Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19
ilustraciones, gráficas, tablas
- Autores:
-
Chaparro Martínez, Diego Alejandro
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/84775
- Palabra clave:
- 610 - Medicina y salud::616 - Enfermedades
510 - Matemáticas::518 - Análisis numérico
Biomarcadores
COVID-19/epidemiología
Biomarkers
COVID-19/epidemiology
Biomarcadores
Covid-19
Modelación conjunta
Modelos longitudinales
Modelos de sobrevivencia
Covariables endógenas
Covariables tiempo-dependientes
Biomarkers
Endogenous covariables
Joint modeling
Longitudinal models
Survival models
Time-dependent covariables
Análisis estadístico
Statistical analysis
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 |
| dc.title.translated.eng.fl_str_mv |
Joint modeling of longitudinal and survival data: an application to biomarker data in patients with Covid-19 |
| title |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 |
| spellingShingle |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 610 - Medicina y salud::616 - Enfermedades 510 - Matemáticas::518 - Análisis numérico Biomarcadores COVID-19/epidemiología Biomarkers COVID-19/epidemiology Biomarcadores Covid-19 Modelación conjunta Modelos longitudinales Modelos de sobrevivencia Covariables endógenas Covariables tiempo-dependientes Biomarkers Endogenous covariables Joint modeling Longitudinal models Survival models Time-dependent covariables Análisis estadístico Statistical analysis |
| title_short |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 |
| title_full |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 |
| title_fullStr |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 |
| title_full_unstemmed |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 |
| title_sort |
Modelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19 |
| dc.creator.fl_str_mv |
Chaparro Martínez, Diego Alejandro |
| dc.contributor.advisor.spa.fl_str_mv |
González García, Luz Mery |
| dc.contributor.author.spa.fl_str_mv |
Chaparro Martínez, Diego Alejandro |
| dc.subject.ddc.spa.fl_str_mv |
610 - Medicina y salud::616 - Enfermedades 510 - Matemáticas::518 - Análisis numérico |
| topic |
610 - Medicina y salud::616 - Enfermedades 510 - Matemáticas::518 - Análisis numérico Biomarcadores COVID-19/epidemiología Biomarkers COVID-19/epidemiology Biomarcadores Covid-19 Modelación conjunta Modelos longitudinales Modelos de sobrevivencia Covariables endógenas Covariables tiempo-dependientes Biomarkers Endogenous covariables Joint modeling Longitudinal models Survival models Time-dependent covariables Análisis estadístico Statistical analysis |
| dc.subject.decs.spa.fl_str_mv |
Biomarcadores COVID-19/epidemiología |
| dc.subject.decs.eng.fl_str_mv |
Biomarkers COVID-19/epidemiology |
| dc.subject.proposal.spa.fl_str_mv |
Biomarcadores Covid-19 Modelación conjunta Modelos longitudinales Modelos de sobrevivencia Covariables endógenas Covariables tiempo-dependientes |
| dc.subject.proposal.eng.fl_str_mv |
Biomarkers Endogenous covariables Joint modeling Longitudinal models Survival models Time-dependent covariables |
| dc.subject.unesco.spa.fl_str_mv |
Análisis estadístico |
| dc.subject.unesco.eng.fl_str_mv |
Statistical analysis |
| description |
ilustraciones, gráficas, tablas |
| publishDate |
2023 |
| dc.date.accessioned.none.fl_str_mv |
2023-10-05T20:26:23Z |
| dc.date.available.none.fl_str_mv |
2023-10-05T20:26:23Z |
| dc.date.issued.none.fl_str_mv |
2023-10-05 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
| dc.type.content.spa.fl_str_mv |
Text |
| dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
| status_str |
acceptedVersion |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/84775 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/84775 https://repositorio.unal.edu.co/ |
| identifier_str_mv |
Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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spa |
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Bireme |
