A new dependence parameter approach to improve the design of cluster randomized trials with binary outcomes

Power and sample size calculations for cluster randomized trials require prediction of the degree of correlation that will be realized among outcomes of participants in the same cluster. This correlation is typically quantified as the intraclass correlation coefficient (ICC), defined as the Pearson correlation between two members of the same cluster or proportion of the total variance attributable to variance between clusters. It is widely known but perhaps not fully appreciated that for binary outcomes, the ICC is a function of outcome prevalence. Hence, the ICC and the outcome prevalence are intrinsically related, making the ICC poorly generalizable across study conditions and between studies with different outcome prevalences.

We use a simple parametrization of the ICC that aims to isolate that part of the ICC that measures dependence among responses within a cluster from the outcome prevalence. We incorporate this parametrization into sample size calculations for cluster randomized trials and compare our method to the traditional approach using the ICC.

Our dependence parameter, R, may be less influenced by outcome prevalence and has an intuitive meaning that facilitates interpretation. Estimates of R from previous studies can be obtained using simple statistics. Comparison of methods showed that the traditional ICC approach to sample size determination tends to overpower studies under many scenarios, calling for more clusters than truly required.

The methods are developed for equal-sized clusters, whereas cluster size may vary in practice.

The dependence parameter R is an alternative measure of dependence among binary outcomes in cluster randomized trials that has a number of advantages over the ICC.