Nonparametric test of stochastic ordering for multiple longitudinal measures

We present a nonparametric approach that tests whether multiple longitudinal measures tend in the same direction over time. It is not required that each measure have the same number of serial observations, or that the observations be evenly spaced. The test and related estimators of group differences are based on the multivariate rank test of Wei and Lachin (1) and multivariate Mann-Whitney shift estimators of Thall and Lachin (2) and Lachin (3). An example is given using a subset of exercise data from a clinical trial of vesnarinone in congestive heart failure.