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Biometrika 2009 96(2):307-322; doi:10.1093/biomet/asp016
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© 2009 Biometrika Trust

Article

Hierarchically penalized Cox regression with grouped variables

S. Wang and B. Nan

Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. sijiwang{at}umich.edu bnan{at}umich.edu

N. Zhu and J. Zhu

Department of Statistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. nfzhou{at}umich.edu jizhu{at}umich.edu

Received for publication 1 December 2007. Revision received 1 October 2008.
  Abstract

In many biological and other scientific applications, predictors are often naturally grouped. For example, in biological applications, assayed genes or proteins are grouped by biological roles or biological pathways. When studying the dependence of survival outcome on these grouped predictors, it is desirable to select variables at both the group level and the within-group level. In this article, we develop a new method to address the group variable selection problem in the Cox proportional hazards model. Our method not only effectively removes unimportant groups, but also maintains the flexibility of selecting variables within the identified groups. We also show that the new method offers the potential for achieving the asymptotic oracle property.

Key Words: Cox model • Group variable selection • Lasso • Microarray • Oracle property • Regularization


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