Primary Submission Category: Mediation
Powerful Partial Conjunction Hypothesis Testing via Conditioning
Authors: Biyonka Liang, Lu Zhang, Lucas Janson,
Presenting Author: Biyonka Liang*
The testing of causal hypotheses, such as in mediation analysis and settings involving evidence factors, is often formulated as a Partial Conjunction Hypothesis (PCH) test, which combines information across a set of base hypotheses to determine whether some subset is non-null. However, standard methods for testing a PCH can be highly conservative. In this paper, we introduce the conditional PCH (cPCH) test, a new framework for testing a single PCH that directly corrects the conservativeness of standard approaches by conditioning on certain order statistics of the base p-values. Under distributional assumptions commonly encountered in PCH testing, the cPCH test produces uniform null p-values. Through simulations, we demonstrate that the cPCH test uniformly outperforms standard single PCH tests, maintains Type I error control even under model misspecification, and, in certain settings, can also be used to outperform state-of-the-art multiple testing approaches for causal mediation analysis.