Familywise Error Rate Control via Knockoffs
Lucas Janson, Weijie Su

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 -familywise error rate (-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 -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 -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…
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Taxonomy
TopicsStatistical Methods in Clinical Trials · Statistical Methods and Inference · Optimal Experimental Design Methods
