Métodos para identificar asociaciones entre genotipos y múltiples fenotipos

ilustraciones, diagramas

Autores:
Acero Baena, Juan Pablo
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/84474
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/84474
https://repositorio.unal.edu.co/
Palabra clave:
620 - Ingeniería y operaciones afines::621 - Física aplicada
GENOTIPOS
FENOTIPOS
Genotypes
Phenotype
Modelos Lineales
Pruebas Múltiples
Bioestadística
Multiple Testing
Biostatistics
Linear Models
Rights
openAccess
License
Reconocimiento 4.0 Internacional
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network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
dc.title.translated.eng.fl_str_mv Methods to identify associations between genotypes and multiple phenotypes
title Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
spellingShingle Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
620 - Ingeniería y operaciones afines::621 - Física aplicada
GENOTIPOS
FENOTIPOS
Genotypes
Phenotype
Modelos Lineales
Pruebas Múltiples
Bioestadística
Multiple Testing
Biostatistics
Linear Models
title_short Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
title_full Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
title_fullStr Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
title_full_unstemmed Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
title_sort Métodos para identificar asociaciones entre genotipos y múltiples fenotipos
dc.creator.fl_str_mv Acero Baena, Juan Pablo
dc.contributor.advisor.none.fl_str_mv López Kleine, Liliana
dc.contributor.author.none.fl_str_mv Acero Baena, Juan Pablo
dc.subject.ddc.spa.fl_str_mv 620 - Ingeniería y operaciones afines::621 - Física aplicada
topic 620 - Ingeniería y operaciones afines::621 - Física aplicada
GENOTIPOS
FENOTIPOS
Genotypes
Phenotype
Modelos Lineales
Pruebas Múltiples
Bioestadística
Multiple Testing
Biostatistics
Linear Models
dc.subject.lemb.spa.fl_str_mv GENOTIPOS
FENOTIPOS
dc.subject.lemb.eng.fl_str_mv Genotypes
Phenotype
dc.subject.proposal.spa.fl_str_mv Modelos Lineales
Pruebas Múltiples
Bioestadística
dc.subject.proposal.eng.fl_str_mv Multiple Testing
Biostatistics
Linear Models
description ilustraciones, diagramas
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-08-08T14:29:39Z
dc.date.available.none.fl_str_mv 2023-08-08T14:29:39Z
dc.date.issued.none.fl_str_mv 2023
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/84474
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/84474
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 spa
language spa
dc.relation.references.spa.fl_str_mv Agresti, A. (2015). Foundations of linear and generalized linear models. John Wiley & Sons Inc.
Andrews, S. J., Fulton-Howard, B., & Goate, A. (2020). Interpretation of risk loci from genome-wide association studies of Alzheimer’s disease. The Lancet Neurology, 19, 326-335. https://doi.org/10.1016/ s1474-4422(19)30435-1
Benafif, S., Kote-Jarai, Z., & Eeles, R. A. (2018). A Review of Prostate Cancer Genome-Wide Association Studies (GWAS). Cancer Epidemiology Biomarkers Prevention, 27, 845-857. https://doi.org/10. 1158/1055-9965.epi-16-1046
Boca, S. M., & Leek, J. T. (2015). A direct approach to estimating false discovery rates conditional on covariates. bioRxiv. https://doi.org/10.1101/035675
Carlos Fang-Mercado, L., Urrego-´Alvarez, J., Andr´es, E., Merlano-Bar´on, Meza-Torres, C., Hern´andez- Bonfante, L., L´opez-Kleine, L., & Marrugo-Cano, J. (2017). Art´ıculo original Influence of lifestyle, diet and vitamin D on atopy in a population of Afro-descendant Colombian children. Rev Alerg Mex, 64, 277-290.
Chul, G., Park, T., Park, D., & Shin. (1996). A Simple Method for Generating Correlated Binary Variates A Simple Method for Generating Correlated Binary Variates. Source: The American Statistician, 50, 306-310.
Cortés Muñoz, F. (2019). Methodology for estimating association between categorical variables with application to Genome-wide association studies (GWAS) (Tesis doctoral).
