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

Abstract

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.

Keywords:

• Mediation
• power
• indirect effects
• multilevel models
• sample size determination
• experimental design

Article Information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This study was supported by grants from the National Science Foundation (Award Nos. 1437679, 1552535, 1437745, and 1437692).

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions is not intended and should not be inferred.

Notes

1 Core assumptions include (a) stable unit treatment value assumption, (b) sequential ignorability, (c) consistency, (d) no downstream confounders, and (e) no treatment-by-mediator interaction.