Modelling the total time spent in an accident and emergency department and the associated costs

The aim of this paper is to analyse the total length of time spent by a group of patients in an Accident and Emergency (A&E) department using a multistage Markov model. A patient’s pathway through A AND E consists of a sequence of stages, such as triage, examination, and a decision of whether to admit to hospital or not. Using Coxian phase-type distributions, this paper models these stages and illustrates the difference in the distribution of the time spent in A and E for those patients who are admitted to hospital, and those patients who are not. A theoretical approach to modelling the costs accumulated by a group of patients in A and E is also presented. The data analysed refers to the time spent by 53,213 patients in the A & E department of a hospital in Northern Ireland over a one year period.