Reducing the overfitting in the gROC curve estimation

The generalized receiver-operating characteristic, gROC, curve considers the classification ability of diagnostic tests when both larger and lower values of the marker are associated with higher probabilities of being positive. Its empirical estimation implies to select the best classification subse...

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Published in:	Computational statistics Vol. 39; no. 2; pp. 1005 - 1022
Main Authors:	Martínez-Camblor, Pablo, Díaz-Coto, Susana
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024 Springer Nature B.V
Subjects:	Algorithms Classification Computer simulation Economic Theory/Quantitative Economics/Mathematical Methods Empirical analysis Mathematics and Statistics Monte Carlo simulation Original Paper Probability and Statistics in Computer Science Probability Theory and Stochastic Processes Statistics Diagnostic problem gROC curve Binary classification problem Cross-validation Overfitting
ISSN:	0943-4062, 1613-9658
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Abstract	The generalized receiver-operating characteristic, gROC, curve considers the classification ability of diagnostic tests when both larger and lower values of the marker are associated with higher probabilities of being positive. Its empirical estimation implies to select the best classification subsets among those satisfying particular condition. Both strong and weak consistency have already been proved. However, using the same data for both to select the classification subsets and to calculate its gROC curve leads to an over-optimistic estimate of the real performance of the diagnostic criteria on future samples. In this work, the bias of the empirical gROC curve estimator is explored through Monte Carlo simulations. Besides, two cross-validation based algorithms are proposed for reducing the overfitting. The practical application of the proposed algorithms is illustrated through the analysis of a real-world dataset. Simulation results suggest that the empirical gROC curve estimator returns optimistic approximations, especially, in situations in which the diagnostic capacity of the marker is poor and the sample size is small. The new proposed algorithms improve the estimation of the actual diagnostic test accuracy, and get almost unbiased gAUCs in most of the considered scenarios. However, the cross-validation based algorithms reported larger L 1 -errors than the standard empirical estimators, and increment the computational cost of the procedures. As online supplementary material, this manuscript includes an R function which wraps up the implemented routines.
AbstractList	The generalized receiver-operating characteristic, gROC, curve considers the classification ability of diagnostic tests when both larger and lower values of the marker are associated with higher probabilities of being positive. Its empirical estimation implies to select the best classification subsets among those satisfying particular condition. Both strong and weak consistency have already been proved. However, using the same data for both to select the classification subsets and to calculate its gROC curve leads to an over-optimistic estimate of the real performance of the diagnostic criteria on future samples. In this work, the bias of the empirical gROC curve estimator is explored through Monte Carlo simulations. Besides, two cross-validation based algorithms are proposed for reducing the overfitting. The practical application of the proposed algorithms is illustrated through the analysis of a real-world dataset. Simulation results suggest that the empirical gROC curve estimator returns optimistic approximations, especially, in situations in which the diagnostic capacity of the marker is poor and the sample size is small. The new proposed algorithms improve the estimation of the actual diagnostic test accuracy, and get almost unbiased gAUCs in most of the considered scenarios. However, the cross-validation based algorithms reported larger L 1 -errors than the standard empirical estimators, and increment the computational cost of the procedures. As online supplementary material, this manuscript includes an R function which wraps up the implemented routines. The generalized receiver-operating characteristic, gROC, curve considers the classification ability of diagnostic tests when both larger and lower values of the marker are associated with higher probabilities of being positive. Its empirical estimation implies to select the best classification subsets among those satisfying particular condition. Both strong and weak consistency have already been proved. However, using the same data for both to select the classification subsets and to calculate its gROC curve leads to an over-optimistic estimate of the real performance of the diagnostic criteria on future samples. In this work, the bias of the empirical gROC curve estimator is explored through Monte Carlo simulations. Besides, two cross-validation based algorithms are proposed for reducing the overfitting. The practical application of the proposed algorithms is illustrated through the analysis of a real-world dataset. Simulation results suggest that the empirical gROC curve estimator returns optimistic approximations, especially, in situations in which the diagnostic capacity of the marker is poor and the sample size is small. The new proposed algorithms improve the estimation of the actual diagnostic test accuracy, and get almost unbiased gAUCs in most of the considered scenarios. However, the cross-validation based algorithms reported larger L1-errors than the standard empirical estimators, and increment the computational cost of the procedures. As online supplementary material, this manuscript includes an R function which wraps up the implemented routines.
Author	Díaz-Coto, Susana Martínez-Camblor, Pablo
Author_xml	– sequence: 1 givenname: Pablo orcidid: 0000-0001-7845-3905 surname: Martínez-Camblor fullname: Martínez-Camblor, Pablo email: Pablo.Martinez-Camblor@hitchcock.org organization: Department of Anesthesiology, Geisel School of Medicine at Dartmouth, Faculty of Health Sciences, Universidad Autonoma de Chile – sequence: 2 givenname: Susana surname: Díaz-Coto fullname: Díaz-Coto, Susana organization: Department of Epidemiology, Geisel School of Medicine at Dartmouth
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Cites_doi	10.1201/9781439800225 10.1001/jama.1989.03430190084036 10.1177/0962280214541095 10.1146/annurev-statistics-040720-022432 10.1016/j.csda.2017.07.008 10.1007/s10182-020-00385-2 10.1093/biomet/89.2.315 10.1177/0962280217747009 10.1016/j.cgh.2022.03.022 10.1148/radiology.143.1.7063747 10.1002/sim.942 10.1177/0962280218795190 10.1016/j.csda.2010.11.018 10.1002/9780470317082 10.1002/sim.8869 10.1080/02664763.2018.1554628 10.1111/j.0006-341X.2002.00657.x 10.1126/science.171.3977.1217 10.1515/ijb-2020-0091 10.1093/oso/9780198509844.001.0001 10.1007/978-0-387-30164-8_469
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SubjectTerms	Algorithms Classification Computer simulation Economic Theory/Quantitative Economics/Mathematical Methods Empirical analysis Mathematics and Statistics Monte Carlo simulation Original Paper Probability and Statistics in Computer Science Probability Theory and Stochastic Processes Statistics
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Title	Reducing the overfitting in the gROC curve estimation
URI	https://link.springer.com/article/10.1007/s00180-023-01344-6 https://www.proquest.com/docview/2956956584
Volume	39
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