132-10" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>,</span>
-<span id="cb132-11"><a href="#cb132-11" aria-hidden="true" tabindex="-1"></a>    <span class="at">scale =</span> <span class="st">"risk_difference"</span>  <span class="co"># instead of default log-odds ratio</span></span>
-<span id="cb132-12"><a href="#cb132-12" aria-hidden="true" tabindex="-1"></a>  )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb135"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb135-1"><a href="#cb135-1" aria-hidden="true" tabindex="-1"></a>outstandR_maic_rd <span class="ot">&lt;-</span> </span>
+<span id="cb135-2"><a href="#cb135-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
+<span id="cb135-3"><a href="#cb135-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_binY_contX, </span>
+<span id="cb135-4"><a href="#cb135-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_binY_contX,</span>
+<span id="cb135-5"><a href="#cb135-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(</span>
+<span id="cb135-6"><a href="#cb135-6" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> <span class="fu">formula</span>(<span class="st">"y ~ trt"</span>),</span>
+<span id="cb135-7"><a href="#cb135-7" aria-hidden="true" tabindex="-1"></a>                     <span class="at">balance_model =</span> bal_form_contX),</span>
+<span id="cb135-8"><a href="#cb135-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">"logit"</span>)</span>
+<span id="cb135-9"><a href="#cb135-9" aria-hidden="true" tabindex="-1"></a>    ),</span>
+<span id="cb135-10"><a href="#cb135-10" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>,</span>
+<span id="cb135-11"><a href="#cb135-11" aria-hidden="true" tabindex="-1"></a>    <span class="at">scale =</span> <span class="st">"risk_difference"</span>  <span class="co"># instead of default log-odds ratio</span></span>
+<span id="cb135-12"><a href="#cb135-12" aria-hidden="true" tabindex="-1"></a>  )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code>Treatment is guessed as: trt</code></pre>
 </div>
@@ -983,10 +993,13 @@ <h2 class="anchored" data-anchor-id="user-specified-outcome-scales">User-specifi
 <div class="cell-output cell-output-stderr">
 <pre><code>ℹ Starting Bootstrap with 1000 replicates.</code></pre>
 </div>
+<div class="cell-output cell-output-stderr">
+<pre><code>Treatment is guessed as: trt</code></pre>
+</div>
 </div>
 <p>The output now displays the contrast estimates on the probability scale:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb142"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb142-1"><a href="#cb142-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic_rd)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb146"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb146-1"><a href="#cb146-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic_rd)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>Object of class 'outstandR' 
 ITC algorithm: MAIC 
@@ -1023,16 +1036,16 @@ <h2 class="anchored" data-anchor-id="robust-variance-estimation">Robust variance
 <p>Standard errors in population-adjusted analyses can be sensitive to model misspecification. Users can request robust (sandwich) standard errors by setting the <code>var_method</code> argument to <code>"sandwich"</code>.</p>
 <p>The following example demonstrates how to compare the naive model-based standard error with the robust sandwich estimate for a maximum likelihood G-computation analysis:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb144"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb144-1"><a href="#cb144-1" aria-hidden="true" tabindex="-1"></a><span class="co"># standard STC analysis</span></span>
-<span id="cb144-2"><a href="#cb144-2" aria-hidden="true" tabindex="-1"></a>stc_naive <span class="ot">&lt;-</span> </span>
-<span id="cb144-3"><a href="#cb144-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
-<span id="cb144-4"><a href="#cb144-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_binY_contX,</span>
-<span id="cb144-5"><a href="#cb144-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_binY_contX,</span>
-<span id="cb144-6"><a href="#cb144-6" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
-<span id="cb144-7"><a href="#cb144-7" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_contX),</span>
-<span id="cb144-8"><a href="#cb144-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">binomial</span>()),</span>
-<span id="cb144-9"><a href="#cb144-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>,</span>
-<span id="cb144-10"><a href="#cb144-10" aria-hidden="true" tabindex="-1"></a>    <span class="at">var_method =</span> <span class="st">"sample"</span>) <span class="co"># Default</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb148"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb148-1"><a href="#cb148-1" aria-hidden="true" tabindex="-1"></a><span class="co"># standard STC analysis</span></span>
+<span id="cb148-2"><a href="#cb148-2" aria-hidden="true" tabindex="-1"></a>stc_naive <span class="ot">&lt;-</span> </span>
+<span id="cb148-3"><a href="#cb148-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
+<span id="cb148-4"><a href="#cb148-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_binY_contX,</span>
+<span id="cb148-5"><a href="#cb148-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_binY_contX,</span>
+<span id="cb148-6"><a href="#cb148-6" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
+<span id="cb148-7"><a href="#cb148-7" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_contX),</span>
+<span id="cb148-8"><a href="#cb148-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">binomial</span>()),</span>
+<span id="cb148-9"><a href="#cb148-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>,</span>
+<span id="cb148-10"><a href="#cb148-10" aria-hidden="true" tabindex="-1"></a>    <span class="at">var_method =</span> <span class="st">"sample"</span>) <span class="co"># Default</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code></code></pre>
 </div>
@@ -1063,16 +1076,16 @@ <h2 class="anchored" data-anchor-id="robust-variance-estimation">Robust variance
 <div class="cell-output cell-output-stderr">
 <pre><code>! Large computation detected (1000000 simulations). Grab a coffee.</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb155"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb155-1"><a href="#cb155-1" aria-hidden="true" tabindex="-1"></a><span class="co"># STC with robust variance (sandwich estimator)</span></span>
-<span id="cb155-2"><a href="#cb155-2" aria-hidden="true" tabindex="-1"></a>stc_robust <span class="ot">&lt;-</span> </span>
-<span id="cb155-3"><a href="#cb155-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
-<span id="cb155-4"><a href="#cb155-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_binY_contX,</span>
-<span id="cb155-5"><a href="#cb155-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_binY_contX,</span>
-<span id="cb155-6"><a href="#cb155-6" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
-<span id="cb155-7"><a href="#cb155-7" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_contX),</span>
-<span id="cb155-8"><a href="#cb155-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">binomial</span>()),</span>
-<span id="cb155-9"><a href="#cb155-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>,</span>
-<span id="cb155-10"><a href="#cb155-10" aria-hidden="true" tabindex="-1"></a>    <span class="at">var_method =</span> <span class="st">"sandwich"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb159"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb159-1"><a href="#cb159-1" aria-hidden="true" tabindex="-1"></a><span class="co"># STC with robust variance (sandwich estimator)</span></span>
+<span id="cb159-2"><a href="#cb159-2" aria-hidden="true" tabindex="-1"></a>stc_robust <span class="ot">&lt;-</span> </span>
+<span id="cb159-3"><a href="#cb159-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
+<span id="cb159-4"><a href="#cb159-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_binY_contX,</span>
+<span id="cb159-5"><a href="#cb159-5" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_binY_contX,</span>
+<span id="cb159-6"><a href="#cb159-6" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
+<span id="cb159-7"><a href="#cb159-7" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_contX),</span>
+<span id="cb159-8"><a href="#cb159-8" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">binomial</span>()),</span>
+<span id="cb159-9"><a href="#cb159-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>,</span>
+<span id="cb159-10"><a href="#cb159-10" aria-hidden="true" tabindex="-1"></a>    <span class="at">var_method =</span> <span class="st">"sandwich"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code></code></pre>
 </div>
@@ -1105,13 +1118,13 @@ <h2 class="anchored" data-anchor-id="robust-variance-estimation">Robust variance
 </div>
 </div>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb166"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb166-1"><a href="#cb166-1" aria-hidden="true" tabindex="-1"></a><span class="co"># compare standard errors</span></span>
-<span id="cb166-2"><a href="#cb166-2" aria-hidden="true" tabindex="-1"></a><span class="fu">unlist</span>(stc_naive<span class="sc">$</span>results<span class="sc">$</span>contrasts<span class="sc">$</span>var)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb170"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb170-1"><a href="#cb170-1" aria-hidden="true" tabindex="-1"></a><span class="co"># compare standard errors</span></span>
+<span id="cb170-2"><a href="#cb170-2" aria-hidden="true" tabindex="-1"></a><span class="fu">unlist</span>(stc_naive<span class="sc">$</span>results<span class="sc">$</span>contrasts<span class="sc">$</span>var)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>       AB        AC        BC 
 0.2465598 0.1443287 0.1022311 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb168"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb168-1"><a href="#cb168-1" aria-hidden="true" tabindex="-1"></a><span class="fu">unlist</span>(stc_robust<span class="sc">$</span>results<span class="sc">$</span>contrasts<span class="sc">$</span>var)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb172"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb172-1"><a href="#cb172-1" aria-hidden="true" tabindex="-1"></a><span class="fu">unlist</span>(stc_robust<span class="sc">$</span>results<span class="sc">$</span>contrasts<span class="sc">$</span>var)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>       AB        AC        BC 
 0.2278323 0.1256012 0.1022311 </code></pre>
@@ -1130,20 +1143,20 @@ <h2 class="anchored" data-anchor-id="user-defined-covariate-distributions-in-g-c
 <p>This is more robust and streamlines the workflow by removing the need for users to perform these statistical transformations manually.</p>
 <p>First, define the target distributions. We specify a Gamma distribution with “gamma” for <code>X1</code> and a Binomial with “binom” for <code>X2</code>. The other covariates not listed (<code>X3</code>, <code>X4</code>) default to a Normal distribution i.e.&nbsp;“norm”.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb170"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb170-1"><a href="#cb170-1" aria-hidden="true" tabindex="-1"></a><span class="co"># define distributions</span></span>
-<span id="cb170-2"><a href="#cb170-2" aria-hidden="true" tabindex="-1"></a>custom_distns <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="at">X1 =</span> <span class="st">"gamma"</span>, <span class="at">X2 =</span> <span class="st">"binom"</span>)</span>
-<span id="cb170-3"><a href="#cb170-3" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb170-4"><a href="#cb170-4" aria-hidden="true" tabindex="-1"></a><span class="co"># run G-computation ML</span></span>
-<span id="cb170-5"><a href="#cb170-5" aria-hidden="true" tabindex="-1"></a>outstandR_sens <span class="ot">&lt;-</span> </span>
-<span id="cb170-6"><a href="#cb170-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
-<span id="cb170-7"><a href="#cb170-7" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_contY_mixedX,</span>
-<span id="cb170-8"><a href="#cb170-8" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_contY_mixedX,</span>
-<span id="cb170-9"><a href="#cb170-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
-<span id="cb170-10"><a href="#cb170-10" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_mixedX),</span>
-<span id="cb170-11"><a href="#cb170-11" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">gaussian</span>(<span class="at">link =</span> <span class="st">"identity"</span>),</span>
-<span id="cb170-12"><a href="#cb170-12" aria-hidden="true" tabindex="-1"></a>      <span class="at">marginal_distns =</span> custom_distns,</span>
-<span id="cb170-13"><a href="#cb170-13" aria-hidden="true" tabindex="-1"></a>      <span class="at">N =</span> <span class="dv">1000</span>),</span>
-<span id="cb170-14"><a href="#cb170-14" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb174"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb174-1"><a href="#cb174-1" aria-hidden="true" tabindex="-1"></a><span class="co"># define distributions</span></span>
+<span id="cb174-2"><a href="#cb174-2" aria-hidden="true" tabindex="-1"></a>custom_distns <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="at">X1 =</span> <span class="st">"gamma"</span>, <span class="at">X2 =</span> <span class="st">"binom"</span>)</span>
+<span id="cb174-3"><a href="#cb174-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb174-4"><a href="#cb174-4" aria-hidden="true" tabindex="-1"></a><span class="co"># run G-computation ML</span></span>
+<span id="cb174-5"><a href="#cb174-5" aria-hidden="true" tabindex="-1"></a>outstandR_sens <span class="ot">&lt;-</span> </span>
+<span id="cb174-6"><a href="#cb174-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
+<span id="cb174-7"><a href="#cb174-7" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_contY_mixedX,</span>
+<span id="cb174-8"><a href="#cb174-8" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_contY_mixedX,</span>
+<span id="cb174-9"><a href="#cb174-9" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
+<span id="cb174-10"><a href="#cb174-10" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_mixedX),</span>
+<span id="cb174-11"><a href="#cb174-11" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">gaussian</span>(<span class="at">link =</span> <span class="st">"identity"</span>),</span>
+<span id="cb174-12"><a href="#cb174-12" aria-hidden="true" tabindex="-1"></a>      <span class="at">marginal_distns =</span> custom_distns,</span>
+<span id="cb174-13"><a href="#cb174-13" aria-hidden="true" tabindex="-1"></a>      <span class="at">N =</span> <span class="dv">1000</span>),</span>
+<span id="cb174-14"><a href="#cb174-14" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code></code></pre>
 </div>
@@ -1174,7 +1187,7 @@ <h2 class="anchored" data-anchor-id="user-defined-covariate-distributions-in-g-c
 <div class="cell-output cell-output-stderr">
 <pre><code>! Large computation detected (1e+06 simulations). Grab a coffee.</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb181"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb181-1"><a href="#cb181-1" aria-hidden="true" tabindex="-1"></a>outstandR_sens</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb185"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb185-1"><a href="#cb185-1" aria-hidden="true" tabindex="-1"></a>outstandR_sens</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>Object of class 'outstandR' 
 ITC algorithm: GCOMP_ML 
@@ -1210,28 +1223,28 @@ <h4 class="anchored" data-anchor-id="manual-parameter-specification">Manual para
 <p>There are scenarios where manual specification via the <code>marginal_params</code> argument is also necessary. One use case is as a sensitivity analysis, where a researcher wishes to assess the robustness of the relative treatment effect estimates to deviations in the target population’s characteristics of the IPD trial. For instance, if the ALD reports a mean age of 65, a researcher might wish to simulate a target population with a mean age of 70 to test if the conclusions hold for an older cohort. Additionally, manual specification is required for distributions where the method of moments conversion is not natively supported by the package (e.g., specific parameterizations of the Weibull distribution).</p>
 <p>The following code illustrates how to manually override the ALD statistics to simulate an older population.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb183"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb183-1"><a href="#cb183-1" aria-hidden="true" tabindex="-1"></a><span class="co"># manually specify parameters for 'age' (mean=70, sd=10.5)</span></span>
-<span id="cb183-2"><a href="#cb183-2" aria-hidden="true" tabindex="-1"></a><span class="co"># convert mean=70/sd=10.5 to shape/rate manually </span></span>
-<span id="cb183-3"><a href="#cb183-3" aria-hidden="true" tabindex="-1"></a><span class="co"># or pass them if we already know the specific shape/rate</span></span>
-<span id="cb183-4"><a href="#cb183-4" aria-hidden="true" tabindex="-1"></a>target_mean <span class="ot">&lt;-</span> <span class="dv">70</span></span>
-<span id="cb183-5"><a href="#cb183-5" aria-hidden="true" tabindex="-1"></a>target_sd <span class="ot">&lt;-</span> <span class="fl">10.5</span></span>
-<span id="cb183-6"><a href="#cb183-6" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb183-7"><a href="#cb183-7" aria-hidden="true" tabindex="-1"></a>new_params <span class="ot">&lt;-</span> <span class="fu">list</span>(</span>
-<span id="cb183-8"><a href="#cb183-8" aria-hidden="true" tabindex="-1"></a>  <span class="at">X1 =</span> <span class="fu">list</span>(<span class="at">shape =</span> (target_mean<span class="sc">/</span>target_sd)<span class="sc">^</span><span class="dv">2</span>, </span>
-<span id="cb183-9"><a href="#cb183-9" aria-hidden="true" tabindex="-1"></a>            <span class="at">rate =</span> target_mean<span class="sc">/</span>(target_sd<span class="sc">^</span><span class="dv">2</span>)))</span>
-<span id="cb183-10"><a href="#cb183-10" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb183-11"><a href="#cb183-11" aria-hidden="true" tabindex="-1"></a><span class="co"># run G-computation with manual override</span></span>
-<span id="cb183-12"><a href="#cb183-12" aria-hidden="true" tabindex="-1"></a>outstandR_sens <span class="ot">&lt;-</span> </span>
-<span id="cb183-13"><a href="#cb183-13" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
-<span id="cb183-14"><a href="#cb183-14" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_contY_mixedX,</span>
-<span id="cb183-15"><a href="#cb183-15" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_contY_mixedX,</span>
-<span id="cb183-16"><a href="#cb183-16" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
-<span id="cb183-17"><a href="#cb183-17" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_mixedX),</span>
-<span id="cb183-18"><a href="#cb183-18" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">gaussian</span>(<span class="at">link =</span> <span class="st">"identity"</span>),</span>
-<span id="cb183-19"><a href="#cb183-19" aria-hidden="true" tabindex="-1"></a>      <span class="at">marginal_distns =</span> custom_distns,</span>
-<span id="cb183-20"><a href="#cb183-20" aria-hidden="true" tabindex="-1"></a>      <span class="at">marginal_params =</span> new_params, <span class="co"># overrides ALD for X1</span></span>
-<span id="cb183-21"><a href="#cb183-21" aria-hidden="true" tabindex="-1"></a>      <span class="at">N =</span> <span class="dv">1000</span>),</span>
-<span id="cb183-22"><a href="#cb183-22" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb187"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb187-1"><a href="#cb187-1" aria-hidden="true" tabindex="-1"></a><span class="co"># manually specify parameters for 'age' (mean=70, sd=10.5)</span></span>
+<span id="cb187-2"><a href="#cb187-2" aria-hidden="true" tabindex="-1"></a><span class="co"># convert mean=70/sd=10.5 to shape/rate manually </span></span>
+<span id="cb187-3"><a href="#cb187-3" aria-hidden="true" tabindex="-1"></a><span class="co"># or pass them if we already know the specific shape/rate</span></span>
+<span id="cb187-4"><a href="#cb187-4" aria-hidden="true" tabindex="-1"></a>target_mean <span class="ot">&lt;-</span> <span class="dv">70</span></span>
+<span id="cb187-5"><a href="#cb187-5" aria-hidden="true" tabindex="-1"></a>target_sd <span class="ot">&lt;-</span> <span class="fl">10.5</span></span>
+<span id="cb187-6"><a href="#cb187-6" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb187-7"><a href="#cb187-7" aria-hidden="true" tabindex="-1"></a>new_params <span class="ot">&lt;-</span> <span class="fu">list</span>(</span>
+<span id="cb187-8"><a href="#cb187-8" aria-hidden="true" tabindex="-1"></a>  <span class="at">X1 =</span> <span class="fu">list</span>(<span class="at">shape =</span> (target_mean<span class="sc">/</span>target_sd)<span class="sc">^</span><span class="dv">2</span>, </span>
+<span id="cb187-9"><a href="#cb187-9" aria-hidden="true" tabindex="-1"></a>            <span class="at">rate =</span> target_mean<span class="sc">/</span>(target_sd<span class="sc">^</span><span class="dv">2</span>)))</span>
+<span id="cb187-10"><a href="#cb187-10" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb187-11"><a href="#cb187-11" aria-hidden="true" tabindex="-1"></a><span class="co"># run G-computation with manual override</span></span>
+<span id="cb187-12"><a href="#cb187-12" aria-hidden="true" tabindex="-1"></a>outstandR_sens <span class="ot">&lt;-</span> </span>
+<span id="cb187-13"><a href="#cb187-13" aria-hidden="true" tabindex="-1"></a>  <span class="fu">outstandR</span>(</span>
+<span id="cb187-14"><a href="#cb187-14" aria-hidden="true" tabindex="-1"></a>    <span class="at">ipd_trial =</span> AC_IPD_contY_mixedX,</span>
+<span id="cb187-15"><a href="#cb187-15" aria-hidden="true" tabindex="-1"></a>    <span class="at">ald_trial =</span> BC_ALD_contY_mixedX,</span>
+<span id="cb187-16"><a href="#cb187-16" aria-hidden="true" tabindex="-1"></a>    <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
+<span id="cb187-17"><a href="#cb187-17" aria-hidden="true" tabindex="-1"></a>      <span class="at">formula =</span> <span class="fu">list</span>(<span class="at">outcome_model =</span> lin_form_mixedX),</span>
