Feature Screening in Ultrahigh Dimensional Cox's Model.

Survival data with ultrahigh dimensional covariates such as genetic markers have been collected in medical studies and other fields. In this work, we propose a feature screening procedure for the Cox model with ultrahigh dimensional covariates. The proposed procedure is distinguished from the existing sure independence screening (SIS) procedures (Fan, Feng and Wu, 2010, Zhao and Li, 2012) in that the proposed procedure is based on joint likelihood of potential active predictors, and therefore is not a marginal screening procedure. The proposed procedure can effectively identify active predictors that are jointly dependent but marginally independent of the response without performing an iterative procedure. We develop a computationally effective algorithm to carry out the proposed procedure and establish the ascent property of the proposed algorithm. We further prove that the proposed procedure possesses the sure screening property. That is, with the probability tending to one, the selected variable set includes the actual active predictors. We conduct Monte Carlo simulation to evaluate the finite sample performance of the proposed procedure and further compare the proposed procedure and existing SIS procedures. The proposed methodology is also demonstrated through an empirical analysis of a real data example.