A prediction interval for the population-wise error rate

TL;DR

This paper develops an asymptotic prediction interval for the population-wise error rate in clinical trials, accounting for unknown population sizes and ensuring controlled error probability.

Contribution

It introduces a novel method using the delta approach to construct prediction intervals for PWER, validated through simulations and real data examples.

Findings

The prediction interval achieves the desired coverage probability.

The method effectively accounts for unknown population strata sizes.

Simulations confirm the interval's accuracy in practical scenarios.

Abstract

We construct an asymptotic prediction interval for the population-wise error rate (PWER), which is a multiple type I error criterion for clinical trials with overlapping patient populations. The PWER is the probability that a randomly selected patient will receive an ineffective treatment. It must usually be estimated due to unknown population strata sizes, such that only an estimate can be controlled at the given significance level. We apply the delta method to find a prediction interval for the resulting true PWER, we demonstrate by simulations that the interval has the required coverage probability, and illustrate the approach with real data examples.