Open Access
Translator Disclaimer
February 2015 Beyond first-order asymptotics for Cox regression
Donald A. Pierce, Ruggero Bellio
Bernoulli 21(1): 401-419 (February 2015). DOI: 10.3150/13-BEJ572


To go beyond standard first-order asymptotics for Cox regression, we develop parametric bootstrap and second-order methods. In general, computation of $P$-values beyond first order requires more model specification than is required for the likelihood function. It is problematic to specify a censoring mechanism to be taken very seriously in detail, and it appears that conditioning on censoring is not a viable alternative to that. We circumvent this matter by employing a reference censoring model, matching the extent and timing of observed censoring. Our primary proposal is a parametric bootstrap method utilizing this reference censoring model to simulate inferential repetitions of the experiment. It is shown that the most important part of improvement on first-order methods – that pertaining to fitting nuisance parameters – is insensitive to the assumed censoring model. This is supported by numerical comparisons of our proposal to parametric bootstrap methods based on usual random censoring models, which are far more unattractive to implement. As an alternative to our primary proposal, we provide a second-order method requiring less computing effort while providing more insight into the nature of improvement on first-order methods. However, the parametric bootstrap method is more transparent, and hence is our primary proposal. Indications are that first-order partial likelihood methods are usually adequate in practice, so we are not advocating routine use of the proposed methods. It is however useful to see how best to check on first-order approximations, or improve on them, when this is expressly desired.


Download Citation

Donald A. Pierce. Ruggero Bellio. "Beyond first-order asymptotics for Cox regression." Bernoulli 21 (1) 401 - 419, February 2015.


Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 06436799
MathSciNet: MR3322324
Digital Object Identifier: 10.3150/13-BEJ572

Keywords: Censoring , conditional inference , Cox regression , higher-order asymptotics , Parametric bootstrap , partial likelihood

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability


Vol.21 • No. 1 • February 2015
Back to Top