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

Research output: Contribution to journalJournal article

Published

Journal publication date03/2014
JournalStatistics and Computing
Journal number2
Volume24
Number of pages10
Pages155-164
Early online date1/10/12
Original languageEnglish

Abstract

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.