Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data
Autor(a) principal: | |
---|---|
Data de Publicação: | 2017 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/8678 |
Resumo: | In this thesis we propose models based on a reparameterized Birnbaum-Saunder (BS) distribution introduced by Santos-Neto et al. (2012) and Santos-Neto et al. (2014), to analyze survival data. Initially we introduce the Birnbaum-Saunders frailty model where we analyze the cases (i) with (ii) without covariates. Survival models with frailty are used when further information is nonavailable to explain the occurrence time of a medical event. The random effect is the “frailty”, which is introduced on the baseline hazard rate to control the unobservable heterogeneity of the patients. We use the maximum likelihood method to estimate the model parameters. We evaluate the performance of the estimators under different percentage of censured observations by a Monte Carlo study. Furthermore, we introduce a Birnbaum-Saunders regression frailty model where the maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model are investigated. In the following we propose a cure rate Birnbaum-Saunders frailty model. An important advantage of this proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for the model. In addition, we introduce a bivariate Birnbaum-Saunders distribution based on a parameterization of the Birnbaum-Saunders which has the mean as one of its parameters. We discuss the maximum likelihood estimation of the model parameters and show that these estimators can be obtained by solving non-linear equations. We then derive a regression model based on the proposed bivariate Birnbaum-Saunders distribution, which permits us to model data in their original scale. A simulation study is carried out to evaluate the performance of the maximum likelihood estimators. Finally, examples with real-data are performed to illustrate all the models proposed here. |
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Leão, Jeremias da SilvaTomazella, Vera Lucia Damascenohttp://lattes.cnpq.br/8870556978317000Sanchez, Victor Eliseo Leivahttp://lattes.cnpq.br/8210845561629144http://lattes.cnpq.br/10799780624912271b2d7f6b-0a2e-4636-916c-76ee8b7fefc12017-04-25T18:59:25Z2017-04-25T18:59:25Z2017-01-09LEÃO, Jeremias da Silva. Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data. 2017. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8678.https://repositorio.ufscar.br/handle/ufscar/8678In this thesis we propose models based on a reparameterized Birnbaum-Saunder (BS) distribution introduced by Santos-Neto et al. (2012) and Santos-Neto et al. (2014), to analyze survival data. Initially we introduce the Birnbaum-Saunders frailty model where we analyze the cases (i) with (ii) without covariates. Survival models with frailty are used when further information is nonavailable to explain the occurrence time of a medical event. The random effect is the “frailty”, which is introduced on the baseline hazard rate to control the unobservable heterogeneity of the patients. We use the maximum likelihood method to estimate the model parameters. We evaluate the performance of the estimators under different percentage of censured observations by a Monte Carlo study. Furthermore, we introduce a Birnbaum-Saunders regression frailty model where the maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model are investigated. In the following we propose a cure rate Birnbaum-Saunders frailty model. An important advantage of this proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for the model. In addition, we introduce a bivariate Birnbaum-Saunders distribution based on a parameterization of the Birnbaum-Saunders which has the mean as one of its parameters. We discuss the maximum likelihood estimation of the model parameters and show that these estimators can be obtained by solving non-linear equations. We then derive a regression model based on the proposed bivariate Birnbaum-Saunders distribution, which permits us to model data in their original scale. A simulation study is carried out to evaluate the performance of the maximum likelihood estimators. Finally, examples with real-data are performed to illustrate all the models proposed here.Nesta tese propomos modelos baseados na distribuição Birnbaum-Saunders reparametrizada introduzida por Santos-Neto et al. (2012) e Santos-Neto et al. (2014), para análise dados de sobrevivência. Incialmente propomos o modelo de fragilidade Birnbaum-Saunders sem e com covariáveis observáveis. O modelo de fragilidade é caracterizado pela utilização de um efeito aleatório, ou seja, de uma variável aleatória não observável, que representa as informações que não podem ou não foram observadas tais como fatores ambientais ou genéticos, como também, informações que, por algum motivo, não foram consideradas no planejamento do estudo. O efeito aleatório (a “fragilidade”) é introduzido na função de risco de base para controlar a heterogeneidade não observável. Usamos o método de máxima verossimilhança para estimar os parâmetros do modelo. Avaliamos o desempenho dos estimadores sob diferentes percentuais de censura via estudo de simulações de Monte Carlo. Considerando variáveis regressoras, derivamos medidas de diagnóstico de influência. Os métodos de diagnóstico têm sido ferramentas importantes na análise de regressão para detectar anomalias, tais como quebra das pressuposições nos erros, presença de outliers e observações influentes. Em seguida propomos o modelo de fração de cura com fragilidade Birnbaum-Saunders. Os modelos para dados de sobrevivência com proporção de curados (também conhecidos como modelos de taxa de cura ou modelos de sobrevivência com longa duração) têm sido amplamente estudados. Uma vantagem importante do modelo proposto é a possibilidade de considerar conjuntamente a heterogeneidade entre os pacientes por suas fragilidades e a presença de uma fração curada. As estimativas dos parâmetros do modelo foram obtidas via máxima verossimilhança, medidas de influência e diagnóstico foram desenvolvidas para o modelo proposto. Por fim, avaliamos a distribuição bivariada Birnbaum-Saunders baseada na média, como também introduzimos um modelo de regressão para o modelo proposto. Utilizamos os métodos de máxima verossimilhança e método dos momentos modificados, para estimar os parâmetros do modelo. Avaliamos o desempenho dos estimadores via estudo de simulações de Monte Carlo. Aplicações a conjuntos de dados reais ilustram as potencialidades dos