Sample Size Planning for Cluster-Randomized Interventions Probing Multilevel Mediation

Multilevel mediation analyses play an essential role in helping researchers develop, probe, and refine theories of action underlying interventions and document how interventions impact outcomes. However, little is known about how to plan studies with sufficient power to detect such multilevel mediation effects. In this study, we describe how to prospectively estimate power and identify sufficient sample sizes for experiments intended to detect multilevel mediation effects. We outline a simple approach to estimate the power to detect mediation effects with individual- or cluster-level mediators using summary statistics easily obtained from empirical literature and the anticipated magnitude of the mediation effect. We draw on a running example to illustrate several different types of mediation and provide an accessible introduction to the design of multilevel mediation studies. The power formulas are implemented in the R package PowerUpR and the PowerUp software (causalevaluation.org).