Sample size requirements for evaluating intervention effects in three-level cluster randomized clinical trials

Experimental clinical trial settings are now often extended to community entities beyond academic research centers. In such settings, a cluster randomized clinical trial (cluster-RCT) design can be useful to rigorously test the effectiveness of a new intervention. Investigators are most commonly interested in assessing the following three types of intervention effects: overall intervention effect, change in intervention effect over time, and local intervention effect at the end of the study. At the design stage of the cluster-RCT, it is essential to estimate a sample size sufficient for adequate statistical power to evaluate the different intervention effects. However, the sample size estimation must account for the multilevel data structure that is necessitated by the nature of the cluster-RCT design. In this review, we consider a three-level data structure and summarize sample size approaches for testing intervention effects within a unified framework of mixedeffects linear models which offer flexibility in the analysis of multilevel data and hypotheses testing in a cluster-RCT. The sample size methods are presented in closed form and have been validated by simulation studies. Important features of sample size determination for each primary hypothesis are also discussed.