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Revista Colombiana de Estadística
versão impressa ISSN 0120-1751
Rev.Colomb.Estad. vol.42 no.1 Bogotá jan./jun. 2019 Epub 23-Maio-2019
https://doi.org/10.15446/rce.v42n1.68572
Artículos originales de investigación
Modeling Data With Semicompeting Risks: An ApModeling Data With Semicompeting Risks: An Aplication to Chronic Kidney Disease in Colombia
Modelo para datos con riesgos semi competitivos: una aplicación a insuficiencia renal crónica en Colombia
a Departamento de Estadística, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil. E-mail: lizapat@ime.usp.br
b Laboratorio Clínico, Hospital Pablo Tobón Uribe, Medellín, Colombia. tunes@ime.usp.br
c Laboratorio Clínico, Hospital Pablo Tobón Uribe, Medellín, Colombia. mmunera@hptu.org.co
In this paper, the structure of semicompeting risks data, defined by Fine, Jiang & Chappell (2001), is studied. Two events are of interest: a nonterminal and a terminal event, the last one, can censor the non-terminal event, but not vice versa. Due to the possible dependence between the times until the occurrence of such events, two approaches are evaluated: modelling the bivariate survival function through Archimedean copulas and a shared frailty model. A simulation is conducted to examine its performance and both approaches are applied to a real data set of patients with chronic kidney disease (CKD).
Key words: Archimedean Copula; Frailty model; Semicompeting risks; Survival
En este trabajo se estudia la estructura de datos con riesgos semicompetitivos definida por Fine et al. (2001). En esta estructura existen dos eventos de interés; uno intermedio y otro terminal, este último puede censurar el evento intermedio, pero no viceversa. Dada la posible dependencia, entre los tiempos hasta la ocurrencia de tales eventos, dos tipos de enfoques son evaluados: uno, modelando la función de supervivencia bivariada a través de cópulas Arquimedianas y el otro por medio de un modelo con fragilidad compartida. El desempeño se observa a través de simulación. Ambos enfoques son aplicados a un conjunto de datos reales de pacientes con insuficiencia renal crónica, que pueden o no presentar una recaída de la enfermedad luego de ser tratados con diálisis.
Palabras clave: Cópulas arquimedianas; Modelo de fragilidad; Riesgos semicompetitivos; Supervivencia
References
Breslow, N. (1972), 'Contribuição para a discusssão do artigo de D. R. Cox', Journal of the Royal Statistical Society, Serie B 34, 216-217. [ Links ]
Breslow, N. (1975), 'Analysis of survival data under the proportional hazards model', International Statistical Review 43, 45-58. [ Links ]
Campbell, G. (1981), 'Nonparametric bivariate estimation with randomly censored data', Bitrka 68, 417-422. [ Links ]
Campbell, G. & Foldes, A. (1980), Large sample properties of nonparametric bivariate estimators with censored data, Technical report, Indiana, USA. [ Links ]
Clayton, D. (1978), 'A model for association in bivariate life tables and its application in epidemiological studies of family tendency in chronic disease incidence', Biometrika 65, 141-151. [ Links ]
Cuenta del Alto Costo (2014), Fondo Colombiano de Enfermedades de Alto Costo. Enfermedad Renal Crónica en Colombia. Resolución 4700 de 2008, Bogotá. [ Links ]
Dabrowska, D. M. (1988), 'Kaplan-meier estimate on the plane', Annals of Statistics 16, 1475-1489. [ Links ]
Fine, J., Jiang, H. & Chappell, R. (2001), 'On semicompeting risk', Biometrika 88, 907-919. [ Links ]
Fiocco, M., Putter, H. & van Houwelingen, H. (2008), 'Reduced-rank proportional hazards regression and simulation-based prediction for multi-state models', Statistics in Medicine 27, 4340-4358. [ Links ]
Fix, E. & Neyman, J. (1951), 'A simple stochastic model for recovery, relapse, death and loss of patients', Human Biology 23, 205-241. [ Links ]
Gómez, R. A. (2006), 'Renal disease in colombia', Renal failure 28, 643-647. [ Links ]
Hanley, J. A. & Parnes, M. N. (1983), 'Nonparametric estimation of a multivariate distribution in the presence of censoring', Biometrics 39, 129-139. [ Links ]
Hsieh, J., Wang, W. & Ding, A. (2008), 'Regression analysis based on semicompeting risk data', Journal of the Royal Statistical Society , Serie B 70, 3-20. [ Links ]
Jiang, H., Fine, J., Kosorok, R. & Chappell, R. (2005), 'Pseudo self-consistent estimation of a copula model with informative censoring', Scandinavian Journal of Statistics 32, 1-20. [ Links ]
Kaplan, E. & Meier, P. (1958), 'Nonparametric estimation from incomplete observations', Journal of the American Statistical Association 53, 457-481. [ Links ]
Klein, J. & Moeschberger, M. (2003), Survival Analysis: Techniques for Censored and Truncated Data, 2 edn, Springer. [ Links ]
Lakhal, L. and Rivest, L. & Abdous, B. (2008), 'Estimating survival and association in a semicompeting risk model', Biometrics 64, 180-188. [ Links ]
Lin, D. Y. & Ying, Z. (1993), 'A simple nonparametric estimator of the bivariate survival function under univariate censoring', Biometrika 80, 573-582. [ Links ]
Martín-Cleary, C. & Ortiz, A. (2014), 'Ckd hotspots around the world: where, why and what the lessons are. a ckj review series', Clinical Kidney Journal 7, 519-523. [ Links ]
Nelsen, R. (2006), An Introduction to Copulas, 2 edn, Springer. [ Links ]
Oakes, D. (1989), 'Bivariate survival models induced by frailties', Journal of the American Statistical Association 84, 487-492. [ Links ]
Patiño, E. G. (2012), Análise de dados com riscos semicompetitivos, Dissertação de Mestrado, Universidade de São Paulo, Instituto de Matemática e Estatística. Departamento de Estatística, São Paulo. [ Links ]
Prentice, R. L. & Cai, J. (1992), 'Covariance and survival function estimation using censored multivariate failure time data', Biometrika 79, 495-512. [ Links ]
Rivest, L.-P. & Wells, M. (2001), 'A martingale approach to the copula-graphic estimator for the survival function under dependent censoring', Journal of Multivariate analysis 79, 138-155. [ Links ]
Romeo, J. S. (2005), Modelagem Bayesiana para dados de sobrevivência bivariados atrvés de cópulas, Tese de Doutorado, Universidade de São Paulo, Instituto de Matemática e Estatística. Departamento de Estatística, São Paulo. [ Links ]
Tsai, W. Y., Leurgans, S. & Crowley, J. (1986), 'Nonparametric estimation of a bivariate survival function in the presence of censoring', Annals of Statistics 14, 1351-1365. [ Links ]
Wienke, A. (2011), Frailty Models in Survival Analysis, CRC Press, Güstrow. [ Links ]
Xu, J., Kalbeisch, J. & Tai, B. (2010), 'Statistical analysis of illness-death processes and semicompeting risks data', Biometrics 66, 716-725. [ Links ]
Zheng, M. & Klein, J. (1982), 'Estimates of marginal survival for dependent competing risk based on an assumed copula', Biometrika 82, 127-138. [ Links ]
Received: April 2018; Accepted: November 2018
This is an open-access article distributed under the terms of the Creative Commons Attribution License
