This article considers modeling of receiver operating characteristic (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 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. 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, the authors 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. (Publisher Abstract)