Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada.
School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON, Canada.
Int J Epidemiol. 2023 Oct 5;52(5):1634-1647. doi: 10.1093/ije/dyad062.
It is well-known that designing a cluster randomized trial (CRT) requires an advance estimate of the intra-cluster correlation coefficient (ICC). In the case of longitudinal CRTs, where outcomes are assessed repeatedly in each cluster over time, estimates for more complex correlation structures are required. Three common types of correlation structures for longitudinal CRTs are exchangeable, nested/block exchangeable and exponential decay correlations-the latter two allow the strength of the correlation to weaken over time. Determining sample sizes under these latter two structures requires advance specification of the within-period ICC and cluster autocorrelation coefficient as well as the intra-individual autocorrelation coefficient in the case of a cohort design. How to estimate these coefficients is a common challenge for investigators. When appropriate estimates from previously published longitudinal CRTs are not available, one possibility is to re-analyse data from an available trial dataset or to access observational data to estimate these parameters in advance of a trial. In this tutorial, we demonstrate how to estimate correlation parameters under these correlation structures for continuous and binary outcomes. We first introduce the correlation structures and their underlying model assumptions under a mixed-effects regression framework. With practical advice for implementation, we then demonstrate how the correlation parameters can be estimated using examples and we provide programming code in R, SAS, and Stata. An Rshiny app is available that allows investigators to upload an existing dataset and obtain the estimated correlation parameters. We conclude by identifying some gaps in the literature.
众所周知，设计集群随机试验（CRT）需要预先估计簇内相关系数（ICC）。在纵向 CRT 中，随着时间的推移，每个簇中的结果会反复评估，因此需要更复杂的相关结构的估计值。纵向 CRT 的三种常见相关结构类型是可交换、嵌套/块可交换和指数衰减相关——后两种允许相关性随时间减弱。在后两种结构下确定样本量需要预先指定每个时期的 ICC 和簇自相关系数，以及队列设计的个体内自相关系数。如何估计这些系数是调查人员的常见挑战。当没有来自先前发表的纵向 CRT 的适当估计值时，一种可能性是重新分析可用试验数据集的数据，或者访问观察数据，以便在试验前预先估计这些参数。在本教程中，我们展示了如何针对连续和二项结局估计这些相关结构下的相关参数。我们首先在混合效应回归框架下介绍了这些相关结构及其底层模型假设。然后，我们提供了实用的实施建议，通过示例演示了如何估计相关参数，并提供了 R、SAS 和 Stata 中的编程代码。我们还提供了一个 Rshiny 应用程序，允许调查人员上传现有数据集并获得估计的相关参数。最后，我们确定了文献中的一些空白。