+<span id="cb187-18"><a href="#cb187-18" aria-hidden="true" tabindex="-1"></a>      <span class="at">family =</span> <span class="fu">gaussian</span>(<span class="at">link =</span> <span class="st">"identity"</span>),</span>
+<span id="cb187-19"><a href="#cb187-19" aria-hidden="true" tabindex="-1"></a>      <span class="at">marginal_distns =</span> custom_distns,</span>
+<span id="cb187-20"><a href="#cb187-20" aria-hidden="true" tabindex="-1"></a>      <span class="at">marginal_params =</span> new_params, <span class="co"># overrides ALD for X1</span></span>
+<span id="cb187-21"><a href="#cb187-21" aria-hidden="true" tabindex="-1"></a>      <span class="at">N =</span> <span class="dv">1000</span>),</span>
+<span id="cb187-22"><a href="#cb187-22" aria-hidden="true" tabindex="-1"></a>    <span class="at">seed =</span> <span class="dv">12345</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code></code></pre>
 </div>
@@ -1262,7 +1275,7 @@ <h4 class="anchored" data-anchor-id="manual-parameter-specification">Manual para
 <div class="cell-output cell-output-stderr">
 <pre><code>! Large computation detected (1e+06 simulations). Grab a coffee.</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb194"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb194-1"><a href="#cb194-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_sens)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb198"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb198-1"><a href="#cb198-1" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_sens)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>Object of class 'outstandR' 
 ITC algorithm: GCOMP_ML 
@@ -1300,20 +1313,20 @@ <h2 class="anchored" data-anchor-id="model-diagnostics">Model diagnostics</h2>
 <p>For example, for an MAIC analysis, we can inspect the distribution of weights to check for outliers or near-zero effective sample sizes.</p>
 <p>Figure 2 shows the histogram of MAIC weights.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb196"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb196-1"><a href="#cb196-1" aria-hidden="true" tabindex="-1"></a><span class="co"># check Effective Sample Size</span></span>
-<span id="cb196-2"><a href="#cb196-2" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic<span class="sc">$</span>model<span class="sc">$</span>ESS)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb200"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb200-1"><a href="#cb200-1" aria-hidden="true" tabindex="-1"></a><span class="co"># check Effective Sample Size</span></span>
+<span id="cb200-2"><a href="#cb200-2" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(outstandR_maic<span class="sc">$</span>model<span class="sc">$</span>ESS)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>    ESS 
 151.053 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb198"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb198-1"><a href="#cb198-1" aria-hidden="true" tabindex="-1"></a><span class="co"># histogram of MAIC weights</span></span>
-<span id="cb198-2"><a href="#cb198-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
-<span id="cb198-3"><a href="#cb198-3" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb198-4"><a href="#cb198-4" aria-hidden="true" tabindex="-1"></a><span class="fu">data.frame</span>(<span class="at">weights =</span> outstandR_maic<span class="sc">$</span>model<span class="sc">$</span>weights) <span class="sc">|&gt;</span> </span>
-<span id="cb198-5"><a href="#cb198-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> weights)) <span class="sc">+</span></span>
-<span id="cb198-6"><a href="#cb198-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_histogram</span>(<span class="at">binwidth =</span> <span class="fl">0.1</span>, <span class="at">color =</span> <span class="st">"black"</span>, <span class="at">fill =</span> <span class="st">"lightgray"</span>) <span class="sc">+</span></span>
-<span id="cb198-7"><a href="#cb198-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">"Weights"</span>, <span class="at">y =</span> <span class="st">"Frequency"</span>) <span class="sc">+</span></span>
-<span id="cb198-8"><a href="#cb198-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_minimal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb202"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb202-1"><a href="#cb202-1" aria-hidden="true" tabindex="-1"></a><span class="co"># histogram of MAIC weights</span></span>
+<span id="cb202-2"><a href="#cb202-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
+<span id="cb202-3"><a href="#cb202-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb202-4"><a href="#cb202-4" aria-hidden="true" tabindex="-1"></a><span class="fu">data.frame</span>(<span class="at">weights =</span> outstandR_maic<span class="sc">$</span>model<span class="sc">$</span>weights) <span class="sc">|&gt;</span> </span>
+<span id="cb202-5"><a href="#cb202-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> weights)) <span class="sc">+</span></span>
+<span id="cb202-6"><a href="#cb202-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_histogram</span>(<span class="at">binwidth =</span> <span class="fl">0.1</span>, <span class="at">color =</span> <span class="st">"black"</span>, <span class="at">fill =</span> <span class="st">"lightgray"</span>) <span class="sc">+</span></span>
+<span id="cb202-7"><a href="#cb202-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">"Weights"</span>, <span class="at">y =</span> <span class="st">"Frequency"</span>) <span class="sc">+</span></span>
+<span id="cb202-8"><a href="#cb202-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_minimal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output-display">
 <div>
 <figure class="figure">
@@ -1325,12 +1338,12 @@ <h2 class="anchored" data-anchor-id="model-diagnostics">Model diagnostics</h2>
 <p>Similarly, for G-computation, users can extract the fitted model to check residuals or, in the Bayesian case, inspect MCMC convergence using for example the <code>bayesplot</code> package.</p>
 <p>Figure 3 shows the MCMC trace plots.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb199"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb199-1"><a href="#cb199-1" aria-hidden="true" tabindex="-1"></a><span class="co"># extract stanfit object</span></span>
-<span id="cb199-2"><a href="#cb199-2" aria-hidden="true" tabindex="-1"></a>stan_obj <span class="ot">&lt;-</span> outstandR_gcomp_bayes<span class="sc">$</span>model<span class="sc">$</span>fit </span>
-<span id="cb199-3"><a href="#cb199-3" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb199-4"><a href="#cb199-4" aria-hidden="true" tabindex="-1"></a><span class="co"># use external package for diagnostics</span></span>
-<span id="cb199-5"><a href="#cb199-5" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bayesplot)</span>
-<span id="cb199-6"><a href="#cb199-6" aria-hidden="true" tabindex="-1"></a><span class="fu">mcmc_trace</span>(stan_obj)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb203"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb203-1"><a href="#cb203-1" aria-hidden="true" tabindex="-1"></a><span class="co"># extract stanfit object</span></span>
+<span id="cb203-2"><a href="#cb203-2" aria-hidden="true" tabindex="-1"></a>stan_obj <span class="ot">&lt;-</span> outstandR_gcomp_bayes<span class="sc">$</span>model<span class="sc">$</span>fit </span>
+<span id="cb203-3"><a href="#cb203-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb203-4"><a href="#cb203-4" aria-hidden="true" tabindex="-1"></a><span class="co"># use external package for diagnostics</span></span>
+<span id="cb203-5"><a href="#cb203-5" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bayesplot)</span>
+<span id="cb203-6"><a href="#cb203-6" aria-hidden="true" tabindex="-1"></a><span class="fu">mcmc_trace</span>(stan_obj)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output-display">
 <div>
 <figure class="figure">
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diff --git a/scripts/exercises2.html b/scripts/exercises2.html
index 85b25dd..33e1a64 100644
--- a/scripts/exercises2.html
+++ b/scripts/exercises2.html
@@ -105,7 +105,7 @@
 
 <div id="quarto-content" class="page-columns page-rows-contents page-layout-article">
 <div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
-<div class="quarto-alternate-formats"><h2>Other Formats</h2><ul><li><a href="..\practical_paic.pdf"><i class="bi bi-file-pdf"></i>PDF</a></li></ul></div></div>
+<div class="quarto-alternate-formats"><h2>Other Formats</h2><ul><li><a href="practical_paic.pdf"><i class="bi bi-file-pdf"></i>PDF</a></li></ul></div></div>
 <main class="content" id="quarto-document-content">
 
 <header id="title-block-header" class="quarto-title-block default">
@@ -315,8 +315,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 5.3e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.53 seconds.
+Chain 1: Gradient evaluation took 0.001271 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 12.71 seconds.
 Chain 1: Adjust your expectations accordingly!
 Chain 1: 
 Chain 1: 
@@ -327,15 +327,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 1: Iteration: 1500 / 2000 [ 75%]  (Sampling)
 Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
 Chain 1: 
-Chain 1:  Elapsed Time: 0.223 seconds (Warm-up)
-Chain 1:                0.208 seconds (Sampling)
-Chain 1:                0.431 seconds (Total)
+Chain 1:  Elapsed Time: 0.243 seconds (Warm-up)
+Chain 1:                0.22 seconds (Sampling)
+Chain 1:                0.463 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 1.8e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.
+Chain 2: Gradient evaluation took 2.2e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.
 Chain 2: Adjust your expectations accordingly!
 Chain 2: 
 Chain 2: 
@@ -346,9 +346,9 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 2: Iteration: 1500 / 2000 [ 75%]  (Sampling)
 Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
 Chain 2: 
-Chain 2:  Elapsed Time: 0.216 seconds (Warm-up)
-Chain 2:                0.204 seconds (Sampling)
-Chain 2:                0.42 seconds (Total)
+Chain 2:  Elapsed Time: 0.232 seconds (Warm-up)
+Chain 2:                0.222 seconds (Sampling)
+Chain 2:                0.454 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -369,8 +369,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 2.4e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
+Chain 1: Gradient evaluation took 2.7e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.27 seconds.
 Chain 1: Adjust your expectations accordingly!
 Chain 1: 
 Chain 1: 
@@ -387,15 +387,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
 Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
 Chain 1: 
-Chain 1:  Elapsed Time: 0.229 seconds (Warm-up)
-Chain 1:                0.21 seconds (Sampling)
-Chain 1:                0.439 seconds (Total)
+Chain 1:  Elapsed Time: 0.261 seconds (Warm-up)
+Chain 1:                0.227 seconds (Sampling)
+Chain 1:                0.488 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 1.6e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.
+Chain 2: Gradient evaluation took 2e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.
 Chain 2: Adjust your expectations accordingly!
 Chain 2: 
 Chain 2: 
@@ -412,9 +412,9 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
 Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
 Chain 2: 
-Chain 2:  Elapsed Time: 0.211 seconds (Warm-up)
-Chain 2:                0.216 seconds (Sampling)
-Chain 2:                0.427 seconds (Total)
+Chain 2:  Elapsed Time: 0.227 seconds (Warm-up)
+Chain 2:                0.237 seconds (Sampling)
+Chain 2:                0.464 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -570,8 +570,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 2.5e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
+Chain 1: Gradient evaluation took 3.3e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.33 seconds.
 Chain 1: Adjust your expectations accordingly!
 Chain 1: 
 Chain 1: 
@@ -582,15 +582,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 1: Iteration: 1500 / 2000 [ 75%]  (Sampling)
 Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
 Chain 1: 
-Chain 1:  Elapsed Time: 0.225 seconds (Warm-up)
-Chain 1:                0.205 seconds (Sampling)
-Chain 1:                0.43 seconds (Total)
+Chain 1:  Elapsed Time: 0.257 seconds (Warm-up)
+Chain 1:                0.235 seconds (Sampling)
+Chain 1:                0.492 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 1.7e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
+Chain 2: Gradient evaluation took 2.3e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds.
 Chain 2: Adjust your expectations accordingly!
 Chain 2: 
 Chain 2: 
@@ -601,9 +601,9 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 2: Iteration: 1500 / 2000 [ 75%]  (Sampling)
 Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
 Chain 2: 
-Chain 2:  Elapsed Time: 0.215 seconds (Warm-up)
-Chain 2:                0.204 seconds (Sampling)
-Chain 2:                0.419 seconds (Total)
+Chain 2:  Elapsed Time: 0.241 seconds (Warm-up)
+Chain 2:                0.231 seconds (Sampling)
+Chain 2:                0.472 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -659,8 +659,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 3.2e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.32 seconds.
+Chain 1: Gradient evaluation took 2.6e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.
 Chain 1: Adjust your expectations accordingly!
 Chain 1: 
 Chain 1: 
@@ -677,15 +677,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
 Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
 Chain 1: 
-Chain 1:  Elapsed Time: 0.227 seconds (Warm-up)
-Chain 1:                0.209 seconds (Sampling)
-Chain 1:                0.436 seconds (Total)
+Chain 1:  Elapsed Time: 0.261 seconds (Warm-up)
+Chain 1:                0.237 seconds (Sampling)
+Chain 1:                0.498 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 1.7e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
+Chain 2: Gradient evaluation took 1.9e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds.
 Chain 2: Adjust your expectations accordingly!
 Chain 2: 
 Chain 2: 
@@ -702,9 +702,9 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
 Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
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+Chain 2:  Elapsed Time: 0.236 seconds (Warm-up)
+Chain 2:                0.244 seconds (Sampling)
+Chain 2:                0.48 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -1029,8 +1029,8 @@ <h4 class="anchored" data-anchor-id="exercises-1">Exercises</h4>
 <pre><code>
 SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
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+Chain 1: Gradient evaluation took 3.6e-05 seconds
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 Chain 1: Adjust your expectations accordingly!
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+Chain 1:                0.108 seconds (Sampling)
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 Chain 1: 
 
 SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.21 seconds.
+Chain 2: Gradient evaluation took 1e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.1 seconds.
 Chain 2: Adjust your expectations accordingly!
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+Chain 2:  Elapsed Time: 0.092 seconds (Warm-up)
+Chain 2:                0.114 seconds (Sampling)
+Chain 2:                0.206 seconds (Total)
 Chain 2: </code></pre>
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+Chain 1:                0.221 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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-Chain 2: Gradient evaluation took 3.8e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.38 seconds.
+Chain 2: Gradient evaluation took 1.2e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds.
 Chain 2: Adjust your expectations accordingly!
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+Chain 2:                0.135 seconds (Sampling)
+Chain 2:                0.258 seconds (Total)
 Chain 2: </code></pre>
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 </details>
diff --git a/vignettes/Binary_outcome_example.Rmd b/vignettes/Binary_outcome_example.Rmd
new file mode 100644
index 0000000..453c3bc
--- /dev/null
+++ b/vignettes/Binary_outcome_example.Rmd
@@ -0,0 +1,915 @@
+---
+title: "Binary data example"
+output: rmarkdown::html_vignette
+vignette: >
+  %\VignetteIndexEntry{Binary data example}
+  %\VignetteEncoding{UTF-8}
+  %\VignetteEngine{knitr::rmarkdown}
+editor_options: 
+  markdown: 
+    wrap: 72
+  chunk_output_type: console
+---
+
+```{r setup, include = FALSE}
+is_simcovariate_installed <- requireNamespace("simcovariates", quietly = TRUE)
+
+knitr::opts_chunk$set(
+  collapse = TRUE,
+  comment = "#>",
+  eval = is_simcovariate_installed
+)
+```
+
+## Introduction
+
+This vignette will demonstrate the use of the `{outstandR}` package to fit the range of types of models to simulated binary data.
+Related vignettes will provide equivalent analyses for continuous and count data.
+
+## Analysis
+
+First, let us load necessary packages.
+
+```{r load-packages, warning=FALSE, message=FALSE}
+# install.packages("outstandR",
+#  repos = c("https://statisticshealtheconomics.r-universe.dev", "https://cloud.r-project.org"))
+#
+# install.packages("simcovariates",
+#  repos = c("https://n8thangreen.r-universe.dev", "https://cloud.r-project.org"))
+
+library(boot)      # non-parametric bootstrap in MAIC and ML G-computation
+library(copula)    # simulating BC covariates from Gaussian copula
+library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation
+library(tidyr)
+library(dplyr)
+library(MASS)
+library(outstandR)
+library(simcovariates)  # from GitHub
+```
+
+### Data
+
+We consider binary outcomes using the log-odds ratio as the measure of
+effect. For example, the binary outcome may be response to treatment or
+the occurrence of an adverse event. For trials *AC* and *BC*, outcome
+$y_i$ for subject $i$ is simulated from a Bernoulli distribution with
+probabilities of success generated from logistic regression.
+
+For the *BC* trial, the individual-level covariates and outcomes are
+aggregated to obtain summaries. The continuous covariates are summarized
+as means and standard deviations, which would be available to the
+analyst in the published study in a table of baseline characteristics in
+the RCT publication. The binary outcomes are summarized in an overall
+event table. Typically, the published study only provides aggregate
+information to the analyst.
+
+The simulation input parameters are given below.
+
+| Parameter | Description | Value |
+|-------------------|----------------------------------|-------------------|
+| `N` | Sample size | 200 |
+| `allocation` | Active treatment vs. placebo allocation ratio (2:1) | 2/3 |
+| `b_trt` | Conditional effect of active treatment vs. comparator (log(0.17)) | -1.77196 |
+| `b_PF` | Conditional effect of each prognostic variable (-log(0.5)) | 0.69315 |
+| `b_EM` | Conditional interaction effect of each effect modifier (-log(0.67)) | 0.40048 |
+| `meanX_AC[1]` | Mean of prognostic factor in AC trial | 0.45 |
+| `meanX_AC[2]` | Mean of prognostic factor in AC trial | 0.45 |
+| `meanX_EM_AC[1]` | Mean of effect modifier in AC trial | 0.45 |
+| `meanX_EM_AC[2]` | Mean of effect modifier in AC trial | 0.45 |
+| `meanX_BC[1]` | Mean of prognostic factor in BC trial | 0.6 |
+| `meanX_BC[2]` | Mean of prognostic factor in BC trial | 0.6 |
+| `meanX_EM_BC[1]` | Mean of effect modifier in BC trial | 0.6 |
+| `meanX_EM_BC[2]` | Mean of effect modifier in BC trial | 0.6 |
+| `sdX` | Standard deviation of prognostic factors (AC and BC) | 0.4 |
+| `sdX_EM` | Standard deviation of effect modifiers | 0.4 |
+| `corX` | Covariate correlation coefficient | 0.2 |
+| `b_0` | Baseline intercept | -0.6 |
+
+Translating to R code.
+
+```{r, warning=FALSE, message=FALSE}
+N <- 200
+allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1)
+b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator
+b_PF <- -log(0.5)       # conditional effect of each prognostic variable
+b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier
+meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial
+meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC
+meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial
+meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC
+sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC)
+sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate
+corX <- 0.2            # covariate correlation coefficient  
+b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value
+```
+
+We shall use the `gen_data()` function available with the
+[simcovariates](https://github.com/n8thangreen/simcovariates) package on
+GitHub. For this, we need to define a list of covariates with distribution `type` and relationship to the outcome `role` as either `prognostic`, `effect_modifier` or both.
+
+```{r}
+covariate_defns_ipd <- list(
+  PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),
+                    role = "prognostic"),
+  PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),
+                    role = "prognostic"),
+  EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),
+                    role = "effect_modifier"),
+  EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),
+                    role = "effect_modifier")
+)
+
+b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)
+
+b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)
+
+num_normal_covs <- length(covariate_defns_ipd)
+cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs)
+diag(cor_matrix) <- 1
+
+rownames(cor_matrix) <- c("PF_cont_1", "PF_cont_2", "EM_cont_1", "EM_cont_2")
+colnames(cor_matrix) <- c("PF_cont_1", "PF_cont_2", "EM_cont_1", "EM_cont_2")
+
+ipd_trial <- simcovariates::gen_data(
+  N = N,
+  b_0 = b_0,
+  b_trt = b_trt,
+  covariate_defns = covariate_defns_ipd,
+  b_prognostic = b_prognostic,
+  b_effect_modifier = b_effect_modifier,
+  cor_matrix = cor_matrix,
+  trt_assignment = list(prob_trt1 = allocation),
+  family = binomial("logit"))
+```
+
+The treatment column in the return data is binary and takes values 0
+and 1. We will include some extra information about treatment names. To
+do this we will define the lable of the two level factor as `A` for 1
+and `C` for 0 as follows.
