Advanced Algorithms for Medical Decision Analysis. Implementation in OpenMarkov

Arias, Manuel; Artaso, Miguel A.; Bermejo, Iñigo; Díez, F. J.; Luque, Manuel; Pérez-Martín, Jorge

doi:10.1007/978-3-319-59758-4_43

Cited by 1 publication

(2 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: Methodsmentioning

confidence: 99%

“…We have reimplemented it as a Markov influence diagram (MID) 14 (see Figure 1) using OpenMarkov, an open source tool developed by our group. 15 The model is available at www.probmodelxml.org/networks. The inaccuracy introduced by the discretization of time into cycles increases with the cycle length: when it approaches 0, all the methods studied in this article converge to the same results as a continuous-time model.…”

Section: Empirical Evaluationmentioning

confidence: 99%

See 1 more Smart Citation

Evaluation of Markov Models with Discontinuities

Pérez-Martín

Bermejo²,

Díez

2019

Med Decis Making

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Empirical Evaluationmentioning

confidence: 99%