Multiple testing with discrete data: proportion of true null hypotheses and two adaptive FDR procedures

TL;DR

This paper introduces a new estimator for the proportion of true null hypotheses in discrete data multiple testing, leading to more powerful adaptive FDR procedures that outperform traditional methods in simulations and real HIV vaccine data.

Contribution

A novel less biased estimator of true null proportion for discrete p-values, enabling improved adaptive FDR procedures with proven conservativeness and higher power.

Findings

Adaptive procedures are more powerful than non-adaptive ones.

The new estimator reduces upward bias compared to existing estimators.

Applied to HIV data, the adaptive procedures detect more significant findings.

Abstract

We consider multiple testing with false discovery rate (FDR) control when p-values have discrete and heterogeneous null distributions. We propose a new estimator of the proportion of true null hypotheses and demonstrate that it is less upwardly biased than Storey's estimator and two other estimators. The new estimator induces two adaptive procedures, i.e., an adaptive Benjamini-Hochberg (BH) procedure and an adaptive Benjamini-Hochberg-Heyse (BHH) procedure. We prove that the the adaptive BH procedure is conservative non-asymptotically. Through simulation studies, we show that these procedures are usually more powerful than their non-adaptive counterparts and that the adaptive BHH procedure is usually more powerful than the adaptive BH procedure and a procedure based on randomized p-value. The adaptive procedures are applied to a study of HIV vaccine efficacy, where they identify more differentially polymorphic positions than the BH procedure at the same FDR level.