Abstract
Background: The use of cluster randomized trials (CRTs) is increasing, along with the variety in their design and analysis. The simplest approach for their sample size calculation is to calculate the sample size assuming individual randomization and inflate this by a design effect to account for randomization by cluster. The assumptions of a simple design effect may not always be met; alternative or more complicated approaches are required.Methods: We summarise a wide range of sample size methods available for cluster randomized trials. For those familiar with sample size calculations for individually randomized trials but with less experience in the clustered case, this manuscript provides formulae for a wide range of scenarios with associated explanation and recommendations. For those with more experience, comprehensive summaries are provided that allow quick identification of methods for a given design, outcome and analysis method.Results: We present first those methods applicable to the simplest two-arm, parallel group, completely randomized design followed by methods that incorporate deviations from this design such as: variability in cluster sizes; attrition; non-compliance; or the inclusion of baseline covariates or repeated measures. The paper concludes with methods for alternative designs.Conclusions: There is a large amount of methodology available for sample size calculations in CRTs. This paper gives the most comprehensive description of published methodology for sample size calculation and provides an important resource for those designing these trials.
Highlights
Cluster randomized trials In a cluster randomized trial, groups or clusters, rather than individuals, are randomly allocated to intervention groups
There may be situations where there are no good estimates of the intracluster correlation coefficient (ICC) available for sample size calculations
The main criteria for use of a stepped-wedge design is when the implementation of the intervention can only be performed sequentially across clusters, perhaps due to resource constraints, and when the intervention is believed to do more good than harm and so it would be considered unethical for some clusters to not receive the intervention at some point during the trial
Summary
Cluster randomized trials In a cluster randomized trial, groups or clusters, rather than individuals, are randomly allocated to intervention groups. Simple methods are available for continuous and binary outcomes that use the coefficient of variation in outcome as a measure of correlation and assume a cluster-level analysis.[27] For continuous outcomes where l1 and l2 are the means in the control and intervention group, respectively, and r1 and r2 the associated within-cluster standard deviations, the number of clusters per group is shown as c þ. There may be situations where there are no good estimates of the ICC available for sample size calculations This occurred in a trial of mental illness because the outcome measure was a newly adaptive questionnaire with unknown properties.[48] In these situations, several approaches might be considered: an educated estimate could be gained from assessment of published ICCs and known patterns in their behaviour for different outcome types and clusters; graphical methods that compare competing designs without requiring knowledge of the ICC49; or an internal pilot could be considered (see later section). Where c represents the number of clusters per group, ni the size of cluster i and n mean cluster size
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