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Biometrika Advance Access published online on February 8, 2008
Biometrika, doi:10.1093/biomet/asm083
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© 2008 Biometrika Trust

Articles

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

Hui Zou

School of Statistics, University of Minnesota, 224 Church Street S.E., Minneapolis, Minnesota 55455, U.S.A. hzou{at}stat.umn.edu

Received for publication 1 May 2006. Revision received 1 June 2007.
  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.

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


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