Abstract The bivariate normal multilevel model (MLM) provides a flexible modelling framework for cost- effectiveness analyses (CEAs) alongside cluster randomized trials (CRTs) as well as for sample size calculations of these trials. The bivariate MLM assumes a joint normal distribution for effects and costs, both within (individual level) and between (cluster level) clusters. A typical problem in CEAs is that costs are often associated with right- skewed distributions (e.g., gamma or lognormal), which make it sometimes difficult to justify the modelling of the data based on normality assumptions. The robustness of CEAs of CRTs based on the bivariate normal MLM to non-normal cost distributions at both cluster and individual level are investigated. Normal, gamma, and lognormal distributions are considered using scenarios that differ in the number of clusters, the number of persons per cluster, the covariance parameters of the model, and the level of skewness in the cost data. It is shown that CEA of CRTs, and therefore sample size calculation, based on the bivariate normal MLM, is quite robust against highly skewed costs across a wide range of scenarios. This robustness holds especially with respect to the type I error rate and the power. In terms of bias in variance component estimation and standard errors of fixed effects, large bias can occur in small samples. However, these biases do not appear to translate into any serious deviation of the type I error rate or power from the nominal level.

中文翻译：

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假设对偏斜成本数据采用双变量正态性，整群随机试验的成本效益分析的稳健性

摘要 双变量正态多级模型 (MLM) 为成本效益分析 (CEA) 以及集群随机试验 (CRT) 以及这些试验的样本量计算提供了灵活的建模框架。双变量 MLM 假设效应和成本的联合正态分布，在（个体级别）集群内和（集群级别）集群之间。CEA 中的一个典型问题是成本通常与右偏分布（例如，伽玛或对数正态分布）相关联，这使得有时难以根据正态性假设来证明数据建模的合理性。研究了基于双变量正态 MLM 的 CRT 的 CEA 对集群和个体级别的非正态成本分布的稳健性。正常，伽马，和对数正态分布使用在集群数量、每个集群的人数、模型的协方差参数和成本数据的偏度水平方面不同的场景来考虑。结果表明，CRT 的 CEA 以及因此基于二元正态 MLM 的样本量计算对于各种场景中的高度偏斜成本非常稳健。这种鲁棒性尤其适用于 I 类错误率和功率。就方差分量估计的偏差和固定效应的标准误差而言，小样本中可能会出现大偏差。然而，这些偏差似乎并未转化为 I 类错误率或功率与标称水平的任何严重偏差。以及成本数据的偏度水平。结果表明，CRT 的 CEA 以及因此基于二元正态 MLM 的样本量计算对于各种场景中的高度偏斜成本非常稳健。这种鲁棒性尤其适用于 I 类错误率和功率。就方差分量估计的偏差和固定效应的标准误差而言，小样本中可能会出现大偏差。然而，这些偏差似乎并未转化为 I 类错误率或功率与标称水平的任何严重偏差。以及成本数据的偏度水平。结果表明，CRT 的 CEA 以及因此基于二元正态 MLM 的样本量计算对于各种场景中的高度偏斜成本非常稳健。这种鲁棒性尤其适用于 I 类错误率和功率。就方差分量估计的偏差和固定效应的标准误差而言，小样本中可能会出现大偏差。然而，这些偏差似乎并未转化为 I 类错误率或功率与标称水平的任何严重偏差。就方差分量估计的偏差和固定效应的标准误差而言，小样本中可能会出现大偏差。然而，这些偏差似乎并未转化为 I 类错误率或功率与标称水平的任何严重偏差。就方差分量估计的偏差和固定效应的标准误差而言，小样本中可能会出现大偏差。然而，这些偏差似乎并未转化为 I 类错误率或功率与标称水平的任何严重偏差。