School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia.
Monash University Accident Research Centre, Monash University, Clayton, VIC, Australia.
Clin Trials. 2022 Jun;19(3):316-325. doi: 10.1177/17407745221082227.
When designing and analysing longitudinal cluster randomised trials, such as the stepped wedge, the similarity of outcomes from the same cluster must be accounted for through the choice of a form for the within-cluster correlation structure. Several choices for this structure are commonly considered for application within the linear mixed model paradigm. The first assumes a constant intra-cluster correlation for all pairs of outcomes from the same cluster (the exchangeable/Hussey and Hughes model); the second assumes that correlations of outcomes measured in the same period are higher than outcomes measured in different periods (the block exchangeable model) and the third is the discrete-time decay model, which allows the correlation between pairs of outcomes to decay over time. Currently, there is limited guidance on how to select the most appropriate within-cluster correlation structure.
We simulated continuous outcomes under each of the three considered within-cluster correlation structures for a range of design and parameter choices, and, using the ASReml-R package, fit each linear mixed model to each simulated dataset. We evaluated the performance of the Akaike and Bayesian information criteria for selecting the correct within-cluster correlation structure for each dataset.
For smaller total sample sizes, neither criteria performs particularly well in selecting the correct within-cluster correlation structure, with the simpler exchangeable model being favoured. Furthermore, in general, the Bayesian information criterion favours the exchangeable model. When the cluster auto-correlation (which defines the degree of dependence between observations in adjacent time periods) is large and number of periods is small, neither criteria is able to distinguish between the block exchangeable and discrete time decay models. However, for increasing numbers of clusters, periods, and subjects per cluster period, both the Akaike and Bayesian information criteria perform increasingly well in the detection of the correct within-cluster correlation structure.
With increasing amounts of data, be they number of clusters, periods or subjects per cluster period, both the Akaike and Bayesian information criteria are increasingly likely to select the correct correlation structure. We recommend that if there are sufficient data available when planning a trial, that the Akaike or Bayesian information criterion is used to guide the choice of within-cluster correlation structure in the absence of other compelling justifications for a specific correlation structure. We also suggest that researchers conduct supplementary analyses under alternate correlation structures to gauge sensitivity to the initial choice.
在设计和分析纵向群组随机对照试验（如逐步楔形试验）时，必须通过选择群组内相关结构的形式来考虑来自同一群组的结果之间的相似性。在线性混合模型范例中，通常会考虑几种结构选择。第一种假设同一群组中所有结果对之间的群组内相关性为常数（可交换/Hussey 和 Hughes 模型）；第二种假设同一时期测量的结果之间的相关性高于不同时期测量的结果（块可交换模型），第三种是离散时间衰减模型，它允许结果对之间的相关性随时间衰减。目前，关于如何选择最合适的群组内相关结构的指导有限。
我们模拟了三种考虑中的群组内相关结构下的连续结果，针对一系列设计和参数选择，并使用 ASReml-R 包，将每个线性混合模型拟合到每个模拟数据集。我们评估了 Akaike 和贝叶斯信息准则用于选择每个数据集正确的群组内相关结构的性能。
对于较小的总样本量，两种标准在选择正确的群组内相关结构方面都表现不佳，简单的可交换模型更为有利。此外，通常情况下，贝叶斯信息准则倾向于可交换模型。当群组自相关（定义相邻时间周期之间观测值之间的依赖程度）较大且时期数较小时，两种标准都无法区分块可交换和离散时间衰减模型。但是，随着集群、时期和每个集群时期的受试者数量的增加，Akaike 和贝叶斯信息准则在检测正确的群组内相关结构方面的性能越来越好。
随着数据量的增加，无论是集群数量、时期数量还是每个集群时期的受试者数量，Akaike 和贝叶斯信息准则都越来越有可能选择正确的相关结构。我们建议，如果在计划试验时有足够的数据可用，则在没有其他有力理由选择特定相关结构的情况下，使用 Akaike 或贝叶斯信息准则来指导群组内相关结构的选择。我们还建议研究人员在替代相关结构下进行补充分析，以衡量对初始选择的敏感性。
