Power Analysis for Moderator Effects in Longitudinal Cluster Randomized Designs

Cluster randomized control trials often incorporate a longitudinal component where, for example, students are followed over time and student outcomes are measured repeatedly. Besides examining how intervention effects induce changes in outcomes, researchers are sometimes also interested in exploring whether intervention effects on outcomes are modified by moderator variables at the individual (e.g., gender, race/ethnicity) and/or the cluster level (e.g., school urbanicity) over time. This study provides methods for statistical power analysis of moderator effects in two- and three-level longitudinal cluster randomized designs. Power computations take into account clustering effects, the number of measurement occasions, the impact of sample sizes at different levels, covariates effects, and the variance of the moderator variable. Illustrative examples are offered to demonstrate the applicability of the methods.