Statistical power and optimal design for randomized controlled trials investigating mediation effects

Mediation analyses in randomized controlled trials (RCTs) can unpack potential causal pathways between interventions and outcomes and help the iterative improvement of interventions. When designing RCTs investigating these mechanisms, two key considerations are (a) the sample size needed to achieve adequate statistical power and (b) the efficient use of resources. The current study has developed closed-form statistical power formulas for RCTs investigating mediation effects with and without covariates under the Sobel and joint significance tests. The power formulas are functions of sample size, sample allocation between treatment conditions, effect sizes in the treatment-mediator and mediator-outcome paths, and other common parameters (e.g., significance level, one- or two-tailed test). The power formulas allow us to assess how covariates impact the magnitude of mediation effects and statistical power. Accounting for the potential unequal sampling costs between treatment conditions, we have further developed an optimal design framework to identify optimal sample allocations that provide the maximum statistical power under a fixed budget or use the minimum resources to achieve a target power. Illustrations show that the proposed method can identify more efficient and powerful sample allocations than conventional designs with an equal number of individuals in each treatment condition. We have implemented the methods in the R package odr to improve the accessibility of the work. (PsycInfo Database Record (c) 2025 APA, all rights reserved).