Using Markov Models to Assess the Performance of a Health and Community Care System

Markov chain modelling, in particular phase type modelling, has been previously used for hospital and community care systems, where we describe hospital care as a series of phases, such as acute, rehabilitation, or long-stay and likewise social care in the community may be modelled using phases such as dependent, convalescent, or nursing home. Such an approach allows us to adopt a holistic systems approach to health and community care modelling and management rather than focusing on the improvement of part of the system to the possible detriment of other components. We here extend this approach by showing how the general Markov framework can be exploited to extract various metrics of interest. In particular, we derive formulae for the mean and variance of the number of spells spent by a patient in hospital and in the community, and the expected total length of time in hospital and in community care, subsequent to first admission. Results are obtained for geriatric patients who have been admitted to hospital care. Finally we discuss how covariates, particularly time dependent covariates such as age, can be incorporated into the analysis