Familywise error rate control via knockoffs

By Lucas Janson, Weijie Su. 2015

51 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Molecular Biology, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

1. Jesse Hemerik
2. Jelle J. Goeman
3. Aldo Solari
4. E.J. Candes
5. Jinchi Lv
6. Yingying Fan
7. Lucas Janson
8. Christina Heinze-Deml

In Molecular Biology

1. Jinchi Lv
2. Jesse Hemerik
3. Aldo Solari
4. Jelle J. Goeman
5. E.J. Candes
6. Yingying Fan
7. Lucas Janson
8. Mark Rubin

In Statistics and Probability

1. Jinchi Lv
2. Yingying Fan
3. Jesse Hemerik
4. E.J. Candes
5. Aldo Solari
6. Jelle J. Goeman
7. Lucas Janson
8. Jianqing Fan

Citations in the corpus

• Only closed testing procedures are admissible for controlling false discovery proportions (2019, background): “Closed testing (Marcus et al., 1976) is a fundamental principle of familywise error rate (FWER) control in multiple hypothesis testing. Indeed, almost every known procedure controlling FWER has been shown to be a special case of closed testing, and many procedures have been explicitly constructed as”
• Panning for Gold: Model-free Knockoffs for High-dimensional Controlled Variable Selection (2016, methodology): “3Using the methods of Janson and Su (2016), other error rates such as the k-familywise error rate can also be controlled using MF knockoffs, but we focus on FDR for this paper.”