Sample size requirement to detect an intervention effect at the end of follow-up in a longitudinal cluster randomized...

It is often anticipated in a longitudinal cluster randomized clinical trial (cluster-RCT) that the course of outcome over time will diverge between intervention arms. In these situations, testing the significance of a local intervention effect at the end of the trial may be more clinically relevant than evaluating overall mean differences between treatment groups. In this paper, we present a closed-form power function for detecting this local intervention effect based on maximum likelihood estimates from a mixed-effects linear regression model for three-level continuous data. Sample size requirements for the number of units at each data level are derived from the power function. The power function and the corresponding sample size requirements are verified by a simulation study. Importantly, it is shown that sample size requirements computed with the proposed power function are smaller than that required when testing group mean difference using data only at the end of trial and ignoring the course of outcome over the entire study period.