Incorporating prognostic factors into causal estimators: A comparison of methods for randomised controlled trials with a time-to-event outcome
Article first published online: 19 JUN 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 31, Issue 26, pages 3073–3088, 20 November 2012
How to Cite
Hampson, L. V. and Metcalfe, C. (2012), Incorporating prognostic factors into causal estimators: A comparison of methods for randomised controlled trials with a time-to-event outcome. Statist. Med., 31: 3073–3088. doi: 10.1002/sim.5411
- Issue published online: 11 OCT 2012
- Article first published online: 19 JUN 2012
- Manuscript Accepted: 16 MAR 2012
- Manuscript Received: 6 JUL 2011
- causal models;
- prognostic factors;
- proportional hazards;
In randomised controlled trials, the effect of treatment on those who comply with allocation to active treatment can be estimated by comparing their outcome to those in the comparison group who would have complied with active treatment had they been allocated to it. We compare three estimators of the causal effect of treatment on compliers when this is a parameter in a proportional hazards model and quantify the bias due to omitting baseline prognostic factors. Causal estimates are found directly by maximising a novel partial likelihood; based on a structural proportional hazards model; and based on a ‘corrected dataset’ derived after fitting a rank-preserving structural failure time model. Where necessary, we extend these methods to incorporate baseline covariates. Comparisons use simulated data and a real data example. Analysing the simulated data, we found that all three methods are accurate when an important covariate was included in the proportional hazards model (maximum bias 5.4%). However, failure to adjust for this prognostic factor meant that causal treatment effects were underestimated (maximum bias 11.4%), because estimators were based on a misspecified marginal proportional hazards model. Analysing the real data example, we found that adjusting causal estimators is important to correct for residual imbalances in prognostic factors present between trial arms after randomisation. Our results show that methods of estimating causal treatment effects for time-to-event outcomes should be extended to incorporate covariates, thus providing an informative compliment to the corresponding intention-to-treat analysis. Copyright © 2012 John Wiley & Sons, Ltd.