On comparing methods for discriminating between actually negative and actually positive subjects with FROC type data.

The task of searching and detecting multiple abnormalities depicted on an image, or a series of images, is a common problem in different areas such as military target detection or diagnostic medical imaging. A free response receiver operating characteristic (FROC) approach for assessing performance in many of these scenarios entails marking the locations of suspected abnormalities and indicating a level of suspicion at each of the marked locations. One of the important characteristics of a system being evaluated under the FROC paradigm is its performance in the conventional ROC domain, namely classifying a subject (or a unit of interest) as "negative" or "positive" in regard to the presence of the abnormality (or any of the abnormalities) of interest. With FROC data we can compare subjects by specifying a function of multiple scores within a subject. This approach allows formulating subject-based ROC type indices that can be estimated using existing ROC concepts. In this article we focus on indices that reflect the ability of the system to discriminate between actually negative and actually positive subjects. We consider a previously proposed index that is based on the comparison of the highest scores on subjects and two new indices that are based on potentially more stable comparison functions, namely comparison of average scores and stochastic dominance. Based on these indices we develop nonparametric procedures for comparing subject-based discriminative ability of diagnostic systems being evaluated under the FROC paradigm. We also investigate the properties of the statistical procedures in a simulation study.