In this article, we develop methods for sample size and power calculations in four-level intervention studies when intervention assignment is carried out at any level, with a particular focus on cluster randomized trials (CRTs). CRTs involving four levels are becoming popular in health care research, where the effects are measured, for example, from evaluations (level 1) within participants (level 2) in divisions (level 3) that are nested in clusters (level 4). In such multi-level CRTs, we consider three types of intraclass correlations between different evaluations to account for such clustering: that of the same participant, that of different participants from the same division, and that of different participants from different divisions in the same cluster. Assuming arbitrary link and variance functions, with the proposed correlation structure as the true correlation structure, closed-form sample size formulas for randomization carried out at any level (including individually randomized trials within a four-level clustered structure) are derived based on the generalized estimating equations approach using the model-based variance and using the sandwich variance with an independence working correlation matrix. We demonstrate that empirical power corresponds well with that predicted by the proposed method for as few as 8 clusters, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator, under both balanced and unbalanced designs.
翻译:在本条中,我们在四级干预研究中制定方法,在任何级别进行干预派任时进行抽样规模和权力计算,特别侧重于集群随机试验。涉及四级的幼儿保育队在保健研究中越来越受欢迎,例如,从以群组(第4级)嵌入的司级(第3级)参与者(第2级)的评价(第1级)中衡量影响,在这种多级幼儿保育队中,我们考虑不同评价之间的三类类内相关关系,以顾及这种集群:同一参加者、同一司的不同参与者以及同一组内不同司的不同参与者。假设任意联系和差异功能,与拟议的相关性结构作为真正的相关性结构,在任何级别(包括按四级分组结构中个别随机试验)进行随机化的封闭式抽样规模公式,根据通用估计方程法,使用模型差异,并使用与独立工作关联矩阵的三明治差异。我们证明,实证能力与拟议方法所预测的相同,即少数不同司、同一组内不同司和同一组不同司的不同参与者的参与者,假设有任意联系和差异功能。假设的关联结构结构结构结构结构结构结构结构结构结构结构,同时用平衡的模型分析数据,根据平衡模型,根据平衡模型进行。