Cluster Randomized Trials with a Pretest and Posttest: Equivalence of Three-, Two- and One-Level Analyses, and Sample Size Calculation

In a cluster randomized trial clusters of persons, for instance, schools or health centers, are assigned to treatments, and all persons in the same cluster get the same treatment. Although less powerful than individual randomization, cluster randomization is a good alternative if individual randomization is impossible or leads to severe treatment contamination (carry-over). Focusing on cluster randomized trials with a pretest and post-test of a quantitative outcome, this paper shows the equivalence of four methods of analysis: a three-level mixed (multilevel) regression for repeated measures with as levels cluster, person, and time, and allowing for unstructured between-cluster and within-cluster covariance matrices; a two-level mixed regression with as levels cluster and person, using change from baseline as outcome; a two-level mixed regression with as levels cluster and time, using cluster means as data; a one-level analysis of cluster means of change from baseline. Subsequently, similar equivalences are shown between a constrained mixed model and methods using the pretest as covariate. All methods are also compared on a cluster randomized trial on mental health in children. From these equivalences follows a simple method to calculate the sample size for a cluster randomized trial with baseline measurement, which is demonstrated step-by-step.