1UEM - Universidade Estadual de Maringá, Centro de Ciências Exatas, Departamento de Estatística, Maringá-PR, Brasil. Adjoint professor. Email: casantos@uem.br
2USP - Universidade de São Paulo, FMRP - Faculdade de Medicina de Ribeirão Preto, Departamento de Medicina Social, Ribeirão Preto-SP, Brasil. Professor. Email: jorge.achcar@pq.cnpq.br
In this paper, we introduce a Bayesian analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different "frailties" or latent variables are considered to capture the correlation among the survival times for the same individual. We assume Weibull or generalized Gamma distributions considering right censored lifetime data. We develop the Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods.
Key words: Bayesian methods, Bivariate distribution, MCMC methods, Survivaldistribution, Weibull distribution.
En este artículo, se introduce un análisis bayesiano para datos multivariados de sobrevivencia en presencia de un vector de covariables y observaciones censuradas. Diferentes "fragilidades" o variables latentes son consideradas para capturar la correlación entre los tiempos de sobrevivencia para un mismo individuo. Asumimos distribuciones Weibull o Gamma generalizadas considerando datos de tiempo de vida a derecha. Desarrollamos el análisis bayesiano usando métodos Markov Chain Monte Carlo (MCMC).
Palabras clave: distribución bivariada, distribución de sobrevivencia, distribución Weibull, métodos bayesianos, métodos MCMC.
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References
1. Chib, S. & Greenberg, E. (1995), `Understanding the Metropolis-Hastings algorithm´, The American Statistician(49), 327-335.
2. Clayton, D. (1991), `A Monte Carlo Method for Bayesian inference in frailty models´, Biometrics(47), 467-485.
3. Clayton, D. & Cuzick, J. (1985), `Multivariate generalizations of the proportional hazards model´, Journal of the Royal Statistical Society A(148), 82-117.
4. Cox, D. R. (1972), `Regression models and life tables´, Journal of the Royal Statistical Society B(34), 187-220.
5. Cox, D. R. & Oakes, D. (1984), Analysis of Survival Data, Chapman & Hall, London.
6. Gelfand, A. E. & Smith, A. F. M. (1990), `Sampling based approaches to calculating marginal densities´, Journal of the American Statistical Association(85), 398-409.
7. Gelman, A. & Rubin, D. B. (1992), `Inference from iterative simulation using multiple sequences (with discussion)´, Statistical Science 7(4), 457-472.
8. Hager, H. W. & Bain, L. J. (1970), `Inferential procedures for the generalized gamma distribution´, Journal of the American Statistical Association(65), 1601-1609.
9. Kalbfleisch, J. D. (1978), `Nonparametric Bayesian analysis of survival time data´, Journal of the Royal Statistical Society B(40), 214-221.
10. McGilchrist, C. A. & Aisbett, C. W. (1991), `Regression with frailty in survival analysis´, Biometrics(47), 461-466.
11. Oakes, D. (1986), `Semiparametric inference in a model for association in bivariate survival data´, Biometrika 73, 353-361.
12. Oakes, D. (1989), `Bivariate survival models induced by frailties´, Journal of the American Statistical Association 84, 487-493.
13. Parr, V. B. & Webster, J. T. (1965), `A method for discriminating between failure density functions used in reliability predictions´, Technometrics(7), 1-10.
14. Shih, J. A. & Louis, T. A. (1992), Models and analysis for multivariate failure time data, Technical Report , Division of Biostatistics, University of Minnesota.
15. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. & Van der Linde, A. (2002), `Bayesian measures of model complexity and fit (with discussion)´, Journal of the Royal Statistical Society B(64), 583-639.
16. Spiegelhalter, D. J., Thomas, A., Best, N. G. & Lunn, D. (2003), WinBugs version 1.4 user manual, Institute of Public Health and Department of Epidemiology & Public Health, London. *http://www.mrc-bsu.com.ac.uk/bugs
17. Stacy, E. W. & Mihram, G. A. (1965), `Parameter estimation for a generalized gamma distribution´, Technometrics(7), 349-358.
18. Weibull, W. (1951), `A statistical distribution function of wide applicability´, Journal of Applied Mechanics 18(3), 292-297.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv34n1a06,
AUTHOR = {Santos, Carlos Aparecido and Alberto Achcar, Jorge},
TITLE = {{A Bayesian Analysis in the Presence of Covariates for Multivariate Survival Data: An example of Application}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2011},
volume = {34},
number = {1},
pages = {111-131}
}