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形式，其差异体现在集群在对照与干预状态间转换的时间点、集群内部进行观测的时间节点以及每个时间点的观测次数。由于集群内及不同时间点观测数据间的相关性，识别最有效的试验设计具有复杂性。本文系统综述了用于识别最优整群随机试验设计的统计学与计算方法，并将实验设计中针对相关观测数据的实验设计方法推广至整群试验场景。我们识别出三大类方法：基于特定模型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广义方法；以及通过组合优化算法选择最优实验单元子集的方法。还讨论了权重取整为整数集群数的方法及非高斯模型的扩展应用。通过多个整群试验案例比较不同方法，涵盖确定集群序列最优分配方案、在高斯与非高斯模型下选择单次观测的最优数量（含可交换与指数衰减协方差结构）等问题。