A note on path-based variable selection in the penalized proportional hazards model

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Abstract

We propose an efficient and adaptive shrinkage method for variable selection in the Cox model. The method constructs a piecewise-linear regularization path connecting the maximum partial likelihood estimator and the origin. Then a model is selected along the path. We show that the constructed path is adaptive in the sense that, with a proper choice of regularization parameter, the fitted model works as well as if the true underlying submodel were given in advance. A modified algorithm of the least-angle-regression type efficiently computes the entire regularization path of the new estimator. Furthermore, we show that, with a proper choice of shrinkage parameter, the method is consistent in variable selection and efficient in estimation. Simulation shows that the new method tends to outperform the lasso and the smoothly-clipped-absolute-deviation estimators with moderate samples. We apply the methodology to data concerning nursing homes.

Original languageEnglish (US)
Pages (from-to)241-247
Number of pages7
JournalBiometrika
Volume95
Issue number1
DOIs
StatePublished - Mar 1 2008

Keywords

  • Adaptive path
  • Lasso
  • Oracle property
  • Penalized partial likelihood
  • Smoothly-clipped-absolute deviation penalty
  • Variable selection

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