Testing and confidence intervals for high dimensional proportional hazards models

Ethan X. Fang, Yang Ning, Han Liu

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


The paper considers the problem of hypothesis testing and confidence intervals in high dimensional proportional hazards models. Motivated by a geometric projection principle, we propose a unified likelihood ratio inferential framework, including score, Wald and partial likelihood ratio statistics for hypothesis testing. Without assuming model selection consistency, we derive the asymptotic distributions of these test statistics, establish their semiparametric optimality and conduct power analysis under Pitman alternatives. We also develop new procedures to construct pointwise confidence intervals for the baseline hazard function and conditional hazard function. Simulation studies show that all tests proposed perform well in controlling type I errors. Moreover, the partial likelihood ratio test is empirically more powerful than the other tests. The methods proposed are illustrated by an example of a gene expression data set.

Original languageEnglish (US)
Pages (from-to)1415-1437
Number of pages23
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number5
StatePublished - Nov 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Censored data
  • High dimensional inference
  • Proportional hazards model
  • Sparsity
  • Survival analysis


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