Nonparametric estimation of the threshold at an operating point on the ROC curve

In the problem of binary classification or diagnostic testing, the classification algorithm or diagnostic test produces a continuous decision variable which is compared to a critical value (or threshold). Test values above (or below) that threshold are called positive (or negative) for disease. There are two types of errors at every threshold value. The relationship between these two types is the receiver operating characteristic curve (ROC). The present work is concerned with the inverse problem; i.e., given the ROC curve (or its estimate) of a particular classification rule, what is the value of the threshold ξ that leads to a specific operating point on that curve, i.e., a specific pair of the two types ∗Waleed A. Yousef is a D.Sc. in Computer Engineering and a research fellow at the Center for Devices and Radiological Health (CDRH) (Email: [email protected]). Subrata Kundu is a Ph.D. in statistics and a professor of statistics at GWU. Robert F. Wagner is a Ph.D. in Physics and a senior biomedical research scientist at the CDRH. Waleed Yousef thanks Professor Hosam M. Mahmoud of statistics department at GWU for affording the time for valuable discussions. The authors thank Marina Kondratovich, Ph.D. of the Division of Biostatistics at CDRH/FDA for helpful comments.