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

Biometrical Journal. Biometrische Zeitschrift
Xiongzhi ChenJoseph F Heyse

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, that is, an adaptive Benjamini-Hochberg (BH) procedure and an adaptive Benjamini-Hochberg-Heyse (BHH) procedure. We prove that the adaptive BH (aBH) procedure is conservative nonasymptotically. Through simulation studies, we show that these procedures are usually more powerful than their nonadaptive counterparts and that the adaptive BHH procedure is usually more powerful than the aBH 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.

References

Jun 17, 2006·Bioinformatics·Stan Pounds, Cheng Cheng
May 5, 2010·Genetics·Paul L Auer, R W Doerge
Mar 5, 2015·Bioinformatics·Isaac DialsinghNaomi S Altman

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Citations

Jan 21, 2020·Biometrical Journal. Biometrische Zeitschrift·Xiongzhi Chen
May 6, 2020·Biometrical Journal. Biometrische Zeitschrift·Xiongzhi ChenSanat K Sarkar
Aug 11, 2020·Biometrical Journal. Biometrische Zeitschrift·Xiongzhi Chen, Rebecca W Doerge

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