modelos abordados.Não recebi financiamentoengUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarAnálise de diagnósticoDistribuição Birnbaum-SaundersEstimação de máxima verossimilhançaModelos de fragilidadeModelos de fração de curaBirnbaum-Saunders distributionCure rate modelDiagnostic analysisFrailty modelLikelihood estimationCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICAModeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival dataModelagem baseada na distribuição Birnbaum-Saunders reparametrizada para análise de dados de sobrevivênciainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisOnline600600ceb2c79a-7b68-4784-a3a7-b6fb90af1437info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTeseJSL.pdfTeseJSL.pdfapplication/pdf1918523https://repositorio.ufscar.br/bitstream/ufscar/8678/1/TeseJSL.pdf4d551d58b97032091209f65b7428e992MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/8678/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTTeseJSL.pdf.txtTeseJSL.pdf.txtExtracted texttext/plain230158https://repositorio.ufscar.br/bitstream/ufscar/8678/3/TeseJSL.pdf.txtbdc73ee47b7769eb33cd34c268da0338MD53THUMBNAILTeseJSL.pdf.jpgTeseJSL.pdf.jpgIM Thumbnailimage/jpeg5683https://repositorio.ufscar.br/bitstream/ufscar/8678/4/TeseJSL.pdf.jpg349c7d48b9918caed6897495ab37deaaMD54ufscar/86782023-09-18 18:31:51.773oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:51Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data |
dc.title.alternative.por.fl_str_mv |
Modelagem baseada na distribuição Birnbaum-Saunders reparametrizada para análise de dados de sobrevivência |
title |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data |
spellingShingle |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data Leão, Jeremias da Silva Análise de diagnóstico Distribuição Birnbaum-Saunders Estimação de máxima verossimilhança Modelos de fragilidade Modelos de fração de cura Birnbaum-Saunders distribution Cure rate model Diagnostic analysis Frailty model Likelihood estimation CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
title_short |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data |
title_full |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data |
title_fullStr |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data |
title_full_unstemmed |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data |
title_sort |
Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data |
author |
Leão, Jeremias da Silva |
author_facet |
Leão, Jeremias da Silva |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/1079978062491227 |
dc.contributor.author.fl_str_mv |
Leão, Jeremias da Silva |
dc.contributor.advisor1.fl_str_mv |
Tomazella, Vera Lucia Damasceno |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8870556978317000 |
dc.contributor.advisor-co1.fl_str_mv |
Sanchez, Victor Eliseo Leiva |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/8210845561629144 |
dc.contributor.authorID.fl_str_mv |
1b2d7f6b-0a2e-4636-916c-76ee8b7fefc1 |
contributor_str_mv |
Tomazella, Vera Lucia Damasceno Sanchez, Victor Eliseo Leiva |
dc.subject.por.fl_str_mv |
Análise de diagnóstico Distribuição Birnbaum-Saunders Estimação de máxima verossimilhança Modelos de fragilidade Modelos de fração de cura |
topic |
Análise de diagnóstico Distribuição Birnbaum-Saunders Estimação de máxima verossimilhança Modelos de fragilidade Modelos de fração de cura Birnbaum-Saunders distribution Cure rate model Diagnostic analysis Frailty model Likelihood estimation CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
dc.subject.eng.fl_str_mv |
Birnbaum-Saunders distribution Cure rate model Diagnostic analysis Frailty model Likelihood estimation |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
description |
In this thesis we propose models based on a reparameterized Birnbaum-Saunder (BS) distribution introduced by Santos-Neto et al. (2012) and Santos-Neto et al. (2014), to analyze survival data. Initially we introduce the Birnbaum-Saunders frailty model where we analyze the cases (i) with (ii) without covariates. Survival models with frailty are used when further information is nonavailable to explain the occurrence time of a medical event. The random effect is the “frailty”, which is introduced on the baseline hazard rate to control the unobservable heterogeneity of the patients. We use the maximum likelihood method to estimate the model parameters. We evaluate the performance of the estimators under different percentage of censured observations by a Monte Carlo study. Furthermore, we introduce a Birnbaum-Saunders regression frailty model where the maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model are investigated. In the following we propose a cure rate Birnbaum-Saunders frailty model. An important advantage of this proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for the model. In addition, we introduce a bivariate Birnbaum-Saunders distribution based on a parameterization of the Birnbaum-Saunders which has the mean as one of its parameters. We discuss the maximum likelihood estimation of the model parameters and show that these estimators can be obtained by solving non-linear equations. We then derive a regression model based on the proposed bivariate Birnbaum-Saunders distribution, which permits us to model data in their original scale. A simulation study is carried out to evaluate the performance of the maximum likelihood estimators. Finally, examples with real-data are performed to illustrate all the models proposed here. |
publishDate |
2017 |
dc.date.accessioned.fl_str_mv |
2017-04-25T18:59:25Z |
dc.date.available.fl_str_mv |
2017-04-25T18:59:25Z |
dc.date.issued.fl_str_mv |
2017-01-09 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
LEÃO, Jeremias da Silva. Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data. 2017. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8678. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/8678 |
identifier_str_mv |
LEÃO, Jeremias da Silva. Modeling based on a reparameterized Birnbaum-Saunders distribution for analysis of survival data. 2017. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8678. |
url |
https://repositorio.ufscar.br/handle/ufscar/8678 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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600 600 |
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ceb2c79a-7b68-4784-a3a7-b6fb90af1437 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
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