+
+```{r}
+ipd_trial$trt <- factor(ipd_trial$trt, labels = c("C", "A"))
+```
+
+Similarly, to obtain the aggregate data we will simulate IPD but with
+the additional summarise step. We set different mean values `meanX_BC`
+and `meanX_EM_BC` but otherwise use the same parameter values as for the
+$AC$ trial.
+
+First, simulate the underlying IPD similarly for the AC trial.
+
+```{r generate-ald-data}
+covariate_defns_ald <- list(
+  PF_cont_1 = list(type = continuous(mean = meanX_BC[1], sd = sdX[1]),
+                    role = "prognostic"),
+  PF_cont_2 = list(type = continuous(mean = meanX_BC[2], sd = sdX[2]),
+                    role = "prognostic"),
+  EM_cont_1 = list(type = continuous(mean = meanX_EM_BC[1], sd = sdX_EM[1]),
+                    role = "effect_modifier"),
+  EM_cont_2 = list(type = continuous(mean = meanX_EM_BC[2], sd = sdX_EM[2]),
+                    role = "effect_modifier")
+)
+
+BC.IPD <- simcovariates::gen_data(
+  N = N,
+  b_0 = b_0,
+  b_trt = b_trt,
+  covariate_defns = covariate_defns_ald,
+  b_prognostic = b_prognostic,
+  b_effect_modifier = b_effect_modifier,
+  cor_matrix = cor_matrix,
+  trt_assignment = list(prob_trt1 = allocation),
+  family = binomial("logit"))
+
+BC.IPD$trt <- factor(BC.IPD$trt, labels = c("C", "B"))
+```
+
+Next, we aggregate these data. We `summarise()` the covariates, sample sizes and outcomes separately and then bind the results together.
+
+```{r}
+# covariate summary statistics
+# assume same between treatments
+cov.X <- 
+  BC.IPD %>%
+  as.data.frame() |> 
+  dplyr::select(matches("^(PF|EM)"), trt) |> 
+  tidyr::pivot_longer(
+    cols = starts_with("PF") | starts_with("EM"),
+    names_to = "variable",
+    values_to = "value") |>
+  group_by(variable) %>%
+  summarise(
+    mean = mean(value),
+    sd = sd(value)
+  ) %>%
+  tidyr::pivot_longer(
+    cols = c("mean", "sd"),
+    names_to = "statistic",
+    values_to = "value") %>%
+  ungroup() |> 
+  mutate(trt = NA)
+
+# outcome
+summary.y <- 
+  BC.IPD |> 
+  as.data.frame() |> 
+  dplyr::select(y, trt) %>%
+  tidyr::pivot_longer(cols = "y",
+               names_to = "variable",
+               values_to = "value") %>%
+  group_by(variable, trt) %>%
+  summarise(
+    mean = mean(value),
+    sd = sd(value),
+    sum = sum(value)
+  ) %>%
+  tidyr::pivot_longer(
+    cols = c("mean", "sd", "sum"),
+    names_to = "statistic",
+    values_to = "value") %>%
+  ungroup()
+
+# sample sizes
+summary.N <- 
+  BC.IPD |> 
+  group_by(trt) |> 
+  count(name = "N") |> 
+  tidyr::pivot_longer(
+    cols = "N",
+    names_to = "statistic",
+    values_to = "value") |> 
+  mutate(variable = NA_character_) |> 
+  dplyr::select(variable, statistic, value, trt)
+  
+ald_trial <- rbind.data.frame(cov.X, summary.y, summary.N)
+```
+
+This general format of the data sets are in a 'long' style consisting of
+the following.
+
+#### `ipd_trial`: Individual patient data
+
+-   `PF_*`: Patient measurements prognostic factors
+-   `EM_*`: Patient measurements effect modifiers
+-   `trt`: Treatment label (factor)
+-   `y`: Indicator of whether event was observed (two level factor)
+
+#### `ald_trial`: Aggregate-level data
+
+-   `variable`: Covariate name. In the case of treatment arm sample size
+    this is `NA`
+-   `statistic`: Summary statistic name from mean, standard deviation or
+    sum
+-   `value`: Numerical value of summary statistic
+-   `trt`: Treatment label. Because we assume a common covariate
+    distribution between treatment arms this is `NA`
+
+Our final data look like the following.
+
+```{r}
+head(ipd_trial)
+```
+
+There are 4 correlated continuous covariates generated per subject,
+simulated from a multivariate normal distribution. Treatment `trt` takes
+either new treatment *A* or standard of care / status quo *C*. The ITC
+is 'anchored' via *C*, the common treatment.
+
+```{r}
+ald_trial
+```
+
+In this case, we have 4 covariate mean and standard deviation values;
+and the event total, average and sample size for each treatment *B* and
+*C*.
+
+#### Regression model
+
+The true logistic outcome model which we use to simulate the data is
+
+$$
+\text{logit}(p_{t}) = \beta_0 + \beta_{PF} (X_3 + X_4) + [\beta_{t} + \beta_{EM} (X_1 + X_2)] \; \text{I}(t \neq C)
+$$
+
+$\text{I}()$ is an indicator function taking value 1 if true and 0
+otherwise. That is, for treatment $C$ the right hand side becomes
+$\beta_0 + \beta_{PF} (X_3 + X_4)$ and for comparator treatments $A$ or $B$
+there is an additional $\beta_t + \beta_{EM} (X_1 + X_2)$ component
+consisting of the effect modifier terms and the coefficient for the
+treatment parameter, $\beta_t$ (or `b_trt` in the R code), i.e. the log
+odds-ratio (LOR) for the logit model. Finally, $p_{t}$ is the
+probability of experiencing the event of interest for treatment $t$.
+
+### Output statistics
+
+We will obtain the *marginal treatment effect* and *marginal variance*.
+The definition by which of these are calculated depends on the type of
+data and outcome scale. For our current example of binary data and
+log-odds ratio the marginal treatment effect is
+
+$$
+\log\left( \frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \right) = \log(n_B n_{\bar{C}}) - \log(n_C n_{\bar{B}})
+$$
+
+and marginal variance is
+
+$$
+\frac{1}{n_C} + \frac{1}{n_{\bar{C}}} + \frac{1}{n_B} + \frac{1}{n_{\bar{B}}}
+$$
+
+where $n_B, n_C$ are the number of events in each arm and $\bar{C}$ is
+the compliment of $C$, so e.g. $n_{\bar{C}} = N_C - n_c$. Other outcome
+scales will be discussed below.
+
+## Model fitting in R
+
+The `{outstandR}` package has been written to be easy to use and
+essentially consists of a single function, `outstandR()`. This can be
+used to run all of the different types of model, which when combined
+with their specific parameters we will call *strategies*. The first two
+arguments of `outstandR()` are the individual patient and
+aggregate-level data, respectively.
+
+A `strategy` argument of `outstandR` takes functions called
+`strategy_*()`, where the wildcard `*` is replaced by the name of the
+particular method required, e.g. `strategy_maic()` for MAIC. Each
+specific example is provided below.
+
+### Model formula
+
+We will take advantage of the in-built R formula object to define the
+models. This will allow us to easily pull out components of the object and
+consistently use it. Defining $EM\_cont\_1, EM\_cont\_2$ as effect
+modifiers, $PF\_cont\_1, PF\_cont\_2$ as prognostic variables and $Z$
+the treatment indicator then the formula used in this model is
+
+$$
+y = PF\_cont\_1 + PF\_cont\_2 + Z + Z \times EM\_cont\_1 + Z \times EM\_cont\_2
+$$
+
+Notice that this does not include the link function of interest so
+appears as a linear regression. This corresponds to the following `R`
+`formula` object we will pass as an argument to the strategy function.
+
+```{r}
+lin_form <- list(
+  outcome_model = as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"),
+  balance_model = as.formula("~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2")
+)
+```
+
+Note that the more succinct formula
+
+```{r, eval=FALSE}
+y ~ PF_cont_1 + PF_cont_2 + trt*(EM_cont_1 + EM_cont_2)
+```
+
+would additionally include $X_1, X_2$ as prognostic factors so is not
+equivalent (but this may be what you actually want).
+To recover the original formula it can be modified as follows.
+
+```{r, eval=FALSE}
+y ~ PF_cont_1 + PF_cont_2 + trt*(EM_cont_1 + EM_cont_2) - EM_cont_1 - EM_cont_2
+```
+
+We note that the MAIC approach does not strictly use a regression in the
+same way as the other methods so should not be considered directly
+comparable in this sense but we have decided to use a consistent syntax
+across models using 'formula'.
+
+### Matching-Adjusted Indirect Comparison (MAIC)
+
+A single call to `outstandR()` is sufficient to run the model. We pass
+to the `strategy` argument the `strategy_maic()` function with arguments
+`formula = lin_form` as defined above and
+`family = binomial(link = "logit")` for binary data and logistic link.
+
+Internally, using the individual patient level data for *AC* firstly we
+perform non-parametric bootstrap of the `maic.boot` function with
+`R = 1000` replicates. This function fits treatment coefficient for the
+marginal effect for *A* vs *C*. The returned value is an object of class
+`boot` from the `{boot}` package. We then calculate the bootstrap mean
+and variance in the wrapper function `maic_boot_stats`.
+
+```{r outstandR_maic}
+outstandR_maic <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_maic(
+              formula = lin_form,
+              family = binomial(link = "logit")))
+```
+
+The returned object is of class `outstandR`.
+
+```{r outstandR_maic-print, warning=FALSE, message=FALSE}
+str(outstandR_maic)
+```
+
+We see that this is a list object with 2 parts. The first contains
+statistics between each pair of treatments. These are the mean
+contrasts, variances and confidence intervals (CI), respectively. The
+default CI is for 95% but can be altered in `outstandR` with the `CI`
+argument. The second element of the list contains the absolute effect
+estimates.
+
+A `print` method is available for `outstandR` objects for more
+human-readable output
+
+```{r}
+outstandR_maic
+```
+
+#### Outcome scale
+
+If we do not explicitly specify the outcome scale, the default is that
+used to fit to the data in the regression model. As we saw, in this
+case, the default is log-odds ratio corresponding to the `"logit"` link
+function for binary data. However, we can change this to some other
+scale which may be more appropriate for a particular analysis. So far
+implemented in the package, the links and their corresponding relative
+treatment effect scales are as follows:
+
+| Data Type  | Model   | Scale           | Argument            |
+|:-----------|---------|:----------------|:--------------------|
+| Binary     | `logit` | Log-odds ratio  | `log_odds`          |
+| Count      | `log`   | Log-risk ratio  | `log_relative_risk` |
+| Continuous | `mean`  | Mean difference | `risk_difference`   |
+
+The full list of possible transformed treatment effect scales will be:
+log-odds ratio, log-risk ratio, mean difference, risk difference, hazard
+ratio, hazard difference.
+
+For binary data the marginal treatment effect and variance are
+
+-   **Log-risk ratio**
+
+Treatment effect is
+
+$$
+\log(n_B/N_B) - \log(n_A/N_A)
+$$
+
+and variance
+
+$$
+\frac{1}{n_B} - \frac{1}{N_B} + \frac{1}{n_A} - \frac{1}{N_A}
+$$
+
+-   **Risk difference**
+
+Treatment effect is
+
+$$
+\frac{n_B}{N_B} - \frac{n_A}{N_A}
+$$
+
+and variance
+
+$$
+\frac{n_B}{N_B} \left( 1 - \frac{n_B}{N_B} \right) + \frac{n_A}{N_A} \left( 1 - \frac{n_A}{N_A} \right)
+$$
+
+To change the outcome scale, we can pass the `scale` argument in the
+`outstandR()` function. For example, to change the scale to risk
+difference, we can use the following code.
+
+```{r outstandR_maic_lrr}
+outstandR_maic_lrr <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_maic(formula = lin_form,
+                                     family = binomial(link = "logit")),
+            scale = "log_relative_risk")
+```
+
+```{r}
+outstandR_maic_lrr
+```
+
+### Parametric G-computation with maximum-likelihood estimation
+
+G-computation marginalizes the conditional estimates by separating the
+regression modelling from the estimation of the marginal treatment
+effect for *A* versus *C*. First, a regression model of the observed
+outcome $y$ on the covariates $x$ and treatment $z$ is fitted to the
+*AC* IPD:
+
+$$
+g(\mu_n) = \beta_0 + \boldsymbol{x}_n \boldsymbol{\beta_{PF}} + (\beta_z + \boldsymbol{x_n^{EM}} \boldsymbol{\beta_{EM}}) \; \mbox{I}(t \neq C)
+$$
+
+In the context of G-computation, this regression model is often called
+the “Q-model.” Having fitted the Q-model, the regression coefficients
+are treated as nuisance parameters. The parameters are applied to the
+simulated covariates $x*$ to predict hypothetical outcomes for each
+subject under both possible treatments. Namely, a pair of predicted
+outcomes, also called potential outcomes, under *A* and under *C*, is
+generated for each subject.
+
+By plugging treatment *C* into the regression fit for every simulated
+observation, we predict the marginal outcome mean in the hypothetical
+scenario in which all units are under treatment *C*:
+
+$$
+\hat{\mu}_0 = \int_{x^*} g^{-1} (\hat{\beta}_0 + x^* \hat{\beta}_1 ) p(x^*) \; \text{d}x^*
+$$
+
+As performed for the previous approaches, call `outstandR()` but change
+the strategy to `strategy_gcomp_ml()`,
+
+```{r outstandR_gcomp_ml}
+outstandR_gcomp_ml <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_gcomp_ml(
+              formula = lin_form,
+              family = binomial(link = "logit")))
+```
+
+```{r}
+outstandR_gcomp_ml
+```
+
+Once again, let us change the outcome scale to LRR
+
+```{r outstandR_gcomp_ml_lrr}
+outstandR_gcomp_ml_lrr <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_gcomp_ml(
+              formula = lin_form,
+              family = binomial(link = "logit")),
+            scale = "log_relative_risk")
+```
+
+```{r}
+outstandR_gcomp_ml_lrr
+```
+
+### Bayesian G-computation with MCMC
+
+The difference between Bayesian G-computation and its maximum-likelihood
+counterpart is in the estimated distribution of the predicted outcomes.
+The Bayesian approach also marginalizes, integrates or standardizes over
+the joint posterior distribution of the conditional nuisance parameters
+of the outcome regression, as well as the joint covariate distribution.
+
+Draw a vector of size $N^*$ of predicted outcomes $y^*_z$ under each set
+intervention $z^* \in \{0, 1\}$ from its posterior predictive
+distribution under the specific treatment. This is defined as
+$p(y^*_{z^*} \mid \mathcal{D}_{AC}) = \int_{\beta} p(y^*_{z^*} \mid \beta) p(\beta \mid \mathcal{D}_{AC}) d\beta$
+where $p(\beta \mid \mathcal{D}_{AC})$ is the posterior distribution of
+the outcome regression coefficients $\beta$, which encode the
+predictor-outcome relationships observed in the *AC* trial IPD. This is
+given by:
+
+$$
+p(y^*_{^z*} \mid \mathcal{D}_{AC}) = \int_{x^*} p(y^* \mid z^*, x^*, \mathcal{D}_{AC}) p(x^* \mid \mathcal{D}_{AC})\; \text{d}x^*
+$$
+
+$$
+= \int_{x^*} \int_{\beta} p(y^* \mid z^*, x^*, \beta) p(x^* \mid \beta) p(\beta \mid \mathcal{D}_{AC})\; d\beta \; \text{d}x^*
+$$
+
+In practice, the integrals above can be approximated numerically, using
+full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling.
+
+The average, variance and interval estimates of the marginal treatment
+effect can be derived empirically from draws of the posterior density.
+
+The strategy function to plug-in to the `outstandR()` call for this
+approach is `strategy_gcomp_bayes()`,
+
+```{r outstandR_gcomp_bayes, message=FALSE, eval=FALSE}
+outstandR_gcomp_bayes <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_gcomp_bayes(
+              formula = lin_form,
+              family = binomial(link = "logit")))
+```
+
+```{r outstandR_gcomp_bayes_eval, echo=FALSE, message=FALSE}
+xx <- capture.output(
+  outstandR_gcomp_bayes <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_gcomp_bayes(
+                formula = lin_form,
+                family = binomial(link = "logit"))))
+```
+
+```{r}
+outstandR_gcomp_bayes
+```
+
+As before, we can change the outcome scale to LRR.
+
+```{r outstandR_gcomp_bayes_lrr, eval=FALSE}
+outstandR_gcomp_bayes_lrr <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_gcomp_bayes(
+              formula = lin_form,
+              family = binomial(link = "logit")),
+            scale = "log_relative_risk")
+```
+
+```{r outstandR_gcomp_bayes_lrr_eval, echo=FALSE}
+xx <- capture.output(
+  outstandR_gcomp_bayes_lrr <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_gcomp_bayes(
+                formula = lin_form,
+                family = binomial(link = "logit")),
+              scale = "log_relative_risk"))
+```
+
+```{r}
+outstandR_gcomp_bayes_lrr
+```
+
+### Multiple imputation marginalisation
+
+The final method is to obtain the marginalized treatment effect for
+aggregate level data study, obtained by integrating over the covariate
+distribution from the aggregate level data $BC$ study
+
+$$
+\Delta^{\text{marg}} = \mathbb{E}_{X \sim f_{\text{BC}}(X)} \left[ \mu_{T=1}(X) - \mu_{T=0}(X) \right]
+= \int \left[ \mu_{T=1}(X) - \mu_{T=0}(X) \right] f_{\text{BC}}(X) \; \text{d}X
+$$
+
+The aggregate level data likelihood is
+
+$$
+\hat{\Delta}_{BC} \sim \mathcal{N}(\Delta^{\text{marg}}, SE^2)
+$$
+
+The multiple imputation marginalisation strategy function is
+`strategy_mim()`,
+
+```{r outstandR_mim, eval=FALSE}
+outstandR_mim <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_mim(
+              formula = lin_form,
+              family = binomial(link = "logit")))
+```
+
+```{r outstandR_mim_eval, echo=FALSE}
+xx <- capture.output(
+  outstandR_mim <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_mim(
+                formula = lin_form,
+                family = binomial(link = "logit"))))
+```
+
+```{r}
+outstandR_mim
+```
+
+Change the outcome scale again for LRR,
+
+```{r outstandR_mim_lrr, eval=FALSE}
+outstandR_mim_lrr <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_mim(
+              formula = lin_form,
+              family = binomial(link = "logit")),
+            scale = "log_relative_risk")
+```
+
+```{r outstandR_mim_lrr_eval, echo=FALSE}
+xx <- capture.output(
+  outstandR_mim_lrr <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_mim(
+                formula = lin_form,
+                family = binomial(link = "logit")),
+              scale = "log_relative_risk"))
+```
+
+```{r}
+outstandR_mim_lrr
+```
+
+## Model comparison
+
+#### $AC$ effect in $BC$ population
+
+The true $AC$ effect on the log OR scale in the $BC$ (aggregate trial
+data) population is
+$\beta_t^{AC} + \beta_{EM} (\bar{X}^{AC}_1 + \bar{X}_2^{AC})$.
