A procedure for multiple testing of partial conjunction hypotheses based on a hazard rate inequality

TL;DR

This paper introduces CoFilter, a new two-step procedure for multiple testing of partial conjunction hypotheses that reduces conservativeness and improves detection power, validated through genome-wide association studies.

Contribution

The paper proposes a novel two-step method, CoFilter, that filters p-values before applying multiple testing procedures, enhancing power in detecting signals across studies.

Findings

CoFilter effectively controls false discovery rate in genome studies.

The method reduces conservativeness of partial conjunction testing.

Validation on Crohn's disease data demonstrates practical utility.

Abstract

The partial conjunction null hypothesis is tested in order to discover a signal that is present in multiple studies. The standard approach of carrying out a multiple test procedure on the partial conjunction (PC) $p$-values can be extremely conservative. We suggest alleviating this conservativeness, by eliminating many of the conservative PC $p$-values prior to the application of a multiple test procedure. This leads to the following two step procedure: first, select the set with PC $p$-values below a selection threshold; second, within the selected set only, apply a family-wise error rate or false discovery rate controlling procedure on the conditional PC $p$-values. The conditional PC $p$-values are valid if the null p-values are uniform and the combining method is Fisher. The proof of their validity is based on a novel inequality in hazard rate order of partial sums of order statistics which may be of independent interest. We also provide the conditions for which the false discovery rate controlling procedures considered will be below the nominal level. We demonstrate the potential usefulness of our novel method, CoFilter (conditional testing after filtering), for analyzing multiple genome wide association studies of Crohn's disease.