Power and sample size of cluster randomized trials

This dissertation consists of three papers on clustered randomized clinical trials (CRTs). The first paper focuses on trials with two intervention groups of equal cluster size with a normally distributed outcome variable. We show that the number of clusters in each group and the cluster size contribute unequally to study power, and the number of clusters is the dominant factor. We also show the existence of an upper bound on power when the number of clusters is fixed and the cluster size tends to infinity. We report a minimum required number of clusters for a prespecified study power and cluster size. The minimum required number of clusters can serve as a feasibility criterion. We exploit our methods on the upper bound of power and indicate that a small increase in the number of clusters can substantially decrease the required cluster size.;The second paper focuses on the power and sample size of comparison of multiple intervention groups using analysis of variance (ANOVA). We provide power and sample size formulas under the framework of ANOVA in CRTs. We show all of the analogues to the two-group comparison in the multiple groups comparison, such as the importance of the number of clusters, the upper bound of power, and the minimum required number of clusters. We present the upper bound of power, the minimum required number of clusters, and cluster size.;The third paper focuses on trials with two groups when cluster size varies. We show that study power decreases with the coefficient of variation (CV) of cluster size for a given sample size. Again, we show that all of the analogues in the two-group comparison with equal cluster size apply to trials with unequal cluster size, such as the importance of the number of clusters, the upper bound of power, and the minimum required number of clusters. We present the upper bound of power, the minimum required number of clusters, and cluster size. We also investigate the relative efficiency of trials with un-equal versus equal cluster size.