Discrete Weibull regression model with cure fraction in survival data
DOI:
https://doi.org/10.17268/sel.mat.2019.01.11Keywords:
Mixture model, regression, Discrete Weibull distribution, EM algorithmAbstract
This paper presents a regression model for discrete time data with cure fraction. For this purpose, we considered a mixture model, in which times are modeled through the discrete Weibull distribution and the cure probability modeled with covariates by using the logit link function. Considering that the model is a mixture, the estimation of the parameters was performed by EM algorithm. The behavior of the estimating algorithm was tested with Monte Carlo simulation experiments and an application for real data was added.
References
Berkson J and Gage, R. P. Survival Curve for Cancer Patients Following Treatment, Journal of the American Statistical Association, 4(1952), pp. 501–515.
Brunello, G. H. V. and E. G. Nakano, Inferencia bayesiana no modelo Weibull discreto em dados com presenca de censuras, Tendencias em Matemática Aplicada e Computacional, 16(2015), pp. 97–110.
Byington, M. R. L. Estudo de fatores prognósticos em pacientes submetidos ao transplante de medula ´ossea para tratamento de leucemia mielóide cronica, Dissertacao de Mestrado em Saúde coletiva - Instituto de medicina social, Universidade do Estado do Rio de Janeiro, 1999.
Fernandes, L. M. Inferencia bayesiana em modelos discretos com fracao de cura, Dissertacao de Mestrado em Estatística – Departamento de Estatística, Universidade de Brasília, 2015.
McLachlan, G. and Peel, D. Finite Mixture Models, Wiley & Sons, Canada, 2000.
Nakagawa, T. and Osaki, S. The discrete weibull distribution, IEEE Transactions on Reliability, 24(1975), 300 – 301.
Nakano, E. Y. and Carrasco, C. G. Uma avaliacao do Uso de um Modelo Contínuo na Análise de Dados Discretos de Sobrevivencia, Tendencias em Matemática Aplicada e Computacional, 7(2006), 91 – 100.
Core Team, R. A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/, 2015.
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