title: Multivariate non-parametric methods for Mann-Whitney statistics to analyse cross-over studies with two treatment sequences.
abstract: A non-parametric strategy for the analysis of ordinal data from cross-over studies with two treatment sequences and d(> or = 2) periods is examined through Mann-Whitney rank measures of association. For each period, these statistics estimate the probability of larger response for a randomly selected patient in one group relative to a randomly selected patient in the other group. Such estimates are as well formed for comparisons between groups for u pairs of periods with the same treatment. Methods for U-statistics are used to produce a consistent estimate of the covariance matrix for the (d + u) Mann-Whitney estimates. The effects of periods and treatments on the respective Mann-Whitney estimates are evaluated through linear (or log-linear) models. For estimation of the parameters in these models, a modified weighted least squares method is applied through a (2d - 1) < or = (d + u) dimensional basis which effectively addresses potentially near singularities in the estimated covariance matrix of the Mann-Whitney estimates. The proposed methods are applicable to response variables with an interval or an ordered categorical scale. Their scope additionally has capabilities for controlling strata in the design of a cross-over study or concomitant variables for which covariance adjustment is of interest for reduction of variance. Applications of the methods are illustrated through three cross-over studies with different specifications for the two sequences of two treatments during two to four periods.
authors.affiliation: Professional Services Division, SAS Institute Inc., Cary, NC 27513, USA. sasjwj@unx.sas.com
authors.forename: J W
authors.initials: JW
authors.lastname: Jung
authors.forename: G G
authors.initials: GG
authors.lastname: Koch
mesh_terms: D000818:Animals; D001145:Arrhythmias, Cardiac / Q000188:drug therapy; D002985:Clinical Protocols; D018592:Cross-Over Studies; D005260:Female; D006339:Heart Rate; D016018:Least-Squares Analysis; D051379:Mice; D015999:Multivariate Analysis; D010424:Pentobarbital / Q000378:metabolism; D016032:Randomized Controlled Trials as Topic; D012890:Sleep; D018709:Statistics, Nonparametric; D018781:Tension-Type Headache / Q000628:therapy
chemical_list: D010424:Pentobarbital