Regularization for cox's proportional hazards model with NP-dimensionality1

Jelena Bradic, Jianqing Fan, Jiancheng Jiang

Research output: Contribution to journalArticlepeer-review

64 Scopus citations

Abstract

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of nonconcave penalized methods for nonpolynomial (NP) dimensional data with censoring in the framework of Cox's proportional hazards model. A class of folded-concave penalties are employed and both LASSO and SCAD are discussed specifically. We unveil the question under which dimensionality and correlation restrictions can an oracle estimator be constructed and grasped. It is demonstrated that nonconcave penalties lead to significant reduction of the "irrepresentable condition" needed for LASSO model selection consistency. The large deviation result for martingales, bearing interests of its own, is developed for characterizing the strong oracle property. Moreover, the nonconcave regularized estimator, is shown to achieve asymptotically the information bound of the oracle estimator. A coordinate-wise algorithm is developed for finding the grid of solution paths for penalized hazard regression problems, and its performance is evaluated on simulated and gene association study examples.

Original languageEnglish (US)
Pages (from-to)3092-3120
Number of pages29
JournalAnnals of Statistics
Volume39
Issue number6
DOIs
StatePublished - Dec 2011

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Hazard rate
  • LASSO
  • Large deviation
  • Oracle
  • SCAD

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