Statistical power and sample size requirements for three level hierarchical cluster randomized trials

Cluster randomized clinical trials (cluster-RCT), where the community entities serve as clusters, often yield data with three hierarchy levels. For example, interventions are randomly assigned to the clusters (level three unit). Health care professionals (level two unit) within the same cluster are trained with the randomly assigned intervention to provide care to subjects (level one unit). In this study, we derived a closed form power function and formulae for sample size determination required to detect an intervention effect on outcomes at the subject's level. In doing so, we used a test statistic based on maximum likelihood estimates from a mixed-effects linear regression model for three level data. A simulation study follows and verifies that theoretical power estimates based on the derived formulae are nearly identical to empirical estimates based on simulated data. Recommendations at the design stage of a cluster-RCT are discussed.