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Abers, M. S., Delmonte, O. M., Ricotta, E. E., Fintzi, J., Fink, D. L., de Jesus, A. A. A., . . . others (2021). An immune-based biomarker signature is associated with mortality in covid-19 patients. Journal of Clinical Investigations insight, 6 (1). Andersen, P. K., y Gill, R. D. (1982). Cox’s regression model for counting processes: a large sample study. The Annals of Statistics, 1100–1120. Bondell, H. D., Krishna, A., y Ghosh, S. K. (2010). Joint variable selection for fixed and random effects in linear mixed-effects models. Biometrics, 66 (4), 1069–1077. Copaescu, A., James, F., Mouhtouris, E., Vogrin, S., Smibert, O. C., Gordon, C. L., . . . Trubiano, J. A. (2021). The role of immunological and clinical biomarkers to predict clinical covid-19 severity and response to therapy—a prospective longitudinal study. Frontiers in Immunology, 12 , 646095. Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34 (2), 187–202. Cox, D. R., y Hinkley, D. V. (1979). Theoretical statistics. CRC Press. Davidian, M., Diggle, P., Follmann, D., Louis, T. A., Taylor, J., Zeger, S., . . . others (2004). Discussion of joint modeling longitudinal and survival data. Statistica Sinica, 14 (3), 621–624. Davis, C. S. (2002). Statistical methods for the analysis of repeated measurements (Inf.Téc.). New York: Springer. Dempster, A. (1977). Maximum likelihood from incomplete data via em algorithm. Journal Royal Statistics Society B., 39 (1), 1–38. Faucett, C. L., y Thomas, D. C. (1996). Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. Statistics in medicine, 15 (15), 1663–1685. Fitzmaurice, G. M., Laird, N. M., y Ware, J. H. (2012). Applied longitudinal analysis (Vol. 998). Boston, MA: John Wiley & Sons. Freedman, D. A. (2008). Survival analysis: A primer. The American Statistician, 62 (2), 110–119. Grambsch, P. M., y Therneau, T. M. (1994). Proportional hazards tests and diagnostics based on weighted residuals. Biometrika, 81 (3), 515–526. Guan, W.-j., Ni, Z.-y., Hu, Y., Liang, W.-h., Ou, C.-q., He, J.-x., . . . others (2020). Clinical characteristics of coronavirus disease 2019 in china. New England Journal of Medicine, 382 (18), 1708–1720. Jones, R. H., y Boadi-Boateng, F. (1991). Unequally spaced longitudinal data with AR (1) serial correlation. Biometrics, 47 , 161–175. Kalbfleisch, J. D., y Prentice, R. L. (2011). The statistical analysis of failure time data. Hoboken, Nwe Jersey; John Wiley & Sons. Klein, J. P., y Moeschberger, M. L. (2003). Survival analysis: techniques for censored and truncated data (Vol. 1230). Springer. Lasso, G., Khan, S., Allen, S. A., Mariano, M., Florez, C., Orner, E. P., . . . others (2022). Longitudinally monitored immune biomarkers predict the timing of Covid19 outcomes. PLoS Computational Biology, 18 (1), e1009778. Little, R. J., y Rubin, D. B. (2019). Statistical analysis with missing data (Vol. 793). Hoboken, New Jersey; John Wiley & Sons. Martinussen, T. (2009). The frailty model. l. duchateau and p. janssen (2008). New York: Springer, 978-0-387-72834-6 (hardback). Standford, California: Wiley Online Library. Miller, A. (2002). Subset selection in regression. Boca Raton, Florida: Chapman and Hall/CRC. Nobre, J., y Singer, J. (2007). Residual analysis for linear mixed models. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 49 (6), 863–875. Ponti, G., Maccaferri, M., Ruini, C., Tomasi, A., y Ozben, T. (2020). Biomarkers associated with Covid-19 disease progression. Critical Reviews in Clinical Laboratory Sciences, 57 (6), 389–399. Press, W. H., Teukolsky, S. A., Vetterling, W. T., y Flannery, B. P. (2007). Numerical recipes 3rd edition: The art of scientific computing. New York: Cambridge University Press. Páramo Hernández, J. A. (2021). Coagulación, Dímero d y Covid-19. Accedido en 20-10-2022 a https://www.covid-19.seth.es/coagulacion-dimero-d-y-covid-19/. Riley, R. S., Gilbert, A. R., Dalton, J. B., Pai, S., y McPherson, R. A. (2016). Widely used types and clinical applications of D-Dimer assay. Laboratory Medicine, 47 (2), 90–102. Rizopoulos, D. (2010). Jm: An r package for the joint modeling of longitudinal and time-to-event data. Journal of Statistical Software, 35 , 1–33. Rizopoulos, D. (2012a). Fast fitting of joint models for longitudinal and event time data using a pseudo-adaptive gaussian quadrature