Variable selection for Cox's proportional hazards model and frailty model

• 成果类型: Article
• 署名作者: Fan, JQ; Li, RZ
• 署名单位: Chinese University of Hong Kong; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 74-99
• 关键词: generalized cross-validation; survival-data; likelihood; shrinkage; Lasso

摘要

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 per-form 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.