Semiparametric Generalized Inverse-Gaussian Frailty Models
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFMG |
Texto Completo: | http://hdl.handle.net/1843/32840 |
Resumo: | In this work we introduce a new frailty model for clustered survival data using the Generalized Inverse- Gaussian (GIG) distribution for the frailty. Assuming this distribution implies in a exible model that is mathematically advantageous since closed expressions are avaliable for the unconditional survival and density functions. The parametric and semiparametric versions of the GIG frailty model are presented. We focus on the semiparametric approach that is based on the piecewise exponential distribution. An EM algorithm is proposed to estimate the parameters under this approach. The exibility of the proposed model comes from working with a two-parameter frailty distribution. One of the parameters will determine the frailty distribution and our interest will be in adjusting the di erent special cases of the GIG distribution obtained by changing the value of this parameter. These include the Inverse-Gaussian, Reciprocal Inverse-Gaussian, Hyperbolic and Positive Hyperbolic distributions. With this, we have in hand the exibility of testing di erent frailties, making it possible to accomodate distinct correlation structures that might not be captured by tting a single model. We present simulation studies under both parametric and semiparametric approaches. In the parametric simulation study, we explore parameter estimation in nite samples sizes under correct model speci cation. A comparison to other models in the literature such as gamma and generalized exponential frailty models is made under the semiparametric approach where the proposed frailty shows competitive results under misspeci cation. We illustrate the applicability of the GIG frailty model through two real data examples. The rst consists on data obtained from the Therapeutically Applicable Research to Generate E ective Treatments (TARGET) 2 initiative, where we chose to investigate the e ect of two genetic variables on the lifetime of children diagnosed with neuroblastoma cancer. To illustrate the application of the proposed methodology to clustered survival data, we also include the t to the well known kidney catheter data set. In the real data examples we compared the t of the proposed model with the t of the gamma and generalized exponential frailty models under parametric and semiparametric approaches. Through the TARGET Neuroblastoma data set we were able to show that the gamma frailty model, being the most popular choice, su ers with convergence issues that the other models did not present. In addition, in this example, the GIG frailty proved to be the most robust regarding the speci cation of the baseline hazard function |
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Wagner Barreto de Souzahttp://lattes.cnpq.br/8823986506327201Vinícius Diniz Mayrinkhttp://lattes.cnpq.br/8630527146732066Luiza Sette Câmara Piancastelli2020-03-11T18:09:41Z2020-03-11T18:09:41Z2019-07-01http://hdl.handle.net/1843/32840In this work we introduce a new frailty model for clustered survival data using the Generalized Inverse- Gaussian (GIG) distribution for the frailty. Assuming this distribution implies in a exible model that is mathematically advantageous since closed expressions are avaliable for the unconditional survival and density functions. The parametric and semiparametric versions of the GIG frailty model are presented. We focus on the semiparametric approach that is based on the piecewise exponential distribution. An EM algorithm is proposed to estimate the parameters under this approach. The exibility of the proposed model comes from working with a two-parameter frailty distribution. One of the parameters will determine the frailty distribution and our interest will be in adjusting the di erent special cases of the GIG distribution obtained by changing the value of this parameter. These include the Inverse-Gaussian, Reciprocal Inverse-Gaussian, Hyperbolic and Positive Hyperbolic distributions. With this, we have in hand the exibility of testing di erent frailties, making it possible to accomodate distinct correlation structures that might not be captured by tting a single model. We present simulation studies under both parametric and semiparametric approaches. In the parametric simulation study, we explore parameter estimation in nite samples sizes under correct model speci cation. A comparison to other models in the literature such as gamma and generalized exponential frailty models is made under the semiparametric approach where the proposed frailty shows competitive results under misspeci cation. We illustrate the applicability of the GIG frailty model through two real data examples. The rst consists on data obtained from the Therapeutically Applicable Research to Generate E ective Treatments (TARGET) 2 initiative, where we chose to investigate the e ect of two genetic variables on the lifetime of children diagnosed with