Bayesian adjusted R2 for the meta-analytic evaluation of surrogate time-to-event endpoints in clinical trials

A two-stage model for evaluating both trial-level and patient-level surrogacy of correlated time-to-event endpoints has been introduced, using patient-level data when multiple clinical trials are available. However, the associated maximum likelihood approach often suffers from numerical problems when different baseline hazards among trials and imperfect estimation of treatment effects are assumed. To address this issue, we propose performing the second-stage, trial-level evaluation of potential surrogates within a Bayesian framework, where we may naturally borrow information across trials while maintaining these realistic assumptions. Posterior distributions on surrogacy measures of interest may then be used to compare measures or make decisions regarding the candidacy of a specific endpoint. We perform a simulation study to investigate differences in estimation performance between traditional maximum likelihood and new Bayesian representations of common meta-analytic surrogacy measures, while assessing sensitivity to data characteristics such as number of trials, trial size, and amount of censoring. Furthermore, we present both frequentist and Bayesian trial-level surrogacy evaluations of time to recurrence for overall survival in two meta-analyses of adjuvant therapy trials in colon cancer. With these results, we recommend Bayesian evaluation as an attractive and numerically stable alternative in the multitrial assessment of potential surrogate endpoints.