A priori power analysis in longitudinal three-level multilevel models: an example with therapist effects

Over the last few years, three-level longitudinal models have become more common in psychotherapy research, particularly in therapist-effect or group-effect studies. Thus far, limited attention has been paid to power analysis in these models. This article demonstrates the effects of intraclass correlation, level of randomization, sample size, covariates and drop-out on power, using data from a routine outcome monitoring study. Results indicate that randomization at the patient level is the most efficient, and that increasing the number of measurements does not increase power much. Adding a covariate or having a 25% drop-out rate had limited effects on study power in our data. In addition, the results demonstrate that sufficient power can be reached with small sample sizes, but that larger sample sizes are needed to prevent estimation bias for the model parameters and standard errors.