A Bayesian Analysis in the Presence of Covariates for Multivariate Survival Data: An example of Application

SANTOS, CARLOS APARECIDO; ALBERTO ACHCAR, JORGE

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Revista Colombiana de Estadística

versión impresa ISSN 0120-1751

Rev.Colomb.Estad. v.34 n.1 Bogotá ene./jun. 2011

A Bayesian Analysis in the Presence of Covariates for Multivariate Survival Data: An example of Application

Análisis bayesiano en presencia de covariables para datos de sobrevivencia multivariados: un ejemplo de aplicación

CARLOS APARECIDO SANTOS¹, JORGE ALBERTO ACHCAR²

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

Abstract

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.

Resumen

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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[Recibido en julio de 2009. Aceptado en enero de 2011]

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}    

}