title: Permutation-based inference for the AUC: A unified approach for continuous and discontinuous data.
abstract: We investigate rank-based studentized permutation methods for the nonparametric Behrens-Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner-Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation-based range-preserving confidence intervals. Extensive simulation studies show that the permutation-based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application.
authors: Institute of Statistics, University of Ulm, Helmholtzstrasse 20, 89081, Ulm, Germany. markus.pauly@uni-ulm.de.
authors: Markus
authors: M
authors: Pauly
authors: Department of Medical Statistics, University of Goettingen, Humboldtallee 32, 37073, Goettingen, Germany.
authors: Thomas
authors: T
authors: Asendorf
authors: Department of Mathematical Sciences, University of Texas at Dallas, 800 W Campbell Road, Richardson, TX, 75080, USA.
authors: Frank
authors: F
authors: Konietschke
mesh_terms: D019540:Area Under Curve; D001699:Biometry / Q000379:methods*; D011336:Probability; D012372:ROC Curve; D012984:Software
keywords: Confidence intervals; Permutation tests; ROC curve; Studentized statistics