The area under the generalized receiver-operating characteristic curve

Martínez-Camblor Pablo (), Pérez-Fernández Sonia and Díaz-Coto Susana
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Martínez-Camblor Pablo: Department of Biomedical Data Science, Geisel School of Medicine at Dartmouth, 7 Lebanon Street, Suite 309, Hinman Box 7261, Hanover, NH 03755, USA
Pérez-Fernández Sonia: Department of Statistics, Oviedo University, Oviedo, Asturies, Spain
Díaz-Coto Susana: Department of Statistics, Oviedo University, Oviedo, Asturies, Spain

The International Journal of Biostatistics, 2022, vol. 18, issue 1, 293-306

Abstract: The receiver operating-characteristic (ROC) curve is a well-known graphical tool routinely used for evaluating the discriminatory ability of continuous markers, referring to a binary characteristic. The area under the curve (AUC) has been proposed as a summarized accuracy index. Higher values of the marker are usually associated with higher probabilities of having the characteristic under study. However, there are other situations where both, higher and lower marker scores, are associated with a positive result. The generalized ROC (gROC) curve has been proposed as a proper extension of the ROC curve to fit these situations. Of course, the corresponding area under the gROC curve, gAUC, has also been introduced as a global measure of the classification capacity. In this paper, we study in deep the gAUC properties. The weak convergence of its empirical estimator is provided while deriving an explicit and useful expression for the asymptotic variance. We also obtain the expression for the asymptotic covariance of related gAUCs and propose a non-parametric procedure to compare them. The finite-samples behavior is studied through Monte Carlo simulations under different scenarios, presenting a real-world problem in order to illustrate its practical application. The R code functions implementing the procedures are provided as Supplementary Material.

Keywords: area under the curve; diagnostic problem; generalized receiver-operating characteristic curve; summarized indices; two-sample problem (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/ijb-2020-0091

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