Dudoit, S., Gilbert, H. N., & van der Laan, M. J. (2008). Resampling-Based Empirical Bayes Multiple Testing Procedures for Controlling Generalized Tail Probability and Expected Value Error Rates: Focus on the False Discovery Rate and Simulation Study. Biometrical Journal, 50, 716-744. https: //doi.org/10.1002/bimj.200710473
Ehret, G. B. (2010). Genome-Wide Association Studies: Contribution of Genomics to Understanding Blood Pressure and Essential Hypertension. Current hypertension reports, 12, 17-25. https://doi.org/10. 1007/s11906-009-0086-6
Emrich, L. J., & Piedmonte, M. R. (1991). A Method for Generating High-Dimensional Multivariate Binary Variates. The American Statistician, 45, 302. https://doi.org/10.2307/2684460
Fernández-Santiago, R., & Sharma, M. (2022). What have we learned from genome-wide association studies (GWAS) in Parkinson disease? Ageing Research Reviews, 101648. https://doi.org/10.1016/j.arr. 2022.101648
Fang-Mercado, L. C., Urrego- Álvarez, J. R., Merlano-Barón, A. E., Meza-Torres, C., Hernández-Bonfante, L., López-Kleine, L., & Marrugo-Cano, J. (2017). Influencia del estilo de vida, la dieta y la vitamina D en la atopia en niños colombianos afrodescendientes. Revista Alergia México, 64, 277. https : //doi.org/10.29262/ram.v64i3.275
Frayling, T. M. (2007). Genome–wide association studies provide new insights into type 2 diabetes aetiology. Nature Reviews Genetics, 8, 657-662. https://doi.org/10.1038/nrg2178
Gibbons, J. D., & Chakraborti, S. (2021). Nonparametric statistical inference. Crc Press.
Guide, G. G. U. (s.f.). Manhattan Plot. www.jmp.com. Consultado el 19 de junio de 2023, desde https://www. jmp.com/support/downloads/JMPG101 documentation/Content/JMPGUserGuide/GR G 0022. htm
Guo, B., & Wu, B. (2018). Integrate multiple traits to detect novel trait–gene association using GWAS summary data with an adaptive test approach (R. Schwartz, Ed.). Bioinformatics, 35, 2251-2257. https://doi.org/10.1093/bioinformatics/bty961
Johnson, R. A., & Wichern, D. W. (2019). Applied multivariate statistical analysis. Pearson.
Liu, Z., & Lin, X. (2017). Multiple phenotype association tests using summary statistics in genome-wide association studies. Biometrics, 74, 165-175. https://doi.org/10.1111/biom.12735
Loos, R. J. F. (2020). 15 years of genome-wide association studies and no signs of slowing down. Nature Communications, 11. https://doi.org/10.1038/s41467-020-19653-5
Otto, L.-G., Mondal, P., Brassac, J., Preiss, S., Degenhardt, J., He, S., Reif, J. C., & Sharbel, T. F. (2017). Use of genotyping-by-sequencing to determine the genetic structure in the medicinal plant chamomile, and to identify flowering time and alpha-bisabolol associated SNP-loci by genome-wide association mapping. BMC Genomics, 18. https://doi.org/10.1186/s12864-017-3991-0
MedlinePlus. (2022). ¿Cuáles son los riesgos y las limitaciones de las pruebas genéticas: MedlinePlus Genetics. medlineplus.gov. https://medlineplus.gov/spanish/genetica/entender/pruebas/riesgoslimitaciones/
Parra-Galindo, M.-A., Piñeros-Niño, C., Soto-Sedano, J. C., & Mosquera-Vasquez, T. (2019). Chromosomes I and X Harbor Consistent Genetic Factors Associated with the Anthocyanin Variation in Potato. Agronomy, 9, 366. https://doi.org/10.3390/agronomy9070366
Ravishanker, N., & Dey, D. K. (2020). A First Course in Linear Model Theory. CRC Press.
