Meta-analysis of time-to-event outcomes using a hazard-based approach: Comparison with other models, robustness and meta-regression

The goal of meta-analysis is to provide a full and comprehensive summary of related studies which have addressed a similar question. A joint analysis of survival probabilities reported at a predetermined set of time points for a number of published studies is presented by employing three different models: two generalized linear models with normal errors, the first with fixed effects only, the second with additional random effects, and finally a hazard-based approach using a Poisson correlated gamma frailty model. Each trial contributing to the meta-analysis provides several survival proportions for each treatment. Such values clearly cannot be treated as independent data but correlations between them can be incorporated using a mixed model approach. The three methods are illustrated with data from 17 randomized controlled trials that tested the addition of chemotherapy to radiotherapy in postoperative malignant glioma in adults. A second issue addressed concerns the robustness of the Poisson correlated gamma frailty model under departures from the assumptions on censoring mechanism and on length of follow-up of each trial involved in the meta-analysis. In order to study this aspect of the Poisson correlated gamma frailty model a sensitivity analysis is performed. Results from the analysis show that the model is robust. The last issue described deals with the problem of heterogeneity between studies since it is well known that exploring the possible reasons for heterogeneity is an important aspect of conducting a meta-analysis. The causes of heterogeneity can be investigated by employing covariates at the study level. To exploit this aspect the Poisson correlated gamma frailty model is used for a meta-regression analysis of published survival curves on breast cancer data. The analysis performed has shown that the random effects model presents less variability when study-level covariates are incorporate in the model.