  When people evaluate the performance of a diagnostic test, it is important to
control both True Positive Rate (TPR) and False Positive Rate (FPR). In the
literature, most researchers propose the partial area under the ROC curve
(pAUC) with restrictions on FPR to assess a binary classification system, which
is named as FPR pAUC. It could be artificially designed to measure the area
controlled by TPR and FPR, but is often misleading conceptually and
practically. A new and intuitive method, named two-way pAUC, is provided in
this paper, which focuses directly on the partial area under the ROC curve with
both horizontal and vertical restrictions. We propose a nonparametric estimator
of two-way pAUC, obtain its asymptotic normality properties and conduct the
measure comparison by bootstrap method. Further, in order to evaluate possible
covariate effects on two-way pAUC, regression analysis framework is constructed
and corresponding theoretical properties are established. Simulation and real
application are conducted to support our methods.
