rcpmcp

Regional Consistency Probability under Multiple Comparison Procedures

Overview

rcpmcp is an R package for computing regional consistency probabilities (RCPs) and disjunctive power in multi-regional clinical trials (MRCTs) with multiple primary endpoints under multiplicity adjustment procedures.

When multiple primary endpoints are employed, familywise error rate (FWER) control via the Bonferroni procedure leads to monotone inflation of the null RCP with increasing number of endpoints if unadjusted consistency thresholds are used. This package implements:

• Closed-form RCP computation via the multivariate normal distribution (Bonferroni)
• Monte Carlo simulation for Bonferroni, Holm, Hochberg, and Hommel procedures
• Adjusted consistency thresholds (Method 1 and Method 2) that correct for null RCP inflation
• Sample size determination under the Bonferroni procedure
• General allocation ratio r (default 1 for equal allocation); the treatment effect estimate has variance (r + 1)^2 sigma^2 / (r N), so RCPs and adjusted thresholds are invariant to r once the sample size achieves the target power

Regional consistency is evaluated following the Japanese Ministry of Health, Labour and Welfare (MHLW, 2007) guidance:

• Method 1: Region 1 retains at least a fraction gamma_M1 of the overall treatment effect
• Method 2: All regional estimates exceed the threshold gamma_M2

Installation

# Install from GitHub
# install.packages("devtools")
devtools::install_github("gosukehommaEX/rcpmcp")

Main Functions

Function	Description
rcpmcp_single()	RCP and power for a fixed number of endpoints K. Supports region-specific treatment effects and unknown-variance sensitivity analysis under approach = "simulation".
rcpmcp_multiple()	RCP and power across K = 1, ..., K_max endpoints. Inherits the simulation extensions of rcpmcp_single().
rcpmcp_get_gamma()	Adjusted consistency thresholds via root-finding
ssmcp_single()	Sample size for a fixed K (Bonferroni)
ssmcp_multiple()	Sample size across K = 1, ..., K_max (Bonferroni)

Examples

1. RCP for a fixed number of endpoints (closed-form)

library(rcpmcp)

# K = 3 independent endpoints, closed-form solution (Bonferroni)
result <- rcpmcp_single(
  delta    = c(0.2, 0.2, 0.2),
  Sigma    = diag(3),
  N        = 200,
  fs       = c(0.1, 0.45, 0.45),
  K        = 3,
  gamma_M1 = 0.5,
  gamma_M2 = 0,
  alpha    = 0.025
)
print(result)

2. RCP via Monte Carlo simulation (all four MCP methods)

result_sim <- rcpmcp_single(
  delta    = c(0.2, 0.2, 0.2),
  Sigma    = diag(3),
  N        = 200,
  fs       = c(0.1, 0.45, 0.45),
  K        = 3,
  gamma_M1 = 0.5,
  gamma_M2 = 0,
  alpha    = 0.025,
  approach = "simulation",
  nsim     = 10000,
  seed     = 1
)
print(result_sim)

3. Sample size determination and adjusted thresholds

# Step 1: Determine sample size for each K = 1, ..., 5 (Bonferroni)
ss <- ssmcp_multiple(
  delta        = rep(0.2, 5),
  Sigma        = diag(5),
  fs           = c(0.1, 0.45, 0.45),
  K_max        = 5,
  alpha        = 0.025,
  target_power = 0.8
)
print(ss)

# Step 2: Compute adjusted consistency thresholds
gamma_res <- rcpmcp_get_gamma(
  Sigma    = diag(5),
  N        = ss$result$N,
  fs       = c(0.1, 0.45, 0.45),
  K_max    = 5,
  gamma_M1 = 0.5,
  gamma_M2 = 0,
  alpha    = 0.025
)
print(gamma_res)

