Null Distribution of Volume Under Ordered Three-Class ROC Surface (VUS) With Continuous Measurements

• Published in: IEEE signal processing letters Vol. 25; no. 12; pp. 1855 - 1859
• Main Authors: Liu, Shun, Sun, Xu, Xu, Weichao, Zhang, Yun, Dai, Jisheng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Abnormalities; Algorithms; Approximation algorithms; Computer simulation; Diagnostic systems; Gaussian distribution; Normal distribution; Normality; Null distribution; Signal processing algorithms; three-class ROC surface; Time complexity; volume under the ROC surface (VUS)
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2018.2877930

Receiver operating characteristic (ROC) analysis has become an indispensable tool in medical care, with a major application to characterizing the performance of binary diagnostic tests in clinical practice. In many circumstances, however, the diagnostic test has three outcomes, that is, the abnormalities are two sided. To deal with this scenario, this letter develops a recursive algorithm for computing the exact null distribution of the volume under the ordered three-class ROC surface (VUS) for samples following continuous distributions. Based on the asymptotic normality, an approximately normal distribution with exact mean and variance is also proposed, which is hoped to be useful for large-sample scenarios. Moreover, an efficient rank-based formula, in linearithmic time, is established for nonparametric estimation of VUS. Monte Carlo simulations verify the usefulness of the theoretical and algorithmic findings in this letter.