Efficient Design of Cluster Randomized Trials and Individually Randomized Group Treatment Trials

For cluster randomized trials and individually randomized group treatment trials that compare two treatments on a continuous outcome, designs are presented that minimize the number of subjects or the amount of research budget, when aiming for a desired power level. These designs optimize the treatment-to-control allocation ratio of study participants but also optimize the choice between the number of clusters/groups versus the number of persons per cluster/group. Given that optimal designs require prior knowledge of parameters from the analysis model, which are often unknown during the design stage-especially outcome variances-maximin designs are introduced. These designs ensure a prespecified power level for plausible ranges of the unknown parameters and maximize power for the worst-case values of these parameters. The present study not only reviews but also extends the existing literature by deriving optimal and maximin designs when the number of clusters/groups are fixed because of practical constraints. How to calculate sample sizes in such practical designs and how much budget may be saved are illustrated for an empirical example. To facilitate sample size calculation for each of the variants of the maximin designs considered, an easy-to-use interactive R Shiny app has been developed and made available.