Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19

El análisis de datos longitudinales es necesario cuando la variable respuesta se mide repetidamente sobre la misma unidad de observación a lo largo del tiempo. Los métodos paramétricos se han empleado tradicionalmente en el análisis de datos longitudinales para estimar los coeficientes que definen l...

Full description

Autores:: Casadiego Rincón, Elkin Javier

Tipo de recurso:: Masters Thesis

Fecha de publicación:: 2021

Institución:: Universidad Santo Tomás

Repositorio:: Repositorio Institucional USTA

Idioma:: spa

id	SANTTOMAS2_ffbd03f2a1bec6ac2fb7dff6c5796986
oai_identifier_str	oai:repository.usta.edu.co:11634/35397
network_acronym_str	SANTTOMAS2
network_name_str	Repositorio Institucional USTA
repository_id_str
dc.title.spa.fl_str_mv	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19
title	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19
spellingShingle	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19 Longitudinal data analysis radial basis kernel function regression spline time-varying coef- cient model viral load CD4 T lymphocytes count HIV/AIDS COVID-19 Estadistica VIH HIV Análisis de datos longitudinales funciones de base radial kernel regresión spline modelos de coeficientes dinámicos carga viral conteo de linfocitos CD4,
title_short	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19
title_full	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19
title_fullStr	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19
title_full_unstemmed	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19
title_sort	Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19
dc.creator.fl_str_mv	Casadiego Rincón, Elkin Javier
dc.contributor.advisor.none.fl_str_mv	Sosa Martinez, Juan Camilo
dc.contributor.author.none.fl_str_mv	Casadiego Rincón, Elkin Javier
dc.contributor.orcid.spa.fl_str_mv	https://orcid.org/0000-0001-7432-4014
dc.contributor.googlescholar.spa.fl_str_mv	https://scholar.google.com/citations?user=armR6koAAAAJ&hl=es
dc.contributor.cvlac.spa.fl_str_mv	https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001359814
dc.contributor.corporatename.spa.fl_str_mv	Universidad Santo Tomas
dc.subject.keyword.spa.fl_str_mv	Longitudinal data analysis radial basis kernel function regression spline time-varying coef- cient model viral load CD4 T lymphocytes count HIV/AIDS COVID-19
topic	Longitudinal data analysis radial basis kernel function regression spline time-varying coef- cient model viral load CD4 T lymphocytes count HIV/AIDS COVID-19 Estadistica VIH HIV Análisis de datos longitudinales funciones de base radial kernel regresión spline modelos de coeficientes dinámicos carga viral conteo de linfocitos CD4,
dc.subject.lemb.spa.fl_str_mv	Estadistica VIH HIV
dc.subject.proposal.spa.fl_str_mv	Análisis de datos longitudinales funciones de base radial kernel regresión spline modelos de coeficientes dinámicos carga viral conteo de linfocitos CD4,
description	El análisis de datos longitudinales es necesario cuando la variable respuesta se mide repetidamente sobre la misma unidad de observación a lo largo del tiempo. Los métodos paramétricos se han empleado tradicionalmente en el análisis de datos longitudinales para estimar los coeficientes que definen la relación entre el predictor lineal y la variable respuesta, sin embargo las técnicas paramétricas no son apropiadas cuando no se cumplen los supuestos acerca de la variable respuesta y la componente aleatoria del modelo, o cuando el valor esperado de la variable respuesta (o una función de esta variable vía una función de enlace) no resulta ser una función conocida de los efectos fijos y aleatorios, razones por las que los modelos paramétricos pueden llevar a conclusiones alejadas de la tendencia promedio del conjunto de datos. En estos casos, las técnicas de regresión no paramétricas, en las que en lugar de parámetros se emplean funciones locales suavizadas que dependen del tiempo, denominados coeficientes o parámetros dinámicos, constituyen una alternativa muy poderosa de modelamiento en el análisis de datos longitudinales, puesto que permiten establecer una dependencia funcional más flexible entre la variable respuesta y las covariables. Este trabajo propone desarrollar técnicas de estimación e inferencia para modelos de coeficientes dinámicos no paramétricos generalizados, particularmente cuando la variable respuesta es de conteo, ilustrando su aplicación en el efecto de la carga viral sobre el conteo de células CD4, en pacientes con HIV/AIDS sometidos a un tratamiento antirretroviral, y también en la predicción de casos de COVID-19.
publishDate	2021
dc.date.accessioned.none.fl_str_mv	2021-08-27T12:15:31Z
dc.date.available.none.fl_str_mv	2021-08-27T12:15:31Z
dc.date.issued.none.fl_str_mv	2021-08-25
dc.type.local.spa.fl_str_mv	Tesis de maestría
dc.type.version.none.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.category.spa.fl_str_mv	Formación de Recurso Humano para la Ctel: Trabajo de grado de Maestría
dc.type.coar.none.fl_str_mv	http://purl.org/coar/resource_type/c_bdcc
dc.type.drive.none.fl_str_mv	info:eu-repo/semantics/masterThesis
format	http://purl.org/coar/resource_type/c_bdcc
status_str	acceptedVersion
dc.identifier.citation.spa.fl_str_mv	Casadiego, E. ( 2021). Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19 (Tesis de maestría). Universidad Santo Tomás, Bogotá, Colombia.
