Nonparametric tests for two-group comparisons of dependent observations obtained at varying time points

We propose new tests for two-group comparisons of repeated measures of a response where the repeated measures might be obtained at arbitrary time points that differ over individuals. The tests are almost U-statistics in that the kernel contains some unknown parameters that need to be estimated from the data. Our methods are designed for settings in which response means of one group are strictly greater than the response means of the other group. The tests do not make any assumptions regarding the distribution of the repeated measures except that one of the tests assumes that the repeated measures can be grouped into distinct periods of observations (e.g., around fixed follow-up time points) such that the covariance between scores only depends on the periods the observations belong to and that the covariance matrices are the same in the two groups. The tests are valid even if the probability that a response is observed depends on the level of response provided that the missing data mechanism is the same in both groups. Inference can conveniently be based on resampling. We provide asymptotic results for the test statistics. We investigate size and power of the tests and use them to assess differences in viral load decline for drug-resistant and drug-sensitive human immunodeficiency virus (HIV)-1 infected patients.