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Permutation‐based inference for the AUC: A unified approach for continuous and discontinuous data
Author(s) -
Pauly Markus,
Asendorf Thomas,
Konietschke Frank
Publication year - 2016
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201500105
Subject(s) - studentized range , resampling , permutation (music) , mathematics , confidence interval , consistency (knowledge bases) , statistics , test statistic , inference , random permutation , studentized residual , statistical hypothesis testing , algorithm , standard error , computer science , discrete mathematics , artificial intelligence , physics , symmetric group , acoustics
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.