dc.identifier.uri.none.fl_str_mv	http://hdl.handle.net/11634/35397
dc.identifier.reponame.spa.fl_str_mv	reponame:Repositorio Institucional Universidad Santo Tomás
dc.identifier.instname.spa.fl_str_mv	instname:Universidad Santo Tomás
dc.identifier.repourl.spa.fl_str_mv	repourl:https://repository.usta.edu.co
identifier_str_mv	Casadiego, E. ( 2021). Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19 (Tesis de maestría). Universidad Santo Tomás, Bogotá, Colombia. reponame:Repositorio Institucional Universidad Santo Tomás instname:Universidad Santo Tomás repourl:https://repository.usta.edu.co
url	http://hdl.handle.net/11634/35397
dc.language.iso.spa.fl_str_mv	spa
language	spa
dc.relation.references.spa.fl_str_mv	Ahmadi, A., Fadaei, Y., Shirani, M., and Rahmani, F. (2020). Modeling and forecasting trend of covid-19 epidemic in iran until may 13, 2020. Medical Journal of the Islamic Republic of Iran, 34:27. Barbosa, I., de Lima, K., and de Almeida Medeiros, A. (2020). Covid-19 in brazil: analysis of the pandemic short-term scenario in relation to other countries. Int. J. Dev. Res, 10(6):36840{36845. Batista, M. (2020). Estimation of the nal size of the covid-19 epidemic. MedRxiv. doi, 10:16{20023606. Cai, Z., Fan, J., and Li, R. (2000). E cient estimation and inferences for varying-coe cient models. Journal of the American Statistical Association, 95(451):888{902. Cameron, A. C. and Trivedi, P. K. (2013). Regression analysis of count data, volume 53. Cambridge university press. Carroll, C., Bhattacharjee, S., Chen, Y., Dubey, P., Fan, J., Gajardo, A., Zhou, X., Mueller, H.-G., and Wang, J.-L. (2020). Time dynamics of covid-19. medRxiv. Clara-Rahola, J. (2020). An empirical model for the spread and reduction of the covid19 pandemic. Studies of Applied Economics, 38(2). Cuevas, A. (2004). El an alisis estad stico de grandes masas de datos: algunas tendencias recientes. De la aritm etica al an alisis: historia y desarrollos recientes en matem aticas, page 59. Davidian, M. (2007). Applied Longitudinal Data Analysis. de Pereda Sebasti an, D., Ramos, A. M., and Ivorr, B. (2010). Modelizaci on matem atica de la difusi on de una epidemia de peste porcina entre granjas. PhD thesis, Tesis de Maester. Universidad Complutese de Madrid. 19, 21. D az-Narv aez, V., San-Mart n-Rold an, D., Calzadilla-N u~nez, A., San-Mart n-Rold an, P., Parody-Mu~noz, A., and Robledo-Veloso, G. (2020). Which curve provides the best explanation of the growth in con rmed covid-19 cases in chile? Revista Latino-Americana de Enfermagem, 28. Egger, M., May, M., Ch^ene, G., Phillips, A. N., Ledergerber, B., Dabis, F., Costagliola, D., Monforte, A. D., De Wolf, F., Reiss, P., et al. (2002). Prognosis of hiv-1-infected patients starting highly active antiretroviral therapy: a collaborative analysis of prospective studies. The Lancet, 360(9327):119{129. Ekum, M. and Ogunsanya, A. (2020). Application of hierarchical polynomial regression models to predict transmission of covid-19 at global level. Int. J. Clin. Biostat. Biom, 6:027. Fan, J. and Zhang, W. (2008). Statistical methods with varying coe cient models. Statistics and its Interface, 1(1):179. Faraway, J. J. (2016). Extending the linear model with R: generalized linear, mixed e ects and nonpara- metric regression models. CRC press. Fischl, M. A., Giuliano, M., Vella, S., Ribaudo, H. J., Collier, A. C., Erice, A., Dehlinger, M., Eron, Joseph J., J., Saag, M. S., Hammer, S. M., and Morse, G. D. (2003). A Randomized Trial of 2 Di erent 4-Drug Antiretroviral Regimens versus a 3-Drug Regimen, in Advanced Human Immunode ciency Virus Disease. The Journal of Infectious Diseases, 188(5):625{634. Ford, N., Stinson, K., Gale, H., Mills, E. J., Stevens, W., Gonz alez, M. P., Markby, J., and Hill, A. (2015). Cd4 changes among virologically suppressed patients on antiretroviral therapy: a systematic review and meta-analysis. Journal of the International AIDS Society, 18(1):20061. Gonzalo-Gil, E., Ikediobi, U., and Sutton, R. E. (2017). Mechanisms of virologic control and clinical characteristics of hiv+ elite/viremic controllers. The Yale journal of biology and medicine, 90(2):245. Hastie, T. and Tibshirani, R. (1993). Varying-coe cient models. Journal of the Royal Statistical Society: Series B (Methodological), 55(4):757{779. Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coe cient models with longitudinal data. Biometrika, 85(4):809{822. Huang, Y., Chen, J., and Yan, C. (2012). Mixed-e ects joint models with skew-normal distribution for hiv dynamic response with missing and mismeasured time-varying covariate. The international journal of biostatistics, 8(1). Huang, Y. and Lu, T. (2016). Bayesian inference on partially linear mixed-e ects joint models for longitudinal data with multiple features. Computational Statistics, 32. Hughes, M. D., Johnson, V. A., Hirsch, M. S., Bremer, J. W., Elbeik, T., Erice, A., Kuritzkes, D. R., Scott, W. A., Spector, S. A., Basgoz, N., et al. (1997). Monitoring plasma hiv-1 rna levels in addition to cd4+ lymphocyte count improves assessment of antiretroviral therapeutic response. Annals of internal medicine, 126(12):929{938. Kasilingam, D., Sathiya Prabhakaran, S. P., Rajendran, D. K., Rajagopal, V., Santhosh Kumar, T., and Soundararaj, A. (2020). Exploring the growth of covid-19 cases using exponential modelling across 42 countries and predicting signs of early containment using machine learning. Transboundary and Emerging Diseases. Kermack, W. O. and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, 115(772):700{721. Korenromp, E. L., Williams, B. G., Schmid, G. P., and Dye, C. (2009). Clinical prognostic value of rna viral load and cd4 cell counts during untreated hiv1 infection a quantitative review. PloS one, 4(6):e5950. Kumar, N. (2015). Review of innovation di usion models. Lederman, M. M., Connick, E., Landay, A., Kuritzkes, D. R., Spritzler, J., St. Clair, M., Kotzin, B. L.,Fox, L., Heath Chiozzi, M., Leonard, J. M., et al. (1998). Immunologic responses associated with 12weeks of combination antiretroviral therapy consisting of zidovudine, lamivudine, and ritonavir: resultsof aids clinical trials group protocol 315.Journal of Infectious Diseases, 178(1):70–79. León Isorna, S. (2015). Modelización estadística de datos longitudinales. Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., Tong, Y., Ren, R., Leung, K. S., Lau, E. H., Wong, J. Y.,et al. (2020). Early transmission dynamics in wuhan, china, of novel coronavirus–infected pneumonia.New England Journal of Medicine. Liang, H., Wu, H., and Carroll, R. J. (2003). The relationship between virologic and immunologicresponses in aids clinical research using mixed-effects varying-coefficient models with measurementerror.Biostatistics, 4(2):297–312. Lipsitz, S. R., Ibrahim, J., and Molenberghs, G. (2000). Using a box–cox transformation in the analysisof longitudinal data with incomplete responses.Journal of the Royal Statistical Society: Series C(Applied Statistics), 49(3):287–296. Lu, T. and Huang, Y. (2017). Bayesian inference on mixed-effects varying-coefficient joint models withskew-t distribution for longitudinal data with multiple features.Statistical methods in medical research,26(3):1146–1164. Lu, Y. and Zhang, R. (2009). Smoothing spline estimation of generalised varying-coefficient mixed model.Journal of Nonparametric Statistics, 21(7):815–825. Luo, J. (2020). Predictive monitoring of covid-19.SUTD Data-Driven Innovation Lab. Ma, J. (2020). Estimating epidemic exponential growth rate and basic reproduction number.InfectiousDisease Modelling, 5:129–141 Manrique Abril, F., Gonz ́alez-Chord ́a, V. M., Guti ́errez Lesmes, O. A., Tellez Pi ̃nerez, C. F., Herrera-Amaya, G. M., et al. (2020). Modelo sir de la pandemia de covid-19 en colombia. Marschner, I. C., Collier, A. C., Coombs, R. W., D’aquila, R. T., DeGruttola, V., Fischl, M. A., Hammer,S. M., Hughes, M. D., Johnson, V. A., Katzenstein, D. A., et al. (1998). Use of changes in plasma levelsof human immunodeficiency virus type 1 rna to assess the clinical benefit of antiretroviral therapy.Journal of Infectious Diseases, 177(1):40–47. Mercker, M., Betzin, U., and Wilken, D. (2020). What influences covid-19 infection rates: A statisticalapproach to identify promising factors applied to infection data from germany.medRxiv. Mill ́an-O ̃nate, J., Rodriguez-Morales, A. J., Camacho-Moreno, G., Mendoza-Ram ́ırez, H., Rodr ́ıguez-Sabogal, I. A., and ́Alvarez-Moreno, C. (2020). A new emerging zoonotic virus of concern: the 2019novel coronavirus (sars cov-2).Infectio, 24(3):187–192. Ministerio (2014). Guía de práctica clínica basada en la evidencia científica para la atención de la infección por vih/sida en adolescentes (con 13 años de edad o más) y adultos. Montgomery, D., Peck, E., and Vining, G. G. (2006). Introducción al análisis de regresión lineal. México:Limusa Wiley. Park, T. and Jeong, S. (2018). Analysis of poisson varying-coefficient models with autoregression.Sta-tistics, 52(1):34–49. Pelinovsky, E., Kurkin, A., Kurkina, O., Kokoulina, M., and Epifanova, A. (2020). Logistic equation andcovid-19.Chaos, Solitons & Fractals, 140:110241. Ramsay, J., Hooker, G., and Graves, S. (2009). Functional data analysis with r and matlab: Springerscience & business media. S ̧ent ̈urk, D. and M ̈uller, H.