Penalized bayesian optimal designs for nonlinear models of Continuous Response
Experimental design is an important phase in both scienti_c and industrial research. In recent years, Bayesian optimal designs have become more and more popular, particularly in biomedical research and clinical trials. The Bayesian experimental design approach allows the prior information of unknown...
- Autores:
-
Rudnykh, Svetlana Ivanovna
- Tipo de recurso:
- Work document
- Fecha de publicación:
- 2019
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/75605
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/75605
- Palabra clave:
- Matemáticas::Probabilidades y matemáticas aplicadas
Bayesian optimal designs
Desirability functions
Penalized designs
Diseños óptimos bayesianos
Funciones de deseabilidad
Diseños penalizados
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Penalized bayesian optimal designs for nonlinear models of Continuous Response |
| title |
Penalized bayesian optimal designs for nonlinear models of Continuous Response |
| spellingShingle |
Penalized bayesian optimal designs for nonlinear models of Continuous Response Matemáticas::Probabilidades y matemáticas aplicadas Bayesian optimal designs Desirability functions Penalized designs Diseños óptimos bayesianos Funciones de deseabilidad Diseños penalizados |
| title_short |
Penalized bayesian optimal designs for nonlinear models of Continuous Response |
| title_full |
Penalized bayesian optimal designs for nonlinear models of Continuous Response |
| title_fullStr |
Penalized bayesian optimal designs for nonlinear models of Continuous Response |
| title_full_unstemmed |
Penalized bayesian optimal designs for nonlinear models of Continuous Response |
| title_sort |
Penalized bayesian optimal designs for nonlinear models of Continuous Response |
| dc.creator.fl_str_mv |
Rudnykh, Svetlana Ivanovna |
| dc.contributor.advisor.spa.fl_str_mv |
López Ríos, Víctor Ignacio |
| dc.contributor.author.spa.fl_str_mv |
Rudnykh, Svetlana Ivanovna |
| dc.subject.ddc.spa.fl_str_mv |
Matemáticas::Probabilidades y matemáticas aplicadas |
| topic |
Matemáticas::Probabilidades y matemáticas aplicadas Bayesian optimal designs Desirability functions Penalized designs Diseños óptimos bayesianos Funciones de deseabilidad Diseños penalizados |
| dc.subject.proposal.eng.fl_str_mv |
Bayesian optimal designs Desirability functions Penalized designs |
| dc.subject.proposal.spa.fl_str_mv |
Diseños óptimos bayesianos Funciones de deseabilidad Diseños penalizados |
| description |
Experimental design is an important phase in both scienti_c and industrial research. In recent years, Bayesian optimal designs have become more and more popular, particularly in biomedical research and clinical trials. The Bayesian experimental design approach allows the prior information of unknown parameters to be incorporated into the design process in order to achieve a better design. The Bayesian optimal design theory can, however, produce inadequate designs from a practical perspective that conict with common practice in laboratories or other guidelines established. In this research, the penalized optimal design strategy with the Bayesian approach is suggested to reduce problems associated with the inadequacy of experimental designs from a practical perspective. New optimality criteria, which combine the use of desirability functions and the Bayesian approach, are constructed for linear and nonlinear regression models. The proposed technique based on the use of desirability functions helps to obtain optimal designs that ful_ll Bayesian optimal design criteria and also satisfy practical preferences. The proposed penalized strategy is illustrated with corresponding examples for both linear and nonlinear models. Furthermore, the methodology of choosing the appropriate desirability functions according to the practical design preferences is proposed and illustrated by an example of the Michaelis-Menten model. |
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2019 |
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2019 |
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2020-02-14T19:04:22Z |
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2020-02-14T19:04:22Z |
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Documento de trabajo |
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info:eu-repo/semantics/workingPaper |
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eng |
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eng |
