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

install.packages("SingleArmMRCT")

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