Evaluation of Markov models with discontinuities

Pérez-Martín, Jorge, Bermejo, Iñigo y Díez, Francisco J. . (2019) Evaluation of Markov models with discontinuities.

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Título Evaluation of Markov models with discontinuities
Autor(es) Pérez-Martín, Jorge
Bermejo, Iñigo
Díez, Francisco J.
Materia(s) Ingeniería Informática
Abstract 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.
Palabras clave state-transition models
half-cycle correction
Markov models
within-cycle correction
Editor(es) Society for Medical Decision Making
Fecha 2019-02-07
Formato application/pdf
Identificador bibliuned:95-Jperez-003
DOI - identifier 10.1177/0272989X19837974
Nombre de la revista Medical Decision Making
Número de Volumen 39
Página inicial 414
Página final 420
Idioma eng
Versión de la publicación acceptedVersion
Tipo de recurso Article
Derechos de acceso y licencia http://creativecommons.org/licenses/by-nc-nd/4.0
Tipo de acceso Acceso abierto
Notas adicionales This paper was published (without the appendix) in Medical Decision Making 2019;39:414-420.

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Creado: Wed, 17 Jun 2020, 23:29:16 CET