# Step 3: Compare adjusted vs. unadjusted RCP across K
res_adj <- rcpmcp_multiple(
  delta    = rep(0.2, 5),
  Sigma    = diag(5),
  N        = ss$result$N,
  fs       = c(0.1, 0.45, 0.45),
  K_max    = 5,
  gamma_M1 = gamma_res$result$gamma_M1_adj,
  gamma_M2 = gamma_res$result$gamma_M2_adj,
  alpha    = 0.025
)

res_unadj <- rcpmcp_multiple(
  delta    = rep(0.2, 5),
  Sigma    = diag(5),
  N        = ss$result$N,
  fs       = c(0.1, 0.45, 0.45),
  K_max    = 5,
  gamma_M1 = 0.5,
  gamma_M2 = 0,
  alpha    = 0.025
)

# Step 4: Plot
plot(res_adj,
     overlay      = list(res_unadj),
     group_labels = c("Adjusted", "Unadjusted"))

4. Sensitivity analyses (new in v0.1.1)

The simulation branch of rcpmcp_single() (and rcpmcp_multiple()) supports two extensions for sensitivity analyses:

• Region-specific treatment effects: supply delta as a K-by-S matrix, where element delta[k, s] is the true treatment effect for endpoint k in region s. This allows evaluation of scenarios in which the regional effect departs from the global effect.
• Unknown variance: set variance_known = FALSE to switch the overall test from a Z-statistic (normal critical value) to a t-statistic with degrees of freedom nu = N - 2. The sample variance-covariance matrix is drawn from a Wishart distribution, avoiding the need to generate individual-level data.

The following example combines both extensions. Region 1 has zero treatment effect for all endpoints, while regions 2 and 3 have a treatment effect of 0.2. The variance is treated as unknown.

# Region 1 is null; regions 2-3 have delta = 0.2 for all three endpoints
delta_mat <- matrix(c(0.0, 0.2, 0.2,
                      0.0, 0.2, 0.2,
                      0.0, 0.2, 0.2),
                    nrow = 3, ncol = 3, byrow = TRUE)

result_sens <- rcpmcp_single(
  delta          = delta_mat,
  Sigma          = diag(3),
  N              = 200,
  fs             = c(0.1, 0.45, 0.45),
  K              = 3,
  gamma_M1       = 0.5,
  gamma_M2       = 0,
  alpha          = 0.025,
  approach       = "simulation",
  nsim           = 10000,
  seed           = 1,
  variance_known = FALSE
)
print(result_sens)

Both extensions are only supported under approach = "simulation". The closed-form (approach = "formula") solution is preserved unchanged from earlier versions.

Reproducibility

All figures and tables in the associated manuscript, including the Supporting Information, can be reproduced from the scripts shipped with the package. To keep heavy computation separate from figure rendering, each set of scripts is split into a computation stage that caches intermediate results as .rds files and a rendering stage that reads them.

Location	Contents
inst/scripts/	Main-text Figures 1-4 and Table 1
inst/sup_info/	Supporting Information Figures S1-S6

Within each folder, data_generate_*.R runs all sample-size, adjusted-threshold, closed-form, and Monte Carlo computations and writes the results to data/*.rds, and table_and_figure_*.R reads those files and writes the figures (EPS and PDF) and the LaTeX table to results/.

To reproduce the main-text Figures 1-4 and Table 1, set the working directory to inst/scripts/ and run:

library(rcpmcp)
source("data_generate_main.R")          # computation -> data/*.rds
source("table_and_figure_manuscript.R") # rendering   -> results/

The Supporting Information Figures S1-S6 are reproduced analogously from inst/sup_info/:

library(rcpmcp)
source("data_generate_supplement.R")
source("table_and_figure_supplement.R")

All paths are relative to the working directory, so the data/ and results/ subfolders are created alongside the scripts. The number of Monte Carlo iterations is set by NSIM near the top of each computation script (1000000 for the published results; reduce it for a quick run). Rendering additionally requires the scales, patchwork, and ggh4x packages.

License

GPL (>= 2)