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Albert, J. (2009), Bayesian computation with R, Springer Science & Business Media. Atkinson, A., Bogacka, B. & Zocchi, S. (2000), `Equivalence theory for design augmentation and parsimonious model checking: response surfaces and yield density models', Listy Biometryczne-Biometrical Letters 37(2), 67{95. Bates, D. M. & Watts, D. G. (1988), Nonlinear regression analysis and its applications, John Wiles & Sons, Inc. Bender, R. (2009), Introduction to the use of regression models in epidemiology, in `Cancer Epidemiology', Springer, pp. 179{195. Borchers, H. W. (2018), `Package `adagio': Discrete and global optimization routines', Available: https://CRAN.R-project.org/package=adagio Chaloner, K. & Larntz, K. (1989), `Optimal bayesian design applied to logistic regression experiments', Journal of Statistical Planning and Inference 21(2), 191{208. Cook, D. & Fedorov, V. (1995), `Invited discussion paper constrained optimization of experimental design', Statistics 26(2), 129{148. Del Castillo, E., Montgomery, D. & McCarville, D. (1996), `Modi ed desirability functions for multiples response optimization', Journal of quality technology 28(3), 337{345 Derringer, G. C. (1994), `A balancing act-optimizing a products properties', Quality Progress 27(6), 51{58. Dette, H. & Biedermann, S. (2003), `Robust and e cient designs for the michaelismenten model', Journal of the American Statistical Association 98(463), 679{686. Dette, H. & Sperlich, S. (1994), `A note on bayesian d-optimal designs for a generalization of the exponential growth model', South African Statist. J 28, 103{11 Dragalin, V., Fedorov, V. & Wu, Y. (2008), `Adaptive designs for selecting drug combinations based on e cacy{toxicity response', Journal of Statistical Planning and Inference 138(2), 352{373. Ermakov, S. M. & Zhiglijavsky, A. A. (1987), The Mathematical Theory of Optimum Experiments, Nauka, Moscow. (In Russian). Firth, D. & Hinde, J. (1997), `On bayesian d-optimum design criteria and the equivalence theorem in non-linear models', Journal of the Royal Statistical Society: Series B Statistical Methodology) 59(4), 793{797. Gao, L. & Rosenberger, W. F. (2013), Adaptive bayesian design with penalty based on toxicity-e cacy response, in D. Ucinski, A. C. Atkinson & M. Patan, eds, `mODa 10{Advances in Model-Oriented Design and Analysis', Springer, Heidelberg, pp. 91{ 98. George, P. & Ogot, M. M. (2006), `A compromise experimental design method for parametric polynomial response surface approximations', Journal of Applied Statistics 33(10), 1037{1050 Haines, L. M., Perevozskaya, I. & Rosenberger, W. F. (2003), `Bayesian optimal designs for phase i clinical trials', Biometrics 59(3), 591{600. Kiefer, J. (1959), `Optimum experimental designs', Journal of the Royal Statistical Society: Series B (Methodological) 21(2), 272{304. Kiefer, J., Wolfowitz, J. et al. (1959), `Optimum designs in regression problems', The Annals of Mathematical Statistics 30(2), 271{294. Mukhopadhyay, S. & Haines, L. M. (1995), `Bayesian d-optimal designs for the exponential growth model', Journal of Statistical Planning and Inference 44(3), 385{397. Mullen, K., Ardia, D., Gil, D. L., Windover, D. & Cline, J. (2016), `Deoptim: An r package for global optimization by di erential evolution', Available: https://CRAN.Rproject. org/package=DEoptim. Parker, S. & Gennings, C. (2008), `Penalized Locally Optimal Experimental Designs for Nonlinear Models', Journal of Agricultural, Biological, and Environmental Statistics 13(3), 334{354. Parker, S. M. (2005), Solutions to reduce problems associated with experimental designs for nonlinear models: Conditional analyses and penalized optimal designs, PhD thesis, Virginia Commonwealth University Storn, R. & Price, K. (1997), `Di erential evolution{a simple and e cient heuristicfor global optimization over continuous spaces', Journal of global optimization 11(4), 341{359. Team, R. C. (2018), `R: A language and environment for statistical computing. r foundation for statistical computing, vienna, austria. 2013 (version 3.5.1)', Available: http://www.R-project.org. Tranda r, C. & L opez-Fidalgo, J. (2004), Locally optimal designs for an extension of the michaelis-menten model, in A. Di Bucchianico, H. Ler & H. P. Wynn, eds, `mODa 7{Advances in Model-Oriented Design and Analysis', Physica-Verlag, Heidelberg, pp. 173{181. Yeatts, S. D., Gennings, C. & Crofton, K. M. (2012), `Optimal design for the precise estimation of an interaction threshold: The impact of exposure to a mixture of 18 polyhalogenated aromatic hydrocarbons', Risk Analysis 32(10), 1784{1797 Ypma, J., Borchers, H. & Eddelbuettel, D. (2014), `R package `nloptr': R interface to nlopt', Available: https://CRAN.R-project.org/package=nloptr Zhang, Y. (2006), Bayesian D-optimal design for generalized linear models, PhD thesis, Virginia Tech. |
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Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial-SinDerivadas 4.0 Internacional |
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Acceso abierto |
