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

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.

This version is essentially a different paper than the previous one. A new estimator of the proportion of true null hypotheses has been developed, and it induces two adaptive FDR procedures. One such procedure has been proved to be conservative non-asymptotically, and the other has been empirically shown to be conservative

References in corpus (4)

• Two simple sufficient conditions for FDR control
• Multiple testing with discrete data: proportion of true null hypotheses and two adaptive FDR procedures
• Multiple Test Functions and Adjusted p-Values for Test Statistics with Discrete Distributions
• A discrete modification of the Benjamini-Yekutieli procedure

Cited by in corpus (9)

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• Uniformly consistently estimating the proportion of false null hypotheses via Lebesgue-Stieltjes integral equations
• Familywise Error Rate Controlling Procedures for Discrete Data
• Improved $q$-values for discrete uniform and homogeneous tests: a comparative study
• Empirical Bayes cumulative $\ell$-value multiple testing procedure for sparse sequences
• A grouped, selectively weighted false discovery rate procedure
• Modified estimator for the proportion of true null hypotheses under discrete setup with proven FDR control by the adaptive Benjamini-Hochberg procedure