PENALIZED VARIABLE SELECTION PROCEDURE FOR COX MODELS WITH SEMIPARAMETRIC RELATIVE RISK

• 成果类型: Article
• 署名作者: Du, Pang; Ma, Shuangge; Liang, Hua
• 署名单位: Virginia Polytechnic Institute & State University; Yale University; University of Rochester
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS780
• 发表日期: 2010
• 页码: 2092-2117
• 关键词: hazards regression; partial likelihood; Lasso

摘要

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts. Two penalties are applied sequentially. The first penalty, governing the smoothness of the multivariate nonlinear covariate effect function, provides a smoothing spline ANOVA framework that is exploited to derive an empirical model selection tool for the nonparametric part. The second penalty, either the smoothly-clipped-absolute-deviation (SCAD) penalty or the adaptive LASSO penalty, achieves variable selection in the parametric part. We show that the resulting estimator of the parametric part possesses the oracle property, and that the estimator of the nonparametric part achieves the optimal rate of convergence. The proposed procedures are shown to work well in simulation experiments, and then applied to a real data example on sexually transmitted diseases.