Blinded sample size re-calculation in multiple composite population designs with normal data and baseline adjustments

TL;DR

This paper introduces a new trial design for subpopulation analysis in clinical studies, using composite populations, p-value combination, and blinded sample size re-calculation to ensure error control and adequate power.

Contribution

It proposes a novel design for composite populations with normally distributed endpoints, including methods for sample size re-calculation and error control using multivariate normal distributions.

Findings

Strong control of family-wise type I error rate demonstrated in simulations

Target power is achieved or nearly achieved after sample size re-calculation

Applicable to personalized medicine and targeted therapy trial designs

Abstract

The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms of an accumulation of disjoint population subsets and will therefore be called composite populations. The proposed trial design is applicable to any set of composite populations, considering normally distributed endpoints and random baseline covariates. Treatment effects for composite populations are tested by combining $p$-values, calculated on the subset levels, using the inverse normal combination function to generate test statistics for those composite populations. The family-wise type I error rate for simultaneous testing is controlled in the strong sense by the application of the closed testing procedure. Critical values for intersection hypothesis tests are derived using multivariate normal distributions, reflecting the joint distribution of composite population test statistics under the null hypothesis. For sample size calculation and sample size re-calculation multivariate normal distributions are derived which describe the joint distribution of composite population test statistics under an assumed alternative hypothesis. Simulations demonstrate the strong control of the family-wise type I error rate in fixed designs and re-calculation designs with blinded sample size re-calculation. The target power after sample size re-calculation is typically met or close to being met.