Nonparametric inference for the localization receiver operating characteristic curve and its extension to free-response image localization tasks

The localization receiver operating characteristic (LROC) and the free-response receiver operating characteristic (FROC) curves are popular methods for evaluating the performance of diagnostic tests concerning detecting and locating lesions. However, the existing LROC and FROC curves have some limitations in their definition and estimation methods. In this article, we extend the LROC curve to the free-response tasks where each case can be marked with multiple suspicious locations and propose a nonparametric estimation of the LROC curve to compensate for the limitations of existing LROC and FROC curves. We derive the asymptotic properties for our estimators and propose a bootstrap method for constructing confidence bands for the proposed LROC curve. Simulations are conducted to compare the proposed LROC curve with the existing AFROC curve and to examine the theoretical results. Finally, we apply our method to evaluate the performance of a diagnostic test investigating AI-assisted pulmonary nodule diagnosis.