Analysis of crossover designs with repeated measurements using generalized estimating equations

ilustraciones, gráficas

Autores:
Cruz Gutiérrez, Nelson Alirio
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2023
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
OAI Identifier:
oai:repositorio.unal.edu.co:unal/84334
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/84334
https://repositorio.unal.edu.co/
Palabra clave:
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Análisis funcional
Teoría de la estimación
Functional analysis
Estimation theory
Carry-over effect
Crossover design
Generalized estimating equations
Poisson distribution
Overdispersion count data
Kronecker correlation
Splines estimation
Efecto de arrastre
Diseño cruzado
Ecuaciones de estimación generalizadas
Distribución de Poisson
Datos de conteo de sobredispersión
Correlación de Kronecker
Rights
openAccess
License
Reconocimiento 4.0 Internacional
id UNACIONAL2_e3a2d0b64cfd6f62614f13c87bf910c6
oai_identifier_str oai:repositorio.unal.edu.co:unal/84334
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.eng.fl_str_mv Analysis of crossover designs with repeated measurements using generalized estimating equations
dc.title.translated.spa.fl_str_mv Análisis de diseños crossover con medidas repetidas usando ecuaciones de estimación generalizadas
title Analysis of crossover designs with repeated measurements using generalized estimating equations
spellingShingle Analysis of crossover designs with repeated measurements using generalized estimating equations
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Análisis funcional
Teoría de la estimación
Functional analysis
Estimation theory
Carry-over effect
Crossover design
Generalized estimating equations
Poisson distribution
Overdispersion count data
Kronecker correlation
Splines estimation
Efecto de arrastre
Diseño cruzado
Ecuaciones de estimación generalizadas
Distribución de Poisson
Datos de conteo de sobredispersión
Correlación de Kronecker
title_short Analysis of crossover designs with repeated measurements using generalized estimating equations
title_full Analysis of crossover designs with repeated measurements using generalized estimating equations
title_fullStr Analysis of crossover designs with repeated measurements using generalized estimating equations
title_full_unstemmed Analysis of crossover designs with repeated measurements using generalized estimating equations
title_sort Analysis of crossover designs with repeated measurements using generalized estimating equations
dc.creator.fl_str_mv Cruz Gutiérrez, Nelson Alirio
dc.contributor.advisor.none.fl_str_mv Melo Martínez, Oscar Orlando
Martínez Niño, Carlos Alberto
dc.contributor.author.none.fl_str_mv Cruz Gutiérrez, Nelson Alirio
dc.contributor.researchgroup.spa.fl_str_mv Estadística Aplicada en Investigación Experimental, Industria y Biotecnología
dc.contributor.orcid.spa.fl_str_mv Cruz, N.A. [0000000273705111]
dc.contributor.cvlac.spa.fl_str_mv Cruz, Nelson Alirio [0001562620]
dc.contributor.googlescholar.spa.fl_str_mv Cruz Gutierrez, N.A. [N.A. Cruz]
dc.subject.ddc.spa.fl_str_mv 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
topic 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Análisis funcional
Teoría de la estimación
Functional analysis
Estimation theory
Carry-over effect
Crossover design
Generalized estimating equations
Poisson distribution
Overdispersion count data
Kronecker correlation
Splines estimation
Efecto de arrastre
Diseño cruzado
Ecuaciones de estimación generalizadas
Distribución de Poisson
Datos de conteo de sobredispersión
Correlación de Kronecker
dc.subject.lemb.spa.fl_str_mv Análisis funcional
Teoría de la estimación
dc.subject.lemb.eng.fl_str_mv Functional analysis
Estimation theory
dc.subject.proposal.eng.fl_str_mv Carry-over effect
Crossover design
Generalized estimating equations
Poisson distribution
Overdispersion count data
Kronecker correlation
Splines estimation
dc.subject.proposal.spa.fl_str_mv Efecto de arrastre
Diseño cruzado
Ecuaciones de estimación generalizadas
Distribución de Poisson
Datos de conteo de sobredispersión
Correlación de Kronecker
description ilustraciones, gráficas
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-07-27T20:37:51Z
dc.date.available.none.fl_str_mv 2023-07-27T20:37:51Z
dc.date.issued.none.fl_str_mv 2023-07-25
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/84334
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/84334
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv eng
language eng
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dc.rights.spa.fl_str_mv Derechos reservados al autor, 2023
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Reconocimiento 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento 4.0 Internacional
Derechos reservados al autor, 2023
http://creativecommons.org/licenses/by/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv xix, 147 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Bogotá - Ciencias - Doctorado en Ciencias - Estadística
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
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spelling Reconocimiento 4.0 InternacionalDerechos reservados al autor, 2023http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Melo Martínez, Oscar Orlando8c38749f8042c1ca56178277e80fbb04Martínez Niño, Carlos Alberto11d435600e21e527d05636cecad3f8faCruz Gutiérrez, Nelson Alirio58f9e0d628e1e09de25259a6fa1cc4dcEstadística Aplicada en Investigación Experimental, Industria y BiotecnologíaCruz, N.A. [0000000273705111]Cruz, Nelson Alirio [0001562620]Cruz Gutierrez, N.A. [N.A. Cruz]2023-07-27T20:37:51Z2023-07-27T20:37:51Z2023-07-25https://repositorio.unal.edu.co/handle/unal/84334Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficasExperimental crossover designs are widely used in medicine, agriculture, and other areas of the biological sciences. Due to the characteristics of the crossover design, each experimental unit has longitudinal observations and the presence of drag effects on the response variable. Furthermore, in many scenarios it is not possible to have a washout period between applications of different treatments, which creates problems in estimating treatment effects without