Optimal Design in Cluster-Randomized Trials of Cross-Level Mediation

Recent studies show cluster randomized trials may be well powered to detect mediation or indirect effects in multilevel settings. However, literature has rarely provided guidance on designing cluster-randomized trials aim to assess indirect effects. In this study, we developed closed-form expression to estimate the variance of and the statistical power to detect both individual and contextual indirect effects in cluster-randomized trials (i.e., 2-1-1 mediation). We then investigated the optimal sample allocation under a fixed budget such that researcher can minimize the resources needed for the study while maintaining adequate power. To facilitate end-user calculations, we have also developed freely available software that implements these formulas and the resampling-based approaches.