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SingleArmMRCT

Overview

SingleArmMRCT provides functions to calculate and visualise the Regional Consistency Probability (RCP) for single-arm multi-regional clinical trials (MRCTs) using the Effect Retention Approach (ERA).

The package addresses a critical methodological gap: current Japanese MHLW Method 1 and Method 2 consistency criteria were originally developed for two-arm trials, yet single-arm trials increasingly form the basis of regulatory submissions, particularly in oncology. This package extends classical approaches to the single-arm setting across six endpoint types.

Supported endpoints

Endpoint type	Calculation function	Plot function
Continuous	`rcp1armContinuous()`	`plot_rcp1armContinuous()`
Binary	`rcp1armBinary()`	`plot_rcp1armBinary()`
Count (negative binomial)	`rcp1armCount()`	`plot_rcp1armCount()`
Time-to-event (hazard ratio)	`rcp1armHazardRatio()`	`plot_rcp1armHazardRatio()`
Milestone survival	`rcp1armMilestoneSurvival()`	`plot_rcp1armMilestoneSurvival()`
Restricted mean survival time (RMST)	`rcp1armRMST()`	`plot_rcp1armRMST()`

Consistency evaluation methods

Method 1 (Effect Retention): Evaluates whether Region 1 retains at least a fraction pi of the overall treatment effect.
Method 2 (Simultaneous Positivity): Evaluates whether all regional estimates exceed the null value simultaneously.

Calculation approaches

Each function supports two approaches:

"formula": Closed-form or semi-analytical solution based on normal approximation.
"simulation": Monte Carlo simulation.

Installation

This package is not yet on CRAN. Install from source:

# Install devtools if not already installed
install.packages("devtools")

# Install SingleArmMRCT from local source
devtools::install_local("path/to/SingleArmMRCT")

Dependencies

R >= 4.1.0
ggplot2 >= 3.4.0

Quick start

Continuous endpoint

library(SingleArmMRCT)

# Closed-form solution: N = 100, Region 1 has 10 subjects (f1 = 0.1)
result <- rcp1armContinuous(
  mu  = 0.5,
  mu0 = 0.1,
  sd  = 1,
  Nj  = c(10, 90),
  PI  = 0.5,
  approach = "formula"
)
print(result)

Binary endpoint

result <- rcp1armBinary(
  p  = 0.5,
  p0 = 0.2,
  Nj = c(10, 90),
  PI = 0.5,
  approach = "formula"
)
print(result)

Time-to-event endpoint (hazard ratio)

result <- rcp1armHazardRatio(
  lambda         = log(2) / 10,
  lambda0        = log(2) / 5,
  Nj             = c(10, 90),
  t_a            = 3,
  t_f            = 10,
  lambda_dropout = NULL,
  PI             = 0.5,
  approach       = "formula"
)
print(result)

RMST endpoint

lam0    <- log(2) / 5
tstar   <- 8
mu0_val <- (1 - exp(-lam0 * tstar)) / lam0

result <- rcp1armRMST(
  lambda   = log(2) / 10,
  tau_star = tstar,
  mu0      = mu0_val,
  Nj       = c(10, 90),
  t_a      = 3,
  t_f      = 10,
  PI       = 0.5,
  approach = "formula"
)
print(result)

Visualisation

Each endpoint has a corresponding plot function that generates a faceted plot of RCP as a function of the regional allocation proportion f₁, overlaying formula and simulation results for both Method 1 and Method 2.

# Continuous endpoint: RCP vs f1 for N = 20, 40, 100 with J = 3 regions
p <- plot_rcp1armContinuous(
  mu    = 0.5,
  mu0   = 0.1,
  sd    = 1,
  PI    = 0.5,
  N_vec = c(20, 40, 100),
  J     = 3
)
print(p)

# Milestone survival endpoint
p <- plot_rcp1armMilestoneSurvival(
  lambda = log(2) / 10,
  t_eval = 8,
  S0     = exp(-log(2) * 8 / 5),
  t_a    = 3,
  t_f    = 10,
  PI     = 0.5,
  N_vec  = c(20, 40, 100),
  J      = 3
)
print(p)

Parameter conventions

Symbol	Meaning	Notes
`Nj`	Integer vector of regional sample sizes	e.g., `c(10, 90)` for J = 2 regions
`PI`	Effect retention threshold pi	Typically ≥ 0.5; default 0.5
`f1`	Regional allocation proportion of Region 1	f₁ = Nj[1] / sum(Nj)
`t_a`	Accrual period	Time-to-event endpoints only
`t_f`	Follow-up period	Time-to-event endpoints only
`lambda_dropout`	Dropout hazard rate	`NULL` = no dropout

References

Hayashi N, Itoh Y (2017). A re-examination of Japanese sample size calculation for multi-regional clinical trial evaluating survival endpoint. Japanese Journal of Biometrics, 38(2): 79–92. https://doi.org/10.5691/jjb.38.79

Homma G (2024). Cautionary note on regional consistency evaluation in multiregional clinical trials with binary outcomes. Pharmaceutical Statistics, 23(3):385–398. https://doi.org/10.1002/pst.2358

Wu J (2015). Sample size calculation for the one-sample log-rank test. Pharmaceutical Statistics, 14(1): 26–33. https://doi.org/10.1002/pst.1654

License

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.