Abstract: In this article, we propose a variable selection approach in the Cox model when there is a group structure in a diverging number of covariates. Most of the existing variable selection methods are designed for either individual variable selection or group selection, but not for both. The proposed methods are capable of simultaneous group selection and individual variable selection within selected groups. Computational algorithms are developed for the proposed bi-level selection methods, and the properties of the proposed selection methods are established. The proposed group bridge penalized methods are able to correctly select the important groups and variables simultaneously with high probability in sparse models. Simulation studies indicate that the proposed methods work well and two examples are provided to illustrate the applications of the proposed methods to scientific problems.

Key words and phrases: Bi-level selection, coordinate descent algorithm, Cox regression, group bridge penalty, survival data, variable selection consistency.