+Calculated by
+
+```{r}
+mean_X1 <- ald_trial$value[ald_trial$statistic == "mean" & ald_trial$variable == "EM_cont_1"]
+mean_X2 <- ald_trial$value[ald_trial$statistic == "mean" & ald_trial$variable == "EM_cont_1"]
+
+d_AC_true <- b_trt + b_EM * (mean_X1 + mean_X2)
+```
+
+```{r echo=FALSE}
+# alternative calculations
+# d_AC_true <- b_trt + b_EM * (meanX_EM_BC[1] + meanX_EM_BC[2])
+# 
+# d_C_true <- b_0 + b_trt + b_EM * (ald_trial$mean.X1 + ald_trial$mean.X2) + b_PF * (ald_trial$mean.X3 + ald_trial$mean.X4)
+# d_A_true <- b_0 + b_PF * (ald_trial$mean.X3 + ald_trial$mean.X4)
+# d_C_true - d_A_true
+```
+
+The naive approach is to just convert directly from one population to
+another, ignoring the imbalance in effect modifiers.
+
+```{r}
+d_AC_naive <- 
+  ipd_trial |> 
+  dplyr::group_by(trt) |> 
+  dplyr::summarise(y_sum = sum(y), y_bar = mean(y), n = n()) |> 
+  tidyr::pivot_wider(names_from = trt,
+                     values_from = c(y_sum, y_bar, n)) |> 
+  dplyr::mutate(d_AC =
+                  log(y_bar_A/(1-y_bar_A)) - log(y_bar_C/(1-y_bar_C)),
+                var_AC =
+                  1/(n_A-y_sum_A) + 1/y_sum_A + 1/(n_C-y_sum_C) + 1/y_sum_C)
+```
+
+#### $AB$ effect in $BC$ population
+
+This is the indirect effect. The true $AB$ effect in the $BC$ population
+is $\beta_t^{AC} - \beta_t^{BC}$.
+
+```{r echo=FALSE}
+d_AB_true <- 0
+```
+
+Following the simulation study in Remiro et al (2020) these cancel out
+and the true effect is zero.
+
+The naive comparison calculating $AB$ effect in the $BC$ population is
+
+```{r}
+# reshape to make extraction easier
+ald_out <- ald_trial |> 
+  dplyr::filter(variable == "y" | is.na(variable)) |> 
+  mutate(stat_trt = paste0(statistic, "_", trt)) |> 
+  dplyr::select(stat_trt, value) |> 
+  pivot_wider(names_from = stat_trt, values_from = value)
+
+d_BC <-
+  with(ald_out, log(mean_B/(1-mean_B)) - log(mean_C/(1-mean_C)))
+
+d_AB_naive <- d_AC_naive$d_AC - d_BC
+
+var.d.BC <- with(ald_out, 1/sum_B + 1/(N_B - sum_B) + 1/sum_C + 1/(N_C - sum_C))
+
+var.d.AB.naive <- d_AC_naive$var_AC + var.d.BC
+```
+
+Alternatively, we can compute this using `outstandR`'s built-in `calc_bucher_naive()` function:
+
+```{r}
+naive_results <- calc_bucher_naive(ipd_trial, ald_trial, outcome_model = lin_form, family = binomial(link = "logit"))
+naive_results
+```
+
+Of course, the $BC$ contrast is calculated directly.
+
+## Results
+
+We now combine all outputs and present in plots and tables. For a
+log-odds ratio a table of all contrasts and methods in the $BC$
+population is given below.
+
+```{r echo=FALSE}
+res_tab <- 
+  data.frame(
+    d_true = c(d_AB_true, d_AC_true, d_BC),
+    d_naive = c(d_AB_naive, d_AC_naive$d_AC, d_BC),
+    `MAIC` = unlist(outstandR_maic$results$contrasts$means),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml$results$contrasts$means),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$results$contrasts$means),
+    `MIM` = unlist(outstandR_mim$results$contrasts$means)) |> 
+  round(2)
+
+res_tab_var <- 
+  data.frame(
+    d_true = c(NA, NA, NA),
+    d_naive = c(var.d.AB.naive, d_AC_naive$var_AC, var.d.BC),
+    `MAIC` = unlist(outstandR_maic$results$contrasts$variances),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml$results$contrasts$variances),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$results$contrasts$variances),
+    `MIM` = unlist(outstandR_mim$results$contrasts$variances)) |> 
+  round(2)
+
+knitr::kable(res_tab)
+```
+
+We can see that the different corresponds reasonably well with one
+another.
+
+Next, let us look at the results on the log relative risk scale. First,
+the true values are calculated as
+
+```{r eval=FALSE}
+d_AB_true_lrr <- 0
+d_AC_true_lrr <- log(plogis(d_A_true) / plogis(d_C_true))
+d_AC_true_lrr
+```
+
+so that the summary table is
+
+```{r echo=FALSE}
+res_tab_lrr <- 
+  data.frame(
+    # d_true = c(d_AB_true_lrr, d_AC_true_lrr, d_BC_lrr),
+    # d_naive = c(d_AB_naive_lrr, d_AC_naive_lrr$d_AC, d_BC_lrr),
+    `MAIC` = unlist(outstandR_maic_lrr$results$contrasts$means),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml_lrr$results$contrasts$means),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes_lrr$results$contrasts$means),
+    `MIM` = unlist(outstandR_mim_lrr$results$contrasts$means)) |> 
+  round(2)
+
+res_tab_var_lrr <- 
+  data.frame(
+    # d_true = c(NA, NA, NA),
+    # d_naive = c(var.d.AB.naive, d_AC_naive$var_AC, var.d.BC),
+    `MAIC` = unlist(outstandR_maic_lrr$results$contrasts$variances),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml_lrr$results$contrasts$variances),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes_lrr$results$contrasts$variances),
+    `MIM` = unlist(outstandR_mim_lrr$results$contrasts$variances)) |> 
+  round(2)
+
+knitr::kable(res_tab_lrr)
+```
+
+#### Plots
+
+The same output can be presented in forest plots is as follows. Each
+horizontal bar represent a different method and the facets group these
+by treatment comparison for the $BC$ population. The log-odds ratio and
+log risk ratio plot are given below.
+
+```{r forest-lor, fig.width=8, fig.height=6, warning=FALSE, message=FALSE, echo=FALSE}
+library(ggplot2)
+
+var_dat <- 
+  t(res_tab_var) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "var")
+
+plotdat <- 
+  t(res_tab) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "Estimate") |> 
+  mutate(id = 1:n(),
+         type = as.factor(type)) |> 
+  merge(var_dat) |> 
+  mutate(lo = Estimate + qnorm(0.025) * sqrt(var),
+         hi = Estimate + qnorm(0.975) * sqrt(var))
+
+ggplot(aes(x = Estimate, y = id, col = type), data = plotdat) +
+  geom_vline(xintercept = 0, lty = 2) +
+  geom_point(size = 2) +
+  geom_segment(aes(y = id, yend = id, x = lo, xend = hi), na.rm = TRUE) +
+  xlab("Estimate (Log OR)") +
+  facet_grid(Comparison~., switch = "y", scales = "free_y", space = "free_y") +
+  scale_y_reverse(name = "Comparison in BC population",
+                  breaks = NULL, expand = c(0, 0.6)) +
+  scale_color_manual(values = c("d_naive" = "black", "d_true" = "red", 
+                                "MAIC" = "#E69F00", "Gcomp ML" = "#56B4E9", 
+                                "Gcomp Bayes" = "#009E73", "MIM" = "#F0E442"))
+```
+
+```{r forest-rr, fig.width=8, fig.height=6, warning=FALSE, message=FALSE, echo=FALSE}
+var_dat <- 
+  t(res_tab_var_lrr) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "var")
+
+plotdat <- 
+  t(res_tab_lrr) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "Estimate") |> 
+  mutate(id = 1:n(),
+         type = as.factor(type)) |> 
+  merge(var_dat) |> 
+  mutate(lo = Estimate + qnorm(0.025) * sqrt(var),
+         hi = Estimate + qnorm(0.975) * sqrt(var))
+
+ggplot(aes(x = Estimate, y = id, col = type), data = plotdat) +
+  geom_vline(xintercept = 0, lty = 2) +
+  geom_point(size = 2) +
+  geom_segment(aes(y = id, yend = id, x = lo, xend = hi), na.rm = TRUE) +
+  xlab("Estimate (Log RR)") +
+  facet_grid(Comparison~., switch = "y", scales = "free_y", space = "free_y") +
+  scale_y_reverse(name = "Comparison in BC population",
+                  breaks = NULL, expand = c(0, 0.6)) +
+  scale_color_manual(values = c("d_naive" = "black", "d_true" = "red", 
+                                "MAIC" = "#E69F00", "Gcomp ML" = "#56B4E9", 
+                                "Gcomp Bayes" = "#009E73", "MIM" = "#F0E442"))
+```
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+</style>
+
+
+
+
+</head>
+
+<body>
+
+
+
+
+<h1 class="title toc-ignore">Binary data example</h1>
+
+
+
+<div id="introduction" class="section level2">
+<h2>Introduction</h2>
+<p>This vignette will demonstrate the use of the
+<code>{outstandR}</code> package to fit the range of types of models to
+simulated binary data. Related vignettes will provide equivalent
+analyses for continuous and count data.</p>
+</div>
+<div id="analysis" class="section level2">
+<h2>Analysis</h2>
+<p>First, let us load necessary packages.</p>
+<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="co"># install.packages(&quot;outstandR&quot;,</span></span>
+<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a><span class="co">#  repos = c(&quot;https://statisticshealtheconomics.r-universe.dev&quot;, &quot;https://cloud.r-project.org&quot;))</span></span>
+<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a><span class="co">#</span></span>
+<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a><span class="co"># install.packages(&quot;simcovariates&quot;,</span></span>
+<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a><span class="co">#  repos = c(&quot;https://n8thangreen.r-universe.dev&quot;, &quot;https://cloud.r-project.org&quot;))</span></span>
+<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a></span>
+<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a><span class="fu">library</span>(boot)      <span class="co"># non-parametric bootstrap in MAIC and ML G-computation</span></span>
+<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a><span class="fu">library</span>(copula)    <span class="co"># simulating BC covariates from Gaussian copula</span></span>
+<span id="cb1-9"><a href="#cb1-9" tabindex="-1"></a><span class="fu">library</span>(rstanarm)  <span class="co"># fit outcome regression, draw outcomes in Bayesian G-computation</span></span>
+<span id="cb1-10"><a href="#cb1-10" tabindex="-1"></a><span class="fu">library</span>(tidyr)</span>
+<span id="cb1-11"><a href="#cb1-11" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span>
+<span id="cb1-12"><a href="#cb1-12" tabindex="-1"></a><span class="fu">library</span>(MASS)</span>
+<span id="cb1-13"><a href="#cb1-13" tabindex="-1"></a><span class="fu">library</span>(outstandR)</span>
+<span id="cb1-14"><a href="#cb1-14" tabindex="-1"></a><span class="fu">library</span>(simcovariates)  <span class="co"># from GitHub</span></span></code></pre></div>
+<div id="data" class="section level3">
+<h3>Data</h3>
+<p>We consider binary outcomes using the log-odds ratio as the measure
+of effect. For example, the binary outcome may be response to treatment
+or the occurrence of an adverse event. For trials <em>AC</em> and
+<em>BC</em>, outcome <span class="math inline">\(y_i\)</span> for
+subject <span class="math inline">\(i\)</span> is simulated from a
+Bernoulli distribution with probabilities of success generated from
+logistic regression.</p>
+<p>For the <em>BC</em> trial, the individual-level covariates and
+outcomes are aggregated to obtain summaries. The continuous covariates
+are summarized as means and standard deviations, which would be
+available to the analyst in the published study in a table of baseline
+characteristics in the RCT publication. The binary outcomes are
+summarized in an overall event table. Typically, the published study
+only provides aggregate information to the analyst.</p>
+<p>The simulation input parameters are given below.</p>
+<table>
+<colgroup>
+<col width="26%" />
+<col width="47%" />
+<col width="26%" />
+</colgroup>
+<thead>
+<tr class="header">
+<th>Parameter</th>
+<th>Description</th>
+<th>Value</th>
+</tr>
+</thead>
+<tbody>
+<tr class="odd">
+<td><code>N</code></td>
+<td>Sample size</td>
+<td>200</td>
+</tr>
+<tr class="even">
+<td><code>allocation</code></td>
+<td>Active treatment vs. placebo allocation ratio (2:1)</td>
+<td>2/3</td>
+</tr>
+<tr class="odd">
+<td><code>b_trt</code></td>
+<td>Conditional effect of active treatment vs. comparator
+(log(0.17))</td>
+<td>-1.77196</td>
+</tr>
+<tr class="even">
+<td><code>b_PF</code></td>
+<td>Conditional effect of each prognostic variable (-log(0.5))</td>
+<td>0.69315</td>
+</tr>
+<tr class="odd">
+<td><code>b_EM</code></td>
+<td>Conditional interaction effect of each effect modifier
+(-log(0.67))</td>
+<td>0.40048</td>
+</tr>
+<tr class="even">
+<td><code>meanX_AC[1]</code></td>
+<td>Mean of prognostic factor in AC trial</td>
+<td>0.45</td>
+</tr>
+<tr class="odd">
+<td><code>meanX_AC[2]</code></td>
+<td>Mean of prognostic factor in AC trial</td>
+<td>0.45</td>
+</tr>
+<tr class="even">
+<td><code>meanX_EM_AC[1]</code></td>
+<td>Mean of effect modifier in AC trial</td>
+<td>0.45</td>
+</tr>
+<tr class="odd">
+<td><code>meanX_EM_AC[2]</code></td>
+<td>Mean of effect modifier in AC trial</td>
+<td>0.45</td>
+</tr>
+<tr class="even">
+<td><code>meanX_BC[1]</code></td>
+<td>Mean of prognostic factor in BC trial</td>
+<td>0.6</td>
+</tr>
+<tr class="odd">
+<td><code>meanX_BC[2]</code></td>
+<td>Mean of prognostic factor in BC trial</td>
+<td>0.6</td>
+</tr>
+<tr class="even">
+<td><code>meanX_EM_BC[1]</code></td>
+<td>Mean of effect modifier in BC trial</td>
+<td>0.6</td>
+</tr>
+<tr class="odd">
+<td><code>meanX_EM_BC[2]</code></td>
+<td>Mean of effect modifier in BC trial</td>
+<td>0.6</td>
+</tr>
+<tr class="even">
+<td><code>sdX</code></td>
+<td>Standard deviation of prognostic factors (AC and BC)</td>
+<td>0.4</td>
+</tr>
+<tr class="odd">
+<td><code>sdX_EM</code></td>
+<td>Standard deviation of effect modifiers</td>
+<td>0.4</td>
+</tr>
+<tr class="even">
+<td><code>corX</code></td>
+<td>Covariate correlation coefficient</td>
+<td>0.2</td>
+</tr>
+<tr class="odd">
+<td><code>b_0</code></td>
+<td>Baseline intercept</td>
+<td>-0.6</td>
+</tr>
+</tbody>
+</table>
+<p>Translating to R code.</p>
+<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a>N <span class="ot">&lt;-</span> <span class="dv">200</span></span>
+<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a>allocation <span class="ot">&lt;-</span> <span class="dv">2</span><span class="sc">/</span><span class="dv">3</span>      <span class="co"># active treatment vs. placebo allocation ratio (2:1)</span></span>
+<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a>b_trt <span class="ot">&lt;-</span> <span class="fu">log</span>(<span class="fl">0.17</span>)     <span class="co"># conditional effect of active treatment vs. common comparator</span></span>
+<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a>b_PF <span class="ot">&lt;-</span> <span class="sc">-</span><span class="fu">log</span>(<span class="fl">0.5</span>)       <span class="co"># conditional effect of each prognostic variable</span></span>
+<span id="cb2-5"><a href="#cb2-5" tabindex="-1"></a>b_EM <span class="ot">&lt;-</span> <span class="sc">-</span><span class="fu">log</span>(<span class="fl">0.67</span>)     <span class="co"># conditional interaction effect of each effect modifier</span></span>
+<span id="cb2-6"><a href="#cb2-6" tabindex="-1"></a>meanX_AC <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fl">0.45</span>, <span class="fl">0.45</span>)       <span class="co"># mean of normally-distributed covariate in AC trial</span></span>
+<span id="cb2-7"><a href="#cb2-7" tabindex="-1"></a>meanX_BC <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fl">0.6</span>, <span class="fl">0.6</span>)         <span class="co"># mean of each normally-distributed covariate in BC</span></span>
+<span id="cb2-8"><a href="#cb2-8" tabindex="-1"></a>meanX_EM_AC <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fl">0.45</span>, <span class="fl">0.45</span>)    <span class="co"># mean of normally-distributed EM covariate in AC trial</span></span>
+<span id="cb2-9"><a href="#cb2-9" tabindex="-1"></a>meanX_EM_BC <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fl">0.6</span>, <span class="fl">0.6</span>)      <span class="co"># mean of each normally-distributed EM covariate in BC</span></span>
+<span id="cb2-10"><a href="#cb2-10" tabindex="-1"></a>sdX <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fl">0.4</span>, <span class="fl">0.4</span>)     <span class="co"># standard deviation of each covariate (same for AC and BC)</span></span>
+<span id="cb2-11"><a href="#cb2-11" tabindex="-1"></a>sdX_EM <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fl">0.4</span>, <span class="fl">0.4</span>)  <span class="co"># standard deviation of each EM covariate</span></span>
+<span id="cb2-12"><a href="#cb2-12" tabindex="-1"></a>corX <span class="ot">&lt;-</span> <span class="fl">0.2</span>            <span class="co"># covariate correlation coefficient  </span></span>
+<span id="cb2-13"><a href="#cb2-13" tabindex="-1"></a>b_0 <span class="ot">&lt;-</span> <span class="sc">-</span><span class="fl">0.6</span>            <span class="co"># baseline intercept coefficient  ##TODO: fixed value</span></span></code></pre></div>
+<p>We shall use the <code>gen_data()</code> function available with the
+<a href="https://github.com/n8thangreen/simcovariates">simcovariates</a>
+package on GitHub. For this, we need to define a list of covariates with
+distribution <code>type</code> and relationship to the outcome
+<code>role</code> as either <code>prognostic</code>,
+<code>effect_modifier</code> or both.</p>
+<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a>covariate_defns_ipd <span class="ot">&lt;-</span> <span class="fu">list</span>(</span>
+<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a>  <span class="at">PF_cont_1 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_AC[<span class="dv">1</span>], <span class="at">sd =</span> sdX[<span class="dv">1</span>]),</span>
+<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;prognostic&quot;</span>),</span>
+<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a>  <span class="at">PF_cont_2 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_AC[<span class="dv">2</span>], <span class="at">sd =</span> sdX[<span class="dv">2</span>]),</span>
+<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;prognostic&quot;</span>),</span>
+<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a>  <span class="at">EM_cont_1 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_EM_AC[<span class="dv">1</span>], <span class="at">sd =</span> sdX_EM[<span class="dv">1</span>]),</span>
+<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;effect_modifier&quot;</span>),</span>
+<span id="cb3-8"><a href="#cb3-8" tabindex="-1"></a>  <span class="at">EM_cont_2 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_EM_AC[<span class="dv">2</span>], <span class="at">sd =</span> sdX_EM[<span class="dv">2</span>]),</span>
+<span id="cb3-9"><a href="#cb3-9" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;effect_modifier&quot;</span>)</span>
+<span id="cb3-10"><a href="#cb3-10" tabindex="-1"></a>)</span>
+<span id="cb3-11"><a href="#cb3-11" tabindex="-1"></a></span>
+<span id="cb3-12"><a href="#cb3-12" tabindex="-1"></a>b_prognostic <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="at">PF_cont_1 =</span> b_PF, <span class="at">PF_cont_2 =</span> b_PF)</span>
+<span id="cb3-13"><a href="#cb3-13" tabindex="-1"></a></span>
+<span id="cb3-14"><a href="#cb3-14" tabindex="-1"></a>b_effect_modifier <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="at">EM_cont_1 =</span> b_EM, <span class="at">EM_cont_2 =</span> b_EM)</span>
+<span id="cb3-15"><a href="#cb3-15" tabindex="-1"></a></span>
+<span id="cb3-16"><a href="#cb3-16" tabindex="-1"></a>num_normal_covs <span class="ot">&lt;-</span> <span class="fu">length</span>(covariate_defns_ipd)</span>
+<span id="cb3-17"><a href="#cb3-17" tabindex="-1"></a>cor_matrix <span class="ot">&lt;-</span> <span class="fu">matrix</span>(corX, num_normal_covs, num_normal_covs)</span>
+<span id="cb3-18"><a href="#cb3-18" tabindex="-1"></a><span class="fu">diag</span>(cor_matrix) <span class="ot">&lt;-</span> <span class="dv">1</span></span>
+<span id="cb3-19"><a href="#cb3-19" tabindex="-1"></a></span>
+<span id="cb3-20"><a href="#cb3-20" tabindex="-1"></a><span class="fu">rownames</span>(cor_matrix) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;PF_cont_1&quot;</span>, <span class="st">&quot;PF_cont_2&quot;</span>, <span class="st">&quot;EM_cont_1&quot;</span>, <span class="st">&quot;EM_cont_2&quot;</span>)</span>
+<span id="cb3-21"><a href="#cb3-21" tabindex="-1"></a><span class="fu">colnames</span>(cor_matrix) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;PF_cont_1&quot;</span>, <span class="st">&quot;PF_cont_2&quot;</span>, <span class="st">&quot;EM_cont_1&quot;</span>, <span class="st">&quot;EM_cont_2&quot;</span>)</span>
+<span id="cb3-22"><a href="#cb3-22" tabindex="-1"></a></span>
+<span id="cb3-23"><a href="#cb3-23" tabindex="-1"></a>ipd_trial <span class="ot">&lt;-</span> simcovariates<span class="sc">::</span><span class="fu">gen_data</span>(</span>
+<span id="cb3-24"><a href="#cb3-24" tabindex="-1"></a>  <span class="at">N =</span> N,</span>
+<span id="cb3-25"><a href="#cb3-25" tabindex="-1"></a>  <span class="at">b_0 =</span> b_0,</span>
+<span id="cb3-26"><a href="#cb3-26" tabindex="-1"></a>  <span class="at">b_trt =</span> b_trt,</span>
+<span id="cb3-27"><a href="#cb3-27" tabindex="-1"></a>  <span class="at">covariate_defns =</span> covariate_defns_ipd,</span>
+<span id="cb3-28"><a href="#cb3-28" tabindex="-1"></a>  <span class="at">b_prognostic =</span> b_prognostic,</span>
+<span id="cb3-29"><a href="#cb3-29" tabindex="-1"></a>  <span class="at">b_effect_modifier =</span> b_effect_modifier,</span>
