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

Jianoing Fan, Runze Li

Research output: Contribution to journalArticle

283 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)74-99
Number of pages26
JournalAnnals of Statistics
Volume30
Issue number1
DOIs
StatePublished - Feb 1 2002

Fingerprint

Frailty Model
Cox Proportional Hazards Model
Penalized Likelihood
Variable Selection
Oracle Property
Subset Selection
Selection Procedures
Regularization Parameter
Penalty Function
Linear regression
Hazard Models
Proportional Hazards
Model Complexity
Likelihood Methods
Survival Analysis
Semiparametric Model
Generalized Linear Model
Standard error
Parametric Model
Penalty

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Variable selection for Cox's proportional hazards model and frailty model. / Fan, Jianoing; Li, Runze.

In: Annals of Statistics, Vol. 30, No. 1, 01.02.2002, p. 74-99.

Research output: Contribution to journalArticle

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