Empirical Bayes large-scale multiple testing for high-dimensional binary outcome data

TL;DR

This paper develops empirical Bayes methods for large-scale multiple testing in high-dimensional binary data, introducing new procedures that accurately control the false discovery rate and establishing their theoretical guarantees.

Contribution

It introduces novel empirical Bayes procedures with proven uniform FDR control for sparse high-dimensional binary outcomes, addressing limitations of existing methods.

Findings

Default conjugate prior can be overly conservative in FDR estimation.

Proposed procedures achieve accurate FDR control in simulations.

First uniform FDR control result for high-dimensional binary outcome data.

Abstract

This paper explores the multiple testing problem for sparse high-dimensional data with binary outcomes. We propose novel empirical Bayes multiple testing procedures based on a spike-and-slab posterior and then evaluate their performance in controlling the false discovery rate (FDR). A surprising finding is that the procedure using the default conjugate prior (namely, the $\ell$-value procedure) can be overly conservative in estimating the FDR. To address this, we introduce two new procedures that provide accurate FDR control. Sharp frequentist theoretical results are established for these procedures, and numerical experiments are conducted to validate our theory in finite samples. To the best of our knowledge, we obtain the first {\it uniform} FDR control result in multiple testing for high-dimensional data with binary outcomes under the sparsity assumption.