Calculating sample sizes for cluster randomized trials: we can keep it simple and efficient !

Objective: Simple guidelines for efficient sample sizes in cluster randomized trials with unknown intraclass correlation and varying cluster sizes. Methods: A simple equation is given for the optimal number of clusters and sample size per cluster. Here, optimal means maximizing power for a given budget, or minimizing total cost for a given power. The problems of cluster size variation and specification of the intraclass correlation (ICC) outcome are solved in a simple yet efficient way. Results: The optimal number of clusters goes up, and the optimal sample size per cluster, goes down, as the ICC goes up or as the cluster-to-person cost ratio goes down. The available budget and desired power affect the optimal number of clusters, but not the optimal sample size per cluster. Power loss due to cluster size variation is compensated by sampling 10% more clusters. The optimal design for the ICC value halfway the range of realistic ICC values is efficient for the whole range. Conclusions: Efficient sample sizes for cluster randomized trials are easily computed, provided the cost per cluster and per person can be specified. keywords: cluster randomized trials, sample size, power, efficient design, intraclass correlation, varying cluster size