Abstract: 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 existing sure independence screening (SIS) procedures Fan, Feng, and Wu (2010); Zhao and Li, (2012) in that it is based on the 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 it out and establish its ascent property. We further prove that the proposed procedure possesses the sure screening property: with probability tending to one, the selected variable set includes the actual active predictors. We conducted Monte Carlo simulation to evaluate the finite sample performance of the proposed procedure and compare it with existing SIS procedures. The proposed methodology is also demonstrated through an empirical analysis of a data example.

Key words and phrases: Cox’s model, partial likelihood, penalized likelihood, ultrahigh dimensional survival data.