How to design efficient cluster randomised trials

Abstract

Cluster randomised trials have diminishing returns in power and precision as cluster size increases. Making the cluster a lot larger while keeping the number of clusters fixed might yield only a very small increase in power and precision, owing to the intracluster correlation. Identifying the point at which observations start making a negligible contribution to the power or precision of the study—which we call the point of diminishing returns—is important for designing efficient trials. Current methods for identifying this point are potentially useful as rules of thumb but don’t generally work well. We introduce several practical aids to help researchers design cluster randomised trials in which all observations make a material contribution to the study. Power curves enable identification of the point at which observations begin to make a negligible contribution to a study for a given target difference. Under this paradigm, the number needed per arm under individual randomisation gives an upper bound on the cluster size, which should not be exceeded. Corresponding precision curves can be useful for accommodating flexibility in the choice of target difference and show the point at which confidence intervals around the estimated effect size no longer decrease. To design efficient trials, the number of clusters and cluster size should be determined concurrently, not independently. Funders and researchers should be aware of diminishing returns in cluster trials. Researchers should routinely plot power or precision curves when performing sample size calculations so that the implications of cluster sizes can be transparent. Even when data appear to be “free,” in the sense that few resources are needed to obtain the data, excessive cluster sizes can have important ramifications