Design and Analysis Considerations for Cluster Randomized Controlled Trials That Have a Small Number of Clusters
Cluster randomized controlled trials (CRCTs) often require a large number of clusters in order to detect small effects with high probability. However, there are contexts where it may be possible to design a CRCT with a much smaller number of clusters (10 or fewer) and still detect meaningful effects.
The objective is to offer recommendations for best practices in design and analysis for small CRCTs.
I use simulations to examine alternative design and analysis approaches. Specifically, I examine (1) which analytic approaches control Type I errors at the desired rate, (2) which design and analytic approaches yield the most power, (3) what is the design effect of spurious correlations, and (4) examples of specific scenarios under which impacts of different sizes can be detected with high probability.
I find that (1) mixed effects modeling and using Ordinary Least Squares (OLS) on data aggregated to the cluster level both control the Type I error rate, (2) randomization within blocks is always recommended, but how best to account for blocking through covariate adjustment depends on whether the precision gains offset the degrees of freedom loss, (3) power calculations can be accurate when design effects from small sample, spurious correlations are taken into account, and (4) it is very difficult to detect small effects with just four clusters, but with six or more clusters, there are realistic circumstances under which small effects can be detected with high probability.
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