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

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.