Meta-Analysis of Time-to-Event Data Using Non-Parametric Measures

In survival analysis, Kaplan-Meier is by far the most popular non-parametric method of estimating survival probabilities. However, in meta-analysis of time-to-event data, various proposed non-parametric methods of pooling the estimates from multiple studies co-exist, yet still lack universal acceptance. For this purpose, methodology for the meta-analysis of individual patient data with survival end-points is being evaluated, using non-parametric measures. We tackle the problem of combining information from independent two-armed trials in order to compare survival distributions, taking censoring into account. We do not rely on the proportionality, since such a simultaneous assumption across studies may seem arbitrary. To this end, three approaches based on the median ratio, the restricted mean survival time (RMST) and the use of the log(-log) survival function difference, are considered. A detailed guideline on how to implement these measures in a meta-analytic framework is presented, with the aim being to gain an appropriate non-parametric estimator and its corresponding weighting factor. Concerning the latter, we utilize traditional, asymptotic techniques and we also propose an alternative procedure via bootstrapping. We illustrate our methodology via simulation experiments, under various distributional schemes and censoring levels. Finally, the performance of these measures is tested under the assumption of small treatment effects. Simulations show that all three meta-analytic approaches produce similar results with mild levels of bias. The RMST produces the most robust results, consistently across the different scenarios studied. Nevertheless, all three measures share the same qualitative behavior and can offer insights as a useful preliminary analysis.