False discovery rate control for multiple testing based on p-values with c\`adl\`ag distribution functions

TL;DR

This paper introduces BH+, a new FDR control procedure for multiple testing with cdle0g p-value distributions, demonstrating its conservativeness and increased power, especially with mid p-values, across various real-world studies.

Contribution

The paper proposes BH+, a novel FDR procedure applicable to cdle0g p-values, including mid p-values, with proven conservativeness and improved power over existing methods.

Findings

BH+ is at least as powerful as BH for super-uniform p-values.

BH+ outperforms BH when applied to mid p-values.

Application to real studies yields more discoveries.

Abstract

For multiple testing based on p-values with c\`{a}dl\`{a}g distribution functions, we propose an FDR procedure "BH+" with proven conservativeness. BH+ is at least as powerful as the BH procedure when they are applied to super-uniform p-values. Further, when applied to mid p-values, BH+ is more powerful than it is applied to conventional p-values. An easily verifiable necessary and sufficient condition for this is provided. BH+ is perhaps the first conservative FDR procedure applicable to mid p-values. BH+ is applied to multiple testing based on discrete p-values in a methylation study, an HIV study and a clinical safety study, where it makes considerably more discoveries than the BH procedure.