Published

2020-07-01

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

DOI:

https://doi.org/10.15446/rce.v43n2.80288

Keywords:

AUC, Copula function, FGM copula, Gumbel copula, ROC curve, Weak dependence (en)
ABCOR, Cópula FGM, Cópula Gumbel Barnett, COR, Dependencia débil (es)

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Authors

  • Luis Carlos Bravo Melo Universidad del Valle
  • Jennyfer Portilla Yela Universidad del Valle
  • José Rafael Tovar Cuevas Universidad del Valle

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.

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.

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How to Cite

APA

Bravo Melo, L. C., Portilla Yela, J. and Tovar Cuevas, J. R. (2020). Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests. Revista Colombiana de Estadística, 43(2), 315–344. https://doi.org/10.15446/rce.v43n2.80288

ACM

[1]
Bravo Melo, L.C., Portilla Yela, J. and Tovar Cuevas, J.R. 2020. Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests. Revista Colombiana de Estadística. 43, 2 (Jul. 2020), 315–344. DOI:https://doi.org/10.15446/rce.v43n2.80288.

ACS

(1)
Bravo Melo, L. C.; Portilla Yela, J.; Tovar Cuevas, J. R. Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests. Rev. colomb. estad. 2020, 43, 315-344.

ABNT

BRAVO MELO, L. C.; PORTILLA YELA, J.; TOVAR CUEVAS, J. R. Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests. Revista Colombiana de Estadística, [S. l.], v. 43, n. 2, p. 315–344, 2020. DOI: 10.15446/rce.v43n2.80288. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/80288. Acesso em: 28 mar. 2025.

Chicago

Bravo Melo, Luis Carlos, Jennyfer Portilla Yela, and José Rafael Tovar Cuevas. 2020. “Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests”. Revista Colombiana De Estadística 43 (2):315-44. https://doi.org/10.15446/rce.v43n2.80288.

Harvard

Bravo Melo, L. C., Portilla Yela, J. and Tovar Cuevas, J. R. (2020) “Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests”, Revista Colombiana de Estadística, 43(2), pp. 315–344. doi: 10.15446/rce.v43n2.80288.

IEEE

[1]
L. C. Bravo Melo, J. Portilla Yela, and J. R. Tovar Cuevas, “Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests”, Rev. colomb. estad., vol. 43, no. 2, pp. 315–344, Jul. 2020.

MLA

Bravo Melo, L. C., J. Portilla Yela, and J. R. Tovar Cuevas. “Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests”. Revista Colombiana de Estadística, vol. 43, no. 2, July 2020, pp. 315-44, doi:10.15446/rce.v43n2.80288.

Turabian

Bravo Melo, Luis Carlos, Jennyfer Portilla Yela, and José Rafael Tovar Cuevas. “Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests”. Revista Colombiana de Estadística 43, no. 2 (July 1, 2020): 315–344. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/80288.

Vancouver

1.
Bravo Melo LC, Portilla Yela J, Tovar Cuevas JR. Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests. Rev. colomb. estad. [Internet]. 2020 Jul. 1 [cited 2025 Mar. 28];43(2):315-44. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/80288

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