Adaptive procedures for directional false discovery rate control

TL;DR

This paper develops adaptive procedures for controlling the directional false discovery rate in multiple hypothesis testing, enhancing power while maintaining strong error control under independence.

Contribution

It introduces methods that extend adaptive FDR procedures to control the directional FDR, with proven strong control properties when sign declarations are augmented.

Findings

Adaptive procedures improve power in multiple testing.

Proven strong control of directional FDR under independence.

Methods are especially effective when few true nulls are present.

Abstract

In multiple hypothesis testing, it is well known that adaptive procedures can enhance power via incorporating information about the number of true nulls present. Under independence, we establish that two adaptive false discovery rate (FDR) methods, upon augmenting sign declarations, also offer directional false discovery rate (FDR$_\text{dir}$) control in the strong sense. Such FDR$_\text{dir}$ controlling properties are appealing because adaptive procedures have the greatest potential to reap substantial gain in power when the underlying parameter configurations contain little to no true nulls, which are precisely settings where the FDR$_\text{dir}$ is an arguably more meaningful error rate to be controlled than the FDR.