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Revista Colombiana de Estadística

versión impresa ISSN 0120-1751

Rev.Colomb.Estad. vol.42 no.2 Bogotá jul./dic. 2019 

Artículos originales de investigación

Bayesian Inference for the Segmented Weibull Distribution

Inferencia bayesiana para distribuciones Weibull segmentadas

Emílio A. Coelho-Barrosa  , Jorge A. Achcarb  , Edson Z. Martinezc  , Nasser Davarzanid  , Heike I. Grabsche 

aDepartment of Mathematics, Federal University of Technology, Cornélio Procópio, Brazil. E-mail:

bDepartment of Social Medicine, Ribeirão Preto Medical School, University of São Paulo, Ribeirão Preto, Brazil. E-mail:

cDepartment of Social Medicine, Ribeirão Preto Medical School, University of São Paulo, Ribeirão Preto, Brazil. E-mail:

dDepartment of Pathology, GROW School for Oncology and Developmental Biology, Maastricht University Medical Center, Maastricht, The Netherlands. E-mail:

eSection of Pathology & Tumour Biology, Leeds Institute of Cancer and Pathology, University of Leeds, Leeds, United Kingdom. E-mail:


In this paper, we introduce a Bayesian approach for segmented Weibull distributions which could be a good alternative to analyze medical survival data in the presence of censored observations and covariates. With the obtained Bayesian estimated change-points we could get an excellent fit of the proposed model to any data sets. With the proposed methodology, it is also possible to identify survival times intervals where a covariate could have significantly different effects when compared to other lifetime intervals, an important point under a clinical view. The obtained Bayesian estimates are obtained using standard Markov Chain Monte Carlo methods. Some examples with real data sets illustrate the proposed methodology and its potential clinical value.

Key words: Bayesian methods; Censored data; Change-points; Covariates; Segmented Weibull distribution


En este artículo introducimos un nuevo modelo Bayesiano para distribuciones Weibull segmentadas, que puede ser una buena alternativa en el análisis de datos aplicados a la investigación en salud, con la presencia de censuras y covariables. Con este método basado en la estimación de puntos de cambio, hemos obtenido un excelente ajuste a los datos utilizados como ejemplos. De acuerdo con el modelo propuesto, fue posible identificar rangos de valores en las series temporales en que una variable independiente podría tener diferentes efectos. Este es un resultado importante desde el punto de vista clínico. Los estimados bayesianos fueron obtenidos usando métodos de Monte Carlo en Cadenas de Markov. Ejemplos basados en conjuntos de datos reales fueran usados para ilustrar el uso de los modelos propuestos y sus potenciales aplicaciones en investigaciones clínicas.

Palabras-clave: Covariables; Datos censurados; Distribución Weibull segmentada; Métodos bayesianos; Puntos de cambio

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