Rowan, B. A., Seymour, D. K., Chae, E., Lundberg, D. S., & Weigel, D. (2016). Methods for Genotyping-by- Sequencing. Methods in Molecular Biology, 221-242. https://doi.org/10.1007/978-1-4939-6442-0 16
Sevilla, S. D. (2023). Metodolog´ıa de los estudios de asociación genética. Insuficiencia cardíaca, 2, 111-114. Consultado el 6 de junio de 2023, desde http://www.scielo.org.ar/scielo.php?script=sci arttext& pid=S1852-38622007000300006
Shaffer, J., Feingold, E., & Marazita, M. (2012). Genome-wide Association Studies. Journal of Dental Research, 91, 637-641. https://doi.org/10.1177/0022034512446968
Shim, H., Chasman, D. I., Smith, J. D., Mora, S., Ridker, P. M., Nickerson, D. A., Krauss, R. M., & Stephens, M. (2015). A Multivariate Genome-Wide Association Analysis of 10 LDL Subfractions, and Their Response to Statin Treatment, in 1868 Caucasians (P. Aspichueta, Ed.). PLOS ONE, 10, e0120758. https://doi.org/10.1371/journal.pone.0120758
Stephens, M. (2013). A Unified Framework for Association Analysis with Multiple Related Phenotypes (F. Emmert-Streib, Ed.). PLoS ONE, 8, e65245. https://doi.org/10.1371/journal.pone.0065245
VanRaden, P. (2008). Efficient Methods to Compute Genomic Predictions. Journal of Dairy Science, 91, 4414-4423. https://doi.org/10.3168/jds.2007-0980
Wang, K., Zhang, H.-T., Kugathasan, S., Annese, V., Bradfield, J. P., Russell, R. K., Imielinski, M., Glessner, J. T., Hou, C., Wilson, D., Walters, T. D., Kim, C. E., Frackelton, E. C., Lionetti, P., Barabino, A., Limbergen, J. V., Guthery, S. L., Denson, L. A., . . . Hakonarson, H. (2009). Diverse Genomewide Association Studies Associate the IL12/IL23 Pathway with Crohn Disease. 84, 399-405. https: //doi.org/10.1016/j.ajhg.2009.01.026
Weighill, D., Jones, P., Bleker, C., Ranjan, P., Shah, M., Zhao, N., Martin, M., DiFazio, S., Macaya-Sanz, D., Schmutz, J., Sreedasyam, A., Tschaplinski, T., Tuskan, G., & Jacobson, D. (2019). Multi-Phenotype Association Decomposition: Unraveling Complex Gene-Phenotype Relationships. Frontiers in Genetics, 10. https://doi.org/10.3389/fgene.2019.00417
Zhu, X., & Stephens, M. (2017). Bayesian large-scale multiple regression with summary statistics from genome-wide association studies. The Annals of Applied Statistics, 11, 1561-1592. https://doi.org/ 10.1214/17-aoas1046
Zhu, X., Feng, T., Tayo, B. O., Liang, J., Young, J. H., Franceschini, N., Smith, J. A., Yanek, L. R., Sun, Y. V., Edwards, T. L., Chen, W., Nalls, M., Fox, E., Sale, M., Bottinger, E., Rotimi, C., Liu, Y., McKnight, B., Liu, K., . . . Redline, S. (2015). Meta-analysis of Correlated Traits via Summary Statistics from GWASs with an Application in Hypertension. The American Journal of Human Genetics, 96, 21-36. https://doi.org/10.1016/j.ajhg.2014.11.011
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dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
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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 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2López Kleine, Liliana9c5b8dea895d5ed7db5c3cb9b48fb925Acero Baena, Juan Pablo3ab9cf98c7d84bca9ca29bbd3a6383652023-08-08T14:29:39Z2023-08-08T14:29:39Z2023https://repositorio.unal.edu.co/handle/unal/84474Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasLa secuenciación de genomas ha permitido aumentar el conocimiento en varios aspectos de la biología de los