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Evaluating tests for cluster-randomized trials with few clusters under generalized linear mixed models with covariate adjustment: a simulation study
Hongxiang Qiu, Andrea J. Cook, Jennifer F. Bobb
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Generalized linear mixed models (GLMM) are commonly used to analyze clustered data, but when the number of clusters is small to moderate, standard statistical tests may produce elevated type I error rates. Small-sample corrections have been proposed for continuous or binary outcomes without covariate adjustment. However, appropriate tests to use for count outcomes or under covariate-adjusted models remains unknown. An important setting in which this issue arises is in cluster-randomized trials (CRTs). Because many CRTs have just a few clusters (e.g., clinics or health systems), covariate adjustment is particularly critical to address potential chance imbalance and/or low power (e.g., adjustment following stratified randomization or for the baseline value of the outcome). We conducted simulations to evaluate GLMM-based tests of the treatment effect that account for the small (10) or moderate (20) number of clusters under a parallel-group CRT setting across scenarios of covariate adjustment (including adjustment for one or more person-level or cluster-level covariates) for both binary and count outcomes. We find that when the intraclass correlation is non-negligible (≥0.01) and the number of covariates is small (≤2), likelihood ratio tests with a between-within denominator degree of freedom have type I error rates close to the nominal level. When the number of covariates is moderate (≥5), across our simulation scenarios, the relative performance of the tests varied considerably and no method performed uniformly well. Therefore, we recommend adjusting for no more than a few covariates and using likelihood ratio tests with a between-within denominator degree of freedom.
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