Decision_rule_W.F: Decision rule of the F design based on the Win Odds test with...

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

Decision rule of the F design based on the Win Odds test with the specified values of alpha1 and beta1

Description

This is to determine the decision rule for a two-stage design based on the Win Odds test with the specified values of alpha1 and beta1.

Usage

Decision_rule_W.F(p1, p2, alpha1, 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.
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.
t1	The 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.

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
beta1 <- 0.1
Decision_rule_W.F(p1, p2, alpha1, beta1, alpha, beta, lambda = 1)

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