organismos. Una de las principales ramas que ha surgido es el estudio de asociación del genoma completo (Genome Wide Association Studies, GWAS), el cual ha permitido por medio de la asociación entre genotipos y fenotipos, identificar aspectos genotípicos relacionados con enfermedades complejas tales como el Alzheimer , la diabetes, el cáncer, entre otras. Originalmente, la mayor parte de estos estudios se han realizado para un solo fenotipo, por esta razón, tomando como base la metodología presentada por Guo y Wu, 2018 se evaluaron las asociaciones entre genotipos y fenotipos múltiples aplicando los métodos Principal Component Based Association Test, denotado como ET, Omnibus Test (OT) y Adaptative Test (AT), sobre tres bases de datos reales y un set de datos simulados binarios correlacionados. Así mismo, se evaluaron los desempeños de las metodologías comparándolas entre sí, teniendo en cuenta su capacidad para rechazar la mayor cantidad de hipótesis en pruebas múltiples y la potencia en los datos simulados. La comparación y caracterización de los métodos permitió establecer un flujo de trabajo óptimo, una identificación de los puntos positivos y negativos de cada una de las metodologias probadas. Igualmente, en la aplicación a bases de datos reales y simuladas se identificaron los aspectos a considerar para tener un m´etodo más sensible y específico. Se evaluó la mejora propuesta que consistió en la inclusión de la frecuencia y proporción de los alelos raros de cada SNP en el método AT. Estos resultados permitieron observar una mejora en la potencia del método AT, demostrando que la inclusión de dicha frecuencia es un insumo importante para detectar una mejor asociación entre un fenotipo y un genotipo. (Texto tomado de la fuente)Genome sequencing has increased knowledge in various aspects of the biology of organisms. One of the main branches that has emerged is the Genome Wide Association Studies (GWAS), which has allowed, through the association between genotypes and phenotypes, to identify genotypic aspects related to complex diseases such as Alzheimer’s, diabetes, cancer, among others, to identify genotypic aspects related to complex diseases such as Alzheimer’s disease, diabetes, cancer, among others. Originally, most of these studies have been performed for a single phenotype, for this reason, taking as a basis the methodology presented by Guo y Wu, 2018, the associations between genotypes and multiple phenotypes were evaluated by applying the methods ¨textitPrincipal Component Based Association Test, denoted as ET, Omnibus Test (OT) and Adaptative Test (AT), on three real datasets and a correlated binary simulated dataset. The performance of the methodologies was also evaluated by comparing them with each other, taking into account their ability to reject the largest number of hypotheses in multiple testing and the power in the simulated data. The comparison and characterization of the methods allowed establishing an optimal workflow, an identification of the positive and negative points of each of the tested methodologies. Likewise, in the application to real and simulated databases, the aspects to be considered in order to have a more sensitive and specific method were identified. The proposed improvement that consisted in the inclusion of the frequency and proportion of rare alleles of each SNP in the AT method was evaluated. These