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.

翻译：在整群随机试验的分析中，混合模型协方差分析（ANCOVA）是进行协变量调整和处理群内相关性的标准方法。然而，当正态性、线性性或随机截距假设被违反时，混合模型ANCOVA估计量对平均处理效应估计的有效性和效率仍不明确。在潜在结果框架下，我们证明混合模型ANCOVA估计量在任意工作模型错误设定下对平均处理效应仍具有一致性和渐近正态性。若每个集群接受处理的概率为0.5，我们进一步证明混合模型ANCOVA1（不含处理-协变量交互项的ANCOVA）下基于模型的方差估计量仍保持一致，阐明标准软件给出的置信区间即使在模型错误设定下也渐近有效。除稳健性外，我们讨论了几种经典分析方法（包括混合模型ANCOVA、个体水平ANCOVA和集群水平ANCOVA估计量）在分析整群随机试验时的精度差异。这些见解可为实践中的方法选择提供参考。通过模拟研究和三个整群随机试验的分析，我们对分析结果和见解进行了验证。