Individual patient data meta-analysis of time-to-event outcomes: one-stage versus two-stage approaches for estimating the hazard ratio under a random effects model.

Meta-analyses of individual patient data (IPD) provide a strong and authoritative basis for evidence synthesis. IPD are particularly useful when the outcome of interest is the time to an event. Methodological developments now enable the meta-analysis of time-to-event IPD using a single model, allowing treatment effect and across-trial heterogeneity parameters to be estimated simultaneously. This differs from the standard approaches used with aggregate data, and also predominantly with IPD. Facilitated by a simulation study, we investigate what these new 'one-stage' random-effects models offer over standard 'two-stage' approaches. We find that two-stage approaches represent a robust, reliable and easily implementable way to estimate treatment effects and account for heterogeneity. Nevertheless, one-stage models can be used to provide a deeper insight into the data. Software for fitting one-stage Cox models with random effects using Restricted Maximum Likelihood methodology is made available, and its use demonstrated on an IPD meta-analysis assessing post-operative radio therapy for patients with non-small cell lung cancer.