Contents are the authors' sole responsibility and do not necessarily represent official NIH views.
Estimation of treatment effect under non-proportional hazards and conditionally independent censoring†
Article first published online: 4 JUL 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 31, Issue 28, pages 3504–3515, 10 December 2012
How to Cite
Boyd, A. P., Kittelson, J. M. and Gillen, D. L. (2012), Estimation of treatment effect under non-proportional hazards and conditionally independent censoring. Statist. Med., 31: 3504–3515. doi: 10.1002/sim.5440
- Issue published online: 23 NOV 2012
- Article first published online: 4 JUL 2012
- Manuscript Accepted: 18 APR 2012
- Manuscript Received: 3 NOV 2010
- NIH/NCRR Colorado CTSI. Grant Number: UL1 RR025780
- multiplicative hazards model;
- partial likelihood;
- time-varying effects;
- weighted estimator
In clinical trials with time-to-event outcomes, it is common to estimate the marginal hazard ratio from the proportional hazards model, even when the proportional hazards assumption is not valid. This is unavoidable from the perspective that the estimator must be specified a priori if probability statements about treatment effect estimates are desired. Marginal hazard ratio estimates under non-proportional hazards are still useful, as they can be considered to be average treatment effect estimates over the support of the data. However, as many have shown, under non-proportional hazard, the ‘usual’ unweighted marginal hazard ratio estimate is a function of the censoring distribution, which is not normally considered to be scientifically relevant when describing the treatment effect. In addition, in many practical settings, the censoring distribution is only conditionally independent (e.g., differing across treatment arms), which further complicates the interpretation. In this paper, we investigate an estimator of the hazard ratio that removes the influence of censoring and propose a consistent robust variance estimator. We compare the coverage probability of the estimator to both the usual Cox model estimator and an estimator proposed by Xu and O'Quigley (2000) when censoring is independent of the covariate. The new estimator should be used for inference that does not depend on the censoring distribution. It is particularly relevant to adaptive clinical trials where, by design, censoring distributions differ across treatment arms. Copyright © 2012 John Wiley & Sons, Ltd.