neuroblastoma cancer. To illustrate the application of the proposed methodology to clustered survival data, we also include the t to the well known kidney catheter data set. In the real data examples we compared the t of the proposed model with the t of the gamma and generalized exponential frailty models under parametric and semiparametric approaches. Through the TARGET Neuroblastoma data set we were able to show that the gamma frailty model, being the most popular choice, su ers with convergence issues that the other models did not present. In addition, in this example, the GIG frailty proved to be the most robust regarding the speci cation of the baseline hazard functionNeste trabalho, introduzimos um novo modelo de fragilidade para dados de sobrevivência agrupados usando a distribuição inversa-Gaussiana Generalizada (GIG) para a fragilidade. Assumir essa distribuição implica em um modelo exível que é matematicamente vantajoso, uma vez que expressões fechadas estão disponíveis para as funções de sobrevivência e densidade incondicionais. As versões paramétrica e semiparam étrica do modelo de fragilidade GIG são apresentadas. Focamos na abordagem semiparamétrica que é baseada na distribuição exponencial por partes. Um algoritmo EM é proposto para estimar os parâmetros sob esta abordagem. A exibilidade do modelo proposto vem da adoção de uma distribuição de fragilidade com dois parâmetros. Um deles determina a distribuição de fragilidade onde nosso interesse será ajustar os diferentes casos especiais da distribuição GIG, obtidos alterando-se o valor desse parâmetro. Esses casos especiais incluem as distribuições inversa-gaussiana, recíproca inversa-gaussiana, hiperbólica e hiperbólica positiva. Com isso, temos em mãos a exibilidade de testar diferentes fragilidades, possibilitando acomodar estruturas de correlação distintas que poderiam não ser capturadas pelo ajuste de um único modelo. Apresentamos estudos de simulação sob as abordagens paramétrica e semiparam étrica. No estudo de simulação paramétrico, exploramos a estimação dos parâmetros sob tamanhos de amostra nitos e correta especi cação do modelo. A comparação com outros modelos da literatura como os modelos de fragilidade gama e exponencial generalizada é feita sob a abordagem semiparamétrica, onde a fragilidade proposta mostra resultados competitivos sob falta de especi cação. Ilustramos a aplicabilidade do modelo de fragilidade GIG através de dois exemplos de ajuste a dados reais. O primeiro consiste em dados obtidos pelo estudo Therapeutically Applicable Research to Generate E ective Treatments (TARGET) 1 onde investigamos o efeito de duas variáveis genéticas no tempo de vida de crianças diagnosticadas com câncer de neuroblastoma. Para ilustrar a aplicação da metodologia proposta a dados de sobrevivência agrupados, incluímos também o ajuste ao conhecido conjunto de dados de cateter renal (kidney catheter). Nos exemplos de aplicação a dados reais comparamos o ajuste do modelo proposto com os dos modelos de fragilidade gama e exponencial generalizada sob as abordagens paramétrica e semiparamétrica. Através do conjunto de dados de câncer de neuroblastoma do estudo TARGET, foi possível mostrar que o modelo de fragilidade gama, sendo a escolha mais popular, sofre com problemas de convergência que os outros modelos não apresentaram. Além disso, neste exemplo, a fragilidade GIG provou ser a mais robusta quanto à especi cação da função de risco baseengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em EstatísticaUFMGBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/pt/info:eu-repo/semantics/openAccessEstatistica - TesesAlgoritmo EM - TesesProcessos gaussianos - TesesGauss, Aplicações de - TesesGeneralized Inverse-GaussianSemiparametricFrailty modelEM algorithmPiecewise constant hazardsSemiparametric Generalized Inverse-Gaussian Frailty Modelsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALDissertacao Luiza Piancastelli.pdfDissertacao Luiza Piancastelli.pdfapplication/pdf800096https://repositorio.ufmg.br/bitstream/1843/32840/1/Dissertacao%20Luiza%20Piancastelli.pdf5e877bf23e49d083619f3f54922dfc8eMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufmg.br/bitstream/1843/32840/2/license_rdfcfd6801dba008cb6adbd9838b81582abMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82119https://repositorio.ufmg.br/bitstream/1843/32840/3/license.txt34badce4be7e31e3adb4575ae96af679MD53TEXTDissertacao Luiza Piancastelli.pdf.txtDissertacao Luiza Piancastelli.pdf.txtExtracted texttext/plain116324https://repositorio.ufmg.br/bitstream/1843/32840/4/Dissertacao%20Luiza%20Piancastelli.pdf.txtfeea295b17e9045f096e2f5a577d4a75MD541843/328402020-03-12 03:41:44.41oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2020-03-12T06:41:44Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.pt_BR.fl_str_mv |
Semiparametric Generalized Inverse-Gaussian Frailty Models |
title |
Semiparametric Generalized Inverse-Gaussian Frailty Models |
spellingShingle |