-G. (2008). Generalized varying coefficient models for longitudinal data.Biometrika, 95(3):653–666. Sosa, J. and Buitrago, L. (2021). Time-varying coefficient model estimation through radial basis fun-ctions.arXiv preprint arXiv:2103.00315. Sosa, J. and Díaz, L. (2009). Desarrollo de un modelo de coeficientes dinámicos y aleatorios para el análisis longitudinales. PhD thesis, Tesis de maestría, Departamento de Estadística, Universidad Nacional de Colombia, Bogotá, Colombia. Sosa, J. C. and Díaz, L. G. (2012). Random time-varying coefficient model estimation through radial basis functions.Revista Colombiana de Estad ́ıstica, 35(1):167–184. Thiébaut, R., Morlat, P., Jacqmin-Gadda, H., Neau, D., Mercié, P., Dabis, F., Chene, G., et al. (2000).Clinical progression of hiv-1 infection according to the viral response during the first year of antire-troviral treatment.Aids, 14(8):971–978. Trujillo, C. H. S. (2020). Resumen: Consenso colombiano de atención, diagnóstico y manejo de la infección por sars-cov-2/covid-19 en establecimientos de atención de la salud.Infectio, 24(3). Twisk, J. W. (2013). Applied longitudinal data analysis for epidemiology: a practical guide. Cambridge University Press. Wang, P., Zheng, X., Li, J., and Zhu, B. (2020). Prediction of epidemic trends in covid-19 with logistic model and machine learning technics.Chaos, Solitons & Fractals, 139:110058. Wang, Y. (2007). Varying-coefficient models: New models, inference procedures, and applications. WHO (2007). Who case definitions of hiv for surveillance and revised clinical staging and immunological classification of hiv-related disease in adults and children. WHO et al. (2016). Consolidated guidelines on the use of antiretroviral drugs for treating and preventing HIV infection: recommendations for a public health approach. World Health Organization. Wu, C. O. and Tian, X. (2018). Nonparametric Models for Longitudinal Data: With Implementation in R. Chapman and Hall/CRC. Wu, H. and Zhang, J.-T. (2006).Nonparametric regression methods for longitudinal data analysis: mixed-effects modeling approaches, volume 515. John Wiley & Sons. Zeger, S. L. and Diggle, P. J. (1994). Semiparametric models for longitudinal data with application to cd4 cell numbers in hiv seroconverters. Biometrics, pages 689–699.
dc.rights.*.fl_str_mv	Atribución-NoComercial-SinDerivadas 2.5 Colombia
dc.rights.uri.*.fl_str_mv	http://creativecommons.org/licenses/by-nc-nd/2.5/co/
dc.rights.local.spa.fl_str_mv	Abierto (Texto Completo)
dc.rights.accessrights.none.fl_str_mv	info:eu-repo/semantics/openAccess
dc.rights.coar.none.fl_str_mv	http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv	Atribución-NoComercial-SinDerivadas 2.5 Colombia http://creativecommons.org/licenses/by-nc-nd/2.5/co/ Abierto (Texto Completo) http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv	openAccess
dc.format.mimetype.spa.fl_str_mv	application/pdf
dc.coverage.campus.spa.fl_str_mv	CRAI-USTA Bogotá
dc.publisher.spa.fl_str_mv	Universidad Santo Tomás
dc.publisher.program.spa.fl_str_mv	Maestría Estadística Aplicada
dc.publisher.faculty.spa.fl_str_mv	Facultad de Estadística
institution	Universidad Santo Tomás
bitstream.url.fl_str_mv	https://repository.usta.edu.co/bitstream/11634/35397/1/2021elkincasadiego.pdf https://repository.usta.edu.co/bitstream/11634/35397/2/Carta%20aprobaci%c3%b3n%20de%20facultad.pdf https://repository.usta.edu.co/bitstream/11634/35397/3/Derechos%20de%20autor%2024%20ago.%202021.pdf https://repository.usta.edu.co/bitstream/11634/35397/5/license.txt https://repository.usta.edu.co/bitstream/11634/35397/4/license_rdf https://repository.usta.edu.co/bitstream/11634/35397/6/2021elkincasadiego.pdf.jpg https://repository.usta.edu.co/bitstream/11634/35397/7/Carta%20aprobaci%c3%b3n%20de%20facultad.pdf.jpg https://repository.usta.edu.co/bitstream/11634/35397/8/Derechos%20de%20autor%2024%20ago.%202021.pdf.jpg
bitstream.checksum.fl_str_mv	a61d85f214668b776b1e26b91b96e326 308c1741e2615f4b94b75f9523f5fcba 935bd0c6192de90e6a90ee72df0f4981 aedeaf396fcd827b537c73d23464fc27 217700a34da79ed616c2feb68d4c5e06 519ae518f8d14f7751562c1e69effebf a7ed2ec391b873f930e8feae8446ac78 049f82e8da65756a5e3ef183c011d18f
