![]() The Residual and Containment methods have inflated type I error rates when the cluster number is small (<30) and the inflation becomes more severe with increased variation in cluster sizes. Our simulation results suggest that the Between-Within method maintains the nominal type I error rates even when the total number of clusters is as low as 10 and is robust to the variation of the cluster sizes. The results are also illustrated using a real CRT dataset. ![]() Specifically, we illustrate how the intraclass correlation (ICC), sample size, and the variation of cluster sizes affect the type I error and statistical power when different DDF approximation methods in GLMM are used to test intervention effect in CRTs with binary outcomes. ![]() The small sample performances of five DDF approximations for the F test are compared and contrasted under CRT frameworks with simulations. Some DDF approximation methods have been proposed, but their small sample performances in analysing binary outcomes in CRTs with few heterogeneous clusters are not well studied. The most challenging issue for the approximate Wald F test is the estimation of the denominator degrees of freedom (DDF). F tests are commonly used in the generalized linear mixed model (GLMM) to test intervention effects in CRTs. Small number of clusters and large variation of cluster sizes commonly exist in cluster-randomized trials (CRTs) and are often the critical factors affecting the validity and efficiency of statistical analyses.
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