exitprob_mams: Exit Probabilities for Multi-Arm Multi-Stage Design

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Exit Probabilities for Multi-Arm Multi-Stage Design

Description

Computes the exit (rejection) probabilities for a multi-arm multi-stage design.

Usage

exitprob_mams(
  M = NA_integer_,
  r = 1,
  theta = NA_real_,
  corr_known = TRUE,
  kMax = NA_integer_,
  b = NULL,
  a = NULL,
  I = NULL
)

Arguments

M	Number of active treatment arms.
r	Randomization ratio of each active arm to the common control.
theta	A vector of length M representing the true treatment effects for each active arm versus the common control.
corr_known	Logical. If TRUE, the correlation between Wald statistics is derived from the randomization ratio r as r / (r + 1). If FALSE, a conservative correlation of 0 is used.
kMax	Number of sequential looks.
b	A vector of efficacy boundaries for the max-Z statistics.
a	A vector of futility boundaries for the max-Z statistics.
I	A vector of information levels for any active arm versus the common control.

Details

The function assumes a multivariate normal distribution for the Wald statistics and all active arms share the same information level.

Value

A vector exitProb of length kMax containing the probability of rejection at each look.

Author(s)

Kaifeng Lu, [e-mail]

References

Ping Gao, Yingqiu Li. Adaptive multiple comparison sequential design (AMCSD) for clinical trials. Journal of Biopharmaceutical Statistics, 2024, 34(3), 424-440.

Examples

# Setup: 2 active arms vs control and 3 sequential looks.

# Information levels: equal spacing over 3 looks based on a maximum of
# 95 patients per arm, SD = 1.0
I <- 95 / (2 * 1.0^2) * seq(1, 3)/3

# O'Brien-Fleming critical values
b <- c(3.886562, 2.748214, 2.243907)

# Type I error under the global null hypothesis
p0 <- exitprob_mams(M = 2, theta = c(0, 0), kMax = 3, b = b, I = I)
cumsum(p0$exitProbUpper)

# Power under alternative: Treatment effects of 0.3 and 0.5
p1 <- exitprob_mams(M = 2, theta = c(0.3, 0.5), kMax = 3, b = b, I = I)
cumsum(p1$exitProbUpper)

lrstat documentation built on May 13, 2026, 9:06 a.m.