Power to detect moderated effects with random slopes in partially nested designs

Investigations of differential treatment effects through the inclusion of moderating variables advance individualized treatment decisions through improved knowledge of treatment effectiveness across individuals and contexts.Literature has explored planning strategies for partially nested designs with heterogeneous treatment effects but statistical power formulas for detecting moderated effects when the moderator-outcome relationship varies across clusters (i.e., random slopes) are currently unavailable.We derive these formulas and probe the roles of the governing parameters and likely scale required for detecting these moderation effects.Simulation study results suggest that substantial moderation effect heterogeneity warrants much larger sample sizes to consistently detect moderation effects.Power formulas are implemented in R (see Supplemental Materials).or a range of treatments frequently seen in educational research settings collaboration among participants in a cluster (e.g., small-group reading instruction) or a shared facilitator (e.g., patients with the same therapist) can produce dependencies among participant outcomes (Lohr et al. 2014;