Statistical analysis and optimal design for cluster randomized trials

In many intervention studies, therapy outcome evaluations, and educational field trials, random treatment assignment of clusters rather than persons is desirable for political feasibility, logistics, or ecological validity. However, cluster randomized designs are widely regarded as lacking statistical precision. This article considers when and to what extent using a pretreatment covariate can increase experimental precision. To answer this question, the author first optimizes allocation of resources within and between clusters for the no-covariate case. Optimal sample sizes at each level depend on variation within and between clusters and on the cost of sampling at each level. Next, the author considers optimal allocation when a covariate is added. In this case, the explanatory power of the covariate at each level becomes highly relevant for choosing optimal sample sizes. A key conclusion is that statistical analysis that fully uses information about the covariate-outcome relationship can substantially increase the efficiency of the cluster randomized trial, especially when the cost of sampling clusters is high and the covariate accounts for substantial variation between clusters. Recent multilevel studies indicate that these conditions are common.