Generalized linear mixed models (GLMM) are commonly used to analyze clustered data, but when the number of clusters is small to moderate, standard statistical tests may produce elevated type I error rates. Small-sample corrections have been proposed for continuous or binary outcomes without covariate adjustment. However, appropriate tests to use for count outcomes or under covariate-adjusted models remains unknown. An important setting in which this issue arises is in cluster-randomized trials (CRTs). Because many CRTs have just a few clusters (e.g., clinics or health systems), covariate adjustment is particularly critical to address potential chance imbalance and/or low power (e.g., adjustment following stratified randomization or for the baseline value of the outcome). We conducted simulations to evaluate GLMM-based tests of the treatment effect that account for the small (10) or moderate (20) number of clusters under a parallel-group CRT setting across scenarios of covariate adjustment (including adjustment for one or more person-level or cluster-level covariates) for both binary and count outcomes. We find that when the intraclass correlation is non-negligible ($\geq 0.01$) and the number of covariates is small ($\leq 2$), likelihood ratio tests with a between-within denominator degree of freedom have type I error rates close to the nominal level. When the number of covariates is moderate ($\geq 5$), across our simulation scenarios, the relative performance of the tests varied considerably and no method performed uniformly well. Therefore, we recommend adjusting for no more than a few covariates and using likelihood ratio tests with a between-within denominator degree of freedom.

翻译：广义线性混合模型（GLMM）常用于分析聚类数据，但当簇群数量较少或中等时，标准统计检验可能导致第一类错误率升高。针对无协变量调整的连续或二元结局变量，已有学者提出小样本校正方法。然而，适用于计数结局变量或协变量调整模型下的恰当检验方法仍属未知。这一问题在群组随机试验（CRTs）中尤为突出——由于许多CRT仅包含少数簇群（如诊所或卫生系统），协变量调整对于应对潜在的不平衡性和/或低统计效力（例如分层随机化后的调整或对结局基线值的调整）至关重要。我们通过模拟研究，在平行组CRT场景下评估了基于GLMM的治疗效应检验方法。研究考虑了小规模（10个）或中等规模（20个）簇群数量，并涵盖二元结局与计数结局变量在协变量调整（包括调整一个或多个个体水平或簇群水平协变量）下的多种情境。研究发现：当组内相关系数不可忽略（$\geq 0.01$）且协变量数量较少（$\leq 2$）时，采用组间-组内分母自由度的似然比检验的第一类错误率接近名义水平；当协变量数量中等（$\geq 5$）时，各模拟场景下检验方法的相对表现差异显著，未发现任何方法具有普适优越性。因此，我们建议调整的协变量不超过三个，并优先采用组间-组内分母自由度的似然比检验。