The gROC curve and the optimal classification

Martínez-Camblor Pablo () and Pérez-Fernández Sonia ()
Additional contact information
Martínez-Camblor Pablo: Department of Anesthesiology, Geisel School of Medicine at Dartmouth, Lebanon, NH, USA
Pérez-Fernández Sonia: Department of Statistics and Operations Research, Universidad de Oviedo, Oviedo, Asturies, Spain

The International Journal of Biostatistics, 2025, vol. 21, issue 2, 255-270

Abstract: The binary classification problem (BCP) aims to correctly allocate subjects in one of two possible groups. The groups are frequently defined as having or not one characteristic of interest. With this goal, we are allowed to use different types of information. There is a huge number of methods dealing with this problem; including standard binary regression models, or complex machine learning techniques such as support vector machine, boosting, or perceptron, among others. When this information is summarized in a continuous score, we have to define classification regions (or subsets) which will determine whether the subjects are classified as positive, with the characteristic under study, or as negative, otherwise. The standard (or regular) receiver-operating characteristic (ROC) curve assumes that higher values of the marker are associated with higher probabilities of being positive and considers as positive those patients with values within the intervals [c, ∞) ( c ∈ R ) $(c\in \mathbb{R})$ , and plots the true- against the false- positive rates (sensitivity against one minus specificity) for all potential c. The so-called generalized ROC curve, gROC, allows that both higher and lower values of the score are associated with higher probabilities of being positive. The efficient ROC curve, eROC, considers the best ROC curve based on a transformation of the score. In this manuscript, we are interested in studying, comparing and approximating the transformations leading to the eROC and to the gROC curves. We will prove that, when the optimal transformation does not have relative maximum, both curves are equivalent. Besides, we investigate the use of the gROC curve on some theoretical models, explore the relationship between the gROC and the eROC curves, and propose two non-parametric procedures for approximating the transformation leading to the gROC curve. The finite-sample behavior of the proposed estimators is explored through Monte Carlo simulations. Two real-data sets illustrate the practical use of the proposed methods.

Keywords: binary classification problem; eROC curve; gROC curve; optimal transformation; ROC curve (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/ijb-2025-0016 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ijbist:v:21:y:2025:i:2:p:255-270:n:1010

Ordering information: This journal article can be ordered from
https://www.degruyte ... journal/key/ijb/html

DOI: 10.1515/ijb-2025-0016

Access Statistics for this article

The International Journal of Biostatistics is currently edited by Antoine Chambaz, Alan E. Hubbard and Mark J. van der Laan

More articles in The International Journal of Biostatistics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().