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In the analyses of cluster-randomized trials, mixed-model analysis ofcovariance (ANCOVA) is a standard approach for covariate adjustment andhandling within-cluster correlations. However, when the normality, linearity,or the random-intercept assumption is violated, the validity and efficiency ofthe mixed-model ANCOVA estimators for estimating the average treatment effectremain unclear. Under the potential outcomes framework, we prove that themixed-model ANCOVA estimators for the average treatment effect are consistentand asymptotically normal under arbitrary misspecification of its workingmodel. If the probability of receiving treatment is 0.5 for each cluster, wefurther show that the model-based variance estimator under mixed-model ANCOVA1(ANCOVA without treatment-covariate interactions) remains consistent,clarifying that the confidence interval given by standard software isasymptotically valid even under model misspecification. Beyond robustness, wediscuss several insights on precision among classical methods for analyzingcluster-randomized trials, including the mixed-model ANCOVA, individual-levelANCOVA, and cluster-level ANCOVA estimators. These insights may inform thechoice of methods in practice. Our analytical results and insights areillustrated via simulation studies and analyses of three cluster-randomizedtrials.

On the mixed-model analysis of covariance in cluster-randomized trials