Department of Biomedical Data Science, Geisel School of Medicine at Dartmouth, 7 Lebanon Street, Suite 309, Hinman Box 7261, Hanover, NH 03755, USA.
Department of Statistics, Oviedo University, Oviedo, Asturies, Spain.
Int J Biostat. 2021 Mar 24;18(1):293-306. doi: 10.1515/ijb-2020-0091.
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 code functions implementing the procedures are provided as Supplementary Material.
受试者工作特征（ROC）曲线是一种常用于评估连续标志物区分能力的图形工具，通常指的是二分类特征。曲线下面积（AUC）已被提议作为一个概括准确性的指标。标志物的较高值通常与研究特征的更高概率相关。然而，在其他情况下，较高和较低的标志物分数都与阳性结果相关。广义 ROC（gROC）曲线已被提议作为 ROC 曲线的适当扩展，以适应这些情况。当然，也引入了 gROC 曲线的相应面积，gAUC，作为分类能力的全局度量。在本文中，我们深入研究了 gAUC 的性质。在导出渐近方差的显式有用表达式的同时，提供了其经验估计量的弱收敛性。我们还获得了相关 gAUC 之间渐近协方差的表达式，并提出了一种非参数方法来比较它们。通过在不同情况下的蒙特卡罗模拟研究了有限样本行为，提出了一个现实世界的问题来说明其实际应用。实现这些过程的代码函数作为补充材料提供。
