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

Jianqing Fan Runze Li

Statistics Theory and Methods mathscidoc:1912.43259

The Annals of Statistics, 30, (1), 74-99, 2002
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
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@inproceedings{jianqing2002variable,
  title={Variable selection for Cox's proportional hazards model and frailty model},
  author={Jianqing Fan, and Runze Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113326755619819},
  booktitle={The Annals of Statistics},
  volume={30},
  number={1},
  pages={74-99},
  year={2002},
}
Jianqing Fan, and Runze Li. Variable selection for Cox's proportional hazards model and frailty model. 2002. Vol. 30. In The Annals of Statistics. pp.74-99. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113326755619819.
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