The eigendecomposition of a matrix is a general mathematical approach. It can be applied to many problems, which allow a description in terms of matrices.

Markov models are an approach to cope with dynamical processes. As they can be phrased in matrix form, it is often possible to use eigenvalues for the analysis of Markov models.

Broad application is seen in demography: The cohort component technique essentially is a Markovian process. The modelling of the need of LTC is often based on a Markov assumption. Note that @Joel_Wagner recently proposed a more elaborate approach.

Article Old-age care prevalence in Switzerland: drivers and future development

Health care interventions can be analyzed as Markov process, the states corresponding to the various disease states that follow from the intervention. Also Cost Effectiveness Analysis can rely on Markov chains. You may find details here:

Article Markov Models in health care

Chapter Markov Models and Cost Effectiveness Analysis: Applications ...

I have not come across explicit application of eigen decomposition in health economic modeling. I can see it play a role in inverting a transition matrix, but would not expect that the modeler going through a step of eigen decomposition. Instead, I expect that the modeler would simply use readily available software (e.g. Excel) to call for the inverse matrix. That software may apply eigen decomposition 'under the hood'.

Why do you ask this question? It sounds a bit like 'solution looking for a problem'.

Thank you Robert. I saw the application of eigen decomposition in this article. Article Changing Cycle Lengths in State-Transition Models: Challenge...

Regards,

Masnoon.

Hi Masnoon,

It is hard to know what is not included in a methods section of a paper. My guess would be that modelers who do something like this would proudly mention it in their methods.

The paper to which you refer states that most models do not use anything like eigen decomposition when changing cycle length. That is, of course, until they published their paper. I assume that knowledge and application of the paper is still disseminating and that there are at most very few recent papers that apply their methods.

More generally, I would say that the paper is yet another illustration of how important it is to check whether your model represents observations correctly wherever reasonably possible.

I would also like to add that lack of clarity in the methods does not imply that the authors used a correct solution for a problem such as changing model cycle length to something else than the observation cycle length.

Rob

Thanks Rob. It's now clear to me.

Regards,

Masnoon.