The Design of Cluster Randomized Trials With Random Cross-Classifications

Data from cluster randomized trials do not always have a pure hierarchical structure. For instance, students are nested within schools that may be crossed by neighborhoods, and soldiers are nested within army units that may be crossed by mental health–care professionals. It is important that the random cross-classification is taken into account while planning a cluster randomized trial. This article presents sample size equations, such that a desired power level is achieved for the test on treatment effect. Furthermore, it also presents optimal sample sizes given a budgetary constraint, with a special focus on conditional optimal designs where one of the sample sizes is fixed beforehand. The optimal design methodology is illustrated using a postdeployment training to reduce ill-health in armed forces personnel.