rule. Computational Statistics & Data Analysis, 56 (3), 491–501. Rizopoulos, D., Verbeke, G., y Lesaffre, E. (2009). Fully exponential laplace approximations for the joint modelling of survival and longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71 (3), 637–654. Rizopoulos, D., Verbeke, G., y Molenberghs, G. (2008). Shared parameter models under random effects misspecification. Biometrika, 95 (1), 63–74. Rizopoulos, D., Verbeke, G., y Molenberghs, G. (2010). Multiple-imputation-based residuals and diagnostic plots for joint models of longitudinal and survival outcomes. Biometrics, 66 (1), 20–29. Ruppert, D., Wand, M. P., y Carroll, R. J. (2003). Semiparametric regression (n.o 12). Cambridge: Cambridge University Press. Sahu, S. K., Dey, D. K., Aslanidou, H., y Sinha, D. (1997). A Weibull regression model with Gamma frailties for multivariate survival data. Lifetime data analysis, 3, 123–137. Self, S., y Pawitan, Y. (1992). Modeling a marker of disease progression and onset of disease. AIDS Epidemiology: Methodological Issues, 34 , 231–255. Siddiqi, H. K., y Mehra, M. R. (2020). Covid-19 illness in native and immunosuppressed states: A clinical–therapeutic staging proposal. The Journal of Heart and Lung Transplantation, 39 (5), 405–407. Wang, Y., y Taylor, J. M. G. (2001). Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. Journal of the American Statistical Association, 96 (455), 895–905. Waternaux, C., Laird, N. M., y Ware, J. H. (1989). Methods for analysis of longitudinal data: blood-lead concentrations and cognitive development. Journal of the American Statistical Association, 84 (405), 33–41. Wulfsohn, M. S., y Tsiatis, A. A. (1997). A joint model for survival and longitudinal data measured with error. Biometrics, 330–339. Zhou, F., Yu, T., Du, R., Fan, G., Liu, Y., Liu, Z., . . . others (2020). Clinical course and risk factors for mortality of adult inpatients with covid-19 in Wuhan, China: a retrospective cohort study. The Lancet, 395 (10229), 1054–1062. LaMotte, L. R. (2007). A direct derivation of the reml likelihood function. Statistical Papers, 48 (2), 321–327. |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias - Maestría en Ciencias - Estadística |
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Facultad de Ciencias |
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Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2González García, Luz Mery848571137a0f25b45cc391309eda3230Chaparro Martínez, Diego Alejandroc866f051de44183724ec7f91a3bb18712023-10-05T20:26:23Z2023-10-05T20:26:23Z2023-10-05https://repositorio.unal.edu.co/handle/unal/84775Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficas, tablasEl siguiente documento presenta una alternativa para el modelamiento de datos de sobrevivencia, con covariables tiempo-dependientes de carácter endógeno, donde modelos clásicos como el modelo extendido de Cox no son apropiados, ya que no tienen en cuenta la estructura de asociación de la covariable endógena con la ocurrencia del evento. La alternativa bajo la cual se modelan las covariables tiempo-dependientes endógenas, en los modelos de sobrevivencia, se conoce como modelamiento conjunto para datos longitudinales y de sobrevivencia, metodología con aportes recientes que han optimizado el proceso de estimación de parámetros. Este trabajo tiene como objetivo explorar la metodología de modelamiento conjunto para datos longitudinales y de sobrevivencia, lo que hace de este una guía para su uso. Finalmente, para verificar los resultados se desarrolla una aplicación a datos clínicos de biomarcadores, en el contexto de la pandemia del Covid-19, en el que se observan las virtudes del método. (Texto tomado de la fuente).This document presents an alternative for modeling survival data, with endogenous time-dependent covariables, where classical models such as the extended Cox model are not appropriate, since they do not take into account the association structure of the endogenous covariable with the occurrence of the event. The alternative under which the endogenous time-dependent covariables are modeled, in the survival models, it is known as joint modeling for longitudinal and survival