Semiparametric Generalized Inverse-Gaussian Frailty Models Luiza Sette Câmara Piancastelli Generalized Inverse-Gaussian Semiparametric Frailty model EM algorithm Piecewise constant hazards Estatistica - Teses Algoritmo EM - Teses Processos gaussianos - Teses Gauss, Aplicações de - Teses |
title_short |
Semiparametric Generalized Inverse-Gaussian Frailty Models |
title_full |
Semiparametric Generalized Inverse-Gaussian Frailty Models |
title_fullStr |
Semiparametric Generalized Inverse-Gaussian Frailty Models |
title_full_unstemmed |
Semiparametric Generalized Inverse-Gaussian Frailty Models |
title_sort |
Semiparametric Generalized Inverse-Gaussian Frailty Models |
author |
Luiza Sette Câmara Piancastelli |
author_facet |
Luiza Sette Câmara Piancastelli |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Wagner Barreto de Souza |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8823986506327201 |
dc.contributor.advisor-co1.fl_str_mv |
Vinícius Diniz Mayrink |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/8630527146732066 |
dc.contributor.author.fl_str_mv |
Luiza Sette Câmara Piancastelli |
contributor_str_mv |
Wagner Barreto de Souza Vinícius Diniz Mayrink |
dc.subject.por.fl_str_mv |
Generalized Inverse-Gaussian Semiparametric Frailty model EM algorithm Piecewise constant hazards |
topic |
Generalized Inverse-Gaussian Semiparametric Frailty model EM algorithm Piecewise constant hazards Estatistica - Teses Algoritmo EM - Teses Processos gaussianos - Teses Gauss, Aplicações de - Teses |
dc.subject.other.pt_BR.fl_str_mv |
Estatistica - Teses Algoritmo EM - Teses Processos gaussianos - Teses Gauss, Aplicações de - Teses |
description |
In this work we introduce a new frailty model for clustered survival data using the Generalized Inverse- Gaussian (GIG) distribution for the frailty. Assuming this distribution implies in a exible model that is mathematically advantageous since closed expressions are avaliable for the unconditional survival and density functions. The parametric and semiparametric versions of the GIG frailty model are presented. We focus on the semiparametric approach that is based on the piecewise exponential distribution. An EM algorithm is proposed to estimate the parameters under this approach. The exibility of the proposed model comes from working with a two-parameter frailty distribution. One of the parameters will determine the frailty distribution and our interest will be in adjusting the di erent special cases of the GIG distribution obtained by changing the value of this parameter. These include the Inverse-Gaussian, Reciprocal Inverse-Gaussian, Hyperbolic and Positive Hyperbolic distributions. With this, we have in hand the exibility of testing di erent frailties, making it possible to accomodate distinct correlation structures that might not be captured by tting a single model. We present simulation studies under both parametric and semiparametric approaches. In the parametric simulation study, we explore parameter estimation in nite samples sizes under correct model speci cation. A comparison to other models in the literature such as gamma and generalized exponential frailty models is made under the semiparametric approach where the proposed frailty shows competitive results under misspeci cation. We illustrate the applicability of the GIG frailty model through two real data examples. The rst consists on data obtained from the Therapeutically Applicable Research to Generate E ective Treatments (TARGET) 2 initiative, where we chose to investigate the e ect of two genetic variables on the lifetime of children diagnosed with neuroblastoma cancer. To illustrate the application of the proposed methodology to clustered survival data, we also include the t to the well known kidney catheter data set. In the real data examples we compared the t of the proposed model with the t of the gamma and generalized exponential frailty models under parametric and semiparametric approaches. Through the TARGET Neuroblastoma data set we were able to show that the gamma frailty model, being the most popular choice, su ers with convergence issues that the other models did not present. In addition, in this example, the GIG frailty proved to be the most robust regarding the speci cation of the baseline hazard function |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019-07-01 |
dc.date.accessioned.fl_str_mv |
2020-03-11T18:09:41Z |
dc.date.available.fl_str_mv |
2020-03-11T18:09:41Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1843/32840 |
url |
http://hdl.handle.net/1843/32840 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/pt/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/pt/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Estatística |
dc.publisher.initials.fl_str_mv |
UFMG |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFMG instname:Universidade Federal de Minas Gerais (UFMG) instacron:UFMG |
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UFMG |
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Repositório Institucional da UFMG |
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