A distribution-free test of parallelism for two-sample repeated measurements

In this paper, we propose a new two-sample distribution-free procedure for testing group-by-time interaction effect in repeated measurements from a linear mixed model setting. The test statistic is based on the maximum difference of partial sums (MDPS) over time points between the two groups. Although the test has a biomedical focus, it can be applied in fields that the study is designed and monitored to be balanced and complete with equal sample sizes as would be generally done in a controlled experiment. The asymptotic null distribution of the test statistic was also derived based on the maxima of Brownian bridge under two different conditions. The simulations revealed that MDPS performed markedly better than the commonly used unstructured multivariate approach (UMA) to profile analysis. However, the empirical powers of MDPS test were convincingly close to those of the best-fitting linear mixed model (LMM).