CoxKnockoff: Controlled feature selection for the Cox model using knockoffs

Abstract

Although there is a huge literature on feature selection for the Cox model, none of the existing approaches can control the false discovery rate (FDR) unless the sample size tends to infinity. In addition, there is no formal power analysis of the knockoffs framework for survival data in the literature. To address those issues, in this paper, we propose a novel controlled feature selection approach using knockoffs for the Cox model. We establish that the proposed method enjoys the FDR control in finite samples regardless of the number of covariates. Moreover, under mild regularity conditions, we also show that the power of our method is asymptotically one as sample size tends to infinity. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure in the survival setting. Simulation studies confirm that our method has appealing finite-sample performance with desired FDR control and high power. We further demonstrate the performance of our method through a real data example.