  In the analyses of cluster-randomized trials, mixed-model analysis of
covariance (ANCOVA) is a standard approach for covariate adjustment and
handling within-cluster correlations. However, when the normality, linearity,
or the random-intercept assumption is violated, the validity and efficiency of
the mixed-model ANCOVA estimators for estimating the average treatment effect
remain unclear. Under the potential outcomes framework, we prove that the
mixed-model ANCOVA estimators for the average treatment effect are consistent
and asymptotically normal under arbitrary misspecification of its working
model. If the probability of receiving treatment is 0.5 for each cluster, we
further 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 is
asymptotically valid even under model misspecification. Beyond robustness, we
discuss several insights on precision among classical methods for analyzing
cluster-randomized trials, including the mixed-model ANCOVA, individual-level
ANCOVA, and cluster-level ANCOVA estimators. These insights may inform the
choice of methods in practice. Our analytical results and insights are
illustrated via simulation studies and analyses of three cluster-randomized
trials.
