There are multiple cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at that time point. Identifying the most efficient study design is complex though, owing to the correlation between observations within clusters and over time. In this article, we present a review of statistical and computational methods for identifying optimal cluster randomised trial designs. We also adapt methods from the experimental design literature for experimental designs with correlated observations to the cluster trial context. We identify three broad classes of methods: using exact formulae for the treatment effect estimator variance for specific models to derive algorithms or weights for cluster sequences; generalised methods for estimating weights for experimental units; and, combinatorial optimisation algorithms to select an optimal subset of experimental units. We also discuss methods for rounding weights to whole numbers of clusters and extensions to non-Gaussian models. We present results from multiple cluster trial examples that compare the different methods, including problems involving determining optimal allocation of clusters across a set of cluster sequences, and selecting the optimal number of single observations to make in each cluster-period for both Gaussian and non-Gaussian models, and including exchangeable and exponential decay covariance structures.

翻译：整群随机试验存在多种设计，其区别在于集群在对照状态与干预状态间切换的时点、集群内观察的时点以及每个时点观察次数的设定。由于集群内及不同时点间的观察数据存在相关性，确定最高效的研究设计颇具复杂性。本文综述了识别整群随机试验最优设计的统计与计算方法，并将实验设计文献中针对相关观察数据的方法适配至整群试验场景。我们识别出三大类方法：基于特定模型下处理效应估计量方差精确公式推导集群序列算法或权重的方法；估计实验单元权重的通用方法；以及通过组合优化算法选择最优实验单元子集的方法。我们还讨论了将权重取整为整数个集群的方法，以及对非高斯模型的扩展。通过多个整群试验实例，我们展示了不同方法的对比结果，涵盖以下问题：确定集群在集群序列间的最优分配方案、在高斯与非高斯模型下选择每个集群-时段中最佳的单次观察次数，并纳入了可交换与指数衰减协方差结构。