Testing and confidence intervals for high dimensional proportional hazards models

Xingyan Ethan Fang, Yang Ning, Han Liu

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1415-1437
Number of pages23
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume79
Issue number5
DOIs
StatePublished - Nov 1 2017
Externally publishedYes

Fingerprint

Partial Likelihood
Proportional Hazards Model
Hazard Function
Hypothesis Testing
Confidence interval
High-dimensional
Testing
Power Analysis
Likelihood Ratio Statistic
Type I error
Likelihood Ratio
Likelihood Ratio Test
Gene Expression Data
Model Selection
Asymptotic distribution
Test Statistic
Baseline
Optimality
Simulation Study
Projection

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Testing and confidence intervals for high dimensional proportional hazards models. / Fang, Xingyan Ethan; Ning, Yang; Liu, Han.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 79, No. 5, 01.11.2017, p. 1415-1437.

Research output: Contribution to journalArticle

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