A joint likelihood approach to the analysis of length of stay data utilising the continuous-time hidden Markov model and Coxian phase-type distribution

Abstract

The Coxian phase-type distribution is a special case of phase-type distribution which represents the time to absorption of a finite Markov chain in continuous time. The distribution is able to capture subjects’ flow through a system but is unable to highlight if there are different pathways caused by an underlying latent factor. Identifying these different pathways will give healthcare providers a deeper insight and understanding of patient flow and allow them to identify and change any potential issues. This paper combines the Coxian phase-type distribution with the continuous-time hidden Markov model to highlight these paths. The theory of combining the Coxian phase-type distribution with the continuous-time hidden Markov model shall be presented along with a simulation study and an application using Italian healthcare data.

Keywords:

• Continuous-time hidden Markov model
• Coxian phase-type distribution
• Healthcare

Acknowledgements

The authors would like to acknowledge the Department for Employment and Learning Northern Ireland (DEL) for funding the research conducted by H. Mitchell and the Ministry of Health in Italy for use of the data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 A detailed analysis on the Italian healthcare system is contained in France et al. (2005); Nuti et al. (2012).