Meta-analysis of time-to-event data: a comparison of two-stage methods

Meta-analysis is widely used to synthesise results from randomised trials. When the relevant trials collected time-to-event data, individual participant data are commonly sought from all trials. Meta-analyses of time-to-event data are typically performed using variants of the log-rank test, but modern statistical software allows for the use of maximum likelihood methods such as Cox proportional hazards models or interval-censored logistic regression. In this paper, the different approaches to the analysis of time-to-event data are examined and compared with show that log-rank test approaches are in fact first-order approximations to the maximum likelihood methods and that some methods assume proportional hazards, whereas others assume proportional odds. A simulation study is performed to compare the different methods, which shows that log-rank test approaches give biased estimates when the underlying hazard ratio or odds ratio is far from unity. It also shows that proportional hazards methods give biased results when hazards are not proportional, and proportional odds methods give biased results when odds are not proportional. Maximum likelihood models should, therefore, be preferred to log-rank test based methods for the meta-analysis of time-to-event data and any such meta-analysis should investigate whether proportional hazards or proportional odds assumptions are valid. Copyright © 2011 John Wiley & Sons, Ltd.