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 distributions for 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 is illustrated for the proposed method with data from a multicenter study with repeated measurements. A nonparametric estimator for relative potency is provided from the method.

Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments in a Three-Period Crossover Study with Randomly Missing Data

“…Such methods are integrated extensions of those previously described by Jung and Koch (1998) for a parallel design with more than two groups and more than one visit and by Jung and Koch (1999) for a crossover design with two sequence groups and two or more periods. The principal assumptions for the methods are random sampling of patients from a target population of interest, randomization of patients to groups, and sufficient sample sizes for the multivariate Mann-Whitney estimators to have an approximately multivariate normal distribution (e.g., ≥20 patients per group).…”

“…For strictly ordinal data, Mann-Whitney rank measures of association for pairwise comparisons between sequence groups within the respective periods, as discussed by Jung and Koch (1998), provide a nonparametric structure for estimating the parameters 1 , 2 , 3 , 4 , and (with adjustment for the reference identifiers 0 , 1 , 2 , and 3 for the periods). Also, such estimation can have nonparametric covariance adjustment (as discussed by Jung and Koch, 1998;Koch et al, 1998) for no expected differences at baseline among the four sequence groups (on the basis of randomization of patients to the four sequence groups in the study design). Through the resulting estimators, test statistics for hypotheses of interest and corresponding confidence intervals can have consideration.…”

“…(3) is based on the Bradley and Terry (1952) model for paired comparisons; see Semenya et al (1983) and Jung and Koch (1998). More specifically, the Bradley-Terry method in Eq.…”

Stratified Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment

“…As noted by Carr, Hafner, and Koch (1989), Koch (1998, 1999), and Kawaguchi and Koch (2010), such logit transformations correspond to the Fisher (1925) transformation of Somers' version of the Kendall Tau rank correlation coefficient. Also, simulation studies of Carr et al (1989) and Kawaguchi and Koch (2010) support somewhat better statistical properties for the use of this logit transformation than the actual Mann-Whitney estimator when the actual MannWhitney estimator is further from its null value of 0.5.…”

“…Let F F F = ∑ N j=1 F F F j /N denote the sample mean vector for the F F F j . As noted in Davis and Quade (1968), Puri and Sen (1971), Quade (1974), Carr et al (1989), and Koch (1998, 1999), a consistent estimator for the covariance matrix for F F F is given in (A.3).…”