An Overview on Variable Selection for Survival Analysis Jianqing Fan 1 , Gang Li 2 , and Runze Li 3 1 Jianqing Fan, Department of Operation Research and Financial Engineering, Princeton University, NJ 08544 jqfan@princeton.edu 2 Gang Li, Department of Biostatistics, University of California Los Angeles, CA 90095-1772 vli@ucla.edu 3 Runze Li, Department of Statistics, The Pennsylvania State University, University Park, PA16802-2111 rli@stat.psu.edu Summary. Variable selection are fundamental in high-dimensional statistical mod- eling. Many authors have proposed various variable selection criteria and procedures for linear regression models (Miller, 2002). Variable selection for survival data anal- ysis poses many challenges because of complicated data structure, and therefore receives much attention in the recent literature. In this article, we will review var- ious existing variable selection procedures for survival analysis. We further pro- pose a unified framework for variable selection in survival analysis via a nonconcave penalized likelihood approach. The nonconcave penalized likelihood approach dis- tinguishes from the traditional variable selection procedures in that it deletes the non-significant covariates by estimating their coefficients as zero. With a proper choice of the penalty function and the regularization parameter, we demonstrate the resulting estimate possesses an oracle property, namely, it performs as well as if the true submodel were known in advance. We further illustrate the methodology by a real data example. Key words: Accelerated life model, Cox’s model, Cox’s frailty model, marginal hazards model, variable selection. 2000 Mathematics Subject Classification: 62N01 1 Introduction Variable selection is vital to survival analysis. In practice, many covariates are often available as potential risk factors. At the initial stage of modeling, data Contemporary Multivariate Analysis and Experimental Designs—In Celebration of Professor Kai- tai Fangs 65th birthday. Edited by Jianqing Fan and Gang Li. The World Scientific Publisher, 2005.