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

4 Citations (Scopus)

Abstract

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
JournalBiometrics
Volume72
Issue number3
DOIs
StatePublished - Sep 1 2016

Fingerprint

Cox Proportional Hazards Model
Information Criterion
Set theory
Proportional Hazards Models
Reparameterization
Subset Selection
Hazards
Tuning
Oracle Property
Partial Likelihood
Penalized Likelihood
Experiments
Parameter Tuning
Maximum Likelihood
Regularization
Programming
methodology
Estimator
Norm
Unit

Keywords

  • 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

Cite this

Sparse estimation of Cox proportional hazards models via approximated information criteria. / Su, Xiaogang; Wijayasinghe, Chalani S.; Fan, Juanjuan; Zhang, Ying.

In: Biometrics, Vol. 72, No. 3, 01.09.2016, p. 751-759.

Research output: Contribution to journalArticle

Su, Xiaogang ; Wijayasinghe, Chalani S. ; Fan, Juanjuan ; Zhang, Ying. / Sparse estimation of Cox proportional hazards models via approximated information criteria. In: Biometrics. 2016 ; Vol. 72, No. 3. pp. 751-759.
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