Improving the adjusted Benjamini--Hochberg method using e-values in knockoff-assisted variable selection

TL;DR

This paper enhances the knockoff-based multiple testing framework by developing a flexible e-value weighted Benjamini-Hochberg procedure with proven FDR control, showing improved power and performance in simulations and real data.

Contribution

It introduces a generalized, adaptive e-value weighted BH method with bounded p-to-e calibrators, extending prior approaches and demonstrating superior empirical results.

Findings

Large and consistent FDR control in simulations and real data

Improved power over previous knockoff methods in low FDR scenarios

Effective application to HIV-1 drug resistance data

Abstract

Considering the knockoff-based multiple testing framework of Barber and Cand\`es [2015], we revisit the method of Sarkar and Tang [2022] and identify it as a specific case of an un-normalized e-value weighted Benjamini-Hochberg procedure. Building on this insight, we extend the method to use bounded p-to-e calibrators that enable more refined and flexible weight assignments. Our approach generalizes the method of Sarkar and Tang [2022], which emerges as a special case corresponding to an extreme calibrator. Within this framework, we propose three procedures: an e-value weighted Benjamini-Hochberg method, its adaptive extension using an estimate of the proportion of true null hypotheses, and an adaptive weighted Benjamini-Hochberg method. We establish control of the false discovery rate (FDR) for the proposed methods. While we do not formally prove that the proposed methods outperform those of Barber and Cand\`es [2015] and Sarkar and Tang [2022], simulation studies and real-data analysis demonstrate large and consistent improvement over the latter in all cases, and better performance than the knockoff method in scenarios with low target FDR, a small number of signals, and weak signal strength. Simulation studies and a real-data application in HIV-1 drug resistance analysis demonstrate strong finite sample FDR control and exhibit improved, or at least competitive, power relative to the aforementioned methods.