data, methodology with recent contributions that have optimized the parameter estimation process. The aim of this document is to explore the joint modeling methodology for longitudinal and survival data, making it a guide for its use. Finally, to verify the results, an application to clinical biomarker data is developed, in the context of the Covid-19 pandemic, in which the virtues of the method are observed.MaestríaMagíster en Ciencias - EstadísticaEstadística aplicadaxii, 84 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá610 - Medicina y salud::616 - Enfermedades510 - Matemáticas::518 - Análisis numéricoBiomarcadoresCOVID-19/epidemiologíaBiomarkersCOVID-19/epidemiologyBiomarcadoresCovid-19Modelación conjuntaModelos longitudinalesModelos de sobrevivenciaCovariables endógenasCovariables tiempo-dependientesBiomarkersEndogenous covariablesJoint modelingLongitudinal modelsSurvival modelsTime-dependent covariablesAnálisis estadísticoStatistical analysisModelación conjunta de datos longitudinales y de sobrevivencia: una aplicación a datos de biomarcadores en pacientes con Covid-19Joint modeling of longitudinal and survival data: an application to biomarker data in patients with Covid-19Trabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBiremeAbers, M. S., Delmonte, O. M., Ricotta, E. E., Fintzi, J., Fink, D. L., de Jesus, A. A. A., . . . others (2021). An immune-based biomarker signature is associated with mortality in covid-19 patients. Journal of Clinical Investigations insight, 6 (1).Andersen, P. K., y Gill, R. D. (1982). Cox’s regression model for counting processes: a large sample study. The Annals of Statistics, 1100–1120.Bondell, H. D., Krishna, A., y Ghosh, S. K. (2010). Joint variable selection for fixed and random effects in linear mixed-effects models. Biometrics, 66 (4), 1069–1077.Copaescu, A., James, F., Mouhtouris, E., Vogrin, S., Smibert, O. C., Gordon, C. L., . . . Trubiano, J. A. (2021). The role of immunological and clinical biomarkers to predict clinical covid-19 severity and response to therapy—a prospective longitudinal study. Frontiers in Immunology, 12 , 646095.Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34 (2), 187–202.Cox, D. R., y Hinkley, D. V. (1979). Theoretical statistics. CRC Press.Davidian, M., Diggle, P., Follmann, D., Louis, T. A., Taylor, J., Zeger, S., . . . others (2004). Discussion of joint modeling longitudinal and survival data. Statistica Sinica, 14 (3), 621–624.Davis, C. S. (2002). Statistical methods for the analysis of repeated measurements (Inf.Téc.). New York: Springer.Dempster, A. (1977). Maximum likelihood from incomplete data via em algorithm. Journal Royal Statistics Society B., 39 (1), 1–38.Faucett, C. L., y Thomas, D. C. (1996). Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. Statistics in medicine, 15 (15), 1663–1685.Fitzmaurice, G. M., Laird, N. M., y Ware, J. H. (2012). Applied longitudinal analysis (Vol. 998). Boston, MA: John Wiley & Sons.Freedman, D. A. (2008). Survival analysis: A primer. The American Statistician, 62 (2), 110–119.Grambsch, P. M., y Therneau, T. M. (1994). Proportional hazards tests and diagnostics based on weighted residuals. Biometrika, 81 (3), 515–526.Guan, W.-j., Ni, Z.-y., Hu, Y., Liang, W.-h., Ou, C.-q., He, J.-x., . . . others (2020). Clinical characteristics of coronavirus disease 2019 in china. New England Journal of Medicine, 382 (18), 1708–1720.Jones, R. H., y Boadi-Boateng, F. (1991). Unequally spaced longitudinal data with AR (1) serial correlation. Biometrics, 47 , 161–175.Kalbfleisch, J. D., y Prentice, R. L. (2011). The statistical analysis of failure time data. Hoboken, Nwe Jersey; John Wiley & Sons.Klein, J. P., y Moeschberger, M. L. (2003). Survival analysis: techniques for censored and truncated data (Vol. 1230). Springer.Lasso, G., Khan, S., Allen, S. A., Mariano, M., Florez, C., Orner, E. P., . . . others (2022). Longitudinally monitored immune biomarkers predict the timing of Covid19 outcomes. PLoS Computational Biology, 18 (1), e1009778.Little, R. J., y Rubin, D. B. (2019). Statistical analysis with missing data (Vol. 793). Hoboken, New Jersey; John Wiley & Sons.Martinussen, T. (2009). The frailty model. l. duchateau and p. janssen (2008). New York: Springer, 978-0-387-72834-6 (hardback). Standford, California: Wiley Online Library.Miller, A. (2002). Subset selection in regression. Boca Raton, Florida: Chapman and Hall/CRC.Nobre, J., y Singer, J. (2007). Residual analysis for linear mixed models. