Evaluating Informative Cluster Size in Cluster Randomized Trials

In cluster randomized trials, the individual-average treatment effect (i-ATE) can be different from the cluster-average treatment effect (c-ATE) when informative cluster size (ICS) is present, that is, when treatment effects or participant outcomes depend on cluster size. In such scenarios, mixed-effects models and generalized estimating equations (GEEs) with exchangeable correlation structure are biased for both the i-ATE and c-ATE estimands, whereas GEEs with an independence correlation structure or analyses of cluster-level summaries are recommended in practice. However, when cluster size is non-informative, mixed-effects models and GEEs with exchangeable correlation structure can provide unbiased estimation and notable efficiency gains over other methods. Thus, hypothesis tests for ICS would be useful to assess this key phenomenon under cluster randomization. In this work, we develop model-based, model-assisted, and randomization-based tests for ICS in cluster randomized trials. We conduct simulation studies to examine the operating characteristics of these tests, show they have appropriate Type I error rate control and meaningful power, and contrast them to existing model-based tests used in the observational study setting. The proposed tests are then applied to data from a recent cluster randomized trial, and practical recommendations for using these tests are discussed.