Designing Multisite Randomized Trials to Detect (Conditional) Indirect Effects

Multisite mediation studies represent an analytic cornerstone in the development and assessment of theories across a broad array of disciplines because they can critically map out development processes and create opportunities to learn how context constrains or facilitates mediating mechanisms. Despite the widespread use of multisite mediation analyses, a notable missing component is methods for predicting statistical power and sample sizes that position studies to detect such effects. The literature has emphasized the importance of complementing main effect power analyses with mediation effect power analyses (even if considered a secondary objective) because they frequently suggest different designs, sample sizes, and resource allocations. Evaluation of different designs considering competing estimands during planning stages helps to balance competing priorities and strengthen the overall quality of evidence generated from studies. In this study, we develop formulas to predict power and guide the design of multisite studies probing mediation under a linear structural formulation.