Inference in receiver operating characteristic surface analysis via a trinormal model-based testing approach

Samuel Noll, Reinhard Furrer, Benjamin Reiser, Christos T. Nakas

Research output: Contribution to journalArticlepeer-review


Receiver operating characteristic (ROC) analysis is the methodological framework of choice for the assessment of diagnostic markers and classification procedures in general, in both two-class and multiple-class classification problems. We focus on the three-class problem for which inference usually involves formal hypothesis testing using a proxy metric such as the volume under the ROC surface (VUS). In this article, we develop an existing approach from the two-class ROC framework. We define a hypothesis-testing procedure that directly compares two ROC surfaces under the assumption of the trinormal model. In the case of the assessment of a single marker, the corresponding ROC surface is compared with the chance plane, that is, to an uninformative marker. A simulation study investigating the proposed tests with existing ones on the basis of the VUS metric follows. Finally, the proposed methodology is applied to a dataset of a panel of pancreatic cancer diagnostic markers. The described testing procedures along with related graphical tools are supported in the corresponding R-package trinROC, which we have developed for this purpose.

Original languageEnglish
Article numbere249
Issue number1
StatePublished - Jan 2019

Bibliographical note

Publisher Copyright:
© 2020 The Authors. Stat published by John Wiley & Sons Ltd


  • Box–Cox transformation
  • Delta method
  • ROC analysis
  • pancreatic cancer biomarkers
  • trinormal ROC model
  • volume under the ROC surface (VUS)

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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