Optimal Sample Sizes in Experimental Designs With Individuals Nested Within Clusters

This article deals with optimal sample sizes for experimental studies with individuals nested within clusters. Examples are multicenter clinical trials with patients nested within clinics or family practices, studies on absence due to illness with employees nested within work sites, or school-based smoking prevention interventions with pupils nested within schools. Optimal sample sizes are given for models with continuous or binary outcomes and for 1 or 2 treatment factors. Because individuals are nested within clusters, not only the total number of individuals needed to obtain a specified power of the test of treatment effect has to be established but also the number of clusters and the number of individuals per cluster. We show that different outcome variables lead to different optimal sample sizes. Furthermore, the statistically optimal design is not always feasible in practice because of certain limitations, and we show how to calculate the optimal design given restrictions on the sample sizes at both the cluster and individual level. Also, the dropout of clusters and individuals are taken into account.