Balance in cluster randomized trials

This paper explores the role of balancing covariates between treatment groups in the design of cluster randomized trials. General expressions are obtained for two criteria to evaluate designs for parallel group studies with two treatments. The first is the variance of the estimated treatment effect and the second is the extent to which the estimated treatment effect is changed by adjusting for covariates. It is argued that the second of these is more important for cluster randomized trials. Methods of obtaining balanced designs from covariates which are available at the start of a study are proposed. An imbalance measure is used to compare the extent to which designs balance important covariates between the arms of a trial. Several approaches to selecting a well balanced design are possible. A method that randomly selects one member from the class of designs with acceptable bias will allow randomization inference as well as model-based inference. The methods are illustrated with data from a trial of school-based sex education.