results allowed observing an improvement in the power of the AT method, demonstrating that the inclusion of such frequency is an important input to detect a better association between a phenotype and a genotypeMaestríaMagíster en Ciencias - EstadísticaEstadística Genómica66 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá620 - Ingeniería y operaciones afines::621 - Física aplicadaGENOTIPOSFENOTIPOSGenotypesPhenotypeModelos LinealesPruebas MúltiplesBioestadísticaMultiple TestingBiostatisticsLinear ModelsMétodos para identificar asociaciones entre genotipos y múltiples fenotiposMethods to identify associations between genotypes and multiple phenotypesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAgresti, A. (2015). Foundations of linear and generalized linear models. John Wiley & Sons Inc.Andrews, S. J., Fulton-Howard, B., & Goate, A. (2020). Interpretation of risk loci from genome-wide association studies of Alzheimer’s disease. The Lancet Neurology, 19, 326-335. https://doi.org/10.1016/ s1474-4422(19)30435-1Benafif, S., Kote-Jarai, Z., & Eeles, R. A. (2018). A Review of Prostate Cancer Genome-Wide Association Studies (GWAS). Cancer Epidemiology Biomarkers Prevention, 27, 845-857. https://doi.org/10. 1158/1055-9965.epi-16-1046Boca, S. M., & Leek, J. T. (2015). A direct approach to estimating false discovery rates conditional on covariates. bioRxiv. https://doi.org/10.1101/035675Carlos Fang-Mercado, L., Urrego-´Alvarez, J., Andr´es, E., Merlano-Bar´on, Meza-Torres, C., Hern´andez- Bonfante, L., L´opez-Kleine, L., & Marrugo-Cano, J. (2017). Art´ıculo original Influence of lifestyle, diet and vitamin D on atopy in a population of Afro-descendant Colombian children. Rev Alerg Mex, 64, 277-290.Chul, G., Park, T., Park, D., & Shin. (1996). A Simple Method for Generating Correlated Binary Variates A Simple Method for Generating Correlated Binary Variates. Source: The American Statistician, 50, 306-310.Cortés Muñoz, F. (2019). Methodology for estimating association between categorical variables with application to Genome-wide association studies (GWAS) (Tesis doctoral).Dudoit, S., Gilbert, H. N., & van der Laan, M. J. (2008). Resampling-Based Empirical Bayes Multiple Testing Procedures for Controlling Generalized Tail Probability and Expected Value Error Rates: Focus on the False Discovery Rate and Simulation Study. Biometrical Journal, 50, 716-744. https: //doi.org/10.1002/bimj.200710473Ehret, G. B. (2010). Genome-Wide Association Studies: Contribution of Genomics to Understanding Blood Pressure and Essential Hypertension. Current hypertension reports, 12, 17-25. https://doi.org/10. 1007/s11906-009-0086-6Emrich, L. J., & Piedmonte, M. R. (1991). A Method for Generating High-Dimensional Multivariate Binary Variates. The American Statistician, 45, 302. https://doi.org/10.2307/2684460Fernández-Santiago, R., & Sharma, M. (2022). What have we learned from genome-wide association studies (GWAS) in Parkinson disease? Ageing Research Reviews, 101648. https://doi.org/10.1016/j.arr. 2022.101648Fang-Mercado, L. C., Urrego- Álvarez, J. R., Merlano-Barón, A. E., Meza-Torres, C., Hernández-Bonfante, L., López-Kleine, L., & Marrugo-Cano, J. (2017). Influencia del estilo de vida, la dieta y la vitamina D en la atopia en niños colombianos afrodescendientes. Revista Alergia México, 64, 277. https : //doi.org/10.29262/ram.v64i3.275Frayling, T. M. (2007). Genome–wide