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Atribución-NoComercial-SinDerivadas 4.0 InternacionalDerechos reservados - Universidad Nacional de ColombiaAcceso abiertohttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2López Ríos, Víctor Ignacio8161396a-0a77-44a4-a5ef-8d8bc5a9d917-1Rudnykh, Svetlana Ivanovna764f951e-08d2-4fa9-be0d-ffcee4c8b9ac2020-02-14T19:04:22Z2020-02-14T19:04:22Z2019https://repositorio.unal.edu.co/handle/unal/75605Experimental design is an important phase in both scienti_c and industrial research. In recent years, Bayesian optimal designs have become more and more popular, particularly in biomedical research and clinical trials. The Bayesian experimental design approach allows the prior information of unknown parameters to be incorporated into the design process in order to achieve a better design. The Bayesian optimal design theory can, however, produce inadequate designs from a practical perspective that conict with common practice in laboratories or other guidelines established. In this research, the penalized optimal design strategy with the Bayesian approach is suggested to reduce problems associated with the inadequacy of experimental designs from a practical perspective. New optimality criteria, which combine the use of desirability functions and the Bayesian approach, are constructed for linear and nonlinear regression models. The proposed technique based on the use of desirability functions helps to obtain optimal designs that ful_ll Bayesian optimal design criteria and also satisfy practical preferences. The proposed penalized strategy is illustrated with corresponding examples for both linear and nonlinear models. Furthermore, the methodology of choosing the appropriate desirability functions according to the practical design preferences is proposed and illustrated by an example of the Michaelis-Menten model.El diseño experimental es una fase importante tanto en la investigación científica como en la industria. En los últimos años, los diseños óptimos bayesianos se han vuelto cada vez más populares, particularmente en la investigación biomédica y los ensayos clínicos. El enfoque de diseño experimental bayesiano permite incorporar la información previa disponible de parámetros desconocidos en el proceso de diseño y así poder obtener un mejor diseño. Sin embargo, la teoría del diseño _optimo bayesiano puede producir diseños inadecuados desde una perspectiva práctica que entran en contacto con la práctica de laboratorio común u otras pautas establecidas. Con el objetivo de reducir los problemas asociados con la inadecuación de los diseños experimentales desde una perspectiva práctica, en esta investigación, se proponen nuevos criterios de optimalidad que combinan el uso de funciones de deseabilidad y el enfoque bayesiano, tanto para modelos de regresión lineal, como no lineal. La técnica propuesta basada en el uso de las funciones de deseabilidad ayuda a obtener diseños _óptimos penalizados que cumplen con los criterios de diseño _óptimos bayesianos y también satisfacen preferencias prácticas. La estrategia penalizada propuesta se ilustra con los respectivos ejemplos para modelos lineales y no lineales. Además, se propone y se ilustra una metodología a para elegir las funciones de deseabilidad apropiadas de acuerdo con las preferencias experimentales desde un punto de vista práctico mediante un ejemplo del modelo de Michaelis-Menten.Doctora en Ciencias EstadísticaDoctorado144application/pdfengMatemáticas::Probabilidades y matemáticas aplicadasBayesian optimal designsDesirability functionsPenalized designsDiseños óptimos bayesianosFunciones de deseabilidadDiseños penalizadosPenalized bayesian optimal designs for nonlinear models of Continuous ResponseDocumento de trabajoinfo:eu-repo/semantics/workingPaperinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_8042Texthttp://purl.org/redcol/resource_type/WPEscuela de estadísticaUniversidad Nacional de Colombia - Sede MedellínAlbert, J. (2009), Bayesian computation with R, Springer Science & Business Media.Atkinson, A., Bogacka, B. & Zocchi, S. (2000), `Equivalence theory for design augmentation and parsimonious model checking: response surfaces and yield density models', Listy Biometryczne-Biometrical Letters 37(2), 67{95.Bates, D. M. & Watts, D. G. (1988), Nonlinear regression analysis and its applications, John Wiles & Sons, Inc.Bender, R. (2009), Introduction to the use of regression models in epidemiology, in `Cancer Epidemiology', Springer, pp. 179{195.Borchers, H. W. (2018), `Package `adagio': Discrete and global optimization routines', Available: https://CRAN.R-project.org/package=adagioChaloner, K. & Larntz, K. (1989), `Optimal bayesian design applied to logistic regression experiments', Journal of Statistical Planning and Inference 21(2), 