Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 1415-1437 |
| Number of pages | 23 |
| Journal | Journal of the Royal Statistical Society. Series B: Statistical Methodology |
| Volume | 79 |
| Issue number | 5 |
| DOIs | |
| State | Published - Nov 1 2017 |
Funding
We thank the Joint Editor, Associate Editor and the three referees for their helpful comments, which significantly improved the paper. We also thank Professor Bradic for providing very helpful comments. This research is partially supported by National Science Foundation career grants DMS 1454377, IIS1408910 and IIS1332109, and National Institutes of Health grants R01MH102339, R01GM083084 and R01HG06841.
Keywords
- Censored data
- High dimensional inference
- Proportional hazards model
- Sparsity
- Survival analysis
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty