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A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

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  • McGrory, C.A.
  • Pettitt, A.N.
  • Faddy, M.J.

Abstract

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

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  • McGrory, C.A. & Pettitt, A.N. & Faddy, M.J., 2009. "A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4311-4321, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4311-4321
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    References listed on IDEAS

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    1. Bruce Jones & Sally McClean & David Stanford, 2019. "Modelling mortality and discharge of hospitalized stroke patients using a phase-type recovery model," Health Care Management Science, Springer, vol. 22(4), pages 570-588, December.
    2. Bo Henry Lindqvist, 2023. "Phase-type models for competing risks, with emphasis on identifiability issues," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 318-341, April.
    3. Albrecher, Hansjörg & Bladt, Martin & Bladt, Mogens & Yslas, Jorge, 2022. "Mortality modeling and regression with matrix distributions," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 68-87.

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