Optimal permutation tests for the analysis of group randomized trials

Two facts complicate the comparison of interventions in group randomized trials (GRT's), a family of clinical trials in which each member of a particular group receives the same treatment assignment. First, individual outcomes within each group are often correlated. Second, the number of groups in a GRT is often not sufficient to make asymptotic approximations possible. Therefore, the tests used with methods, such as generalized estimating equations (GEE) and penalized quasi likelihood (PQL), originally developed for longitudinal studies, may not be valid. As an alternative, a class of permutation tests is derived to maximize the power of testing for an intervention effect in a GRT while maintaining a nominal test size. The test uses a statistic that is a weighted sum of residuals, with the weights based on the group sizes and the variability of each individual outcome. Through simulation, we demonstrate the importance of weights to a permutation test's power and compare the power of permutation tests, GEE, and PQL. Last, we apply our methods to an actual GRT to study smoking cessation, discuss the findings based on permutation tests, and compare those findings with traditional methods.