+<span id="cb3-30"><a href="#cb3-30" tabindex="-1"></a>  <span class="at">cor_matrix =</span> cor_matrix,</span>
+<span id="cb3-31"><a href="#cb3-31" tabindex="-1"></a>  <span class="at">trt_assignment =</span> <span class="fu">list</span>(<span class="at">prob_trt1 =</span> allocation),</span>
+<span id="cb3-32"><a href="#cb3-32" tabindex="-1"></a>  <span class="at">family =</span> <span class="fu">binomial</span>(<span class="st">&quot;logit&quot;</span>))</span></code></pre></div>
+<p>The treatment column in the return data is binary and takes values 0
+and 1. We will include some extra information about treatment names. To
+do this we will define the lable of the two level factor as
+<code>A</code> for 1 and <code>C</code> for 0 as follows.</p>
+<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a>ipd_trial<span class="sc">$</span>trt <span class="ot">&lt;-</span> <span class="fu">factor</span>(ipd_trial<span class="sc">$</span>trt, <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">&quot;C&quot;</span>, <span class="st">&quot;A&quot;</span>))</span></code></pre></div>
+<p>Similarly, to obtain the aggregate data we will simulate IPD but with
+the additional summarise step. We set different mean values
+<code>meanX_BC</code> and <code>meanX_EM_BC</code> but otherwise use the
+same parameter values as for the <span class="math inline">\(AC\)</span>
+trial.</p>
+<p>First, simulate the underlying IPD similarly for the AC trial.</p>
+<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a>covariate_defns_ald <span class="ot">&lt;-</span> <span class="fu">list</span>(</span>
+<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>  <span class="at">PF_cont_1 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_BC[<span class="dv">1</span>], <span class="at">sd =</span> sdX[<span class="dv">1</span>]),</span>
+<span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;prognostic&quot;</span>),</span>
+<span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a>  <span class="at">PF_cont_2 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_BC[<span class="dv">2</span>], <span class="at">sd =</span> sdX[<span class="dv">2</span>]),</span>
+<span id="cb5-5"><a href="#cb5-5" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;prognostic&quot;</span>),</span>
+<span id="cb5-6"><a href="#cb5-6" tabindex="-1"></a>  <span class="at">EM_cont_1 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_EM_BC[<span class="dv">1</span>], <span class="at">sd =</span> sdX_EM[<span class="dv">1</span>]),</span>
+<span id="cb5-7"><a href="#cb5-7" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;effect_modifier&quot;</span>),</span>
+<span id="cb5-8"><a href="#cb5-8" tabindex="-1"></a>  <span class="at">EM_cont_2 =</span> <span class="fu">list</span>(<span class="at">type =</span> <span class="fu">continuous</span>(<span class="at">mean =</span> meanX_EM_BC[<span class="dv">2</span>], <span class="at">sd =</span> sdX_EM[<span class="dv">2</span>]),</span>
+<span id="cb5-9"><a href="#cb5-9" tabindex="-1"></a>                    <span class="at">role =</span> <span class="st">&quot;effect_modifier&quot;</span>)</span>
+<span id="cb5-10"><a href="#cb5-10" tabindex="-1"></a>)</span>
+<span id="cb5-11"><a href="#cb5-11" tabindex="-1"></a></span>
+<span id="cb5-12"><a href="#cb5-12" tabindex="-1"></a>BC.IPD <span class="ot">&lt;-</span> simcovariates<span class="sc">::</span><span class="fu">gen_data</span>(</span>
+<span id="cb5-13"><a href="#cb5-13" tabindex="-1"></a>  <span class="at">N =</span> N,</span>
+<span id="cb5-14"><a href="#cb5-14" tabindex="-1"></a>  <span class="at">b_0 =</span> b_0,</span>
+<span id="cb5-15"><a href="#cb5-15" tabindex="-1"></a>  <span class="at">b_trt =</span> b_trt,</span>
+<span id="cb5-16"><a href="#cb5-16" tabindex="-1"></a>  <span class="at">covariate_defns =</span> covariate_defns_ald,</span>
+<span id="cb5-17"><a href="#cb5-17" tabindex="-1"></a>  <span class="at">b_prognostic =</span> b_prognostic,</span>
+<span id="cb5-18"><a href="#cb5-18" tabindex="-1"></a>  <span class="at">b_effect_modifier =</span> b_effect_modifier,</span>
+<span id="cb5-19"><a href="#cb5-19" tabindex="-1"></a>  <span class="at">cor_matrix =</span> cor_matrix,</span>
+<span id="cb5-20"><a href="#cb5-20" tabindex="-1"></a>  <span class="at">trt_assignment =</span> <span class="fu">list</span>(<span class="at">prob_trt1 =</span> allocation),</span>
+<span id="cb5-21"><a href="#cb5-21" tabindex="-1"></a>  <span class="at">family =</span> <span class="fu">binomial</span>(<span class="st">&quot;logit&quot;</span>))</span>
+<span id="cb5-22"><a href="#cb5-22" tabindex="-1"></a></span>
+<span id="cb5-23"><a href="#cb5-23" tabindex="-1"></a>BC.IPD<span class="sc">$</span>trt <span class="ot">&lt;-</span> <span class="fu">factor</span>(BC.IPD<span class="sc">$</span>trt, <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">&quot;C&quot;</span>, <span class="st">&quot;B&quot;</span>))</span></code></pre></div>
+<p>Next, we aggregate these data. We <code>summarise()</code> the
+covariates, sample sizes and outcomes separately and then bind the
+results together.</p>
+<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="co"># covariate summary statistics</span></span>
+<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a><span class="co"># assume same between treatments</span></span>
+<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a>cov.X <span class="ot">&lt;-</span> </span>
+<span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a>  BC.IPD <span class="sc">%&gt;%</span></span>
+<span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a>  <span class="fu">as.data.frame</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb6-6"><a href="#cb6-6" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">select</span>(<span class="fu">matches</span>(<span class="st">&quot;^(PF|EM)&quot;</span>), trt) <span class="sc">|&gt;</span> </span>
+<span id="cb6-7"><a href="#cb6-7" tabindex="-1"></a>  tidyr<span class="sc">::</span><span class="fu">pivot_longer</span>(</span>
+<span id="cb6-8"><a href="#cb6-8" tabindex="-1"></a>    <span class="at">cols =</span> <span class="fu">starts_with</span>(<span class="st">&quot;PF&quot;</span>) <span class="sc">|</span> <span class="fu">starts_with</span>(<span class="st">&quot;EM&quot;</span>),</span>
+<span id="cb6-9"><a href="#cb6-9" tabindex="-1"></a>    <span class="at">names_to =</span> <span class="st">&quot;variable&quot;</span>,</span>
+<span id="cb6-10"><a href="#cb6-10" tabindex="-1"></a>    <span class="at">values_to =</span> <span class="st">&quot;value&quot;</span>) <span class="sc">|&gt;</span></span>
+<span id="cb6-11"><a href="#cb6-11" tabindex="-1"></a>  <span class="fu">group_by</span>(variable) <span class="sc">%&gt;%</span></span>
+<span id="cb6-12"><a href="#cb6-12" tabindex="-1"></a>  <span class="fu">summarise</span>(</span>
+<span id="cb6-13"><a href="#cb6-13" tabindex="-1"></a>    <span class="at">mean =</span> <span class="fu">mean</span>(value),</span>
+<span id="cb6-14"><a href="#cb6-14" tabindex="-1"></a>    <span class="at">sd =</span> <span class="fu">sd</span>(value)</span>
+<span id="cb6-15"><a href="#cb6-15" tabindex="-1"></a>  ) <span class="sc">%&gt;%</span></span>
+<span id="cb6-16"><a href="#cb6-16" tabindex="-1"></a>  tidyr<span class="sc">::</span><span class="fu">pivot_longer</span>(</span>
+<span id="cb6-17"><a href="#cb6-17" tabindex="-1"></a>    <span class="at">cols =</span> <span class="fu">c</span>(<span class="st">&quot;mean&quot;</span>, <span class="st">&quot;sd&quot;</span>),</span>
+<span id="cb6-18"><a href="#cb6-18" tabindex="-1"></a>    <span class="at">names_to =</span> <span class="st">&quot;statistic&quot;</span>,</span>
+<span id="cb6-19"><a href="#cb6-19" tabindex="-1"></a>    <span class="at">values_to =</span> <span class="st">&quot;value&quot;</span>) <span class="sc">%&gt;%</span></span>
+<span id="cb6-20"><a href="#cb6-20" tabindex="-1"></a>  <span class="fu">ungroup</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb6-21"><a href="#cb6-21" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">trt =</span> <span class="cn">NA</span>)</span>
+<span id="cb6-22"><a href="#cb6-22" tabindex="-1"></a></span>
+<span id="cb6-23"><a href="#cb6-23" tabindex="-1"></a><span class="co"># outcome</span></span>
+<span id="cb6-24"><a href="#cb6-24" tabindex="-1"></a>summary.y <span class="ot">&lt;-</span> </span>
+<span id="cb6-25"><a href="#cb6-25" tabindex="-1"></a>  BC.IPD <span class="sc">|&gt;</span> </span>
+<span id="cb6-26"><a href="#cb6-26" tabindex="-1"></a>  <span class="fu">as.data.frame</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb6-27"><a href="#cb6-27" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">select</span>(y, trt) <span class="sc">%&gt;%</span></span>
+<span id="cb6-28"><a href="#cb6-28" tabindex="-1"></a>  tidyr<span class="sc">::</span><span class="fu">pivot_longer</span>(<span class="at">cols =</span> <span class="st">&quot;y&quot;</span>,</span>
+<span id="cb6-29"><a href="#cb6-29" tabindex="-1"></a>               <span class="at">names_to =</span> <span class="st">&quot;variable&quot;</span>,</span>
+<span id="cb6-30"><a href="#cb6-30" tabindex="-1"></a>               <span class="at">values_to =</span> <span class="st">&quot;value&quot;</span>) <span class="sc">%&gt;%</span></span>
+<span id="cb6-31"><a href="#cb6-31" tabindex="-1"></a>  <span class="fu">group_by</span>(variable, trt) <span class="sc">%&gt;%</span></span>
+<span id="cb6-32"><a href="#cb6-32" tabindex="-1"></a>  <span class="fu">summarise</span>(</span>
+<span id="cb6-33"><a href="#cb6-33" tabindex="-1"></a>    <span class="at">mean =</span> <span class="fu">mean</span>(value),</span>
+<span id="cb6-34"><a href="#cb6-34" tabindex="-1"></a>    <span class="at">sd =</span> <span class="fu">sd</span>(value),</span>
+<span id="cb6-35"><a href="#cb6-35" tabindex="-1"></a>    <span class="at">sum =</span> <span class="fu">sum</span>(value)</span>
+<span id="cb6-36"><a href="#cb6-36" tabindex="-1"></a>  ) <span class="sc">%&gt;%</span></span>
+<span id="cb6-37"><a href="#cb6-37" tabindex="-1"></a>  tidyr<span class="sc">::</span><span class="fu">pivot_longer</span>(</span>
+<span id="cb6-38"><a href="#cb6-38" tabindex="-1"></a>    <span class="at">cols =</span> <span class="fu">c</span>(<span class="st">&quot;mean&quot;</span>, <span class="st">&quot;sd&quot;</span>, <span class="st">&quot;sum&quot;</span>),</span>
+<span id="cb6-39"><a href="#cb6-39" tabindex="-1"></a>    <span class="at">names_to =</span> <span class="st">&quot;statistic&quot;</span>,</span>
+<span id="cb6-40"><a href="#cb6-40" tabindex="-1"></a>    <span class="at">values_to =</span> <span class="st">&quot;value&quot;</span>) <span class="sc">%&gt;%</span></span>
+<span id="cb6-41"><a href="#cb6-41" tabindex="-1"></a>  <span class="fu">ungroup</span>()</span>
+<span id="cb6-42"><a href="#cb6-42" tabindex="-1"></a></span>
+<span id="cb6-43"><a href="#cb6-43" tabindex="-1"></a><span class="co"># sample sizes</span></span>
+<span id="cb6-44"><a href="#cb6-44" tabindex="-1"></a>summary.N <span class="ot">&lt;-</span> </span>
+<span id="cb6-45"><a href="#cb6-45" tabindex="-1"></a>  BC.IPD <span class="sc">|&gt;</span> </span>
+<span id="cb6-46"><a href="#cb6-46" tabindex="-1"></a>  <span class="fu">group_by</span>(trt) <span class="sc">|&gt;</span> </span>
+<span id="cb6-47"><a href="#cb6-47" tabindex="-1"></a>  <span class="fu">count</span>(<span class="at">name =</span> <span class="st">&quot;N&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb6-48"><a href="#cb6-48" tabindex="-1"></a>  tidyr<span class="sc">::</span><span class="fu">pivot_longer</span>(</span>
+<span id="cb6-49"><a href="#cb6-49" tabindex="-1"></a>    <span class="at">cols =</span> <span class="st">&quot;N&quot;</span>,</span>
+<span id="cb6-50"><a href="#cb6-50" tabindex="-1"></a>    <span class="at">names_to =</span> <span class="st">&quot;statistic&quot;</span>,</span>
+<span id="cb6-51"><a href="#cb6-51" tabindex="-1"></a>    <span class="at">values_to =</span> <span class="st">&quot;value&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb6-52"><a href="#cb6-52" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">variable =</span> <span class="cn">NA_character_</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb6-53"><a href="#cb6-53" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">select</span>(variable, statistic, value, trt)</span>
+<span id="cb6-54"><a href="#cb6-54" tabindex="-1"></a>  </span>
+<span id="cb6-55"><a href="#cb6-55" tabindex="-1"></a>ald_trial <span class="ot">&lt;-</span> <span class="fu">rbind.data.frame</span>(cov.X, summary.y, summary.N)</span></code></pre></div>
+<p>This general format of the data sets are in a ‘long’ style consisting
+of the following.</p>
+<div id="ipd_trial-individual-patient-data" class="section level4">
+<h4><code>ipd_trial</code>: Individual patient data</h4>
+<ul>
+<li><code>PF_*</code>: Patient measurements prognostic factors</li>
+<li><code>EM_*</code>: Patient measurements effect modifiers</li>
+<li><code>trt</code>: Treatment label (factor)</li>
+<li><code>y</code>: Indicator of whether event was observed (two level
+factor)</li>
+</ul>
+</div>
+<div id="ald_trial-aggregate-level-data" class="section level4">
+<h4><code>ald_trial</code>: Aggregate-level data</h4>
+<ul>
+<li><code>variable</code>: Covariate name. In the case of treatment arm
+sample size this is <code>NA</code></li>
+<li><code>statistic</code>: Summary statistic name from mean, standard
+deviation or sum</li>
+<li><code>value</code>: Numerical value of summary statistic</li>
+<li><code>trt</code>: Treatment label. Because we assume a common
+covariate distribution between treatment arms this is
+<code>NA</code></li>
+</ul>
+<p>Our final data look like the following.</p>
+<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a><span class="fu">head</span>(ipd_trial)</span></code></pre></div>
+<p>There are 4 correlated continuous covariates generated per subject,
+simulated from a multivariate normal distribution. Treatment
+<code>trt</code> takes either new treatment <em>A</em> or standard of
+care / status quo <em>C</em>. The ITC is ‘anchored’ via <em>C</em>, the
+common treatment.</p>
+<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a>ald_trial</span></code></pre></div>
+<p>In this case, we have 4 covariate mean and standard deviation values;
+and the event total, average and sample size for each treatment
+<em>B</em> and <em>C</em>.</p>
+</div>
+<div id="regression-model" class="section level4">
+<h4>Regression model</h4>
+<p>The true logistic outcome model which we use to simulate the data
+is</p>
+<p><span class="math display">\[
+\text{logit}(p_{t}) = \beta_0 + \beta_{PF} (X_3 + X_4) + [\beta_{t} +
+\beta_{EM} (X_1 + X_2)] \; \text{I}(t \neq C)
+\]</span></p>
+<p><span class="math inline">\(\text{I}()\)</span> is an indicator
+function taking value 1 if true and 0 otherwise. That is, for treatment
+<span class="math inline">\(C\)</span> the right hand side becomes <span class="math inline">\(\beta_0 + \beta_{PF} (X_3 + X_4)\)</span> and for
+comparator treatments <span class="math inline">\(A\)</span> or <span class="math inline">\(B\)</span> there is an additional <span class="math inline">\(\beta_t + \beta_{EM} (X_1 + X_2)\)</span>
+component consisting of the effect modifier terms and the coefficient
+for the treatment parameter, <span class="math inline">\(\beta_t\)</span> (or <code>b_trt</code> in the R
+code), i.e. the log odds-ratio (LOR) for the logit model. Finally, <span class="math inline">\(p_{t}\)</span> is the probability of experiencing
+the event of interest for treatment <span class="math inline">\(t\)</span>.</p>
+</div>
+</div>
+<div id="output-statistics" class="section level3">
+<h3>Output statistics</h3>
+<p>We will obtain the <em>marginal treatment effect</em> and
+<em>marginal variance</em>. The definition by which of these are
+calculated depends on the type of data and outcome scale. For our
+current example of binary data and log-odds ratio the marginal treatment
+effect is</p>
+<p><span class="math display">\[
+\log\left( \frac{n_B/(N_B-n_B)}{n_C/(N_B-n_{B})} \right) = \log(n_B
+n_{\bar{C}}) - \log(n_C n_{\bar{B}})
+\]</span></p>
+<p>and marginal variance is</p>
+<p><span class="math display">\[
+\frac{1}{n_C} + \frac{1}{n_{\bar{C}}} + \frac{1}{n_B} +
+\frac{1}{n_{\bar{B}}}
+\]</span></p>
+<p>where <span class="math inline">\(n_B, n_C\)</span> are the number of
+events in each arm and <span class="math inline">\(\bar{C}\)</span> is
+the compliment of <span class="math inline">\(C\)</span>, so e.g. <span class="math inline">\(n_{\bar{C}} = N_C - n_c\)</span>. Other outcome
+scales will be discussed below.</p>
+</div>
+</div>
+<div id="model-fitting-in-r" class="section level2">
+<h2>Model fitting in R</h2>
+<p>The <code>{outstandR}</code> package has been written to be easy to
+use and essentially consists of a single function,
+<code>outstandR()</code>. This can be used to run all of the different
+types of model, which when combined with their specific parameters we
+will call <em>strategies</em>. The first two arguments of
+<code>outstandR()</code> are the individual patient and aggregate-level
+data, respectively.</p>
+<p>A <code>strategy</code> argument of <code>outstandR</code> takes
+functions called <code>strategy_*()</code>, where the wildcard
+<code>*</code> is replaced by the name of the particular method
+required, e.g. <code>strategy_maic()</code> for MAIC. Each specific
+example is provided below.</p>
+<div id="model-formula" class="section level3">
+<h3>Model formula</h3>
+<p>We will take advantage of the in-built R formula object to define the
+models. This will allow us to easily pull out components of the object
+and consistently use it. Defining <span class="math inline">\(EM\_cont\_1, EM\_cont\_2\)</span> as effect
+modifiers, <span class="math inline">\(PF\_cont\_1, PF\_cont\_2\)</span>
+as prognostic variables and <span class="math inline">\(Z\)</span> the
+treatment indicator then the formula used in this model is</p>
+<p><span class="math display">\[
+y = PF\_cont\_1 + PF\_cont\_2 + Z + Z \times EM\_cont\_1 + Z \times
+EM\_cont\_2
+\]</span></p>
+<p>Notice that this does not include the link function of interest so
+appears as a linear regression. This corresponds to the following
+<code>R</code> <code>formula</code> object we will pass as an argument
+to the strategy function.</p>
+<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a>lin_form <span class="ot">&lt;-</span> <span class="fu">list</span>(</span>
+<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>  <span class="at">outcome_model =</span> <span class="fu">as.formula</span>(<span class="st">&quot;y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2&quot;</span>),</span>
+<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>  <span class="at">balance_model =</span> <span class="fu">as.formula</span>(<span class="st">&quot;~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2&quot;</span>)</span>
+<span id="cb9-4"><a href="#cb9-4" tabindex="-1"></a>)</span></code></pre></div>
+<p>Note that the more succinct formula</p>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a>y <span class="sc">~</span> PF_cont_1 <span class="sc">+</span> PF_cont_2 <span class="sc">+</span> trt<span class="sc">*</span>(EM_cont_1 <span class="sc">+</span> EM_cont_2)</span></code></pre></div>
+<p>would additionally include <span class="math inline">\(X_1,
+X_2\)</span> as prognostic factors so is not equivalent (but this may be
+what you actually want). To recover the original formula it can be
+modified as follows.</p>
+<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a>y <span class="sc">~</span> PF_cont_1 <span class="sc">+</span> PF_cont_2 <span class="sc">+</span> trt<span class="sc">*</span>(EM_cont_1 <span class="sc">+</span> EM_cont_2) <span class="sc">-</span> EM_cont_1 <span class="sc">-</span> EM_cont_2</span></code></pre></div>
+<p>We note that the MAIC approach does not strictly use a regression in
+the same way as the other methods so should not be considered directly
+comparable in this sense but we have decided to use a consistent syntax
+across models using ‘formula’.</p>
+</div>
+<div id="matching-adjusted-indirect-comparison-maic" class="section level3">
+<h3>Matching-Adjusted Indirect Comparison (MAIC)</h3>
+<p>A single call to <code>outstandR()</code> is sufficient to run the
+model. We pass to the <code>strategy</code> argument the
+<code>strategy_maic()</code> function with arguments
+<code>formula = lin_form</code> as defined above and
+<code>family = binomial(link = &quot;logit&quot;)</code> for binary data and
+logistic link.</p>
+<p>Internally, using the individual patient level data for <em>AC</em>
+firstly we perform non-parametric bootstrap of the
+<code>maic.boot</code> function with <code>R = 1000</code> replicates.
