Meta-analysis of two-arm studies: Modeling the intervention effect from survival probabilities

Pooling the hazard ratios is not always feasible in meta-analyses of two-arm survival studies, because the measure of the intervention effect is not systematically reported. An alternative approach proposed by Moodie et al. is to use the survival probabilities of the included studies, all collected at a single point in time: the intervention effect is then summarised as the pooled ratio of the logarithm of survival probabilities (which is an estimator of the hazard ratios when hazards are proportional). In this article, we propose a generalization of this method. By using survival probabilities at several points in time, this generalization allows a flexible modeling of the intervention over time. The method is applicable to partially proportional hazards models, with the advantage of not requiring the specification of the baseline survival. As in Moodie et al.'s method, the study-level factors modifying the survival functions can be ignored as long as they do not modify the intervention effect. The procedures of estimation are presented for fixed and random effects models. Two illustrative examples are presented.