A linear model method for rank measures of association from longitudinal studies with fixed conditions (visits) for data collection and more than two groups

Abstract

Several statistical methods are available for the analysis of responses with ordinal categories or continuous distributionsfor the respective visits in longitudinal studies. This paper discusses an alternative nonparametric strategy for studies with more than two groups through Mann-Whitney rank measures of association for all pairs of groups. The proposed method is based on U-statistic theory, and it applies a linear or linear logistic model to the Mann-Whitney estimators for the probabilities of better response for each group relative to each of the others. In addition, the ways of adjusting for covariables and managing stratification factors are explained. Analysis of parallel dose-response relationships for two treatments isillustrated for the proposed method with data from a multicenter study with repeated measurements. A nonparametric estimator for relative potency is provided from the method.

Keywords:

• U-statistic
• Mann-Whitney rank measures of association
• Dose response
• Relative potency
• Repeated measures data analysis