Adaptive Storey's null proportion estimator

TL;DR

This paper introduces a new adaptive hyper-parameter selection method for Storey's null proportion estimator in FDR control, improving power while maintaining FDR guarantees, validated through simulations and real data.

Contribution

It proposes a novel class of data-driven hyper-parameters for Storey's estimator, ensuring FDR control and maximizing rejection power, with theoretical convergence guarantees.

Findings

Significant power gains in detecting true positives.

Effective control of FDR with adaptive hyper-parameters.

Robust performance on simulated and real protein data.

Abstract

False discovery rate (FDR) is a commonly used criterion in multiple testing and the Benjamini-Hochberg (BH) procedure is arguably the most popular approach with FDR guarantee. To improve power, the adaptive BH procedure has been proposed by incorporating various null proportion estimators, among which Storey's estimator has gained substantial popularity. The performance of Storey's estimator hinges on a critical hyper-parameter, where a pre-fixed configuration lacks power and existing data-driven hyper-parameters compromise the FDR control. In this work, we propose a novel class of adaptive hyper-parameters and establish the FDR control of the associated BH procedure using a martingale argument. Within this class of data-driven hyper-parameters, we present a specific configuration designed to maximize the number of rejections and characterize the convergence of this proposal to the optimal hyper-parameter under a commonly-used mixture model. We evaluate our adaptive Storey's null proportion estimator and the associated BH procedure on extensive simulated data and a motivating protein dataset. Our proposal exhibits significant power gains when dealing with a considerable proportion of weak non-nulls or a conservative null distribution.