+This function fits treatment coefficient for the marginal effect for
+<em>A</em> vs <em>C</em>. The returned value is an object of class
+<code>boot</code> from the <code>{boot}</code> package. We then
+calculate the bootstrap mean and variance in the wrapper function
+<code>maic_boot_stats</code>.</p>
+<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a>outstandR_maic <span class="ot">&lt;-</span></span>
+<span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb12-3"><a href="#cb12-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(</span>
+<span id="cb12-4"><a href="#cb12-4" tabindex="-1"></a>              <span class="at">formula =</span> lin_form,</span>
+<span id="cb12-5"><a href="#cb12-5" tabindex="-1"></a>              <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)))</span></code></pre></div>
+<p>The returned object is of class <code>outstandR</code>.</p>
+<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" tabindex="-1"></a><span class="fu">str</span>(outstandR_maic)</span></code></pre></div>
+<p>We see that this is a list object with 2 parts. The first contains
+statistics between each pair of treatments. These are the mean
+contrasts, variances and confidence intervals (CI), respectively. The
+default CI is for 95% but can be altered in <code>outstandR</code> with
+the <code>CI</code> argument. The second element of the list contains
+the absolute effect estimates.</p>
+<p>A <code>print</code> method is available for <code>outstandR</code>
+objects for more human-readable output</p>
+<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" tabindex="-1"></a>outstandR_maic</span></code></pre></div>
+<div id="outcome-scale" class="section level4">
+<h4>Outcome scale</h4>
+<p>If we do not explicitly specify the outcome scale, the default is
+that used to fit to the data in the regression model. As we saw, in this
+case, the default is log-odds ratio corresponding to the
+<code>&quot;logit&quot;</code> link function for binary data. However, we can
+change this to some other scale which may be more appropriate for a
+particular analysis. So far implemented in the package, the links and
+their corresponding relative treatment effect scales are as follows:</p>
+<table>
+<thead>
+<tr class="header">
+<th align="left">Data Type</th>
+<th>Model</th>
+<th align="left">Scale</th>
+<th align="left">Argument</th>
+</tr>
+</thead>
+<tbody>
+<tr class="odd">
+<td align="left">Binary</td>
+<td><code>logit</code></td>
+<td align="left">Log-odds ratio</td>
+<td align="left"><code>log_odds</code></td>
+</tr>
+<tr class="even">
+<td align="left">Count</td>
+<td><code>log</code></td>
+<td align="left">Log-risk ratio</td>
+<td align="left"><code>log_relative_risk</code></td>
+</tr>
+<tr class="odd">
+<td align="left">Continuous</td>
+<td><code>mean</code></td>
+<td align="left">Mean difference</td>
+<td align="left"><code>risk_difference</code></td>
+</tr>
+</tbody>
+</table>
+<p>The full list of possible transformed treatment effect scales will
+be: log-odds ratio, log-risk ratio, mean difference, risk difference,
+hazard ratio, hazard difference.</p>
+<p>For binary data the marginal treatment effect and variance are</p>
+<ul>
+<li><strong>Log-risk ratio</strong></li>
+</ul>
+<p>Treatment effect is</p>
+<p><span class="math display">\[
+\log(n_B/N_B) - \log(n_A/N_A)
+\]</span></p>
+<p>and variance</p>
+<p><span class="math display">\[
+\frac{1}{n_B} - \frac{1}{N_B} + \frac{1}{n_A} - \frac{1}{N_A}
+\]</span></p>
+<ul>
+<li><strong>Risk difference</strong></li>
+</ul>
+<p>Treatment effect is</p>
+<p><span class="math display">\[
+\frac{n_B}{N_B} - \frac{n_A}{N_A}
+\]</span></p>
+<p>and variance</p>
+<p><span class="math display">\[
+\frac{n_B}{N_B} \left( 1 - \frac{n_B}{N_B} \right) + \frac{n_A}{N_A}
+\left( 1 - \frac{n_A}{N_A} \right)
+\]</span></p>
+<p>To change the outcome scale, we can pass the <code>scale</code>
+argument in the <code>outstandR()</code> function. For example, to
+change the scale to risk difference, we can use the following code.</p>
+<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a>outstandR_maic_lrr <span class="ot">&lt;-</span></span>
+<span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb15-3"><a href="#cb15-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_maic</span>(<span class="at">formula =</span> lin_form,</span>
+<span id="cb15-4"><a href="#cb15-4" tabindex="-1"></a>                                     <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)),</span>
+<span id="cb15-5"><a href="#cb15-5" tabindex="-1"></a>            <span class="at">scale =</span> <span class="st">&quot;log_relative_risk&quot;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" tabindex="-1"></a>outstandR_maic_lrr</span></code></pre></div>
+</div>
+</div>
+<div id="parametric-g-computation-with-maximum-likelihood-estimation" class="section level3">
+<h3>Parametric G-computation with maximum-likelihood estimation</h3>
+<p>G-computation marginalizes the conditional estimates by separating
+the regression modelling from the estimation of the marginal treatment
+effect for <em>A</em> versus <em>C</em>. First, a regression model of
+the observed outcome <span class="math inline">\(y\)</span> on the
+covariates <span class="math inline">\(x\)</span> and treatment <span class="math inline">\(z\)</span> is fitted to the <em>AC</em> IPD:</p>
+<p><span class="math display">\[
+g(\mu_n) = \beta_0 + \boldsymbol{x}_n \boldsymbol{\beta_{PF}} + (\beta_z
++ \boldsymbol{x_n^{EM}} \boldsymbol{\beta_{EM}}) \; \mbox{I}(t \neq C)
+\]</span></p>
+<p>In the context of G-computation, this regression model is often
+called the “Q-model.” Having fitted the Q-model, the regression
+coefficients are treated as nuisance parameters. The parameters are
+applied to the simulated covariates <span class="math inline">\(x*\)</span> to predict hypothetical outcomes for
+each subject under both possible treatments. Namely, a pair of predicted
+outcomes, also called potential outcomes, under <em>A</em> and under
+<em>C</em>, is generated for each subject.</p>
+<p>By plugging treatment <em>C</em> into the regression fit for every
+simulated observation, we predict the marginal outcome mean in the
+hypothetical scenario in which all units are under treatment
+<em>C</em>:</p>
+<p><span class="math display">\[
+\hat{\mu}_0 = \int_{x^*} g^{-1} (\hat{\beta}_0 + x^* \hat{\beta}_1 )
+p(x^*) \; \text{d}x^*
+\]</span></p>
+<p>As performed for the previous approaches, call
+<code>outstandR()</code> but change the strategy to
+<code>strategy_gcomp_ml()</code>,</p>
+<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" tabindex="-1"></a>outstandR_gcomp_ml <span class="ot">&lt;-</span></span>
+<span id="cb17-2"><a href="#cb17-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb17-3"><a href="#cb17-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
+<span id="cb17-4"><a href="#cb17-4" tabindex="-1"></a>              <span class="at">formula =</span> lin_form,</span>
+<span id="cb17-5"><a href="#cb17-5" tabindex="-1"></a>              <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)))</span></code></pre></div>
+<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" tabindex="-1"></a>outstandR_gcomp_ml</span></code></pre></div>
+<p>Once again, let us change the outcome scale to LRR</p>
+<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" tabindex="-1"></a>outstandR_gcomp_ml_lrr <span class="ot">&lt;-</span></span>
+<span id="cb19-2"><a href="#cb19-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb19-3"><a href="#cb19-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_gcomp_ml</span>(</span>
+<span id="cb19-4"><a href="#cb19-4" tabindex="-1"></a>              <span class="at">formula =</span> lin_form,</span>
+<span id="cb19-5"><a href="#cb19-5" tabindex="-1"></a>              <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)),</span>
+<span id="cb19-6"><a href="#cb19-6" tabindex="-1"></a>            <span class="at">scale =</span> <span class="st">&quot;log_relative_risk&quot;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" tabindex="-1"></a>outstandR_gcomp_ml_lrr</span></code></pre></div>
+</div>
+<div id="bayesian-g-computation-with-mcmc" class="section level3">
+<h3>Bayesian G-computation with MCMC</h3>
+<p>The difference between Bayesian G-computation and its
+maximum-likelihood counterpart is in the estimated distribution of the
+predicted outcomes. The Bayesian approach also marginalizes, integrates
+or standardizes over the joint posterior distribution of the conditional
+nuisance parameters of the outcome regression, as well as the joint
+covariate distribution.</p>
+<p>Draw a vector of size <span class="math inline">\(N^*\)</span> of
+predicted outcomes <span class="math inline">\(y^*_z\)</span> under each
+set intervention <span class="math inline">\(z^* \in \{0, 1\}\)</span>
+from its posterior predictive distribution under the specific treatment.
