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n8thangreen merged 1 commit into from
Jun 19, 2026
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Update naive formulas in exercises2.qmd to use full notation (p_{A(AC… #70

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2 changes: 1 addition & 1 deletion man/outstandR-package.Rd
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122 changes: 61 additions & 61 deletions scripts/exercises2.html
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Expand Up @@ -315,8 +315,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
<pre><code>
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
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<pre><code>
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
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SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
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Expand Down Expand Up @@ -570,8 +570,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
<pre><code>
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
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SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
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Expand Down Expand Up @@ -659,8 +659,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
<pre><code>
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
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Expand Down Expand Up @@ -1029,8 +1029,8 @@ <h4 class="anchored" data-anchor-id="exercises-1">Exercises</h4>
<pre><code>
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Expand Down Expand Up @@ -1359,15 +1359,15 @@ <h4 class="anchored" data-anchor-id="exercises-3">Exercises</h4>
</details>
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<p>3.&nbsp;Calculate the unadjusted (naive) estimates for comparison.</p>
<p>To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let <span class="math inline">\(p_A\)</span> and <span class="math inline">\(p_{C(AC)}\)</span> be the raw probabilities of the event in the IPD trial, and let <span class="math inline">\(p_B\)</span> and <span class="math inline">\(p_{C(BC)}\)</span> be the raw probabilities in the ALD trial.</p>
<p>To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let <span class="math inline">\(p_{A(AC)}\)</span> and <span class="math inline">\(p_{C(AC)}\)</span> be the raw probabilities of the event in the IPD trial, and let <span class="math inline">\(p_{B(BC)}\)</span> and <span class="math inline">\(p_{C(BC)}\)</span> be the raw probabilities in the ALD trial.</p>
<ul>
<li><strong>Naive Anchored Risk Difference:</strong> This assumes the relative effect is transportable without adjustment (the classic Bucher indirect comparison).</li>
</ul>
<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_A - p_{C(AC)}) - (p_B - p_{C(BC)})\]</span></p>
<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_{A(AC)} - p_{C(AC)}) - (p_{B(BC)} - p_{C(BC)})\]</span></p>
<ul>
<li><strong>Naive Unanchored Risk Difference:</strong> This drops the common comparator entirely and assumes absolute exchangeability between the two isolated active arms.</li>
</ul>
<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_A - p_B\]</span></p>
<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_{A(AC)} - p_{B(BC)}\]</span></p>
<div class="callout callout-style-default callout-warning callout-titled">
<div class="callout-header d-flex align-content-center">
<div class="callout-icon-container">
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6 changes: 3 additions & 3 deletions scripts/exercises2.qmd
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Expand Up @@ -605,16 +605,16 @@ cat("Unanchored Risk Difference (A vs B):", round(unanchored_rd, 3), "\n")

3.\ Calculate the unadjusted (naive) estimates for comparison.

To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let $p_A$ and $p_{C(AC)}$ be the raw probabilities of the event in the IPD trial, and let $p_B$ and $p_{C(BC)}$ be the raw probabilities in the ALD trial.
To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let $p_{A(AC)}$ and $p_{C(AC)}$ be the raw probabilities of the event in the IPD trial, and let $p_{B(BC)}$ and $p_{C(BC)}$ be the raw probabilities in the ALD trial.

* **Naive Anchored Risk Difference:** This assumes the relative effect is transportable without adjustment (the classic Bucher indirect comparison).

$$\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_A - p_{C(AC)}) - (p_B - p_{C(BC)})$$
$$\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_{A(AC)} - p_{C(AC)}) - (p_{B(BC)} - p_{C(BC)})$$


* **Naive Unanchored Risk Difference:** This drops the common comparator entirely and assumes absolute exchangeability between the two isolated active arms.

$$\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_A - p_B$$
$$\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_{A(AC)} - p_{B(BC)}$$


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