Deploying the Conditional Randomization Test in High Multiplicity Problems

TL;DR

This paper presents the sequential CRT, a variable selection method combining the conditional randomization test and Selective SeqStep+ to control FDR in high multiplicity settings, with theoretical guarantees and practical applications.

Contribution

It introduces the sequential CRT, integrating CRT and Selective SeqStep+ for FDR control in high-dimensional variable selection.

Findings

The method controls FDR in simulations.

It outperforms some existing methods in power.

Successfully applied to breast cancer data.

Abstract

This paper introduces the sequential CRT, which is a variable selection procedure that combines the conditional randomization test (CRT) and Selective SeqStep+. Valid p-values are constructed via the flexible CRT, which are then ordered and passed through the selective SeqStep+ filter to produce a list of discoveries. We develop theory guaranteeing control on the false discovery rate (FDR) even though the p-values are not independent. We show in simulations that our novel procedure indeed controls the FDR and are competitive with -- and sometimes outperform -- state-of-the-art alternatives in terms of power. Finally, we apply our methodology to a breast cancer dataset with the goal of identifying biomarkers associated with cancer stage.