+This is defined as <span class="math inline">\(p(y^*_{z^*} \mid
+\mathcal{D}_{AC}) = \int_{\beta} p(y^*_{z^*} \mid \beta) p(\beta \mid
+\mathcal{D}_{AC}) d\beta\)</span> where <span class="math inline">\(p(\beta \mid \mathcal{D}_{AC})\)</span> is the
+posterior distribution of the outcome regression coefficients <span class="math inline">\(\beta\)</span>, which encode the predictor-outcome
+relationships observed in the <em>AC</em> trial IPD. This is given
+by:</p>
+<p><span class="math display">\[
+p(y^*_{^z*} \mid \mathcal{D}_{AC}) = \int_{x^*} p(y^* \mid z^*, x^*,
+\mathcal{D}_{AC}) p(x^* \mid \mathcal{D}_{AC})\; \text{d}x^*
+\]</span></p>
+<p><span class="math display">\[
+= \int_{x^*} \int_{\beta} p(y^* \mid z^*, x^*, \beta) p(x^* \mid \beta)
+p(\beta \mid \mathcal{D}_{AC})\; d\beta \; \text{d}x^*
+\]</span></p>
+<p>In practice, the integrals above can be approximated numerically,
+using full Bayesian estimation via Markov chain Monte Carlo (MCMC)
+sampling.</p>
+<p>The average, variance and interval estimates of the marginal
+treatment effect can be derived empirically from draws of the posterior
+density.</p>
+<p>The strategy function to plug-in to the <code>outstandR()</code> call
+for this approach is <code>strategy_gcomp_bayes()</code>,</p>
+<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" tabindex="-1"></a>outstandR_gcomp_bayes <span class="ot">&lt;-</span></span>
+<span id="cb21-2"><a href="#cb21-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb21-3"><a href="#cb21-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_gcomp_bayes</span>(</span>
+<span id="cb21-4"><a href="#cb21-4" tabindex="-1"></a>              <span class="at">formula =</span> lin_form,</span>
+<span id="cb21-5"><a href="#cb21-5" tabindex="-1"></a>              <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)))</span></code></pre></div>
+<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" tabindex="-1"></a>outstandR_gcomp_bayes</span></code></pre></div>
+<p>As before, we can change the outcome scale to LRR.</p>
+<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" tabindex="-1"></a>outstandR_gcomp_bayes_lrr <span class="ot">&lt;-</span></span>
+<span id="cb23-2"><a href="#cb23-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb23-3"><a href="#cb23-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_gcomp_bayes</span>(</span>
+<span id="cb23-4"><a href="#cb23-4" tabindex="-1"></a>              <span class="at">formula =</span> lin_form,</span>
+<span id="cb23-5"><a href="#cb23-5" tabindex="-1"></a>              <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)),</span>
+<span id="cb23-6"><a href="#cb23-6" tabindex="-1"></a>            <span class="at">scale =</span> <span class="st">&quot;log_relative_risk&quot;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" tabindex="-1"></a>outstandR_gcomp_bayes_lrr</span></code></pre></div>
+</div>
+<div id="multiple-imputation-marginalisation" class="section level3">
+<h3>Multiple imputation marginalisation</h3>
+<p>The final method is to obtain the marginalized treatment effect for
+aggregate level data study, obtained by integrating over the covariate
+distribution from the aggregate level data <span class="math inline">\(BC\)</span> study</p>
+<p><span class="math display">\[
+\Delta^{\text{marg}} = \mathbb{E}_{X \sim f_{\text{BC}}(X)} \left[
+\mu_{T=1}(X) - \mu_{T=0}(X) \right]
+= \int \left[ \mu_{T=1}(X) - \mu_{T=0}(X) \right] f_{\text{BC}}(X) \;
+\text{d}X
+\]</span></p>
+<p>The aggregate level data likelihood is</p>
+<p><span class="math display">\[
+\hat{\Delta}_{BC} \sim \mathcal{N}(\Delta^{\text{marg}}, SE^2)
+\]</span></p>
+<p>The multiple imputation marginalisation strategy function is
+<code>strategy_mim()</code>,</p>
+<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" tabindex="-1"></a>outstandR_mim <span class="ot">&lt;-</span></span>
+<span id="cb25-2"><a href="#cb25-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb25-3"><a href="#cb25-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_mim</span>(</span>
+<span id="cb25-4"><a href="#cb25-4" tabindex="-1"></a>              <span class="at">formula =</span> lin_form,</span>
+<span id="cb25-5"><a href="#cb25-5" tabindex="-1"></a>              <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)))</span></code></pre></div>
+<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" tabindex="-1"></a>outstandR_mim</span></code></pre></div>
+<p>Change the outcome scale again for LRR,</p>
+<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" tabindex="-1"></a>outstandR_mim_lrr <span class="ot">&lt;-</span></span>
+<span id="cb27-2"><a href="#cb27-2" tabindex="-1"></a>  <span class="fu">outstandR</span>(ipd_trial, ald_trial,</span>
+<span id="cb27-3"><a href="#cb27-3" tabindex="-1"></a>            <span class="at">strategy =</span> <span class="fu">strategy_mim</span>(</span>
+<span id="cb27-4"><a href="#cb27-4" tabindex="-1"></a>              <span class="at">formula =</span> lin_form,</span>
+<span id="cb27-5"><a href="#cb27-5" tabindex="-1"></a>              <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>)),</span>
+<span id="cb27-6"><a href="#cb27-6" tabindex="-1"></a>            <span class="at">scale =</span> <span class="st">&quot;log_relative_risk&quot;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" tabindex="-1"></a>outstandR_mim_lrr</span></code></pre></div>
+</div>
+</div>
+<div id="model-comparison" class="section level2">
+<h2>Model comparison</h2>
+<div id="ac-effect-in-bc-population" class="section level4">
+<h4><span class="math inline">\(AC\)</span> effect in <span class="math inline">\(BC\)</span> population</h4>
+<p>The true <span class="math inline">\(AC\)</span> effect on the log OR
+scale in the <span class="math inline">\(BC\)</span> (aggregate trial
+data) population is <span class="math inline">\(\beta_t^{AC} +
+\beta_{EM} (\bar{X}^{AC}_1 + \bar{X}_2^{AC})\)</span>. Calculated by</p>
+<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" tabindex="-1"></a>mean_X1 <span class="ot">&lt;-</span> ald_trial<span class="sc">$</span>value[ald_trial<span class="sc">$</span>statistic <span class="sc">==</span> <span class="st">&quot;mean&quot;</span> <span class="sc">&amp;</span> ald_trial<span class="sc">$</span>variable <span class="sc">==</span> <span class="st">&quot;EM_cont_1&quot;</span>]</span>
+<span id="cb29-2"><a href="#cb29-2" tabindex="-1"></a>mean_X2 <span class="ot">&lt;-</span> ald_trial<span class="sc">$</span>value[ald_trial<span class="sc">$</span>statistic <span class="sc">==</span> <span class="st">&quot;mean&quot;</span> <span class="sc">&amp;</span> ald_trial<span class="sc">$</span>variable <span class="sc">==</span> <span class="st">&quot;EM_cont_1&quot;</span>]</span>
+<span id="cb29-3"><a href="#cb29-3" tabindex="-1"></a></span>
+<span id="cb29-4"><a href="#cb29-4" tabindex="-1"></a>d_AC_true <span class="ot">&lt;-</span> b_trt <span class="sc">+</span> b_EM <span class="sc">*</span> (mean_X1 <span class="sc">+</span> mean_X2)</span></code></pre></div>
+<p>The naive approach is to just convert directly from one population to
+another, ignoring the imbalance in effect modifiers.</p>
+<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" tabindex="-1"></a>d_AC_naive <span class="ot">&lt;-</span> </span>
+<span id="cb30-2"><a href="#cb30-2" tabindex="-1"></a>  ipd_trial <span class="sc">|&gt;</span> </span>
+<span id="cb30-3"><a href="#cb30-3" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">group_by</span>(trt) <span class="sc">|&gt;</span> </span>
+<span id="cb30-4"><a href="#cb30-4" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">summarise</span>(<span class="at">y_sum =</span> <span class="fu">sum</span>(y), <span class="at">y_bar =</span> <span class="fu">mean</span>(y), <span class="at">n =</span> <span class="fu">n</span>()) <span class="sc">|&gt;</span> </span>
+<span id="cb30-5"><a href="#cb30-5" tabindex="-1"></a>  tidyr<span class="sc">::</span><span class="fu">pivot_wider</span>(<span class="at">names_from =</span> trt,</span>
+<span id="cb30-6"><a href="#cb30-6" tabindex="-1"></a>                     <span class="at">values_from =</span> <span class="fu">c</span>(y_sum, y_bar, n)) <span class="sc">|&gt;</span> </span>
+<span id="cb30-7"><a href="#cb30-7" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">mutate</span>(<span class="at">d_AC =</span></span>
+<span id="cb30-8"><a href="#cb30-8" tabindex="-1"></a>                  <span class="fu">log</span>(y_bar_A<span class="sc">/</span>(<span class="dv">1</span><span class="sc">-</span>y_bar_A)) <span class="sc">-</span> <span class="fu">log</span>(y_bar_C<span class="sc">/</span>(<span class="dv">1</span><span class="sc">-</span>y_bar_C)),</span>
+<span id="cb30-9"><a href="#cb30-9" tabindex="-1"></a>                <span class="at">var_AC =</span></span>
+<span id="cb30-10"><a href="#cb30-10" tabindex="-1"></a>                  <span class="dv">1</span><span class="sc">/</span>(n_A<span class="sc">-</span>y_sum_A) <span class="sc">+</span> <span class="dv">1</span><span class="sc">/</span>y_sum_A <span class="sc">+</span> <span class="dv">1</span><span class="sc">/</span>(n_C<span class="sc">-</span>y_sum_C) <span class="sc">+</span> <span class="dv">1</span><span class="sc">/</span>y_sum_C)</span></code></pre></div>
+</div>
+<div id="ab-effect-in-bc-population" class="section level4">
+<h4><span class="math inline">\(AB\)</span> effect in <span class="math inline">\(BC\)</span> population</h4>
+<p>This is the indirect effect. The true <span class="math inline">\(AB\)</span> effect in the <span class="math inline">\(BC\)</span> population is <span class="math inline">\(\beta_t^{AC} - \beta_t^{BC}\)</span>.</p>
+<p>Following the simulation study in Remiro et al (2020) these cancel
+out and the true effect is zero.</p>
+<p>The naive comparison calculating <span class="math inline">\(AB\)</span> effect in the <span class="math inline">\(BC\)</span> population is</p>
+<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" tabindex="-1"></a><span class="co"># reshape to make extraction easier</span></span>
+<span id="cb31-2"><a href="#cb31-2" tabindex="-1"></a>ald_out <span class="ot">&lt;-</span> ald_trial <span class="sc">|&gt;</span> </span>
+<span id="cb31-3"><a href="#cb31-3" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">filter</span>(variable <span class="sc">==</span> <span class="st">&quot;y&quot;</span> <span class="sc">|</span> <span class="fu">is.na</span>(variable)) <span class="sc">|&gt;</span> </span>
+<span id="cb31-4"><a href="#cb31-4" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">stat_trt =</span> <span class="fu">paste0</span>(statistic, <span class="st">&quot;_&quot;</span>, trt)) <span class="sc">|&gt;</span> </span>
+<span id="cb31-5"><a href="#cb31-5" tabindex="-1"></a>  dplyr<span class="sc">::</span><span class="fu">select</span>(stat_trt, value) <span class="sc">|&gt;</span> </span>
+<span id="cb31-6"><a href="#cb31-6" tabindex="-1"></a>  <span class="fu">pivot_wider</span>(<span class="at">names_from =</span> stat_trt, <span class="at">values_from =</span> value)</span>
+<span id="cb31-7"><a href="#cb31-7" tabindex="-1"></a></span>
+<span id="cb31-8"><a href="#cb31-8" tabindex="-1"></a>d_BC <span class="ot">&lt;-</span></span>
+<span id="cb31-9"><a href="#cb31-9" tabindex="-1"></a>  <span class="fu">with</span>(ald_out, <span class="fu">log</span>(mean_B<span class="sc">/</span>(<span class="dv">1</span><span class="sc">-</span>mean_B)) <span class="sc">-</span> <span class="fu">log</span>(mean_C<span class="sc">/</span>(<span class="dv">1</span><span class="sc">-</span>mean_C)))</span>
+<span id="cb31-10"><a href="#cb31-10" tabindex="-1"></a></span>
+<span id="cb31-11"><a href="#cb31-11" tabindex="-1"></a>d_AB_naive <span class="ot">&lt;-</span> d_AC_naive<span class="sc">$</span>d_AC <span class="sc">-</span> d_BC</span>
+<span id="cb31-12"><a href="#cb31-12" tabindex="-1"></a></span>
+<span id="cb31-13"><a href="#cb31-13" tabindex="-1"></a>var.d.BC <span class="ot">&lt;-</span> <span class="fu">with</span>(ald_out, <span class="dv">1</span><span class="sc">/</span>sum_B <span class="sc">+</span> <span class="dv">1</span><span class="sc">/</span>(N_B <span class="sc">-</span> sum_B) <span class="sc">+</span> <span class="dv">1</span><span class="sc">/</span>sum_C <span class="sc">+</span> <span class="dv">1</span><span class="sc">/</span>(N_C <span class="sc">-</span> sum_C))</span>
+<span id="cb31-14"><a href="#cb31-14" tabindex="-1"></a></span>
+<span id="cb31-15"><a href="#cb31-15" tabindex="-1"></a>var.d.AB.naive <span class="ot">&lt;-</span> d_AC_naive<span class="sc">$</span>var_AC <span class="sc">+</span> var.d.BC</span></code></pre></div>
+<p>Alternatively, we can compute this using <code>outstandR</code>’s
+built-in <code>calc_bucher_naive()</code> function:</p>
+<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" tabindex="-1"></a>naive_results <span class="ot">&lt;-</span> <span class="fu">calc_bucher_naive</span>(ipd_trial, ald_trial, <span class="at">outcome_model =</span> lin_form, <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">&quot;logit&quot;</span>))</span>
+<span id="cb32-2"><a href="#cb32-2" tabindex="-1"></a>naive_results</span></code></pre></div>
+<p>Of course, the <span class="math inline">\(BC\)</span> contrast is
+calculated directly.</p>
+</div>
+</div>
+<div id="results" class="section level2">
+<h2>Results</h2>
+<p>We now combine all outputs and present in plots and tables. For a
+log-odds ratio a table of all contrasts and methods in the <span class="math inline">\(BC\)</span> population is given below.</p>
+<p>We can see that the different corresponds reasonably well with one
+another.</p>
+<p>Next, let us look at the results on the log relative risk scale.
+First, the true values are calculated as</p>
+<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" tabindex="-1"></a>d_AB_true_lrr <span class="ot">&lt;-</span> <span class="dv">0</span></span>
+<span id="cb33-2"><a href="#cb33-2" tabindex="-1"></a>d_AC_true_lrr <span class="ot">&lt;-</span> <span class="fu">log</span>(<span class="fu">plogis</span>(d_A_true) <span class="sc">/</span> <span class="fu">plogis</span>(d_C_true))</span>
+<span id="cb33-3"><a href="#cb33-3" tabindex="-1"></a>d_AC_true_lrr</span></code></pre></div>
+<p>so that the summary table is</p>
+<div id="plots" class="section level4">
+<h4>Plots</h4>
+<p>The same output can be presented in forest plots is as follows. Each
+horizontal bar represent a different method and the facets group these
+by treatment comparison for the <span class="math inline">\(BC\)</span>
+population. The log-odds ratio and log risk ratio plot are given
+below.</p>
+</div>
+</div>
+
+
+
+<!-- code folding -->
+
+
+<!-- dynamically load mathjax for compatibility with self-contained -->
+<script>
+  (function () {
+    var script = document.createElement("script");
+    script.type = "text/javascript";
+    script.src  = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
+    document.getElementsByTagName("head")[0].appendChild(script);
+  })();
+</script>
+
+</body>
+</html>
diff --git a/vignettes/Continuous_outcome_example.Rmd b/vignettes/Continuous_outcome_example.Rmd
new file mode 100644
index 0000000..e0de130
--- /dev/null
+++ b/vignettes/Continuous_outcome_example.Rmd
@@ -0,0 +1,372 @@
+---
+title: "Continuous data example"
+output: rmarkdown::html_vignette
+vignette: >
+  %\VignetteIndexEntry{Continuous data example}
+  %\VignetteEncoding{UTF-8}
+  %\VignetteEngine{knitr::rmarkdown}
+  editor_options: 
+    markdown: 
+  markdown: 
+    wrap: 72
+  chunk_output_type: console
+---
+
+```{r setup, include = FALSE}
+is_simcovariate_installed <- requireNamespace("simcovariates", quietly = TRUE)
+
+knitr::opts_chunk$set(
+  collapse = TRUE,
+  comment = "#>",
+  eval = is_simcovariate_installed
+)
+```
+
+## Introduction
+
+This is the vignette for performing population adjustment methods with continuous data, in order to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. We will demonstrate how to apply MAIC, G-computation with ML, G-computation with Bayesian inference and multiple imputation marginalisation. The document structure follow the binary data example vignette which should be referred to for more details.
+
+## Example analysis
+
+First, let us load necessary packages.
+
+```{r load-packages, warning=FALSE, message=FALSE}
+# install.packages("outstandR",
+#  repos = c("https://statisticshealtheconomics.r-universe.dev", "https://cloud.r-project.org"))
+#
+# install.packages("simcovariates",
+#  repos = c("https://n8thangreen.r-universe.dev", "https://cloud.r-project.org"))
+
+library(boot)      # non-parametric bootstrap in MAIC and ML G-computation
+library(copula)    # simulating BC covariates from Gaussian copula
+library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation
+library(tidyr)
+library(dplyr)
+library(MASS)
+library(outstandR)
+library(simcovariates)
+```
+
+### Data
+
+We first simulate both the IPD and ALD data. See the binary data example vignette for more details on how this is implemented.
+
+```{r generate-ipd-data, warning=FALSE, message=FALSE}
+N <- 200
+allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1)
+b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator
+b_PF <- -log(0.5)      # conditional effect of each prognostic variable
+b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier
+meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial
+meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC
+meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial
+meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC
+sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC)
+sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate
+corX <- 0.2            # covariate correlation coefficient  
+b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value
+```
+
+The difference with that example is that we change the `family` argument in `gen_data()` to `gaussian(link = "identity")`, corresponding to the continuous data case. The `gen_data()` function is available in the [simcovariates](https://github.com/n8thangreen/simcovariates) package on GitHub.
+
+```{r}
+covariate_defns_ipd <- list(
+  PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),
+                    role = "prognostic"),
+  PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),
+                    role = "prognostic"),
+  EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),
+                    role = "effect_modifier"),
+  EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),
+                    role = "effect_modifier")
+)
+
+b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)
+
+b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)
+
+num_normal_covs <- length(covariate_defns_ipd)
+cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs)
+diag(cor_matrix) <- 1
+
+rownames(cor_matrix) <- c("PF_cont_1", "PF_cont_2", "EM_cont_1", "EM_cont_2")
+colnames(cor_matrix) <- c("PF_cont_1", "PF_cont_2", "EM_cont_1", "EM_cont_2")
+
+ipd_trial <- simcovariates::gen_data(
+  N = N,
+  b_0 = b_0,
+  b_trt = b_trt,
+  covariate_defns = covariate_defns_ipd,
+  b_prognostic = b_prognostic,
+  b_effect_modifier = b_effect_modifier,
+  cor_matrix = cor_matrix,
+  trt_assignment = list(prob_trt1 = allocation),
+  family = gaussian("identity"))
+
+ipd_trial$trt <- factor(ipd_trial$trt, labels = c("C", "A"))
+```
+
+Similarly, for the aggregate data but with the additional summarise step (see binary data example vignette for code).
+
+```{r generate-ald-data, echo=FALSE, warning=FALSE, message=FALSE}
+covariate_defns_ald <- list(
+  PF_cont_1 = list(type = continuous(mean = meanX_BC[1], sd = sdX[1]),
+                    role = "prognostic"),
+  PF_cont_2 = list(type = continuous(mean = meanX_BC[2], sd = sdX[2]),
+                    role = "prognostic"),
+  EM_cont_1 = list(type = continuous(mean = meanX_EM_BC[1], sd = sdX_EM[1]),
+                    role = "effect_modifier"),
+  EM_cont_2 = list(type = continuous(mean = meanX_EM_BC[2], sd = sdX_EM[2]),
+                    role = "effect_modifier")
+)
+
+BC.IPD <- simcovariates::gen_data(
+  N = N,
+  b_0 = b_0,
+  b_trt = b_trt,
+  covariate_defns = covariate_defns_ald,
+  b_prognostic = b_prognostic,
+  b_effect_modifier = b_effect_modifier,
+  cor_matrix = cor_matrix,
+  trt_assignment = list(prob_trt1 = allocation),
+  family = gaussian("identity"))
+
+BC.IPD$trt <- factor(BC.IPD$trt, labels = c("C", "B"))
+
+# covariate summary statistics
+# assume same between treatments
+cov.X <- 
+  BC.IPD %>%
+  as.data.frame() |> 
+  dplyr::select(matches("^(PF|EM)"), trt) |> 
+  tidyr::pivot_longer(
+    cols = starts_with("PF") | starts_with("EM"),
+    names_to = "variable",
+    values_to = "value") |>
+  group_by(variable) %>%
+  summarise(
+    mean = mean(value),
+    sd = sd(value)
+  ) %>%
+  tidyr::pivot_longer(
+    cols = c("mean", "sd"),
+    names_to = "statistic",
+    values_to = "value") %>%
+  ungroup() |> 
+  mutate(trt = NA)
+
+# outcome
+summary.y <- 
+  BC.IPD |> 
+  as.data.frame() |> 
+  dplyr::select(y, trt) %>%
+  tidyr::pivot_longer(cols = "y",
+               names_to = "variable",
+               values_to = "value") %>%
+  group_by(variable, trt) %>%
+  summarise(
+    mean = mean(value),
+    sd = sd(value),
+    sum = sum(value)
+  ) %>%
+  tidyr::pivot_longer(
+    cols = c("mean", "sd", "sum"),
+    names_to = "statistic",
+    values_to = "value") %>%
+  ungroup()
+
+# sample sizes
+summary.N <- 
+  BC.IPD |> 
+  group_by(trt) |> 
+  count(name = "N") |> 
+  tidyr::pivot_longer(
+    cols = "N",
+    names_to = "statistic",
+    values_to = "value") |> 
+  mutate(variable = NA_character_) |> 
+  dplyr::select(variable, statistic, value, trt)
+
+  
+ald_trial <- rbind.data.frame(cov.X, summary.y, summary.N)
+```
+
+This general format of the data sets are in a 'long' style consisting of the following.
+
+#### `ipd_trial`: Individual patient data
+
+-   `PF_*`: Patient measurements prognostic factors
+-   `EM_*`: Patient measurements effect modifiers
+-   `trt`: Treatment label (factor)
+-   `y`: Continuous numeric
+
+#### `ald_trial`: Aggregate-level data
+
+-   `variable`: Covariate name. In the case of treatment arm sample size this is `NA`
+-   `statistic`: Summary statistic name from mean, standard deviation or sum
+-   `value`: Numerical value of summary statistic
+-   `trt`: Treatment label. Because we assume a common covariate distribution between treatment arms this is `NA`
+
+Our data look like the following.
+
+```{r}
+head(ipd_trial)
+```
+
+There are 4 correlated continuous covariates generated per subject, simulated from a multivariate normal distribution. Treatment `trt` takes either new treatment *A* or standard of care / status quo *C*. The ITC is 'anchored' via *C*, the common treatment.
+
+```{r}
+ald_trial
+```
+
+In this case, we have 4 covariate mean and standard deviation values; and the total, average and sample size for each treatment *B* and *C*.
+
+In the following we will implement for MAIC and G-computation methods to obtain the *marginal variance* and the *marginal treatment effect*.
+
+## Model fitting in R
+
+The `{outstandR}` package has been written to be easy to use and essential consists of a single function, `outstandR()`. This can be used to run all of the different types of model, which we will call *strategies*. The first two arguments of `outstandR()` are the individual and aggregate-level data, respectively.
+
+A `strategy` argument of `outstandR` takes functions called `strategy_*()`, where the wildcard `*` is replaced by the name of the particular method required, e.g. `strategy_maic()` for MAIC. Each specific example is provided below.
+
+The formula used in this model, passed as an argument to the strategy function is
+
+```{r lin_form}
+lin_form <- list(
+  outcome_model = as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"),
+  balance_model = as.formula("~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2")
+)
+```
+
+### MAIC
+
+As mentioned above, pass the model specific strategy function to the main `outstandR()` function, in this case use `strategy_maic()`.
+
+```{r outstandR_maic}
+outstandR_maic <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_maic(
+              formula = lin_form,
+              family = gaussian(link = "identity")))
+```
+
+The returned object is of class `outstandR`.
+
+```{r outstandR_maic-print}
+outstandR_maic
+```
+
+### Bayesian G-computation with MCMC
+
+The difference between Bayesian G-computation and its maximum-likelihood counterpart is in the estimated distribution of the predicted outcomes. The Bayesian approach also marginalizes, integrates or standardizes over the joint posterior distribution of the conditional nuisance parameters of the outcome regression, as well as the joint covariate distribution.
