In the analyses of cluster-randomized trials, a standard approach for
covariate adjustment and handling within-cluster correlations is the
mixed-model analysis of covariance (ANCOVA). The mixed-model ANCOVA makes
stringent assumptions, including normality, linearity, and a compound symmetric
correlation structure, which may be challenging to verify and may not hold in
practice. When mixed-model ANCOVA assumptions are violated, the validity and
efficiency of the model-based inference for the average treatment effect are
currently unclear. In this article, we prove that the mixed-model ANCOVA
estimator for the average treatment effect is consistent and asymptotically
normal under arbitrary misspecification of its working model. Under equal
randomization, we further show that the model-based variance estimator for the
mixed-model ANCOVA estimator remains consistent, clarifying that the confidence
interval given by standard software is asymptotically valid even under model
misspecification. Beyond robustness, we also provide a caveat that covariate
adjustment via mixed-model ANCOVA may lead to precision loss compared to no
adjustment when the covariance structure is misspecified, and describe when a
cluster-level ANCOVA becomes more efficient. These results hold under both
simple and stratified randomization, and are further illustrated via
simulations as well as analyses of three cluster-randomized trials