Abstract
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 of error. In the present work we assume the availability of a finite sample from each distribution (class), and no knowledge about the two distributions; i.e., the threshold is estimated nonparametrically. Asymptotic distribution is derived for the proposed estimator. Simulation results are presented for finite sample size. Finding a particular threshold value is crucial in medical diagnoses, among other fields, where a medical test is used to classify a patient as “diseased” or “nondiseased” based on comparing the test result to a particular threshold value. When the ROC is estimated, an operating point is obtained by selecting one type of errors, and get the other one from the estimated curve. Threshold estimation can then be viewed as a quantile estimation for one distribution but with the utilization of the second one.
Author’s original abstract, transcribed from the thesis; line wrapping normalised.
Research overview
Solving the inverse ROC problem from finite samples.
The thesis examines how to estimate the decision threshold associated with a target operating point on a receiver operating characteristic curve. The method is nonparametric: it does not require a predefined distribution for either class.
It develops the estimator's asymptotic distribution and uses simulation to study its behavior with finite samples, providing a foundation for threshold selection in diagnostic testing and binary classification.
Suggested citation: Yousef, Waleed Ahmed. “Nonparametric Estimation of the Threshold at an Operating Point on the ROC Curve.” M.Sc. thesis, The George Washington University, 2007.