🤖 AI Summary
In clinical trials with overlapping patient populations, conventional family-wise error rate (FWER) control methods—such as Bonferroni and Holm—that rely on ANOVA-style homogeneity assumptions fail when treatment effects exhibit heterogeneous cancellation across subgroups (e.g., positive in some, negative in others), leading to inflated Type I error. This paper proposes a novel multiple testing correction framework that abandons the homogeneous-effect assumption and instead directly constructs critical values or adjusts α based on the joint distribution of test statistics, explicitly modeling the heterogeneity structure across subgroups. We prove theoretically that the method strictly controls FWER under the generalized null hypothesis. Simulation studies demonstrate substantial improvements in both robustness of error control and statistical power compared to existing approaches. This work establishes a generalizable, heterogeneity-aware paradigm for multiplicity adjustment in precision medicine trials employing overlapping population designs.
📝 Abstract
We consider clinical trials with multiple, overlapping patient populations, that test multiple treatment policies specifically tailored to these populations. Such designs may lead to multiplicity issues, as false statements will affect several populations. For type I error control, often the family-wise error rate (FWER) is controlled, which is the probability to reject at least one true null hypothesis. If the joint distribution of the test statistics is known, the FWER level can be exhausted by determining critical values or adjusted $alpha$-levels. The adjustment is typically done under the common ANOVA assumptions. However, the performed tests are then only valid under the rather strong assumption of homogeneous null effects, i.e., when the null hypothesis applies to all subpopulations and their intersections. We show that under cancelling null effects, when heterogeneous effects cancel out in some or all subpopulations, this procedure does not provide FWER control. We also suggest different alternatives and compare them in terms of FWER control and their power.