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There are multiple cluster randomised trial designs that vary in when theclusters cross between control and intervention states, when observations aremade within clusters, and how many observations are made at that time point.Identifying the most efficient study design is complex though, owing to thecorrelation between observations within clusters and over time. In thisarticle, we present a review of statistical and computational methods foridentifying optimal cluster randomised trial designs. We also adapt methodsfrom the experimental design literature for experimental designs withcorrelated observations to the cluster trial context. We identify three broadclasses of methods: using exact formulae for the treatment effect estimatorvariance for specific models to derive algorithms or weights for clustersequences; generalised methods for estimating weights for experimental units;and, combinatorial optimisation algorithms to select an optimal subset ofexperimental units. We also discuss methods for rounding weights to wholenumbers of clusters and extensions to non-Gaussian models. We present resultsfrom multiple cluster trial examples that compare the different methods,including problems involving determining optimal allocation of clusters acrossa set of cluster sequences, and selecting the optimal number of singleobservations to make in each cluster-period for both Gaussian and non-Gaussianmodels, and including exchangeable and exponential decay covariance structures.

Optimal Study Designs for Cluster Randomised Trials: An Overview of Methods and Results