Conditional calibration for false discovery rate control under dependence

TL;DR

This paper presents a new method for controlling the false discovery rate in multiple testing with dependent data, improving power over existing procedures by adaptively calibrating thresholds based on dependence structure.

Contribution

The paper introduces a novel class of FDR control methods that adapt thresholds for dependent tests, including the dependence-adjusted Benjamini-Hochberg procedure, with proven dominance over traditional methods.

Findings

dBH procedure outperforms BH under positive dependence

dBH uniformly dominates BY procedure in general dependence scenarios

Simulations show increased power with the new method

Abstract

We introduce a new class of methods for finite-sample false discovery rate (FDR) control in multiple testing problems with dependent test statistics where the dependence is fully or partially known. Our approach separately calibrates a data-dependent p-value rejection threshold for each hypothesis, relaxing or tightening the threshold as appropriate to target exact FDR control. In addition to our general framework we propose a concrete algorithm, the dependence-adjusted Benjamini-Hochberg (dBH) procedure, which adaptively thresholds the q-value for each hypothesis. Under positive regression dependence the dBH procedure uniformly dominates the standard BH procedure, and in general it uniformly dominates the Benjamini-Yekutieli (BY) procedure (also known as BH with log correction). Simulations and real data examples illustrate power gains over competing approaches to FDR control under dependence.