191{208.Cook, D. & Fedorov, V. (1995), `Invited discussion paper constrained optimization of experimental design', Statistics 26(2), 129{148.Del Castillo, E., Montgomery, D. & McCarville, D. (1996), `Modi ed desirability functions for multiples response optimization', Journal of quality technology 28(3), 337{345Derringer, G. C. (1994), `A balancing act-optimizing a products properties', Quality Progress 27(6), 51{58.Dette, H. & Biedermann, S. (2003), `Robust and e cient designs for the michaelismenten model', Journal of the American Statistical Association 98(463), 679{686.Dette, H. & Sperlich, S. (1994), `A note on bayesian d-optimal designs for a generalization of the exponential growth model', South African Statist. J 28, 103{11Dragalin, V., Fedorov, V. & Wu, Y. (2008), `Adaptive designs for selecting drug combinations based on e cacy{toxicity response', Journal of Statistical Planning and Inference 138(2), 352{373.Ermakov, S. M. & Zhiglijavsky, A. A. (1987), The Mathematical Theory of Optimum Experiments, Nauka, Moscow. (In Russian).Firth, D. & Hinde, J. (1997), `On bayesian d-optimum design criteria and the equivalence theorem in non-linear models', Journal of the Royal Statistical Society: Series B Statistical Methodology) 59(4), 793{797.Gao, L. & Rosenberger, W. F. (2013), Adaptive bayesian design with penalty based on toxicity-e cacy response, in D. Ucinski, A. C. Atkinson & M. Patan, eds, `mODa 10{Advances in Model-Oriented Design and Analysis', Springer, Heidelberg, pp. 91{ 98.George, P. & Ogot, M. M. (2006), `A compromise experimental design method for parametric polynomial response surface approximations', Journal of Applied Statistics 33(10), 1037{1050Haines, L. M., Perevozskaya, I. & Rosenberger, W. F. (2003), `Bayesian optimal designs for phase i clinical trials', Biometrics 59(3), 591{600.Kiefer, J. (1959), `Optimum experimental designs', Journal of the Royal Statistical Society: Series B (Methodological) 21(2), 272{304.Kiefer, J., Wolfowitz, J. et al. (1959), `Optimum designs in regression problems', The Annals of Mathematical Statistics 30(2), 271{294.Mukhopadhyay, S. & Haines, L. M. (1995), `Bayesian d-optimal designs for the exponential growth model', Journal of Statistical Planning and Inference 44(3), 385{397.Mullen, K., Ardia, D., Gil, D. L., Windover, D. & Cline, J. (2016), `Deoptim: An r package for global optimization by di erential evolution', Available: https://CRAN.Rproject. org/package=DEoptim.Parker, S. & Gennings, C. (2008), `Penalized Locally Optimal Experimental Designs for Nonlinear Models', Journal of Agricultural, Biological, and Environmental Statistics 13(3), 334{354.Parker, S. M. (2005), Solutions to reduce problems associated with experimental designs for nonlinear models: Conditional analyses and penalized optimal designs, PhD thesis, Virginia Commonwealth UniversityStorn, R. & Price, K. (1997), `Di erential evolution{a simple and e cient heuristicfor global optimization over continuous spaces', Journal of global optimization 11(4), 341{359.Team, R. C. (2018), `R: A language and environment for statistical computing. r foundation for statistical computing, vienna, austria. 2013 (version 3.5.1)', Available: http://www.R-project.org.Tranda r, C. & L opez-Fidalgo, J. (2004), Locally optimal designs for an extension of the michaelis-menten model, in A. Di Bucchianico, H. Ler & H. P. Wynn, eds, `mODa 7{Advances in Model-Oriented Design and Analysis', Physica-Verlag, Heidelberg, pp. 173{181.Yeatts, S. D., Gennings, C. & Crofton, K. M. (2012), `Optimal design for the precise estimation of an interaction threshold: The impact of exposure to a mixture of 18 polyhalogenated aromatic hydrocarbons', Risk Analysis 32(10), 1784{1797Ypma, J., Borchers, H. & Eddelbuettel, D. (2014), `R package `nloptr': R interface to nlopt', Available: https://CRAN.R-project.org/package=nloptrZhang, Y. (2006), Bayesian D-optimal design for generalized linear models, PhD thesis, Virginia Tech.ORIGINAL1140821034.2019.pdf1140821034.2019.pdfapplication/pdf1019313https://repositorio.unal.edu.co/bitstream/unal/75605/1/1140821034.2019.pdf729e0532c5ae7a38527aacd10541122cMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-83991https://repositorio.unal.edu.co/bitstream/unal/75605/2/license.txt6f3f13b02594d02ad110b3ad534cd5dfMD52CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.unal.edu.co/bitstream/unal/75605/3/license_rdf4460e5956bc1d1639be9ae6146a50347MD53THUMBNAIL1140821034.2019.pdf.jpg1140821034.2019.pdf.jpgGenerated Thumbnailimage/jpeg3677https://repositorio.unal.edu.co/bitstream/unal/75605/4/1140821034.2019.pdf.jpg36fe295458787bd40c167dae8c85693fMD54unal/75605oai:repositorio.unal.edu.co:unal/756052023-03-23 09:03:58.45Repositorio Institucional Universidad Nacional de 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