The receiver operating characteristic (ROC) curve is widely used to assess discrimination 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. Incorporating stochastic ordering as an additional constraint into estimation can improve statistical efficiency.
In this talk, we consider modeling of ROC curves using both the order constraint and covariates associated with each score given that the latter often have a substantial impact on discriminative accuracy. The proposed method is based on the indirect ROC regression approach using mean or quantile regression. Estimation is based on linearly constrained optimization problems whose solution can be obtained efficiently. We present theoretical results showing that the proposed estimator is consistent and has smaller mean square error than its unconstrained counterpart, which is further corroborated by simulation studies. The practical usefulness of the approach is demonstrated based on an application to face recognition data.