  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.
