Generalized linear mixed models (GLMM) are a popular tool 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 to address this issue 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:普通线性混合模型(GLMM)是分析集群数据的一种流行工具,但当集群数量小到中等时,标准统计测试可能会产生高一级I型误差率;建议进行小规模的抽样更正,以解决这个问题,而不作连续或二进制结果的调整;然而,用于计数结果或按千变式调整模型(GLMM)使用的适当测试仍然未知;出现这一问题的一个重要环境是分组调整试验(CRTs)中出现的问题。由于许多CRTs只有几组(例如诊所或卫生系统),因此对于解决潜在概率失衡和/或低功率(例如,在分级随机随机调整后进行调整或结果的基线值值);我们进行了模拟,以评价基于GLMMM对计算结果或按千变式调整模型计算结果的处理效果进行的适当测试;在组平行组合CRT(CRTs)中,在组合调整的情景中(包括一个或更多的人级或组级差数调整),对于二进和计结果而言,共变差率调整对于解决潜在的概率差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差差