bitstream.checksumAlgorithm.fl_str_mv	MD5 MD5 MD5 MD5 MD5 MD5 MD5 MD5
repository.name.fl_str_mv	Repositorio Universidad Santo Tomás
repository.mail.fl_str_mv	repositorio@usantotomas.edu.co
_version_	1782026237110124544
spelling	Sosa Martinez, Juan CamiloCasadiego Rincón, Elkin Javierhttps://orcid.org/0000-0001-7432-4014https://scholar.google.com/citations?user=armR6koAAAAJ&hl=eshttps://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001359814Universidad Santo Tomas2021-08-27T12:15:31Z2021-08-27T12:15:31Z2021-08-25Casadiego, E. ( 2021). Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19 (Tesis de maestría). Universidad Santo Tomás, Bogotá, Colombia.http://hdl.handle.net/11634/35397reponame:Repositorio Institucional Universidad Santo Tomásinstname:Universidad Santo Tomásrepourl:https://repository.usta.edu.coEl análisis de datos longitudinales es necesario cuando la variable respuesta se mide repetidamente sobre la misma unidad de observación a lo largo del tiempo. Los métodos paramétricos se han empleado tradicionalmente en el análisis de datos longitudinales para estimar los coeficientes que definen la relación entre el predictor lineal y la variable respuesta, sin embargo las técnicas paramétricas no son apropiadas cuando no se cumplen los supuestos acerca de la variable respuesta y la componente aleatoria del modelo, o cuando el valor esperado de la variable respuesta (o una función de esta variable vía una función de enlace) no resulta ser una función conocida de los efectos fijos y aleatorios, razones por las que los modelos paramétricos pueden llevar a conclusiones alejadas de la tendencia promedio del conjunto de datos. En estos casos, las técnicas de regresión no paramétricas, en las que en lugar de parámetros se emplean funciones locales suavizadas que dependen del tiempo, denominados coeficientes o parámetros dinámicos, constituyen una alternativa muy poderosa de modelamiento en el análisis de datos longitudinales, puesto que permiten establecer una dependencia funcional más flexible entre la variable respuesta y las covariables. Este trabajo propone desarrollar técnicas de estimación e inferencia para modelos de coeficientes dinámicos no paramétricos generalizados, particularmente cuando la variable respuesta es de conteo, ilustrando su aplicación en el efecto de la carga viral sobre el conteo de células CD4, en pacientes con HIV/AIDS sometidos a un tratamiento antirretroviral, y también en la predicción de casos de COVID-19.Longitudinal data analysis is necessary when the response variable is repeatedly measured on the same observation unit over time. The parametric methods have been traditionally used in the analysis of longitudinal data to estimate the coefficients that define the relationship between the linear predictor and the response variable, However, parametric techniques do not work when the assumptions about the response variable and the random component of the model are not fulfilled, or when the expected value of the response variable (or a function of this variable via a link function) is not be a known function of the fixed and random effects, reasons why parametric models can draw conclusions away from the average trend of the data set. In these cases, {non-parametric regression techniques, in which time-dependent smoothed local functions are used instead of parameters, called coefficients or dynamic parameters, constitute a very powerful modeling alternative in the analysis of longitudinal data, since they allow establish a more flexible functional dependence between the response variable and the covariates. In this work, it is proposed to develop estimation and inference techniques for generalized non-parametric dynamic coefficient models, particularly when the response variable is counting, illustrating its application in the effect of viral load on CD4 cell count, in patients with HIV / AIDS undergoing antiretroviral treatment, and also in the prediction of COVID-19 cases.Magister en Estadística Aplicadahttp://unidadinvestigacion.usta.edu.coMaestríaapplication/pdfspaUniversidad Santo TomásMaestría Estadística AplicadaFacultad de EstadísticaAtribución-NoComercial-SinDerivadas 2.5 Colombiahttp://creativecommons.org/licenses/by-nc-nd/2.5/co/Abierto (Texto Completo)info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19Longitudinal data analysisradial