Decision_rule_M.FS: Decision rule for the FS design based on the...

In OptOTrials: Optimal Two-Stage Designs for Ordered Categorical Outcomes

Decision rule for the FS design based on the Mann-Whitney-Wilcoxon test with the specified values of alpha1, alpha2, and beta1

Description

This is the function to determine the decision rule for the FS design based on the Mann-Whitney-Wilcoxon test with the specified values of alpha1, alpha2, and beta1.

Usage

Decision_rule_M.FS(p1, p2, alpha1, alpha2, beta1, alpha, beta, lambda = 1)

Arguments

p1	A vector containing the probabilities of the outcome falling into each level of the control arm.
p2	A vector containging the probabilities of the outcome falling into each level of the control arm.
alpha1	The parameter used to define futility monitoring. Under the null hypothesis, 1 - alpha1 corresponds to the probability of stopping for futility at the interim analysis.
alpha2	The probability of stopping for superiority at the interim analysis when the null hypothesis is true.
beta1	The probability of stopping for futility at the interim analysis when the alternative hypothesis is true.
alpha	Target type I error rate.
beta	Target type II error rate.
lambda	The ratio of sample sizes between the experimental and control groups, defined as sample size (experimental): sample size (control) = lambda:1. The default value is 1.

Value

n1	The total sample size of the control and experimental groups required at the 1st analysis.
t1l	The lower threshold of the test statistic at the 1st analysis.
t1u	The upper threshold of the test statistic at the 1st analysis.
n2	The cumulative total sample size of the control and experimental groups required at the 2nd analysis.
t2	The threshold of the test statistic at the 2nd analysis.
beta2	Under the null hypothesis, 1 - beta2 denotes the probability of stopping for superiority at the interim analysis.

References

Park, Y. (2025). Optimal two-stage group sequential designs based on Mann-Whitney-Wilcoxon test. PloS one, 20(2), e0318211.

Examples

alpha = 0.05; beta = 0.2; 
p1 = c(0.2, 0.5, 0.2, 0.1)
p2 = c(0.4, 0.3, 0.2, 0.1)
alpha1 <- 0.2
alpha2 <- 0.025
beta1 <- 0.1
Decision_rule_M.FS(p1, p2, alpha1, alpha2, beta1, alpha, beta, lambda = 1)

OptOTrials documentation built on Sept. 9, 2025, 5:46 p.m.