Proportional hazards models with random effects to examine centre effects in multicentre cancer clinical trials

In randomized clinical trials comparing treatment effects on diseases such as cancer, a multicentre trial is usually conducted to accrue the required number of patients within a reasonable period of time. The fundamental point of conducting a multicentre trial is that all participating investigators must agree to follow the common study protocol. However, even with every attempt having been made to standardize the methods for diagnosing severity of disease and evaluating response to treatment, for example, they might be applied differently at different centres, and these may vary from comprehensive cancer centres to university hospitals to community hospitals. Therefore, in multicentre trials there is likely to be some degree of variation (heterogeneity) among centres in both the baseline risks and the treatment effects. While we estimate the overall treatment effect using a summary measure such as hazard ratio and usually interpret it as an average treatment effect over the centre, it is necessary to examine the homogeneity of the observed treatment effects across centres, that is, treatment-by-centre interaction. If the data are reasonably consistent with homogeneity of the observed treatment effects across centres, a single summary measure is adequate to describe the trial results and those results will contribute to the scientific generalization, the process of synthesizing knowledge from observations. On the other hand, if heterogeneity of treatment effects is found, we should carefully interpret the trial results and investigate the reason why the variation is seen. In the analyses of multicentre trials, a random effects approach is often used to model the centre effects. In this article, we focus on the proportional hazards models with random effects to examine centre variation in the treatment effects as well as the baseline risks, and review the parameter estimation procedures, frequentist approach-penalized maximum likelihood method--and Bayesian approach--Gibbs sampling method. We also briefly review the models for bivariate responses. We present a few real data examples from the biometrical literature to highlight the issues.