Dependence correction of multiple tests with applications to sparsity

TL;DR

This paper introduces new multiple testing procedures that control the false discovery rate under dependence, especially in sparse settings like genome studies, improving upon existing methods with better dependence correction.

Contribution

It develops dependence correction methods for multiple testing that extend the Benjamini-Yekutieli and Storey procedures, tailored for sparse data scenarios.

Findings

Procedures control FDR at finite sample sizes under dependence.

New tests outperform existing methods in genome data applications.

FDR bounds are adjusted by a dependency factor.

Abstract

The present paper establishes new multiple procedures for simultaneous testing of a large number of hypotheses under dependence. Special attention is devoted to experiments with rare false hypotheses. This sparsity assumption is typically for various genome studies when a portion of remarkable genes should be detected. The aim is to derive tests which control the false discovery rate (FDR) always at finite sample size. The procedures are compared for the set up of dependent and independent $p$-values. It turns out that the FDR bounds differ by a dependency factor which can be used as a correction quantity. We offer sparsity modifications and improved dependence tests which generalize the Benjamini-Yekutieli test and adaptive tests in the sense of Storey. As a byproduct, an early stopped test is presented in order to bound the number of rejections. The new procedures perform well for real genome data examples.