Distribution-Free Marginal Analysis of Repeated Measures

In many clinical trials the principal objective is to assess the effects of treatment on the progression of disease as reflected by a set of K repeated measures on each subject over time. This paper reviews the application of the Wei-Lachin (1) multivariate rank procedure to the marginal analysis of such repeated measures where some observations are missing at random. With Wilcoxon scores, this analysis (2, 3) yields an estimate of the Mann-Whitney difference to reflect the difference between groups in the distributions for each of the K measures. This is especially useful for measures on an ordinal scale. The methods are introduced using analyses of repeated cholesterol measurements at four points in time in the National Cooperative Gallstone Study (4). Based on the vector of Mann-Whitney differences, a variety of summary test statistics can be computed. The nature of the alternative hypotheses and rejection regions are then contrasted for the K df T2-like omnibus test and for two alternate one df tests: the test of stochastic ordering and the test of association. More detailed analyses then are presented using repeated ordinal gradings of the severity of retinopathy in the Diabetes Control and Complications Trial (5, 6, 7). Finally, related methods and group sequential procedures are reviewed.