Choosing the nominal level post-hoc with knockoffs using e-values

TL;DR

This paper introduces a method using e-values to adaptively choose the nominal FDR level post-hoc in knockoff procedures, enhancing power and precision in variable selection without additional costs.

Contribution

It presents a novel post-hoc adjustment technique for knockoff filters using e-values, improving flexibility and performance in variable selection tasks.

Findings

Enhanced FDR control with post-hoc nominal level adjustment

Improved power in low-dimensional, sparse settings

Validated on clinical trial data for drug development

Abstract

The knockoff filter is a powerful tool for controlled variable selection with false discovery rate (FDR) control. In this paper, we leverage e-values to allow the nominal FDR level to be switched post-hoc, after looking at the data and applying the knockoff procedure. This approach addresses a significant limitation of standard knockoffs: while frequently used in high-dimensional regressions, they often lack power in low-dimensional and sparse signal settings. One of the main reasons for this is that the knockoff filter requires a minimum number of selections that depends strictly on the nominal FDR level. By utilizing e-values, we can increase the nominal level in cases where the original procedure makes no discoveries, or decrease it to improve precision when discoveries are abundant. These improvements come without any costs, meaning the results of our post-hoc procedure are always more informative than those of the original knockoff filter. We extend this methodology to recently proposed derandomized knockoff procedures and demonstrate its utility in variable selection problems relevant to drug development using real clinical trial data.