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Doctoral Thesis
DOI
https://doi.org/10.11606/T.11.2011.tde-12092011-170753
Document
Author
Full name
Juliana Betini Fachini
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 2011
Supervisor
Committee
Ortega, Edwin Moises Marcos (President)
Bolfarine, Heleno
Davila, Victor Hugo Lachos
Piedade, Sonia Maria de Stefano
Savian, Taciana Villela
Title in Portuguese
Modelos de regressão com e sem fração de cura para dados bivariados em análise de sobrevivência
Keywords in Portuguese
Análise de sobrevivência
Dados censurados
Modelos matemáticos
Regressão linear
Verosimilhança.
Abstract in Portuguese
Neste trabalho são reunidos diferentes modelos e técnicas para representar situações experimentais ou observacionais de análise de sobrevivência. Para modelar respostas bivariadas e covariáveis foi proposto o modelo de regressão Kumaraswamy-Weibull bivariado. A presen»ca de indivíduos curados foi considerada sob duas diferentes abordagens, originando o modelo de regressão com fração de cura para dados bivariados por meio de cópulas e o modelo de regressão log-linear bivariado com fração de cura. Os parâmetros dos modelos foram esti- mados pelo método de máxima verossimilhança sujeito a restriçãoo nos parâmetros por meio da função barreira adaptada. Adaptou-se uma análise de sensibilidade de forma a considerar as metodologias de Influência Global, Influência Local e Influência Local Total para verificar vários aspectos que envolvem a formulação e ajuste dos modelos propostos. Utilizou-se um conjunto de dados de insuficiência renal e retinopatia diabética são utilizados para exemplificar a aplicação dos modelos propostos.
Title in English
Models with and without fraction of cure for bivariate data in survival analysis
Keywords in English
Bivariate data and censored
Cured fraction
Likelihood subject to restriction on the parameters
Regression models
Sensitivity analysis.
Abstract in English
This work brought together di®erent models and techniques to represent expe- rimental or observational situations in survival analysis. To model bivariate responses and covariates was proposed Kumaraswamy Weibull bivariate regression model. The presence of cured individuals was considered under two di®erent approaches originating the regression model with a cured fraction for bivariate data through copulas and the log-linear bivariate regression model with cured fraction. The parameters of the models were estimated by ma- ximum likelihood method subject to the restriction on the parameters through the adapted barrier function. A sensitivity analysis was adapted considering the methodologies of Global In°uence, Local In°uence and Total Local In°uence to check various aspects of the formulation and adjustment of the models proposed. Data set of renal failure and diabetic retinopathy are used to exemplify the application of the proposed models.
 
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Publishing Date
2011-09-21
 
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