We consider the problem of sample size determination for three-level mixed-effects linear regression models for the analysis of clustered longitudinal data. Three-level designs are used in many areas, but in particular, multi-center randomized longitudinal clinical trials in medical or health-related research. In this case, level 1 represents measurement occasion, level 2 represents subject, and level 3 represents center. The model we consider involves random effects of the time trends at both the subject level and the center level. In the most common case, we have two random effects (constant and linear), at both subject and center levels. The approach presented here is general with respect to sampling proportions, number of groups, and attrition rates over time. In addition, we also develop a cost model, as an aid in selecting the most parsimonius of several possible competing models (i.e., different
combinations of centers, subjects within centers, and measurement occasions). We derive sample size requirements (i.e., power characteristics) for a test of treatment by time interaction(s) for designs based on either subject-level or cluster-level randomization. The general methodology is illustrated using two characteristic examples.
This is joint work with Dulal Bhaumik, Subhash Aryal and Robert Gibbons.