Required sample size to detect mediation in 3-level implementation studies

Statistical tests of mediation are important for advancing implementation science; however, little research has examined the sample sizes needed to detect mediation in 3-level designs (e.g., organization, provider, patient) that are common in implementation research. Using a generalizable Monte Carlo simulation method, this paper examines the sample sizes required to detect mediation in 3-level designs under a range of conditions plausible for implementation studies.

Statistical power was estimated for 17,496 3-level mediation designs in which the independent variable (X) resided at the highest cluster level (e.g., organization), the mediator (M) resided at the intermediate nested level (e.g., provider), and the outcome (Y) resided at the lowest nested level (e.g., patient). Designs varied by sample size per level, intraclass correlation coefficients of M and Y, effect sizes of the two paths constituting the indirect (mediation) effect (i.e., X→M and M→Y), and size of the direct effect. Power estimates were generated for all designs using two statistical models-conventional linear multilevel modeling of manifest variables (MVM) and multilevel structural equation modeling (MSEM)-for both 1- and 2-sided hypothesis tests.

For 2-sided tests, statistical power to detect mediation was sufficient (≥0.8) in only 463 designs (2.6%) estimated using MVM and 228 designs (1.3%) estimated using MSEM; the minimum number of highest-level units needed to achieve adequate power was 40; the minimum total sample size was 900 observations. For 1-sided tests, 808 designs (4.6%) estimated using MVM and 369 designs (2.1%) estimated using MSEM had adequate power; the minimum number of highest-level units was 20; the minimum total sample was 600. At least one large effect size for either the X→M or M→Y path was necessary to achieve adequate power across all conditions.

While our analysis has important limitations, results suggest many of the 3-level mediation designs that can realistically be conducted in implementation research lack statistical power to detect mediation of highest-level independent variables unless effect sizes are large and 40 or more highest-level units are enrolled. We suggest strategies to increase statistical power for multilevel mediation designs and innovations to improve the feasibility of mediation tests in implementation research.