Sparse estimation of Cox proportional hazards models via approximated information criteria

Xiaogang Su, Chalani S. Wijayasinghe, Juanjuan Fan, Ying Zhang

Research output: Contribution to journalArticle

11 Scopus citations


We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the ℓ0 norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularization by borrowing strength from both. It mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a reparameterization step so that it reduces to one unconstrained nonconvex yet smooth programming problem, which can be solved efficiently as in computing the maximum partial likelihood estimator (MPLE). Furthermore, the reparameterization tactic yields an additional advantage in terms of circumventing postselection inference. The oracle property of the proposed method is established. Both simulated experiments and empirical examples are provided for assessment and illustration.

Original languageEnglish (US)
Pages (from-to)751-759
Number of pages9
Issue number3
StatePublished - Sep 1 2016


  • AIC
  • BIC
  • Cox proportional hazards model
  • Regularization
  • Sparse estimation
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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