An issue of statistical analysis in controlled multi-centre studies: how shall we weight the centres?

When analysing data from a controlled multi-centre study, an important issue is how to weight each centre to assess the overall treatment effect. The unweighted analysis, which weights all centres equally, was recommended by many statisticians and the U.S. Food and Drug Administration, and has been routinely utilized as the primary statistical method for many phase III clinical studies in the pharmaceutical industry. The weighted analysis, which weights centres relative to the number of patients in them, was considered not meaningful in the presence of treatment-by-centre interaction. This paper demonstrates why we should hesitate to use the unweighted analysis as the primary statistical method of a study from a statistical power perspective. It also shows that the weighted analysis is meaningful, even in the presence of treatment-by-centre interaction, and that it is generally the preferred approach.