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 49 (6), 863–875.Ponti, G., Maccaferri, M., Ruini, C., Tomasi, A., y Ozben, T. (2020). Biomarkers associated with Covid-19 disease progression. Critical Reviews in Clinical Laboratory Sciences, 57 (6), 389–399.Press, W. H., Teukolsky, S. A., Vetterling, W. T., y Flannery, B. P. (2007). Numerical recipes 3rd edition: The art of scientific computing. New York: Cambridge University Press.Páramo Hernández, J. A. (2021). Coagulación, Dímero d y Covid-19. Accedido en 20-10-2022 a https://www.covid-19.seth.es/coagulacion-dimero-d-y-covid-19/.Riley, R. S., Gilbert, A. R., Dalton, J. B., Pai, S., y McPherson, R. A. (2016). Widely used types and clinical applications of D-Dimer assay. Laboratory Medicine, 47 (2), 90–102.Rizopoulos, D. (2010). Jm: An r package for the joint modeling of longitudinal and time-to-event data. Journal of Statistical Software, 35 , 1–33.Rizopoulos, D. (2012a). Fast fitting of joint models for longitudinal and event time data using a pseudo-adaptive gaussian quadrature rule. Computational Statistics & Data Analysis, 56 (3), 491–501.Rizopoulos, D., Verbeke, G., y Lesaffre, E. (2009). Fully exponential laplace approximations for the joint modelling of survival and longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71 (3), 637–654.Rizopoulos, D., Verbeke, G., y Molenberghs, G. (2008). Shared parameter models under random effects misspecification. Biometrika, 95 (1), 63–74.Rizopoulos, D., Verbeke, G., y Molenberghs, G. (2010). Multiple-imputation-based residuals and diagnostic plots for joint models of longitudinal and survival outcomes. Biometrics, 66 (1), 20–29.Ruppert, D., Wand, M. P., y Carroll, R. J. (2003). Semiparametric regression (n.o 12). Cambridge: Cambridge University Press.Sahu, S. K., Dey, D. K., Aslanidou, H., y Sinha, D. (1997). A Weibull regression model with Gamma frailties for multivariate survival data. Lifetime data analysis, 3, 123–137.Self, S., y Pawitan, Y. (1992). Modeling a marker of disease progression and onset of disease. AIDS Epidemiology: Methodological Issues, 34 , 231–255.Siddiqi, H. K., y Mehra, M. R. (2020). Covid-19 illness in native and immunosuppressed states: A clinical–therapeutic staging proposal. The Journal of Heart and Lung Transplantation, 39 (5), 405–407.Wang, Y., y Taylor, J. M. G. (2001). Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. Journal of the American Statistical Association, 96 (455), 895–905.Waternaux, C., Laird, N. M., y Ware, J. H. (1989). Methods for analysis of longitudinal data: blood-lead concentrations and cognitive development. Journal of the American Statistical Association, 84 (405), 33–41.Wulfsohn, M. S., y Tsiatis, A. A. (1997). A joint model for survival and longitudinal data measured with error. Biometrics, 330–339.Zhou, F., Yu, T., Du, R., Fan, G., Liu, Y., Liu, Z., . . . others (2020). Clinical course and risk factors for mortality of adult inpatients with covid-19 in Wuhan, China: a retrospective cohort study. The Lancet, 395 (10229), 1054–1062.LaMotte, L. R. (2007). A direct derivation of the reml likelihood function. Statistical Papers, 48 (2), 321–327.EstudiantesInvestigadoresPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84775/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1026577391.2023.pdf1026577391.2023.pdfTesis de Maestría en Ciencias - Estadísticaapplication/pdf1469515https://repositorio.unal.edu.co/bitstream/unal/84775/2/1026577391.2023.pdf8e388f0778a8ea7679ccd1960303056eMD52THUMBNAIL1026577391.2023.pdf.jpg1026577391.2023.pdf.jpgGenerated Thumbnailimage/jpeg4523https://repositorio.unal.edu.co/bitstream/unal/84775/3/1026577391.2023.pdf.jpgfd361b40afd308a7a9227f9daefce5bbMD53unal/84775oai:repositorio.unal.edu.co:unal/847752024-08-18 23:13:34.035Repositorio Institucional Universidad Nacional de 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