+
+Pass the `strategy_gcomp_bayes()` strategy function.
+
+```{r outstandR_gcomp_bayes, eval=FALSE}
+outstandR_gcomp_bayes <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_gcomp_bayes(
+              formula = lin_form,
+              family = gaussian(link = "identity")))
+```
+
+```{r outstandR_gcomp_bayes_eval, echo=FALSE}
+xx <- capture.output(
+  outstandR_gcomp_bayes <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_gcomp_bayes(
+                formula = lin_form,
+                family = gaussian(link = "identity"))))
+```
+
+```{r}
+outstandR_gcomp_bayes
+```
+
+### Multiple imputation marginalisation
+
+Finally, the strategy function to pass to `outstandR()` for multiple imputation marginalisation is `strategy_mim()`,
+
+```{r outstandR_mim, eval=FALSE}
+outstandR_mim <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_mim(
+              formula = lin_form,
+              family = gaussian(link = "identity")))
+```
+
+```{r outstandR_mim_eval, echo=FALSE}
+xx <- capture.output(
+  outstandR_mim <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_mim(
+                formula = lin_form,
+                family = gaussian(link = "identity"))))
+```
+
+```{r}
+outstandR_mim
+```
+
+### Model comparison
+
+Combine all outputs for relative effects table of all contrasts and methods.
+
+```{r table-res, echo=FALSE}
+res_tab <- 
+  data.frame(
+    # d_true = c(d_AB_true, d_AC_true, d_BC),
+    # d_naive = c(d_AB_naive, d_AC_naive$d_AC, d_BC),
+    `MAIC` = unlist(outstandR_maic$results$contrasts$means),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml$results$contrasts$means),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$results$contrasts$means),
+    `MIM` = unlist(outstandR_mim$results$contrasts$means)) |> 
+  round(2)
+
+res_tab_var <- 
+  data.frame(
+    # d_true = c(NA, NA, NA),
+    # d_naive = c(var.d.AB.naive, d_AC_naive$var_AC, var.d.BC),
+    `MAIC` = unlist(outstandR_maic$results$contrasts$variances),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml$results$contrasts$variances),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$results$contrasts$variances),
+    `MIM` = unlist(outstandR_mim$results$contrasts$variances)) |> 
+  round(2)
+
+knitr::kable(res_tab)
+```
+
+```{r forest-res, fig.width=8, fig.height=6, warning=FALSE, message=FALSE, echo=FALSE}
+library(ggplot2)
+
+var_dat <- 
+  t(res_tab_var) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "var")
+
+plotdat <- 
+  t(res_tab) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "Estimate") |> 
+  mutate(id = 1:n(),
+         type = as.factor(type)) |> 
+  merge(var_dat) |> 
+  mutate(lo = Estimate + qnorm(0.025) * sqrt(var),
+         hi = Estimate + qnorm(0.975) * sqrt(var))
+
+ggplot(aes(x = Estimate, y = id, col = type), data = plotdat) +
+  geom_vline(xintercept = 0, lty = 2) +
+  geom_point(size = 2) +
+  geom_segment(aes(y = id, yend = id, x = lo, xend = hi), na.rm = TRUE) +
+  xlab("Estimate (Log RR)") +
+  facet_grid(Comparison~., switch = "y", scales = "free_y", space = "free_y") +
+  scale_y_reverse(name = "Comparison in BC population",
+                  breaks = NULL, expand = c(0, 0.6)) +
+  scale_color_manual(values = c("d_naive" = "black", "d_true" = "red", 
+                                "MAIC" = "#E69F00", "Gcomp ML" = "#56B4E9", 
+                                "Gcomp Bayes" = "#009E73", "MIM" = "#F0E442"))
+```
diff --git a/vignettes/Count_outcome_example.Rmd b/vignettes/Count_outcome_example.Rmd
new file mode 100644
index 0000000..a740206
--- /dev/null
+++ b/vignettes/Count_outcome_example.Rmd
@@ -0,0 +1,425 @@
+---
+title: "Count data example"
+output: rmarkdown::html_vignette
+vignette: >
+  %\VignetteIndexEntry{Count data example}
+  %\VignetteEncoding{UTF-8}
+  %\VignetteEngine{knitr::rmarkdown}
+editor_options: 
+  markdown: 
+    wrap: 72
+  chunk_output_type: console
+---
+
+```{r setup, include = FALSE}
+is_simcovariate_installed <- requireNamespace("simcovariates", quietly = TRUE)
+
+knitr::opts_chunk$set(
+  collapse = TRUE,
+  comment = "#>",
+  eval = is_simcovariate_installed
+)
+```
+
+## Introduction
+
+This is the vignette for performing population adjustment methods with
+count data, in order to compare marginal treatment effects when there
+are cross-trial differences in effect modifiers and limited
+patient-level data. We will demonstrate how to apply MAIC, 
+G-computation with ML, G-computation with Bayesian inference and
+multiple imputation marginalisation. The document structure follow the
+binary data example vignette which should be referred to for more
+details.
+
+## Example analysis
+
+First, let us load necessary packages.
+
+```{r load-packages, warning=FALSE, message=FALSE}
+# install.packages("outstandR",
+#  repos = c("https://statisticshealtheconomics.r-universe.dev", "https://cloud.r-project.org"))
+#
+# install.packages("simcovariates",
+#  repos = c("https://n8thangreen.r-universe.dev", "https://cloud.r-project.org"))
+
+library(boot)      # non-parametric bootstrap in MAIC and ML G-computation
+library(copula)    # simulating BC covariates from Gaussian copula
+library(rstanarm)  # fit outcome regression, draw outcomes in Bayesian G-computation
+library(tidyr)
+library(dplyr)
+library(MASS)
+library(outstandR)
+library(simcovariates)
+```
+
+### Data
+
+We first simulate both the IPD and ALD count data. See the binary data
+example vignette for more details on how this is implemented.
+
+```{r generate-ipd-data, warning=FALSE, message=FALSE}
+
+N <- 200
+allocation <- 2/3      # active treatment vs. placebo allocation ratio (2:1)
+b_trt <- log(0.17)     # conditional effect of active treatment vs. common comparator
+b_PF <- -log(0.5)       # conditional effect of each prognostic variable
+b_EM <- -log(0.67)     # conditional interaction effect of each effect modifier
+meanX_AC <- c(0.45, 0.45)       # mean of normally-distributed covariate in AC trial
+meanX_BC <- c(0.6, 0.6)         # mean of each normally-distributed covariate in BC
+meanX_EM_AC <- c(0.45, 0.45)    # mean of normally-distributed EM covariate in AC trial
+meanX_EM_BC <- c(0.6, 0.6)      # mean of each normally-distributed EM covariate in BC
+sdX <- c(0.4, 0.4)     # standard deviation of each covariate (same for AC and BC)
+sdX_EM <- c(0.4, 0.4)  # standard deviation of each EM covariate
+corX <- 0.2            # covariate correlation coefficient  
+b_0 <- -0.6            # baseline intercept coefficient  ##TODO: fixed value
+```
+
+The difference with that example is that we change the `family` argument in
+`gen_data()` to `poisson(link = "log")`, corresponding to the count data
+case. The `gen_data()` function is available in the
+[simcovariates](https://github.com/n8thangreen/simcovariates) package on
+GitHub.
+
+```{r}
+covariate_defns_ipd <- list(
+  PF_cont_1 = list(type = continuous(mean = meanX_AC[1], sd = sdX[1]),
+                    role = "prognostic"),
+  PF_cont_2 = list(type = continuous(mean = meanX_AC[2], sd = sdX[2]),
+                    role = "prognostic"),
+  EM_cont_1 = list(type = continuous(mean = meanX_EM_AC[1], sd = sdX_EM[1]),
+                    role = "effect_modifier"),
+  EM_cont_2 = list(type = continuous(mean = meanX_EM_AC[2], sd = sdX_EM[2]),
+                    role = "effect_modifier")
+)
+
+b_prognostic <- c(PF_cont_1 = b_PF, PF_cont_2 = b_PF)
+
+b_effect_modifier <- c(EM_cont_1 = b_EM, EM_cont_2 = b_EM)
+
+num_normal_covs <- length(covariate_defns_ipd)
+cor_matrix <- matrix(corX, num_normal_covs, num_normal_covs)
+diag(cor_matrix) <- 1
+
+rownames(cor_matrix) <- c("PF_cont_1", "PF_cont_2", "EM_cont_1", "EM_cont_2")
+colnames(cor_matrix) <- c("PF_cont_1", "PF_cont_2", "EM_cont_1", "EM_cont_2")
+
+ipd_trial <- simcovariates::gen_data(
+  N = N,
+  b_0 = b_0,
+  b_trt = b_trt,
+  covariate_defns = covariate_defns_ipd,
+  b_prognostic = b_prognostic,
+  b_effect_modifier = b_effect_modifier,
+  cor_matrix = cor_matrix,
+  trt_assignment = list(prob_trt1 = allocation),
+  family = poisson("log"))
+
+ipd_trial$trt <- factor(ipd_trial$trt, labels = c("C", "A"))
+```
+
+Similarly, for the aggregate data but with the additional summarise step
+(see binary data example vignette for code).
+
+```{r generate-ald-data, echo=FALSE, warning=FALSE, message=FALSE}
+covariate_defns_ald <- list(
+  PF_cont_1 = list(type = continuous(mean = meanX_BC[1], sd = sdX[1]),
+                    role = "prognostic"),
+  PF_cont_2 = list(type = continuous(mean = meanX_BC[2], sd = sdX[2]),
+                    role = "prognostic"),
+  EM_cont_1 = list(type = continuous(mean = meanX_EM_BC[1], sd = sdX_EM[1]),
+                    role = "effect_modifier"),
+  EM_cont_2 = list(type = continuous(mean = meanX_EM_BC[2], sd = sdX_EM[2]),
+                    role = "effect_modifier")
+)
+
+BC.IPD <- simcovariates::gen_data(
+  N = N,
+  b_0 = b_0,
+  b_trt = b_trt,
+  covariate_defns = covariate_defns_ald,
+  b_prognostic = b_prognostic,
+  b_effect_modifier = b_effect_modifier,
+  cor_matrix = cor_matrix,
+  trt_assignment = list(prob_trt1 = allocation),
+  family = poisson("log"))
+
+BC.IPD$trt <- factor(BC.IPD$trt, labels = c("C", "B"))
+
+# covariate summary statistics
+# assume same between treatments
+cov.X <- 
+  BC.IPD %>%
+  as.data.frame() |> 
+  dplyr::select(matches("^(PF|EM)"), trt) |> 
+  tidyr::pivot_longer(
+    cols = starts_with("PF") | starts_with("EM"),
+    names_to = "variable",
+    values_to = "value") |>
+  group_by(variable) %>%
+  summarise(
+    mean = mean(value),
+    sd = sd(value)
+  ) %>%
+  tidyr::pivot_longer(
+    cols = c("mean", "sd"),
+    names_to = "statistic",
+    values_to = "value") %>%
+  ungroup() |> 
+  mutate(trt = NA)
+
+# outcome
+summary.y <- 
+  BC.IPD |> 
+  as.data.frame() |> 
+  dplyr::select(y, trt) %>%
+  tidyr::pivot_longer(cols = "y",
+               names_to = "variable",
+               values_to = "value") %>%
+  group_by(variable, trt) %>%
+  summarise(
+    mean = mean(value),
+    sd = sd(value),
+    sum = sum(value)
+  ) %>%
+  tidyr::pivot_longer(
+    cols = c("mean", "sd", "sum"),
+    names_to = "statistic",
+    values_to = "value") %>%
+  ungroup()
+
+# sample sizes
+summary.N <- 
+  BC.IPD |> 
+  group_by(trt) |> 
+  count(name = "N") |> 
+  tidyr::pivot_longer(
+    cols = "N",
+    names_to = "statistic",
+    values_to = "value") |> 
+  mutate(variable = NA_character_) |> 
+  dplyr::select(variable, statistic, value, trt)
+
+ald_trial <- rbind.data.frame(cov.X, summary.y, summary.N)
+```
+
+This general format of the data sets are in a 'long' style consisting of
+the following.
+
+#### `ipd_trial`: Individual patient data
+
+-   `PF_*`: Patient measurements prognostic factors
+-   `EM_*`: Patient measurements effect modifiers
+-   `trt`: Treatment label (factor)
+-   `y`: Counts
+
+#### `ald_trial`: Aggregate-level data
+
+-   `variable`: Covariate name. In the case of treatment arm sample size
+    this is `NA`
+-   `statistic`: Summary statistic name from mean, standard deviation or
+    sum
+-   `value`: Numerical value of summary statistic
+-   `trt`: Treatment label. Because we assume a common covariate
+    distribution between treatment arms this is `NA`
+
+Our data look like the following.
+
+```{r}
+head(ipd_trial)
+```
+
+There are 4 correlated continuous covariates generated per subject,
+simulated from a multivariate normal distribution. Treatment `trt` takes
+either new treatment *A* or standard of care / status quo *C*. The ITC
+is 'anchored' via *C*, the common treatment.
+
+```{r}
+ald_trial
+```
+
+In this case, we have 4 covariate mean and standard deviation values;
+and the total, average and sample size for each treatment *B* and *C*.
+
+In the following we will implement for MAIC and G-computation
+methods to obtain the *marginal variance* and the *marginal treatment
+effect*.
+
+## Model fitting in R
+
+The `{outstandR}` package has been written to be easy to use and
+essential consists of a single function, `outstandR()`. This can be used
+to run all of the different types of model, which we will call
+*strategies*. The first two arguments of `outstandR()` are the
+individual and aggregate-level data, respectively.
+
+A `strategy` argument of `outstandR` takes functions called
+`strategy_*()`, where the wildcard `*` is replaced by the name of the
+particular method required, e.g. `strategy_maic()` for MAIC. Each
+specific example is provided below.
+
+The formula used in this model, passed as an argument to the strategy
+function is
+
+```{r lin_form}
+lin_form <- list(
+  outcome_model = as.formula("y ~ PF_cont_1 + PF_cont_2 + trt:EM_cont_1 + trt:EM_cont_2"),
+  balance_model = as.formula("~ PF_cont_1 + PF_cont_2 + EM_cont_1 + EM_cont_2")
+)
+```
+
+### MAIC
+
+As mentioned above, pass the model specific strategy function to the
+main `outstandR()` function, in this case use `strategy_maic()`.
+
+```{r outstandR_maic}
+outstandR_maic <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_maic(
+              formula = lin_form,
+              family = poisson(link = "log")))
+```
+
+The returned object is of class `outstandR`.
+
+```{r outstandR_maic-print}
+outstandR_maic
+```
+
+### Parametric G-computation with maximum-likelihood estimation
+
+G-computation marginalizes the conditional estimates by separating the
+regression modelling from the estimation of the marginal treatment
+effect for *A* versus *C*. Pass the `strategy_gcomp_ml()` strategy
+function.
+
+```{r outstandR_gcomp_ml, message=FALSE, warning=FALSE}
+outstandR_gcomp_ml <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_gcomp_ml(
+              formula = lin_form,
+              family = poisson(link = "log")))
+outstandR_gcomp_ml
+```
+
+### Bayesian G-computation with MCMC
+
+The difference between Bayesian G-computation and its maximum-likelihood
+counterpart is in the estimated distribution of the predicted outcomes.
+The Bayesian approach also marginalizes, integrates or standardizes over
+the joint posterior distribution of the conditional nuisance parameters
+of the outcome regression, as well as the joint covariate distribution.
+
+Pass the `strategy_gcomp_bayes()` strategy function.
+
+```{r outstandR_gcomp_bayes, eval=FALSE, message=FALSE, warning=FALSE}
+outstandR_gcomp_bayes <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_gcomp_bayes(
+              formula = lin_form,
+              family = poisson(link = "log")))
+```
+
+```{r outstandR_gcomp_bayes_eval, echo=FALSE, message=FALSE, warning=FALSE}
+xx <- capture.output(
+  outstandR_gcomp_bayes <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_gcomp_bayes(
+                formula = lin_form,
+                family = poisson(link = "log"))))
+```
+
+```{r}
+outstandR_gcomp_bayes
+```
+
+### Multiple imputation marginalisation
+
+Finally, the strategy function to pass to `outstandR()` for multiple
+imputation marginalisation is `strategy_mim()`,
+
+```{r outstandR_mim, eval=FALSE}
+outstandR_mim <-
+  outstandR(ipd_trial, ald_trial,
+            strategy = strategy_mim(
+              formula = lin_form,
+              family = poisson(link = "log")))
+```
+
+```{r outstandR_mim_eval, echo=FALSE}
+xx <- capture.output(
+  outstandR_mim <-
+    outstandR(ipd_trial, ald_trial,
+              strategy = strategy_mim(
+                formula = lin_form,
+                family = poisson(link = "log"))))
+```
+
+```{r}
+outstandR_mim
+```
+
+### Model comparison
+
+Combine all outputs for relative effects table of all contrasts and
+methods.
+
+```{r table-res, echo=FALSE}
+res_tab <- 
+  data.frame(
+    # d_true = c(d_AB_true, d_AC_true, d_BC),
+    # d_naive = c(d_AB_naive, d_AC_naive$d_AC, d_BC),
+    `MAIC` = unlist(outstandR_maic$results$contrasts$means),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml$results$contrasts$means),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$results$contrasts$means),
+    `MIM` = unlist(outstandR_mim$results$contrasts$means)) |> 
+  round(2)
+
+res_tab_var <- 
+  data.frame(
+    # d_true = c(NA, NA, NA),
+    # d_naive = c(var.d.AB.naive, d_AC_naive$var_AC, var.d.BC),
+    `MAIC` = unlist(outstandR_maic$results$contrasts$variances),
+    `Gcomp ML` = unlist(outstandR_gcomp_ml$results$contrasts$variances),
+    `Gcomp Bayes` = unlist(outstandR_gcomp_bayes$results$contrasts$variances),
+    `MIM` = unlist(outstandR_mim$results$contrasts$variances)) |> 
+  round(2)
+
+knitr::kable(res_tab)
+```
+
+```{r forest-res, fig.width=8, fig.height=6, warning=FALSE, message=FALSE, echo=FALSE}
+library(ggplot2)
+
+var_dat <- 
+  t(res_tab_var) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "var")
+
+plotdat <- 
+  t(res_tab) |> 
+  as.data.frame() |> 
+  tibble::rownames_to_column("type") |>
+  reshape2::melt(variable.name = "Comparison",
+                 value.name = "Estimate") |> 
+  mutate(id = 1:n(),
+         type = as.factor(type)) |> 
+  merge(var_dat) |> 
+  mutate(lo = Estimate + qnorm(0.025) * sqrt(var),
+         hi = Estimate + qnorm(0.975) * sqrt(var))
+
+ggplot(aes(x = Estimate, y = id, col = type), data = plotdat) +
+  geom_vline(xintercept = 0, lty = 2) +
+  geom_point(size = 2) +
+  geom_segment(aes(y = id, yend = id, x = lo, xend = hi), na.rm = TRUE) +
+  xlab("Estimate (Log RR)") +
+  facet_grid(Comparison~., switch = "y", scales = "free_y", space = "free_y") +
+  scale_y_reverse(name = "Comparison in BC population",
+                  breaks = NULL, expand = c(0, 0.6)) +
+  scale_color_manual(values = c("d_naive" = "black", "d_true" = "red", 
+                                "MAIC" = "#E69F00", "Gcomp ML" = "#56B4E9", 
+                                "Gcomp Bayes" = "#009E73", "MIM" = "#F0E442"))
+```