association studies provide new insights into type 2 diabetes aetiology. Nature Reviews Genetics, 8, 657-662. https://doi.org/10.1038/nrg2178Gibbons, J. D., & Chakraborti, S. (2021). Nonparametric statistical inference. Crc Press.Guide, G. G. U. (s.f.). Manhattan Plot. www.jmp.com. Consultado el 19 de junio de 2023, desde https://www. jmp.com/support/downloads/JMPG101 documentation/Content/JMPGUserGuide/GR G 0022. htmGuo, B., & Wu, B. (2018). Integrate multiple traits to detect novel trait–gene association using GWAS summary data with an adaptive test approach (R. Schwartz, Ed.). Bioinformatics, 35, 2251-2257. https://doi.org/10.1093/bioinformatics/bty961Johnson, R. A., & Wichern, D. W. (2019). Applied multivariate statistical analysis. Pearson.Liu, Z., & Lin, X. (2017). Multiple phenotype association tests using summary statistics in genome-wide association studies. Biometrics, 74, 165-175. https://doi.org/10.1111/biom.12735Loos, R. J. F. (2020). 15 years of genome-wide association studies and no signs of slowing down. Nature Communications, 11. https://doi.org/10.1038/s41467-020-19653-5Otto, L.-G., Mondal, P., Brassac, J., Preiss, S., Degenhardt, J., He, S., Reif, J. C., & Sharbel, T. F. (2017). Use of genotyping-by-sequencing to determine the genetic structure in the medicinal plant chamomile, and to identify flowering time and alpha-bisabolol associated SNP-loci by genome-wide association mapping. BMC Genomics, 18. https://doi.org/10.1186/s12864-017-3991-0MedlinePlus. (2022). ¿Cuáles son los riesgos y las limitaciones de las pruebas genéticas: MedlinePlus Genetics. medlineplus.gov. https://medlineplus.gov/spanish/genetica/entender/pruebas/riesgoslimitaciones/Parra-Galindo, M.-A., Piñeros-Niño, C., Soto-Sedano, J. C., & Mosquera-Vasquez, T. (2019). Chromosomes I and X Harbor Consistent Genetic Factors Associated with the Anthocyanin Variation in Potato. Agronomy, 9, 366. https://doi.org/10.3390/agronomy9070366Ravishanker, N., & Dey, D. K. (2020). A First Course in Linear Model Theory. CRC Press.Rowan, B. A., Seymour, D. K., Chae, E., Lundberg, D. S., & Weigel, D. (2016). Methods for Genotyping-by- Sequencing. Methods in Molecular Biology, 221-242. https://doi.org/10.1007/978-1-4939-6442-0 16Sevilla, S. D. (2023). Metodolog´ıa de los estudios de asociación genética. Insuficiencia cardíaca, 2, 111-114. Consultado el 6 de junio de 2023, desde http://www.scielo.org.ar/scielo.php?script=sci arttext& pid=S1852-38622007000300006Shaffer, J., Feingold, E., & Marazita, M. (2012). Genome-wide Association Studies. Journal of Dental Research, 91, 637-641. https://doi.org/10.1177/0022034512446968Shim, H., Chasman, D. I., Smith, J. D., Mora, S., Ridker, P. M., Nickerson, D. A., Krauss, R. M., & Stephens, M. (2015). A Multivariate Genome-Wide Association Analysis of 10 LDL Subfractions, and Their Response to Statin Treatment, in 1868 Caucasians (P. Aspichueta, Ed.). PLOS ONE, 10, e0120758. https://doi.org/10.1371/journal.pone.0120758Stephens, M. (2013). A Unified Framework for Association Analysis with Multiple Related Phenotypes (F. Emmert-Streib, Ed.). 