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Partial AUC and VUS using minmax combination method
Journal of the Korean Data & Information Science Society 2021;32:1-14
Published online January 31, 2021;
© 2021 Korean Data and Information Science Society.

Chong Sun Hong1 · Dong Hui Lim2

12Department of Statistics, Sungkyunkwan University
Correspondence to: 1Professor, Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-Ro, Jongno-Gu, Seoul 03063, Korea. E-mail:
2Graduate student, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea.
Received November 18, 2020; Revised December 4, 2020; Accepted December 7, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
There exist many methods using truncated functions or nonparametric statistics in order to estimate the AUC (area under the ROC curve), partial AUC, two-way partial AUC and VUS (volume under the ROC surface), partial VUS, three-way partial VUS. Among many methods of estimating AUC in multivariate variables, the minmax combination method defines the sensitivity and specificity using the maximum and minimum values of the variables, and maximizes AUC or partial AUC. In this study, the VUS is estimated by expanding the min-max combination. Moreover, the partial AUC, two-way partial AUC, partial VUS and three-way partial VUS estimation using the min-max combination are expressed as truncated functions. The two-way partial AUC and the three-way partial VUS are obtained for the truncated functions set in various distributions, and the utility and expected effects are discussed through empirical data.
Keywords : Nonparametric, partial, sensitivity, specificity, truncation.