The design of cluster randomized crossover trials

The inefficiency induced by between-cluster variation in cluster randomized
(CR) trials can be reduced by implementing a crossover (CO) design. In a
simple CO trial, each subject receives each treatment in random order. A
powerful characteristic of this design is that each subject serves as its own
control. In a CR CO trial, clusters of subjects are randomly allocated to a
sequence of interventions. Under this design, each subject is either included
in only one of the treatment periods (CO at cluster level) or in both periods
(CO at subject level). In this study, the efficiency of both CR CO trials relative
to the CR trial without CO is demonstrated. Furthermore, the optimal
allocation of clusters and subjects given a fixed budget or desired power
level is discussed.