Cluster Randomized and Multi-Level Designs
Quantify how within-cluster correlation inflates the sample size required for a cluster randomized trial. Enter the sample size that would be needed under individual randomization, the number of individuals per cluster, and the expected ICC. The calculator applies the standard design effect to show the inflation caused by clustering and the resulting number of clusters.
In a parallel cluster randomized trial with equal cluster sizes, the standard design effect is the factor by which the sample size from an individually randomized design is inflated to account for correlation among observations within the same cluster.
Here, m is the number of individuals per cluster and ρ is the intraclass correlation coefficient (ICC). When the ICC is zero, individuals within clusters are statistically independent and the design effect is 1. As the ICC or cluster size increases, the design effect increases and more participants are needed to obtain the same statistical information.
A cluster randomized trial cannot generally enroll a fractional cluster. Therefore, after applying the design effect, the calculator rounds the required number of clusters upward and reports the resulting achievable total sample size.
If individual-level attrition is anticipated, the calculator first inflates the cluster-adjusted sample size by dividing by the expected retention proportion. For example, 10% attrition corresponds to retaining 90% of enrolled participants.
The effective sample size expresses the information contained in the clustered sample on an approximately independent-observation scale. Before any additional attrition adjustment, it is obtained by dividing the actual clustered sample size by the design effect.
Validation example: Kerry and Bland report an ICC of 0.019 with 50 individuals per cluster. The published design effect is 1.93. The calculator evaluates 1 + (50 - 1)(0.019) = 1.931, which rounds to 1.93.
This calculator uses the simple equal-cluster-size design effect. It is intended for the standard parallel cluster design where the cluster size is reasonably constant. Unequal cluster sizes, stepped-wedge designs, multiple levels of clustering, covariate adjustment, cluster dropout, and other complex design features may require more specialized sample-size methods.
Donner, A., Birkett, N., & Buck, C. (1981). Randomization by cluster: Sample size requirements and analysis. American Journal of Epidemiology, 114(6), 906–914. doi:10.1093/oxfordjournals.aje.a113261.
Kerry, S. M., & Bland, J. M. (1998). The intracluster correlation coefficient in cluster randomisation. BMJ, 316, 1455.
Teerenstra, S., Eldridge, S., Graffy, J., van Achterberg, T., & van Tulder, M. (2015). Methods for sample size determination in cluster randomized trials. International Journal of Epidemiology, 44(3), 1051–1067.