Doctoral Thesis
DOI
https://doi.org/10.11606/T.17.2014.tde-23092014-120646
Document
Author
Full name
Emilio Augusto Coelho Barros
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Ribeirão Preto, 2014
Supervisor
Committee
Achcar, Jorge Alberto (President)
Martinez, Edson Zangiacomi
Ruffino Netto, Antonio
Santos, Carlos Aparecido dos
Souza, Aparecida Doniseti Pires de
Title in Portuguese
Modelagem em análise de sobrevivência para dados médicos bivariados utilizando funções cópulas e fração de cura
Keywords in Portuguese
Fracão de cura
Funcões cópulas
Inferência Bayesiana.
Abstract in Portuguese
Title in English
Modeling in survival analysis for medical data using bivariate copula functions and cure fraction.
Keywords in English
Bayesian inference.
copula function
Cure fraction
Abstract in English
Mixture and non-mixture lifetime models are applied to analyze survival data when some individuals may never experience the event of interest. Dierent statistical models are proposed to analyze survival data in the presence of cure fraction. In this thesis, we propose the use of new models. From the univariate case, we consider that the lifetime data have a three-parameter Burr XII distribution, which includes the popular Weibull mixture model as a special case. We consider a general survival model where the scale and shape parameters of the Burr XII distribution depends on covariates. Also considering the univariate case the two-parameters exponentiated exponential distribution is used. The two-parameter exponentiated exponential or the generalized exponential distribution is a particular member of the exponentiated Weibull distribution introduced by Mudholkar and Srivastava (1993). We also consider in this case a general survival model where the scale, shape and cured fraction parameters of the exponentiated exponential distribution depends on covariates. We also introduce the univariate Weibull distributions in presence of cure fraction, censored data and covariates. Two models are explored in this case: the mixture model and non-mixture model. When we have two lifetimes associated with each unit (bivariate data), we can use some bivariate distributions: as special case the Block and Basu bivariate lifetime distribution. We also presents estimates for the parameters included in Block and Basu bivariate lifetime distribution in presence of covariates and cure fraction, applied to analyze survival data when some individuals may never experience the event of interest and two lifetimes are associated with each unit. We also consider in bivariate case the bivariate Weibull distributions derived from copula functions in presence of cure fraction, censored data and covariates. Two copula functions are explored in this paper: the Farlie-Gumbel-Morgenstern copula (FGM) and the Gumbel copula. Classical and Bayesian procedures are used to get point and condence intervals of the unknown parameters. Illustrations of the proposed methodologies are given considering medicals data sets.