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

Abstract

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