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February 2002 Variable Selection for Cox's proportional Hazards Model and Frailty Model
Jianqing Fan, Runze Li
Ann. Statist. 30(1): 74-99 (February 2002). DOI: 10.1214/aos/1015362185


A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in Fan and Li (2001a). It has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance. Such a property is called an oracle property. The proposed procedures were illustrated in the context of linear regression, robust linear regression and generalized linear models. In this paper, the nonconcave penalized likelihood approach is extended further to the Cox proportional hazards model and the Cox proportional hazards frailty model, two commonly used semi-parametric models in survival analysis. As a result, new variable selection procedures for these two commonly-used models are proposed. It is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function. Further, with a proper choice of the regularization parameter and the penalty function, the proposed estimators possess an oracle property. Standard error formulae are derived and their accuracies are empirically tested. Simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection, and they reduce model complexity as effectively as the best subset variable selection. Compared with the LASSO, which is the penalized likelihood method with the $L_1$ -penalty, proposed by Tibshirani, the newly proposed approaches have better theoretic properties and finite sample performance.


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Jianqing Fan. Runze Li. "Variable Selection for Cox's proportional Hazards Model and Frailty Model." Ann. Statist. 30 (1) 74 - 99, February 2002.


Published: February 2002
First available in Project Euclid: 5 March 2002

zbMATH: 1012.62106
MathSciNet: MR1892656
Digital Object Identifier: 10.1214/aos/1015362185

Primary: 62F12 , 62N02

Keywords: Cox’s regression model , frailty model , Lasso , partial likelihood , penalized likelihood , profile likelihood

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.30 • No. 1 • February 2002
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