Estimating False Discovery Proportion Under Arbitrary Covariance Dependence

TL;DR

This paper introduces a principal factor approximation method to accurately estimate and control the false discovery proportion in high-dimensional multiple testing with arbitrary dependence among test statistics.

Contribution

It proposes a novel dependence-adjusted approach for FDP estimation and control, improving over existing methods in correlated high-dimensional testing scenarios.

Findings

Accurately estimates FDP under arbitrary dependence.

Outperforms Efron's method in simulations.

Demonstrates effectiveness on real data applications.

Abstract

Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any SNPs are associated with some traits and those tests are correlated. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In the current paper, we propose a novel method based on principal factor approximation, which successfully subtracts the common dependence and weakens significantly the correlation structure, to deal with an arbitrary dependence structure. We derive an approximate expression for false discovery proportion (FDP) in large scale multiple testing when a common threshold is used and provide a consistent estimate of realized FDP. This result has important applications in controlling FDR and FDP. Our estimate of realized FDP compares favorably with Efron (2007)'s approach, as demonstrated in the simulated examples. Our approach is further illustrated by some real data applications. We also propose a dependence-adjusted procedure, which is more powerful than the fixed threshold procedure.