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Threshold interval for linear combination scores maximizing the partial AUC and VUS
Journal of the Korean Data & Information Science Society 2019;30:759-70
Published online July 31, 2019;
© 2019 Korean Data and Information Science Society.

Chong Sun Hong1 · Hae Seon Jeon2 · Hye Soo Shin3

123Department of Statistics, Sungkyunkwan University
Correspondence to: Professor, Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-Ro, Jongno-Gu, Seoul, 03063, Korea. E-mail:
Received June 26, 2019; Revised July 12, 2019; Accepted July 13, 2019.
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.
For the ROC curve and surface expressed as linear combination score random variables in realistic classification models, there are many research literature estimating linear coefficients to maximize the AUC (area under the ROC curve), VUS (volume under the ROC surface) and pAUC (partial AUC) for a certain interval. In this paper, a standardized pAUC statistic is proposed to compare of other pAUCs which have the same length of intervals, so that an alternative pAUC approach method can be developed to estimate the linear coefficients corresponding to the interval with high discriminant power. The partial VUS approach method is extended to ROC surfaces for estimating the linear coefficient. Moreover, it is found that the optimal thresholds are included in these intervals obtained by these methods.
Keywords : AUC, sensitivity, specificity, TPR, threshold, VUS.