Variable Selection in Partial Linear Cox Model

• Activity Number: 603
• Type: Contributed
• Date/Time: Thursday, August 6, 2009 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): Pang Du*+ and Shuangge Ma and Hua Liang
• Companies: Virginia Polytechnic Institute and State University and Yale University and University of Rochester
• Keywords: Variable selection ; Partial linear model ; Porportional hazards ; penalized partial likelihood ; non-concave penalty

Abstract

Variable selection is an important issue in survival analysis. In this paper, we propose a partial linear Cox model where the covariates are divided into parametric and nonparametric components. A doubly penalized partial likelihood is then minimized to obtain the estimates of the unknown coefficient vector for the parametric component and the unknown nonlinear pattern function for the nonparametric component. The first penalty, either the smoothly-clipped-absolute-deviation penalty or the adaptive LASSO penalty, achieves variable selection in the parametric component. The second penalty, often an $L_{2}$-penalty on the nonlinear pattern function, governs the smoothness of its estimate. A model selection tool for the nonparametric component is also developed based on the Kullback-Leibler geometry. The proposed techniques are then evaluated by simulated data and real example applications.