Familywise Error Rate Control via Knockoffs

TL;DR

This paper introduces a new knockoffs-based method for controlling the $k$-familywise error rate in linear regression, which is exact in finite samples and more powerful than existing methods.

Contribution

It develops a novel knockoffs procedure for $k$-FWER control in linear regression that does not require noise variance knowledge and is tailored to the regression setting.

Findings

Controls $k$-FWER exactly in finite samples

Provides superior power compared to alternative methods

Successfully applied to identify drug-resistance mutations

Abstract

We present a novel method for controlling the $k$-familywise error rate ($k$-FWER) in the linear regression setting using the knockoffs framework first introduced by Barber and Cand\`es. Our procedure, which we also refer to as knockoffs, can be applied with any design matrix with at least as many observations as variables, and does not require knowing the noise variance. Unlike other multiple testing procedures which act directly on $p$-values, knockoffs is specifically tailored to linear regression and implicitly accounts for the statistical relationships between hypothesis tests of different coefficients. We prove that knockoffs controls the $k$-FWER exactly in finite samples and show in simulations that it provides superior power to alternative procedures over a range of linear regression problems. We also discuss extensions to controlling other Type I error rates such as the false exceedance rate, and use it to identify candidates for mutations conferring drug-resistance in HIV.