Background:

Sample size calculations for longitudinal cluster randomised trials, such as crossover and stepped-wedge trials, require estimates of the assumed correlation structure. This includes both within-period intra-cluster correlations, which importantly differ from conventional intra-cluster correlations by their dependence on period, and also cluster autocorrelation coefficients to model correlation decay. There are limited resources to inform these estimates. In this article, we provide a repository of correlation estimates from a bank of real-world clustered datasets. These are provided under several assumed correlation structures, namely exchangeable, block-exchangeable and discrete-time decay correlation structures.

Methods:

Longitudinal studies with clustered outcomes were collected to form the CLustered OUtcome Dataset bank. Forty-four available continuous outcomes from 29 datasets were obtained and analysed using each correlation structure. Patterns of within-period intra-cluster correlation coefficient and cluster autocorrelation coefficients were explored by study characteristics.

Results:

The median within-period intra-cluster correlation coefficient for the discrete-time decay model was 0.05 (interquartile range: 0.02–0.09) with a median cluster autocorrelation of 0.73 (interquartile range: 0.19–0.91). The within-period intra-cluster correlation coefficients were similar for the exchangeable, block-exchangeable and discrete-time decay correlation structures. Within-period intra-cluster correlation coefficients and cluster autocorrelations were found to vary with the number of participants per cluster-period, the period-length, type of cluster (primary care, secondary care, community or school) and country income status (high-income country or low- and middle-income country). The within-period intra-cluster correlation coefficients tended to decrease with increasing period-length and slightly decrease with increasing cluster-period sizes, while the cluster autocorrelations tended to move closer to 1 with increasing cluster-period size. Using the CLustered OUtcome Dataset bank, an RShiny app has been developed for determining plausible values of correlation coefficients for use in sample size calculations.

Discussion:

This study provides a repository of intra-cluster correlations and cluster autocorrelations for longitudinal cluster trials. This can help inform sample size calculations for future longitudinal cluster randomised trials.

中文翻译：

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来自集群结果数据集库的集群内相关性为纵向集群试验的设计提供信息

背景：

纵向整群随机试验（例如交叉和阶梯楔形试验）的样本量计算需要估计假定的相关结构。这包括周期内集群内相关性，它与传统集群内相关性的重要区别在于它们对周期的依赖性，还包括集群自相关系数来模拟相关性衰减。为这些估计提供信息的资源有限。在本文中，我们提供了一个来自真实世界集群数据集的相关性估计存储库。这些是在几个假设的相关结构下提供的，即可交换的、块可交换的和离散时间衰减相关结构。

方法：

收集具有聚类结果的纵向研究以形成聚类结果数据集库。使用每个相关结构获得并分析了来自 29 个数据集的 44 个可用的连续结果。通过研究特征探索了周期内簇内相关系数和簇自相关系数的模式。

结果：

离散时间衰减模型的周期内簇内相关系数中位数为 0.05（四分位数范围：0.02-0.09），簇自相关中位数为 0.73（四分位数范围：0.19-0.91）。可交换、块可交换和离散时间衰减相关结构的周期内簇内相关系数相似。期间集群内相关系数和集群自相关被发现随每个集群周期的参与者数量、周期长度、集群类型（初级保健、二级保健、社区或学校）和国家收入状况（高-收入国家或低收入和中等收入国家）。周期内簇内相关系数随着周期长度的增加而减小，随着簇周期大小的增加而略有减小，而簇自相关随着簇周期大小的增加而趋于接近 1。使用 Clustered OUtcome 数据集库，开发了一个 RShiny 应用程序，用于确定用于样本量计算的相关系数的合理值。

讨论：

本研究为纵向集群试验提供了集群内相关性和集群自相关的存储库。这有助于为未来的纵向整群随机试验计算样本量。