Permutation-based inference for the AUC: A unified approach for continuous and discontinuous data.

Area of Science:

• Statistics
• Nonparametric Statistics
• Biostatistics

Background:

• The Behrens-Fisher problem involves comparing variances between two independent groups.
• Inference for the area under the receiver operating characteristic (ROC) curve is crucial in diagnostic test evaluation.
• Existing rank-based methods lacked robust theoretical underpinnings for certain scenarios.

Purpose of the Study:

• To provide a theoretical foundation for rank-based studentized permutation methods for the Behrens-Fisher problem.
• To establish the asymptotic normality of the Brunner-Munzel rank statistic under the alternative hypothesis.
• To demonstrate the consistency and invertibility of the Neubert and Brunner studentized permutation test for confidence interval computation.

Main Methods:

• Investigated rank-based studentized permutation methods.
• Proved asymptotic standard normality of the Brunner-Munzel rank statistic.
• Derived permutation-based range-preserving confidence intervals.
• Conducted extensive simulation studies.

Main Results:

• The studentized permutation distribution of the Brunner-Munzel rank statistic is asymptotically standard normal, even under the alternative.
• The Neubert and Brunner studentized permutation test is consistent.
• Confidence intervals for treatment effects can be computed by inverting the permutation test.
• Permutation-based confidence intervals maintain preassigned coverage probability accurately, even for small sample sizes.

Conclusions:

• The study provides the missing theoretical foundation for studentized permutation tests in the Behrens-Fisher problem.
• The proposed methods offer reliable confidence intervals for treatment effects, applicable even with limited data.
• Freely available R software facilitates the application of these advanced statistical techniques.