Continuous‐time Markov models for geriatric patient behaviour

Previous research has shown that the flow of patients around departments of geriatric medicine and ex‐patients in the community may be modelled by the application of a mixed exponential distribution where the number of terms in the mixture corresponds to the number of stages of patient care. A common scenario is that there are two stages for in‐patient care (acute and long stay) and one for ex‐patients in the community. However, current hospital planning models assume that patients all move through the system at the same rate, i.e. a one‐compartment approach, thereby ignoring the effects of inherent heterogeneity for individual patients in the system — much of which may be explained by considering patient care as comprising a number of states. This paper uses a continuous‐time Markov model to describe the movement of a cohort of patients entering the system at time t=0. The modelling of in‐patient geriatric care has already been considered. Our present approach enables us to study the whole system of geriatric care and therefore not only to look at the time patients spend in hospital but also the subsequent time patients spend in the community. The model is fitted to data from St George's Hospital, London, consisting of data from 6994 geriatric patients admitted between 1969 and 1984. The model is fitted using the method of maximum likelihood, unlike previous work that has applied the method of least squares. © 1998 John Wiley & Sons, Ltd.