Using the “Risk Combination” method to estimate the survival function in the presence of competing risks dependent:: A simulation study.
Abstract
In this paper we compare different structures of dependence for the risks that compete in a trivariate competing risk model, using the C-Vines and D-Vines copula techniques, through statistical simulation. The vines can obtain multivariate flexibility and are able to capture all the possible range of dependencies between the competing risks, which are of great interest in financial markets, social, genetic among others problems. Then, we estimated survival function for the minimum time, both for the independent case, through the Kaplan Meier estimator and for the dependent case, in which we will use the risk combination method, which is an extension of the copula graphic estimator. The C-DVines copulas work with a cascade of bivariate copulas, which can be selected independently and allow a wide range of possibilities for characterizing the dependence of competing risks, we study particular cases where two of the three risks have equal dependence and the remaining risk is independent to the previous ones. We also study the case where two risks are equally dependent and the other is highly dependent. In addition, a particular case where the three risks have different dependence is analyzed. In all the cases studied, the risk combination method is a good alternative to estimate the marginal distribution functions and the survival function when there is a dependence between the risks of a dependent competing risks model.Keywords
C-Vines, D-Vines, Risk pooling method, Copula Graphic
Author Biography
Osnamir Elias Bru Cordero
Estudiante Doctorado en Estadística
Mario César Jaramillo Elorza
Escuela de Estadística, Docente
References
- Lo, S. and Wilke, R. A, “A copula model for dependent competing risks”, Journal of the Royal Statistical Society, vol. 59, no. 2, pp. 359-376, 2010. DOI: https://doi.org/10.1111/j.1467-9876.2009.00695.x
- M. Zheng, J. P. Klein, “Estimates of marginal survival for dependent
- competing risks based on an assumed copula”Biometrika, vol. 82, no 1, pp. 127-138, 1995. DOI: https://doi.org/10.1093/biomet/82.1.127
- Nelsen, R. B, “An introduction to copulas”, Springer, second edn, New York, 2006.
- Tsiatis, A, “A nonidentifiability aspect of the problem of competing risks”, Proc. Natl. Acad. Sci, USA. 72(1), pp. 20-22, 1975. DOI: https://doi.org/10.1073/pnas.72.1.20
- Meeker,W. Q. and Escobar, L. A. and Hong, Y, “Using Accelerated Life Tests Results to Predict Product Field Reliability”, Technometrics, vol. 51, no. 2, pp. 146-161, 2009. DOI: https://doi.org/10.1198/TECH.2009.0016
- B. Schweizer, A. Sklar, “Probabilistic Metric Spaces”, Dover Publications,
- New York, 1983.
- Paz-Sabogal., M. C., Lopera-Gómez., C. M. and Yañez-Canal., S. “Extensión del estimador cópula gráfico para un modelo con más de dos riesgos competitivos dependientes”, Revista Ingeniería y Competitividad-Univalle 16(1), 2014.
- M. Pintilie, “Competing Risks: Apractical Perspective”, Jhon Wiley and Sons, 2006. DOI: https://doi.org/10.1002/9780470870709
- Meeker, W. Q. and Escobar, L. A, “Statistical methods for reliability data”,
- New York: John Wiley and Sons, 1998.
- Escarela, G. and Carriere, J., “Fitting competing risks with an assumed
- copula”, Statistical Methods in Medical Research 12, 33-349, 2003.
- Brechman, E. C. and Shepsmeier, U., “Modeling dependence with C- and D-vine copula: The r package cdvine”, Journal of statistical software 52, 2013. DOI: https://doi.org/10.18637/jss.v052.i03
- Aas, K., Czado, C., Frigessi, A. and Bakken, H., “Pair-copula constructions of multiple dependence”, Mathematics and Economics 44(2), 182-198, 2009. DOI: https://doi.org/10.1016/j.insmatheco.2007.02.001
- Lu, J. C., and Bhattacharyya, G. K., “Some new constructions of bivariate Weibull models”, Annals of the Institute of Statistical Mathematics, 42(3), 543-559, 1990. DOI: https://doi.org/10.1007/BF00049307
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