Recent advances in stochastic modeling and data analysis

Markov chain modelling has been previously used for hospital and community care systems, where the states in hospital care are described as 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. This approach allows us to adopt a unified 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 to show how the non-homogeneous Markov framework can be used to extract various metrics of interest. In particular, we use time-dependent covariates to obtain the mean and variance of the number of spells spent by a patient in hospital and in the community, and the expected total lengths of time in hospital and in the community.peer-reviewe