Measures of between-cluster variability in cluster randomized trials with binary outcomes.

Cluster randomized trials (CRTs) are increasingly used to evaluate the effectiveness of health-care interventions. A key feature of CRTs is that the observations on individuals within clusters are correlated as a result of between-cluster variability. Sample size formulae exist which account for such correlations, but they make different assumptions regarding the between-cluster variability in the intervention arm of a trial, resulting in different sample size estimates. We explore the relationship for binary outcome data between two common measures of between-cluster variability: k, the coefficient of variation and rho, the intracluster correlation coefficient. We then assess how the assumptions of constant k or rho across treatment arms correspond to different assumptions about intervention effects. We assess implications for sample size estimation and present a simple solution to the problems outlined.