basis kernel functionregression splinetime-varying coef- cient modelviral loadCD4 T lymphocytes countHIV/AIDSCOVID-19EstadisticaVIHHIVAnálisis de datos longitudinalesfunciones de base radial kernelregresión splinemodelos de coeficientes dinámicoscarga viralconteo de linfocitos CD4,Tesis de maestríainfo:eu-repo/semantics/acceptedVersionFormación de Recurso Humano para la Ctel: Trabajo de grado de Maestríahttp://purl.org/coar/resource_type/c_bdccinfo:eu-repo/semantics/masterThesisCRAI-USTA BogotáAhmadi, A., Fadaei, Y., Shirani, M., and Rahmani, F. (2020). Modeling and forecasting trend of covid-19 epidemic in iran until may 13, 2020. Medical Journal of the Islamic Republic of Iran, 34:27.Barbosa, I., de Lima, K., and de Almeida Medeiros, A. (2020). Covid-19 in brazil: analysis of the pandemic short-term scenario in relation to other countries. Int. J. Dev. Res, 10(6):36840{36845.Batista, M. (2020). Estimation of the nal size of the covid-19 epidemic. MedRxiv. doi, 10:16{20023606.Cai, Z., Fan, J., and Li, R. (2000). E cient estimation and inferences for varying-coe cient models. Journal of the American Statistical Association, 95(451):888{902.Cameron, A. C. and Trivedi, P. K. (2013). Regression analysis of count data, volume 53. Cambridge university press.Carroll, C., Bhattacharjee, S., Chen, Y., Dubey, P., Fan, J., Gajardo, A., Zhou, X., Mueller, H.-G., and Wang, J.-L. (2020). Time dynamics of covid-19. medRxiv.Clara-Rahola, J. (2020). An empirical model for the spread and reduction of the covid19 pandemic. Studies of Applied Economics, 38(2).Cuevas, A. (2004). El an alisis estad stico de grandes masas de datos: algunas tendencias recientes. De la aritm etica al an alisis: historia y desarrollos recientes en matem aticas, page 59.Davidian, M. (2007). Applied Longitudinal Data Analysis.de Pereda Sebasti an, D., Ramos, A. M., and Ivorr, B. (2010). Modelizaci on matem atica de la difusi on de una epidemia de peste porcina entre granjas. PhD thesis, Tesis de Maester. Universidad Complutese de Madrid. 19, 21.D az-Narv aez, V., San-Mart n-Rold an, D., Calzadilla-N u~nez, A., San-Mart n-Rold an, P., Parody-Mu~noz, A., and Robledo-Veloso, G. (2020). Which curve provides the best explanation of the growth in con rmed covid-19 cases in chile? Revista Latino-Americana de Enfermagem, 28.Egger, M., May, M., Ch^ene, G., Phillips, A. N., Ledergerber, B., Dabis, F., Costagliola, D., Monforte, A. D., De Wolf, F., Reiss, P., et al. (2002). Prognosis of hiv-1-infected patients starting highly active antiretroviral therapy: a collaborative analysis of prospective studies. The Lancet, 360(9327):119{129.Ekum, M. and Ogunsanya, A. (2020). Application of hierarchical polynomial regression models to predict transmission of covid-19 at global level. Int. J. Clin. Biostat. Biom, 6:027.Fan, J. and Zhang, W. (2008). Statistical methods with varying coe cient models. Statistics and its Interface, 1(1):179.Faraway, J. J. (2016). Extending the linear model with R: generalized linear, mixed e ects and nonpara- metric regression models. CRC press.Fischl, M. A., Giuliano, M., Vella, S., Ribaudo, H. J., Collier, A. C., Erice, A., Dehlinger, M., Eron, Joseph J., J., Saag, M. S., Hammer, S. M., and Morse, G. D. (2003). A Randomized Trial of 2 Di erent 4-Drug Antiretroviral Regimens versus a 3-Drug Regimen, in Advanced Human Immunode ciency Virus Disease. The Journal of Infectious Diseases, 188(5):625{634.Ford, N., Stinson, K., Gale, H., Mills, E. J., Stevens, W., Gonz alez, M. P., Markby, J., and Hill, A. (2015). Cd4 changes among virologically suppressed patients on antiretroviral therapy: a systematic review and meta-analysis. Journal of the International AIDS Society, 18(1):20061.Gonzalo-Gil, E., Ikediobi, U., and Sutton, R. E. (2017). Mechanisms of virologic control and clinical characteristics of hiv+ elite/viremic controllers. The Yale journal of biology and medicine, 90(2):245.Hastie, T. and Tibshirani, R. (1993). Varying-coe cient models. Journal of the Royal Statistical Society: Series B (Methodological), 55(4):757{779.Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coe cient models with longitudinal data. Biometrika, 85(4):809{822.Huang, Y., Chen, J., and Yan, C. (2012). Mixed-e ects joint models with skew-normal distribution for hiv dynamic response with missing and mismeasured time-varying covariate. The international journal of biostatistics, 8(1).Huang, Y. and Lu, T. (2016). Bayesian inference on partially linear mixed-e ects joint models for longitudinal data with multiple features. Computational Statistics, 32.Hughes, M. D., Johnson, V. A., Hirsch, M. S., Bremer, J. W., Elbeik, T., Erice, A., Kuritzkes, D. R., Scott, W. A., Spector, S. A., Basgoz, N., et al. (1997). Monitoring plasma hiv-1 rna levels in addition to cd4+ lymphocyte count improves assessment of antiretroviral therapeutic response. Annals of internal medicine, 126(12):929{938.Kasilingam, D., Sathiya Prabhakaran, S. P., Rajendran, D. K., Rajagopal, V., Santhosh Kumar, T., and Soundararaj, A. (2020). Exploring the growth of covid-19 cases using exponential modelling across 42 countries and predicting signs of early containment using machine learning. Transboundary and Emerging Diseases.Kermack, W. O. and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, 115(772):700{721.Korenromp, E. L., Williams, B. G., Schmid, G. P., and Dye, C. (2009). Clinical prognostic value of rna viral load and cd4 cell counts during untreated hiv1 infection a quantitative review. PloS one, 4(6):e5950.Kumar, N. (2015). Review of innovation di usion models.Lederman, M. M., Connick, E., Landay, A., Kuritzkes, D. R., Spritzler, J., St. Clair, M., Kotzin, B. L.,Fox, L., Heath Chiozzi, M., Leonard, J. M., et al. (1998). Immunologic responses associated with 12weeks of combination antiretroviral therapy consisting of zidovudine, lamivudine, and ritonavir: resultsof aids clinical trials group protocol 315.Journal of Infectious Diseases, 178(1):70–79.León Isorna, S. (2015). Modelización estadística de datos longitudinales.Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., Tong, Y., Ren, R., Leung, K. S., Lau, E. H., Wong, J. Y.,et al. (2020). Early transmission dynamics in wuhan, china, of novel coronavirus–infected pneumonia.New England Journal of Medicine.Liang, H., Wu, H., and Carroll, R. J. (2003). The relationship between virologic and immunologicresponses in aids clinical research using mixed-effects varying-coefficient models with measurementerror.Biostatistics, 4(2):297–312.Lipsitz, S. R., Ibrahim, J., and Molenberghs, G. (2000). Using a box–cox transformation in the analysisof longitudinal data with incomplete responses.Journal of the Royal Statistical Society: Series C(Applied Statistics), 49(3):287–296.Lu, T. and Huang, Y. (2017). Bayesian inference on mixed-effects varying-coefficient joint models withskew-t distribution for longitudinal data with multiple features.Statistical methods in medical research,26(3):1146–1164.Lu, Y. and Zhang, R. (2009). Smoothing spline estimation of generalised varying-coefficient mixed model.Journal of Nonparametric Statistics, 21(7):815–825.Luo, J. (2020). Predictive monitoring of covid-19.SUTD Data-Driven Innovation Lab.Ma, J. (2020). Estimating epidemic exponential growth rate and basic reproduction number.InfectiousDisease Modelling, 5:129–141Manrique Abril, F., Gonz ́alez-Chord ́a, V. M., Guti ́errez Lesmes, O. A., Tellez Pi ̃nerez, C. F., Herrera-Amaya, G. M., et al. (2020). Modelo sir de la pandemia de covid-19 en colombia.Marschner, I. C., Collier, A. C., Coombs, R. W., D’aquila, R. T., DeGruttola, V., Fischl, M. A., Hammer,S. M., Hughes, M. D., Johnson, V. A., Katzenstein, D. A., et al. (1998). Use of changes in plasma levelsof human immunodeficiency virus type 1 rna to assess the clinical benefit of antiretroviral therapy.Journal of Infectious Diseases, 177(1):40–47.Mercker, M., Betzin, U., and Wilken, D. (2020). What influences covid-19 infection rates: A statisticalapproach to identify promising factors applied to infection data from germany.medRxiv.Mill ́an-O ̃nate, J., Rodriguez-Morales, A. J., Camacho-Moreno, G., Mendoza-Ram ́ırez, H., Rodr ́ıguez-Sabogal, I. A., and ́Alvarez-Moreno, C. (2020). A new emerging zoonotic virus of concern: the 2019novel coronavirus (sars cov-2).Infectio, 24(3):187–192.Ministerio (2014). Guía de práctica clínica basada en la evidencia científica para la atención de la infección por vih/sida en adolescentes (con 13 años de edad o más) y adultos.Montgomery, D., Peck, E., and Vining, G. G. (2006). Introducción al análisis de regresión lineal. México:Limusa Wiley.Park, T. and Jeong, S. (2018). Analysis of poisson varying-coefficient models with autoregression.Sta-tistics, 52(1):34–49.Pelinovsky, E., Kurkin, A., Kurkina, O., Kokoulina, M., and Epifanova, A. (2020). Logistic equation andcovid-19.Chaos, Solitons & Fractals, 140:110241.Ramsay, J., Hooker, G., and Graves, S. (2009). Functional data analysis with r and matlab: Springerscience & business media.S ̧ent ̈urk, D. and M ̈uller, H.