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Calculating sample sizes for cluster randomized trials: we can keep it simple and efficient!
Gerard J P van Breukelen1, Math J J M Candel
1Department of Methodology and Statistics, CAPHRI School for Public Health and Primary Care, Maastricht University, Maastricht, The Netherlands. gerard.vbreukelen@maastrichtuniversity.nl
Objective:
Simple guidelines for calculating efficient sample sizes in cluster randomized trials with unknown intraclass correlation (ICC) 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 ICC of the 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, desired power, and effect size only affect the number of clusters and not the sample size per cluster, which is between 7 and 70 for a wide range of cost ratios and ICCs. Power loss because of cluster size variation is compensated by sampling 10% more clusters. The optimal design for the ICC halfway the range of realistic ICC values is a good choice for the first stage of a two-stage design. The second stage is needed only if the first stage shows the ICC to be higher than assumed.
Conclusion:
Efficient sample sizes for cluster randomized trials are easily computed, provided the cost per cluster and cost per person are specified.
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