A Bayesian hierarchical survival model for the institutional effects in a multi-centre cancer clinical trial

In randomized clinical trials comparing treatment effects on diseases such as cancer, a multi-centre trial is usually conducted to accrue the required number of patients in a reasonable period of time. While we interpret the average treatment effect, it is necessary to examine the homogeneity of the observed treatment effects across institutions, that is, treatment-by-institution interaction. If the homogeneity is confirmed, the conclusions concerning treatment effects can be generalized to a broader patient population. In this paper, a Bayesian hierarchical survival model is used to investigate the institutional effects on the efficacy of treatment as well as on the baseline risk. The marginal posterior distributions are estimated by a Markov chain Monte Carlo method, that is, Gibbs sampling, to overcome current computational limitations. The robustness of the inferences to the distributional assumption for the random effects is also examined. We illustrate the methods with analyses of data from a multi-centre cancer clinical trial, which investigated the efficacy of immunochemotherapy as an adjuvant treatment after curative resection of gastric cancer. In this trial there is little difference in the treatment effects across institutions and the treatment is shown to be effective, while there appears to be substantial variation in the baseline risk across institutions. This result indicates that the observed treatment effects might be generalized to a broader patient population.