a proper model specification. As a solution to this problem, this thesis deals with crossover designs without a washout period and with repeated measures. First, a methodology is developed for the analysis of crossover designs when the response variable is a Poisson count. For the estimation, generalized estimation equations are used assuming that there is no washout period and that the experimental unit was observed once per period. Furthermore, this methodology is easily extended to any response variable that belongs to the exponential family. Then, the above methodology is extended to crossover designs with repeated measures within each period, that is, when an experimental unit is observed more than once in each period. For this model, a family of correlation structures that takes into account the particularities of the design, that is, the correlation between and within the periods, is built. Finally, an extension of the generalized estimating equations is developed. It includes a parametric component to model treatment effects and a nonparametric component to model time effects and carry-over effects. The non-parametric component is estimated from splines inserted into the generalized estimation equations. Additionally, the codes for the application of the methodology in any crossover design in the R statistical software are given. The advantages of the proposed methodology are evidenced through simulation exercises and, theoretically, by exploring the asymptotic properties of the estimators obtained. The performance of the methodology is also compared with the usual methodologies on some real data from crossover designs. The methodology built in this thesis allows to analyze any crossover design as long as the observed response variable belongs to the exponential family, regardless of whether there is a washout period or not. It also allows modeling repeated measurements within each period and broadens the correlation structures used in the generalized estimation equations.Los diseños experimentales crossover se usan ampliamente en medicina, agricultura y otras áreas de las ciencias biológicas. Por las características del diseño crossover, cada unidad experimental tiene observaciones longitudinales y presencia de efectos de arrastre en la variable respuesta. Además, en muchos escenarios no es posible dejar un período de lavado entre aplicaciones de diferentes tratamientos, lo que genera problemas al estimar los efectos del tratamiento sin una especificación adecuada del modelo. Como solución a lo anterior, esta tesis trata sobre diseños crossover sin período de lavado y con medidas repetidas. En primer lugar, se desarrolla una metodología para el análisis de diseños crossover cuando la variable de respuesta es un conteo de Poisson. Para la estimación se utilizan ecuaciones de estimación generalizadas asumiendo que no existe período de lavado y que la unidad experimental fue observada una vez por período. Además, esta metodología es fácilmente extensible a cualquier variable de respuesta que pertenezca a la familia exponencial. En un segundo lugar, la metodología anterior se extiende a diseños cruzados con medidas repetidas dentro de cada período, es decir, cuando una unidad experimental es observada más de una vez en cada período. Para este modelo se construye una familia de estructuras de correlación que toman en cuenta las particularidades del diseño, es decir, la correlación entre y dentro de los periodos. En tercer lugar, se proporciona una extensión de las ecuaciones de estimación generalizadas que incluye un componente paramétrico para modelar los efectos del tratamiento y un componente no paramétrico para modelar los efectos del tiempo y los efectos carry-over. El componente no paramétrico se estima a partir de Splines insertados en las ecuaciones de estimación generalizadas. Adicionalmente, se dan los códigos para la aplicación de la metodología en cualquier diseño crossover en el software estadístico R. Las ventajas de la metodología propuesta se evidencian en ejercicios de simulación y explorando teóricamente las propiedades asintóticas de los estimadores obtenidos. También se compara el rendimiento de la metodología con las metodologías habituales sobre algunos datos reales de diseños cruzados. La metodología construida en esta tesis permite analizar cualquier diseño crossover siempre que la variable respuesta observada pertenezca a la familia exponencial, sin importar si hay periodo de lavado o no. Además, permite modelar medidas repetidas dentro de cada periodo y amplía las estructuras de correlación dentro de las ecuaciones de estimación generalizadas. (Texto tomado de la fuente)DoctoradoDoctor en Ciencias - Estadísticaxix, 147 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasAnálisis funcionalTeoría de la estimaciónFunctional analysisEstimation theoryCarry-over effectCrossover designGeneralized estimating equationsPoisson distributionOverdispersion count dataKronecker correlationSplines estimationEfecto de arrastreDiseño cruzadoEcuaciones de estimación generalizadasDistribución de PoissonDatos de conteo de sobredispersiónCorrelación de KroneckerAnalysis of crossover designs with repeated measurements using generalized estimating equationsAnálisis de diseños crossover con medidas repetidas usando ecuaciones de estimación generalizadasTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDAgresti, A. 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Journal of Applied Statistics, 39(9):2067–2079.EstudiantesInvestigadoresPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84334/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53ORIGINAL1072719347.2023.pdf1072719347.2023.pdfTesis de Maestría en Ciencias - Estadísticaapplication/pdf1966429https://repositorio.unal.edu.co/bitstream/unal/84334/4/1072719347.2023.pdfa3f8dcc7af0945688b0bc7c9faac0a86MD54THUMBNAIL1072719347.2023.pdf.jpg1072719347.2023.pdf.jpgGenerated Thumbnailimage/jpeg4413https://repositorio.unal.edu.co/bitstream/unal/84334/5/1072719347.2023.pdf.jpgf8f33c6433f580728db6f6dc0dee0758MD55unal/84334oai:repositorio.unal.edu.co:unal/843342024-08-16 23:48:24.407Repositorio Institucional Universidad Nacional de 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