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Multivariate methods for measures of association for quantifying variation among two or more groups in longitudinal or crossover studies

JIN-WHAN JUNG. Multivariate Methods for Measures of Association for Quantifying Variation among Two or More Groups in Longitudinal or Crossover Studies (Under the direction of Gary G. Koch.) Several statistical methods of parametric or nonparametric nature have been examined for both longitudinal and crossover studies in which the response criteria have ordinal categories or continuous distributions. However, not many methods are available for quantifying variation among groups with rank measures of association in either longitudinal or crossover studies. Carr et al (1989), Uesaka (1993), Tudor and Koch (1994), Semenya et al (1983), Lachin (1992) and Schnell et al (1995) proposed methods using rank measures of association in comparing two groups in multivariate situations or several groups in univariate situations. In this research, attention is focused on methods for rank measures of association among two or more groups in longitudinal or crossover studies. Rank measures of association for variation among groups are formed using Mann-Whitney (1947) statistics for pairwise comparisons between groups in longitudinal studies and crossover studies with product multinomial distributions for ordered categorical response variables. The previously described approach is not computationally practical with continuous responses. Thus, another approach with U-statistic theory for Mann-Whitney measures is examined in the longitudinal study with more than two groups (8 groups). Extensions to crossover studies with two or more sequence groups and two or more periods are also addressed in a similar way as those for the longitudinal study. The covariance matrix for Mann-Whitney statistics is asymptotically singular, so the classical weighted least squares method (WLS) may not be appropriate to estimate parameters f3 in linear models for describing variation. A modified weighted least squares method(MWLS) is proposed through the subspace of a 8(8 1) /2 dimensional basis. MWLS and WLS methods are compared to each other under various conditions in terms of relative efficiencies, closeness to true covariance matrix, and statistical power. Additionally, ways to manage the ties of responses, ways to deal with randomly missing data, ways to adjust for continuous or ordered covariables, and ways to manage stratified samples are examined for the proposed methods.