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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.2 Bogotá July/Dec. 2020 Epub Dec 05, 2020
https://doi.org/10.15446/rce.v43n2.80288
Original articles of research
Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests
Uso de funciones cópula para estimar el área bajo la curva característica de operación para dos pruebas de diagnóstico dependientes
1Statistics School, Universidad del Valle, Cali, Colombia
When performing validation studies on diagnostic classification procedures, one or more biomarkers are typically measured in individuals. Some of these biomarkers may provide better information; moreover, more than one biomarker may be significant and may exhibit dependence between them. This proposal intends to estimate the Area Under the Receiver Operating Characteristic Curve (AUC) for classifying individuals in a screening study. We analyze the dependence between the results of the tests by means of copula-type dependence (using FGM and Gumbel-Barnett copula functions), and studying the respective AUC under this type of dependence. Three different dependence-level values were evaluated for each copula function considered. In most of the reviewed literature, the authors assume a normal model to represent the performance of the biomarkers used for clinical diagnosis. There are situations in which assuming normality is not possible because that model is not suitable for one or both biomarkers. The proposed statistical model does not depend on some distributional assumption for the biomarkers used for diagnosis procedure, and additionally, it is not necessary to observe a strong or moderate linear dependence between them.
Key words: AUC; Copula function; FGM copula; Gumbel copula; ROC curve; Weak dependence
Cuando se realizan estudios de validación en procedimientos de clasificación diagnóstica, normalmente se miden uno o más biomarcadores en los individuos. Algunos biomarcadores pueden proporcionar mejor información que otros y en muchos casos, más de uno puede ser necesario. Cuando se utilizan varios biomarcadores para hacer clasificación, se presenta dependencia entre ellos. En este trabajo se estima el área bajo la curva característica de operación (ABCOR) para establecer la capacidad clasificadora de dos biomarcadores en un procedimiento para diagnóstico clínico. Se estudia mediante copulas (FGM y Gumbel-Barnett) la dependencia entre pruebas y se estima la respectiva área bajo la curva, asumiendo tres niveles para cada estructura de dependencia. En la literatura revisada los autores asumen un modelo normal para representar el comportamiento de los biomarcadores utilizados para el diagnóstico clínico. Hay situaciones en las que no es posible asumir este modelo porque no es adecuado para uno o ambos biomarcadores. El método estadístico propuesto no depende de un supuesto distribucional para los biomarcadores utilizados en el procedimiento de diagnóstico y tampoco es necesario considerar una dependencia lineal fuerte o moderada entre ellos.
Palabras clave: ABCOR; Cópula FGM; Cópula Gumbel Barnett; COR; Dependencia débil
Acknowledgements
We thank the program "Development of applied research to contribute to an effective and sustainable model of dengue intervention in Santander, Casanare and Valle del Cauca" of the AEDES Knowledge and Cooperation Network (RedAedes), Comfandi and the clinical and epidemiological experts participating in the consultations. This work was partially supported by the Science, Technology and Innovation Fund - FCTel of SGR, Colombia - BPIN 2013000100011 and the AEDES and Comfandi Network. The participation of the second author was partially financed by a scholarship from the Virginia Gutierrez de Pineda Program for Young Researches and Innovators of the Administrative Department of Science, Technology and Innovation (Colciencias) in Colombia.
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Received: January 2019; Accepted: April 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
