Power and Sample Size Determination for Multilevel Mediation in Three-Level Cluster-Randomized Trials

Mediation analyses supply a principal lens to probe the pathways through which a treatment acts upon an outcome because they can dismantle and test the core components of treatments and test how these components function as a coordinated system or theory of action. Experimental evaluation of mediation effects in addition to total effects has become increasingly common but literature has developed only limited guidance on how to plan mediation studies with multi-tiered hierarchical or clustered structures. In this study, we provide methods for computing the power to detect mediation effects in three-level cluster-randomized designs that examine individual- (level one), intermediate- (level two) or cluster-level (level three) mediators. We assess the methods using a simulation and provide examples of a three-level clinic-randomized study (individuals nested within therapists nested within clinics) probing an individual-, intermediate- or cluster-level mediator using the R package PowerUpR and its Shiny application.