Calculating power for multilevel implementation trials in mental health: Meaningful effect sizes, intraclass correlation coefficients, and proportions of variance explained by covariates

Implement Res Pract. 2024 Sep 26:5:26334895241279153. doi: 10.1177/26334895241279153. eCollection 2024 Jan-Dec.

Abstract

Background: Despite the ubiquity of multilevel sampling, design, and analysis in mental health implementation trials, few resources are available that provide reference values of design parameters (e.g., effect size, intraclass correlation coefficient [ICC], and proportion of variance explained by covariates [covariate R 2]) needed to accurately determine sample size. The aim of this study was to provide empirical reference values for these parameters by aggregating data on implementation and clinical outcomes from multilevel implementation trials, including cluster randomized trials and individually randomized repeated measures trials, in mental health. The compendium of design parameters presented here represents plausible values that implementation scientists can use to guide sample size calculations for future trials.

Method: We searched NIH RePORTER for all federally funded, multilevel implementation trials addressing mental health populations and settings from 2010 to 2020. For all continuous and binary implementation and clinical outcomes included in eligible trials, we generated values of effect size, ICC, and covariate R2 at each level via secondary analysis of trial data or via extraction of estimates from analyses in published research reports. Effect sizes were calculated as Cohen d; ICCs were generated via one-way random effects ANOVAs; covariate R2 estimates were calculated using the reduction in variance approach.

Results: Seventeen trials were eligible, reporting on 53 implementation and clinical outcomes and 81 contrasts between implementation conditions. Tables of effect size, ICC, and covariate R2 are provided to guide implementation researchers in power analyses for designing multilevel implementation trials in mental health settings, including two- and three-level cluster randomized designs and unit-randomized repeated-measures designs.

Conclusions: Researchers can use the empirical reference values reported in this study to develop meaningful sample size determinations for multilevel implementation trials in mental health. Discussion focuses on the application of the reference values reported in this study.

Keywords: cluster randomized trial; covariate R2; effect size; hybrid effectiveness-implementation trial; implementation research; intraclass correlation coefficient; mental health; multilevel power analysis; sample size.

Plain language summary

To improve the planning and execution of implementation research in mental health settings, researchers need accurate estimates of several key metrics to help determine what sample size should be obtained at each level of a multi-level study (e.g., number of patients, doctors, and clinics). These metrics include the (1) effect size, which indicates how large of a difference in the primary outcome is expected between a treatment and control group, (2) intraclass correlation coefficient, which describes how similar two people in the same group might be, and (3) covariate R 2, which indicates how much of the variability in an outcome is explained by a background variable, such as level of health at the start of a study. We collected data from mental health implementation trials conducted between 2010 and 2020. We extracted information about each of these metrics and aggregated the results for researchers to use in planning their own studies. Seventeen trials were eligible, and we were able to obtain statistical information on 53 different outcome variables from these studies. We provide a set of values which will assist in sample size calculations for future mental health implementation trials.