Efficient design of partially nested randomized trials: A maximin approach

For two-treatment randomized trials with clustering in one of the treatment arms and 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 (such as therapy groups) versus the number of persons per cluster (therapy group) in the arm with clustering. Optimal designs require prior knowledge of parameters from the analysis model, which are unknown during the design stage. We present maximin designs which address this by ensuring a pre-specified power level for plausible ranges of the unknown parameters, while maximizing the power for worst-case values of these parameters. Maximin designs are also derived when the number of clusters, or the cluster size is fixed due to practical constraints. An empirical example illustrates how to calculate sample sizes for such practical designs and shows how much these maximin designs can reduce the required research budgets compared to designs with equal subject numbers in treatment and control. A user-friendly R Shiny app facilitates these sample size calculations.