Adaptive Lasso for Cox's proportional hazards model

Hao Helen Zhang, Wenbin Lu

Research output: Contribution to journalArticlepeer-review

386 Scopus citations


We investigate the variable selection problem for Coxs proportional hazards model, and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience. The new method is based on a penalized log partial likelihood with the adaptively weighted L 1 penalty on regression coefficients, providing what we call the adaptive Lasso estimator. The method incorporates different penalties for different coefficients: unimportant variables receive larger penalties than important ones, so that important variables tend to be retained in the selection process, whereas unimportant variables are more likely to be dropped. Theoretical properties, such as consistency and rate of convergence of the estimator, are studied. We also show that, with proper choice of regularization parameters, the proposed estimator has the oracle properties. The convex optimization nature of the method leads to an efficient algorithm. Both simulated and real examples show that the method performs competitively.

Original languageEnglish (US)
Pages (from-to)691-703
Number of pages13
Issue number3
StatePublished - 2007


  • Adaptive Lasso
  • Lasso
  • Penalized partial likelihood
  • Proportional hazards model
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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