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The American Journal of Human Genetics, 96, 21-36. https://doi.org/10.1016/j.ajhg.2014.11.011EstudiantesLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84474/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53ORIGINALTRABAJO_DE_GRADO_VERSION_FINAL_ENTREGA.pdfTRABAJO_DE_GRADO_VERSION_FINAL_ENTREGA.pdfTrabajo final de Maestría en ciencias Estadística, Juan Pablo Aceroapplication/pdf976081https://repositorio.unal.edu.co/bitstream/unal/84474/4/TRABAJO_DE_GRADO_VERSION_FINAL_ENTREGA.pdf2369a7817bdb6ce383cb80bff3a75d82MD54unal/84474oai:repositorio.unal.edu.co:unal/844742023-08-08 09:30:38.128Repositorio Institucional Universidad Nacional de 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WwgdHJhdGFtaWVudG8gZGUgZGF0b3MgcGVyc29uYWxlcywgZGUgYWN1ZXJkbyBjb24gbGEgbGV5IDE1ODEgZGUgMjAxMiBlbnRlbmRpZW5kbyBxdWUgc2UgZW5jdWVudHJhbiBiYWpvIG1lZGlkYXMgcXVlIGdhcmFudGl6YW4gbGEgc2VndXJpZGFkLCBjb25maWRlbmNpYWxpZGFkIGUgaW50ZWdyaWRhZCwgeSBzdSB0cmF0YW1pZW50byB0aWVuZSB1bmEgZmluYWxpZGFkIGhpc3TDs3JpY2EsIGVzdGFkw61zdGljYSBvIGNpZW50w61maWNhIHNlZ8O6biBsbyBkaXNwdWVzdG8gZW4gbGEgUG9sw610aWNhIGRlIFRyYXRhbWllbnRvIGRlIERhdG9zIFBlcnNvbmFsZXMuCgoKClBBUlRFIDIuIEFVVE9SSVpBQ0nDk04gUEFSQSBQVUJMSUNBUiBZIFBFUk1JVElSIExBIENPTlNVTFRBIFkgVVNPIERFIE9CUkFTIEVOIEVMIFJFUE9TSVRPUklPIElOU1RJVFVDSU9OQUwgVU5BTC4KClNlIGF1dG9yaXphIGxhIHB1YmxpY2FjacOzbiBlbGVjdHLDs25pY2EsIGNvbnN1bHRhIHkgdXNvIGRlIGxhIG9icmEgcG9yIHBhcnRlIGRlIGxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhIHkgZGUgc3VzIHVzdWFyaW9zIGRlIGxhIHNpZ3VpZW50ZSBtYW5lcmE6CgphLglDb25jZWRvIGxpY2VuY2lhIGVuIGxvcyB0w6lybWlub3Mgc2XDsWFsYWRvcyBlbiBsYSBwYXJ0ZSAxIGRlbCBwcmVzZW50ZSBkb2N1bWVudG8sIGNvbiBlbCBvYmpldGl2byBkZSBxdWUgbGEgb2JyYSBlbnRyZWdhZGEgc2VhIHB1YmxpY2FkYSBlbiBlbCBSZXBvc2l0b3JpbyBJbnN0aXR1Y2lvbmFsIGRlIGxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhIHkgcHVlc3RhIGEgZGlzcG9zaWNpw7NuIGVuIGFjY2VzbyBhYmllcnRvIHBhcmEgc3UgY29uc3VsdGEgcG9yIGxvcyB1c3VhcmlvcyBkZSBsYSBVbml2ZXJzaWRhZCBOYWNpb25hbCBkZSBDb2xvbWJpYSAgYSB0cmF2w6lzIGRlIGludGVybmV0LgoKCgpQQVJURSAzIEFVVE9SSVpBQ0nDk04gREUgVFJBVEFNSUVOVE8gREUgREFUT1MgUEVSU09OQUxFUy4KCkxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhLCBjb21vIHJlc3BvbnNhYmxlIGRlbCBUcmF0YW1pZW50byBkZSBEYXRvcyBQZXJzb25hbGVzLCBpbmZvcm1hIHF1ZSBsb3MgZGF0b3MgZGUgY2Fyw6FjdGVyIHBlcnNvbmFsIHJlY29sZWN0YWRvcyBtZWRpYW50ZSBlc3RlIGZvcm11bGFyaW8sIHNlIGVuY3VlbnRyYW4gYmFqbyBtZWRpZGFzIHF1ZSBnYXJhbnRpemFuIGxhIHNlZ3VyaWRhZCwgY29uZmlkZW5jaWFsaWRhZCBlIGludGVncmlkYWQgeSBzdSB0cmF0YW1pZW50byBzZSByZWFsaXphIGRlIGFjdWVyZG8gYWwgY3VtcGxpbWllbnRvIG5vcm1hdGl2byBkZSBsYSBMZXkgMTU4MSBkZSAyMDEyIHkgZGUgbGEgUG9sw610aWNhIGRlIFRyYXRhbWllbnRvIGRlIERhdG9zIFBlcnNvbmFsZXMgZGUgbGEgVW5pdmVyc2lkYWQgTmFjaW9uYWwgZGUgQ29sb21iaWEuIFB1ZWRlIGVqZXJjZXIgc3VzIGRlcmVjaG9zIGNvbW8gdGl0dWxhciBhIGNvbm9jZXIsIGFjdHVhbGl6YXIsIHJlY3RpZmljYXIgeSByZXZvY2FyIGxhcyBhdXRvcml6YWNpb25lcyBkYWRhcyBhIGxhcyBmaW5hbGlkYWRlcyBhcGxpY2FibGVzIGEgdHJhdsOpcyBkZSBsb3MgY2FuYWxlcyBkaXNwdWVzdG9zIHkgZGlzcG9uaWJsZXMgZW4gd3d3LnVuYWwuZWR1LmNvIG8gZS1tYWlsOiBwcm90ZWNkYXRvc19uYUB1bmFsLmVkdS5jbyIKClRlbmllbmRvIGVuIGN1ZW50YSBsbyBhbnRlcmlvciwgYXV0b3Jpem8gZGUgbWFuZXJhIHZvbHVudGFyaWEsIHByZXZpYSwgZXhwbMOtY2l0YSwgaW5mb3JtYWRhIGUgaW5lcXXDrXZvY2EgYSBsYSBVbml2ZXJzaWRhZCBOYWNpb25hbCBkZSBDb2xvbWJpYSBhIHRyYXRhciBsb3MgZGF0b3MgcGVyc29uYWxlcyBkZSBhY3VlcmRvIGNvbiBsYXMgZmluYWxpZGFkZXMgZXNwZWPDrWZpY2FzIHBhcmEgZWwgZGVzYXJyb2xsbyB5IGVqZXJjaWNpbyBkZSBsYXMgZnVuY2lvbmVzIG1pc2lvbmFsZXMgZGUgZG9jZW5jaWEsIGludmVzdGlnYWNpw7NuIHkgZXh0ZW5zacOzbiwgYXPDrSBjb21vIGxhcyByZWxhY2lvbmVzIGFjYWTDqW1pY2FzLCBsYWJvcmFsZXMsIGNvbnRyYWN0dWFsZXMgeSB0b2RhcyBsYXMgZGVtw6FzIHJlbGFjaW9uYWRhcyBjb24gZWwgb2JqZXRvIHNvY2lhbCBkZSBsYSBVbml2ZXJzaWRhZC4gCgo=