Statistical power in partially nested designs probing multilevel mediation

Objective: Analysis of the intermediate behaviors and mechanisms through which innovative therapies come to shape outcomes is a critical objective in many areas of psychotherapy research because it supports the iterative exploration, development and refinement of theories and therapies. Despite widespread interest in the intermediate behaviors and mechanisms that convey treatment effects, there is limited guidance on how to effectively and efficiently design studies to detect such mediated effects in the types of partially nested designs that commonly arise in psychotherapy research. In this study, we develop statistical power formulas to identify requisite sample sizes and guide the planning of studies probing mediation under two- and three-level partially nested designs. Method: We investigate multilevel mediation in partially nested structures and models for two- and three-level designs. Results: Well-powered studies probing mediation using partially nested designs will typically require moderate to large sample sizes or moderate to large effects. Discussion: We implement these formulas in the R package PowerUpR and a simple Shiny web application (https://poweruprshiny.shinyapps.io/PartiallyNestedMediationPower/) and demonstrate their use to plan studies using partially nested designs.