-G. (2008). Generalized varying coefficient models for longitudinal data.Biometrika, 95(3):653–666.Sosa, J. and Buitrago, L. (2021). Time-varying coefficient model estimation through radial basis fun-ctions.arXiv preprint arXiv:2103.00315.Sosa, J. and Díaz, L. (2009). Desarrollo de un modelo de coeficientes dinámicos y aleatorios para el análisis longitudinales. PhD thesis, Tesis de maestría, Departamento de Estadística, Universidad Nacional de Colombia, Bogotá, Colombia.Sosa, J. C. and Díaz, L. G. (2012). Random time-varying coefficient model estimation through radial basis functions.Revista Colombiana de Estad ́ıstica, 35(1):167–184.Thiébaut, R., Morlat, P., Jacqmin-Gadda, H., Neau, D., Mercié, P., Dabis, F., Chene, G., et al. (2000).Clinical progression of hiv-1 infection according to the viral response during the first year of antire-troviral treatment.Aids, 14(8):971–978.Trujillo, C. H. S. (2020). Resumen: Consenso colombiano de atención, diagnóstico y manejo de la infección por sars-cov-2/covid-19 en establecimientos de atención de la salud.Infectio, 24(3).Twisk, J. W. (2013). Applied longitudinal data analysis for epidemiology: a practical guide. Cambridge University Press.Wang, P., Zheng, X., Li, J., and Zhu, B. (2020). Prediction of epidemic trends in covid-19 with logistic model and machine learning technics.Chaos, Solitons & Fractals, 139:110058.Wang, Y. (2007). Varying-coefficient models: New models, inference procedures, and applications.WHO (2007). Who case definitions of hiv for surveillance and revised clinical staging and immunological classification of hiv-related disease in adults and children.WHO et al. (2016). Consolidated guidelines on the use of antiretroviral drugs for treating and preventing HIV infection: recommendations for a public health approach. World Health Organization.Wu, C. O. and Tian, X. (2018). Nonparametric Models for Longitudinal Data: With Implementation in R. Chapman and Hall/CRC.Wu, H. and Zhang, J.-T. (2006).Nonparametric regression methods for longitudinal data analysis: mixed-effects modeling approaches, volume 515. John Wiley & Sons.Zeger, S. L. and Diggle, P. J. (1994). Semiparametric models for longitudinal data with application to cd4 cell numbers in hiv seroconverters. Biometrics, pages 689–699.ORIGINAL2021elkincasadiego.pdf2021elkincasadiego.pdfTrabajo de Gradoapplication/pdf690817https://repository.usta.edu.co/bitstream/11634/35397/1/2021elkincasadiego.pdfa61d85f214668b776b1e26b91b96e326MD51open accessCarta aprobación de facultad.pdfCarta aprobación de facultad.pdfCarta aprobación facultadapplication/pdf16121https://repository.usta.edu.co/bitstream/11634/35397/2/Carta%20aprobaci%c3%b3n%20de%20facultad.pdf308c1741e2615f4b94b75f9523f5fcbaMD52metadata only accessDerechos de autor 24 ago. 2021.pdfDerechos de autor 24 ago. 2021.pdfDerechos de autorapplication/pdf458994https://repository.usta.edu.co/bitstream/11634/35397/3/Derechos%20de%20autor%2024%20ago.%202021.pdf935bd0c6192de90e6a90ee72df0f4981MD53metadata only accessLICENSElicense.txtlicense.txttext/plain; charset=utf-8807https://repository.usta.edu.co/bitstream/11634/35397/5/license.txtaedeaf396fcd827b537c73d23464fc27MD55open accessCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repository.usta.edu.co/bitstream/11634/35397/4/license_rdf217700a34da79ed616c2feb68d4c5e06MD54open accessTHUMBNAIL2021elkincasadiego.pdf.jpg2021elkincasadiego.pdf.jpgIM Thumbnailimage/jpeg7148https://repository.usta.edu.co/bitstream/11634/35397/6/2021elkincasadiego.pdf.jpg519ae518f8d14f7751562c1e69effebfMD56open accessCarta aprobación de facultad.pdf.jpgCarta aprobación de facultad.pdf.jpgIM Thumbnailimage/jpeg6303https://repository.usta.edu.co/bitstream/11634/35397/7/Carta%20aprobaci%c3%b3n%20de%20facultad.pdf.jpga7ed2ec391b873f930e8feae8446ac78MD57open accessDerechos de autor 24 ago. 2021.pdf.jpgDerechos de autor 24 ago. 2021.pdf.jpgIM Thumbnailimage/jpeg9070https://repository.usta.edu.co/bitstream/11634/35397/8/Derechos%20de%20autor%2024%20ago.%202021.pdf.jpg049f82e8da65756a5e3ef183c011d18fMD58open access11634/35397oai:repository.usta.edu.co:11634/353972022-10-25 03:03:45.846open accessRepositorio Universidad Santo Tomásrepositorio@usantotomas.edu.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

Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19

Publicaciones similares