Using the potential outcome framework to estimate optimal sample size for cluster randomized trials: a simulation-based algorithm

In cluster randomized trials (CRTs) groups rather than individuals are randomized to different interventions. Individuals' responses within clusters are commonly more similar than those across clusters. This dependency introduces complexity when calculating the number of clusters required to reach a specified statistical power for nominal significance levels and effect sizes. Current CRTs' sample size estimation approaches rely on asymptotic-based formulae or Monte Carlo methods. We propose a new Monte Carlo procedure which is based on the potential outcomes framework. By explicitly defining the causal estimand, the data generating, the sampling, and the treatment assignment mechanisms, this procedure allows for sample size calculations in a broad range of study designs including sample size calculations in finite and infinite populations. It can also address financial and administrative considerations by allowing for unequal allocation of clusters. The R package CRTsampleSearch implements the method and we provide examples for using this package.