Abstract

The receiver operating characteristic (ROC) curve is widely used to assess discriminative accuracy of two groups based on a continuous score. In a variety of applications, the distributions of such scores across the two groups exhibit a stochastic ordering. Specific examples include calibrated biomarkers in medical diagnostics or the output of matching algorithms in biometric recognition. Incorporating stochastic ordering as an additional constraint into estimation can improve statistical efficiency. In this article, we consider modeling of ROC curves using both the order constraint and covariates associated with each score given that the latter (e.g., demographic characteristics of the underlying subjects) often have a substantial impact on discriminative accuracy. The proposed method is based on the indirect ROC regression approach using a location-scale model, and quadratic optimization is used to implement the order constraint. The statistical properties of the proposed order-constrained least squares estimator are studied. Based on the theoretical results developed herein, we deduce that the proposed estimator can achieve substantial reductions in mean squared error relative to its unconstrained counterpart. Simulation studies corroborate the superior performance of the proposed approach. Its practical usefulness is demonstrated in an application to face recognition data from the “Good, Bad, and Ugly” face challenge, a domain in which accounting for covariates has hardly been studied.

摘要

接收者操作特征（ROC）曲线被广泛用于基于连续评分评估两组的判别准确性。在各种应用中，这两组分数的分布表现出随机排序。具体示例包括医疗诊断中的校准生物标志物或生物识别中匹配算法的输出。将随机排序作为估计的附加约束可以提高统计效率。在本文中，我们考虑使用顺序约束和与每个分数相关的协变量对 ROC 曲线进行建模，因为后者（例如，基础受试者的人口统计特征）通常对判别准确性有重大影响。所提出的方法基于使用位置尺度模型的间接 ROC 回归方法，并使用二次优化来实现顺序约束。研究了所提出的阶次约束最小二乘估计器的统计特性。基于本文开发的理论结果，我们推断出所提出的估计器相对于其无约束对应物可以显着降低均方误差。仿真研究证实了所提出方法的优越性能。它的实用性在来自“好、坏、丑”人脸挑战的人脸识别数据的应用中得到了证明，该领域几乎没有研究过对协变量的解释。研究了所提出的阶次约束最小二乘估计器的统计特性。基于本文开发的理论结果，我们推断出所提出的估计器相对于其无约束对应物可以显着降低均方误差。仿真研究证实了所提出方法的优越性能。它的实用性在来自“好、坏、丑”人脸挑战的人脸识别数据的应用中得到了证明，该领域几乎没有研究过对协变量的解释。研究了所提出的阶次约束最小二乘估计器的统计特性。基于本文开发的理论结果，我们推断出所提出的估计器相对于其无约束对应物可以显着降低均方误差。仿真研究证实了所提出方法的优越性能。它的实用性在来自“好、坏、丑”人脸挑战的人脸识别数据的应用中得到了证明，该领域几乎没有研究过对协变量的解释。仿真研究证实了所提出方法的优越性能。它的实用性在来自“好、坏、丑”人脸挑战的人脸识别数据的应用中得到了证明，该领域几乎没有研究过对协变量的解释。仿真研究证实了所提出方法的优越性能。它的实用性在来自“好、坏、丑”人脸挑战的人脸识别数据的应用中得到了证明，该领域几乎没有研究过对协变量的解释。