The Annals of Statistics

Penalized variable selection procedure for Cox models with semiparametric relative risk

Pang Du, Shuangge Ma, and Hua Liang

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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.

Article information

Ann. Statist., Volume 38, Number 4 (2010), 2092-2117.

First available in Project Euclid: 11 July 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62N01: Censored data models 62N03: Testing
Secondary: 62N02: Estimation

Backfitting partially linear models penalized variable selection proportional hazards penalized partial likelihood smoothing spline ANOVA


Du, Pang; Ma, Shuangge; Liang, Hua. Penalized variable selection procedure for Cox models with semiparametric relative risk. Ann. Statist. 38 (2010), no. 4, 2092--2117. doi:10.1214/09-AOS780.

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