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Estimating parametric semi-Markov models from panel data using phase-type approximations

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<mark>Journal publication date</mark>03/2014
<mark>Journal</mark>Statistics and Computing
Issue number2
Number of pages10
Pages (from-to)155-164
Publication StatusPublished
Early online date1/10/12
<mark>Original language</mark>English


Inference for semi-Markov models under panel data presents considerable computational difficulties. In general the likelihood is intractable, but a tractable likelihood with the form of a hidden Markov model can be obtained if the sojourn times in each of the states are assumed to have phase-type distributions. However, using phase-type distributions directly may be undesirable as they require estimation of parameters which may be poorly identified. In this article, an approach to fitting semi-Markov models with standard parametric sojourn distributions is developed. The method involves establishing a family of Coxian phase-type distribution approximations to the parametric distribution and merging approximations for different states to obtain an approximate semi-Markov process with a tractable likelihood. Approximations are developed for Weibull and Gamma distributions and demonstrated on data relating to post-lung-transplantation patients.