title: A Cochran-Armitage-type and a score-free global test for multivariate ordinal data.
abstract: We propose a Cochran-Armitage-type and a score-free global test that can be used to assess the presence of an association between a set of ordinally scaled covariates and an outcome variable within the range of generalized linear models. Both tests are developed within the framework of the well-established 'global test' methodology and as such are feasible in high-dimensional data situations under any correlation and enable adjustment for covariates. The Cochran-Armitage-type test, for which an intimate connection with the traditional score-based Cochran-Armitage test is shown, rests upon explicit assumptions on the distances between the covariates' ordered categories. The score-free test, in contrast, parametrizes these distances and thus keeps them flexible, rendering it ideally suited for covariates measured on an ordinal scale. As confirmed by means of simulations, the Cochran-Armitage-type test focuses its power on set-outcome relationships where the distances between the covariates' categories are equal or close to those assumed, whereas the score-free test spreads its power over a wide range of possible set-outcome relationships, putting more emphasis on monotonic than on non-monotonic ones. Based on the tests' power properties, it is discussed when to favour one or the other, and the practical merits of both of them are illustrated by an application in the field of rehabilitation medicine. Our proposed tests are implemented in the R package globaltest. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Biostatistics, Institute for Molecular Life Sciences, Radboud university medical center, P.O. Box 9101, Nijmegen, 6500 HB, The Netherlands.|Department of Medical Informatics, Biometry and Epidemiology, Ludwig-Maximilians University Munich, Marchioninistr. 15, Munich, 81377, Germany.
authors.forename: Monika
authors.initials: M
authors.lastname: Jelizarow
authors.affiliation: Department of Medical Informatics, Biometry and Epidemiology, Ludwig-Maximilians University Munich, Marchioninistr. 15, Munich, 81377, Germany.|Department of Statistics, Ludwig-Maximilians University Munich, Ludwigstr. 33, Munich, 80539, Germany.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Mansmann
authors.affiliation: Biostatistics, Institute for Molecular Life Sciences, Radboud university medical center, P.O. Box 9101, Nijmegen, 6500 HB, The Netherlands.|Department of Medical Statistics and Bioinformatics, Leiden University Medical Center, P.O. Box 9600, Leiden, 2300 RC, The Netherlands.
authors.forename: Jelle J
authors.initials: JJ
authors.lastname: Goeman
mesh_terms: D006801:Humans; D016014:Linear Models; D015999:Multivariate Analysis
keywords: Cochran-Armitage test for trend; generalized linear model; global test; logit model; multivariate ordinal data