Multi-centre trial analysis revisited

Analyses of multi-centre trials must consider the effects of the individual centres and the possibility of non-constancy of treatment effect differences among centres. This usually means an ANOVA with terms for centres, treatments, and centre x treatment interactions in practice, at least in the U.S.A. Empirical and conventional Bayes methods provide attractive alternatives to conventional ANOVAs for analysing and reporting the findings from multi-centre trials and do not require more restrictive assumptions than the ANOVA approach. These approaches require regarding the centre effects as random instead of fixed, a view which often will reasonably describe outcomes of clinical trials in spite of the fact that the individual centres certainly do not comprise a random sample of all possible centres. The components of these approaches are well understood and have been employed in related applications such as meta-analysis. Combining them in a way that makes their application to routine multi-centre trial analysis relatively straightforward does not appear to have been described previously, and is what forms the topic of this paper. The empirical Bayes approach leads to useful graphical displays, including one with the data superimposed on probability contours of the joint distribution of the individual centre means and standard deviations, which provides a handy way to identify possible outliers. Covariates can be incorporated without difficulty. The Bayes approach, implemented with Gibbs sampling, provides a convenient way to construct posterior and predictive distributions for a variety of useful statistics. We compare the result of empirical and conventional Bayes analyses with the result of fixed and mixed model ANOVAs applied to data from a multi-centre trial.