Division of Public Health Sciences, Department of Surgery, Washington University School of Medicine, St. Louis, Missouri.
Division of Biostatistics, Washington University School of Medicine, St. Louis, Missouri.
Stat Med. 2019 Sep 10;38(20):3733-3746. doi: 10.1002/sim.8153. Epub 2019 Jun 4.
Cluster randomized trials (CRTs) were originally proposed for use when randomization at the subject level is practically infeasible or may lead to a severe estimation bias of the treatment effect. However, recruiting an additional cluster costs more than enrolling an additional subject in an individually randomized trial. Under budget constraints, researchers have proposed the optimal sample sizes in two-level CRTs. CRTs may have a three-level structure, in which two levels of clustering should be considered. In this paper, we propose optimal designs in three-level CRTs with a binary outcome, assuming a nested exchangeable correlation structure in generalized estimating equation models. We provide the variance of estimators of three commonly used measures: risk difference, risk ratio, and odds ratio. For a given sampling budget, we discuss how many clusters and how many subjects per cluster are necessary to minimize the variance of each measure estimator. For known association parameters, the locally optimal design is proposed. When association parameters are unknown but within predetermined ranges, the MaxiMin design is proposed to maximize the minimum of relative efficiency over the possible ranges, that is, to minimize the risk of the worst scenario.
群组随机试验（CRTs）最初是为了当在个体水平进行随机化在实践上不可行或可能导致治疗效果的严重估计偏差时提出的。然而，招募额外的群组比在个体随机试验中招募额外的个体花费更多。在预算限制下，研究人员已经提出了两水平 CRT 中的最佳样本量。CRTs 可能具有三级结构，其中应考虑两个层次的聚类。在本文中，我们假设广义估计方程模型中的嵌套可交换相关结构，针对二分类结局提出了三级 CRT 的最佳设计。我们提供了三种常用测量值的估计量的方差：风险差、风险比和优势比。对于给定的抽样预算，我们讨论了需要多少个群组和每个群组中的多少个个体来最小化每个测量值估计量的方差。对于已知的关联参数，我们提出了局部最优设计。当关联参数未知但在预定范围内时，我们提出了最大化最小相对效率的 MaxiMin 设计，即在可能的范围内，即最小化最坏情况的风险。
