Evaluation of Markov models with discontinuities

Background. Several methods, such as the half-cycle correction and the life-table method, were developed to attenuate the error introduced in Markov models by the discretization of time. Elbasha and Chhatwal have proposed alternative “corrections” based on numerical integration techniques. They pres...

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Detalles Bibliográficos
Autores: Bermejo, Iñigo, Pérez Martín, Jorge, Díez Vegas, Francisco Javier
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/12447
Acceso en línea:https://hdl.handle.net/20.500.14468/12447
Access Level:acceso abierto
Palabra clave:state-transition models
half-cycle correction
Markov models
within-cycle correction
discontinuities
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repository_id_str
spelling Evaluation of Markov models with discontinuitiesBermejo, IñigoPérez Martín, JorgeDíez Vegas, Francisco Javierstate-transition modelshalf-cycle correctionMarkov modelswithin-cycle correctiondiscontinuitiesBackground. Several methods, such as the half-cycle correction and the life-table method, were developed to attenuate the error introduced in Markov models by the discretization of time. Elbasha and Chhatwal have proposed alternative “corrections” based on numerical integration techniques. They present an example whose results suggest that the trapezoidal rule, which is equivalent to the half-cycle correction, is not as accurate as Simpson’s 1/3 and 3/8 rules. However, they did not take into consideration the impact of discontinuities. Objective. To propose a method for evaluating Markov models with discontinuities. Design. Applying the trapezoidal rule, we derive a method that consists of adjusting the model by setting the cost at each point of discontinuity to the mean of the left and right limits of the cost function. We then take from the literature a model with a cycle length of 1 year and a discontinuity on the cost function and compare our method with other “corrections” using as the gold standard an equivalent model with a cycle length of 1 day. Results. As expected, for this model, the life-table method is more accurate than assuming that transitions occur at the beginning or the end of cycles. The application of numerical integration techniques without taking into account the discontinuity causes large errors. The model with averaged cost values yields very small errors, especially for the trapezoidal and the 1/3 Simpson rules. Conclusion. In the case of discontinuities, we recommend applying the trapezoidal rule on an averaged model because this method has a mathematical justification, and in our empirical evaluation, it was more accurate than the sophisticated 3/8 Simpson rule.Society for Medical Decision Makinge-Spacio UNED20242024-05-2020192019-02-0720192019-02-07journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14468/12447reponame:e-spacio. Repositorio Institucional de la UNEDinstname:Universidad Nacional de Educación a DistanciaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.esoai:e-spacio.uned.es:20.500.14468/124472026-06-06T12:38:31Z
dc.title.none.fl_str_mv Evaluation of Markov models with discontinuities
title Evaluation of Markov models with discontinuities
spellingShingle Evaluation of Markov models with discontinuities
Bermejo, Iñigo
state-transition models
half-cycle correction
Markov models
within-cycle correction
discontinuities
title_short Evaluation of Markov models with discontinuities
title_full Evaluation of Markov models with discontinuities
title_fullStr Evaluation of Markov models with discontinuities
title_full_unstemmed Evaluation of Markov models with discontinuities
title_sort Evaluation of Markov models with discontinuities
dc.creator.none.fl_str_mv Bermejo, Iñigo
Pérez Martín, Jorge
Díez Vegas, Francisco Javier
author Bermejo, Iñigo
author_facet Bermejo, Iñigo
Pérez Martín, Jorge
Díez Vegas, Francisco Javier
author_role author
author2 Pérez Martín, Jorge
Díez Vegas, Francisco Javier
author2_role author
author
dc.contributor.none.fl_str_mv e-Spacio UNED
dc.subject.none.fl_str_mv state-transition models
half-cycle correction
Markov models
within-cycle correction
discontinuities
topic state-transition models
half-cycle correction
Markov models
within-cycle correction
discontinuities
description Background. Several methods, such as the half-cycle correction and the life-table method, were developed to attenuate the error introduced in Markov models by the discretization of time. Elbasha and Chhatwal have proposed alternative “corrections” based on numerical integration techniques. They present an example whose results suggest that the trapezoidal rule, which is equivalent to the half-cycle correction, is not as accurate as Simpson’s 1/3 and 3/8 rules. However, they did not take into consideration the impact of discontinuities. Objective. To propose a method for evaluating Markov models with discontinuities. Design. Applying the trapezoidal rule, we derive a method that consists of adjusting the model by setting the cost at each point of discontinuity to the mean of the left and right limits of the cost function. We then take from the literature a model with a cycle length of 1 year and a discontinuity on the cost function and compare our method with other “corrections” using as the gold standard an equivalent model with a cycle length of 1 day. Results. As expected, for this model, the life-table method is more accurate than assuming that transitions occur at the beginning or the end of cycles. The application of numerical integration techniques without taking into account the discontinuity causes large errors. The model with averaged cost values yields very small errors, especially for the trapezoidal and the 1/3 Simpson rules. Conclusion. In the case of discontinuities, we recommend applying the trapezoidal rule on an averaged model because this method has a mathematical justification, and in our empirical evaluation, it was more accurate than the sophisticated 3/8 Simpson rule.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-02-07
2019
2019-02-07
2024
2024-05-20
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14468/12447
url https://hdl.handle.net/20.500.14468/12447
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Society for Medical Decision Making
publisher.none.fl_str_mv Society for Medical Decision Making
dc.source.none.fl_str_mv reponame:e-spacio. Repositorio Institucional de la UNED
instname:Universidad Nacional de Educación a Distancia
instname_str Universidad Nacional de Educación a Distancia
reponame_str e-spacio. Repositorio Institucional de la UNED
collection e-spacio. Repositorio Institucional de la UNED
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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