The development of gravity models for hospital patient flows under system change: a Bayesian modelling approach

This paper discusses models for the impact on patient referral flows from homes to hospitals of reconfigurations of emergency hospital services. Such system change might involve new hospital sites, or expanded bed numbers at some sites, together with possible closure of emergency units at other hospitals. In terms of a gravity model for the flows of patients, this corresponds to removing a destination or adding a new one. While retaining a gravity type approach to this problem, the relevance of supply weighting by distance within the broader accessibility concept is stressed since the independence from irrelevant alternatives property is generally inapplicable. This accessibility based approach may be implemented as a general linear model, with a Poisson outcome, and a Bayesian estimation and predictive approach is adopted. In the context of patient hospitalisations, this facilitates prediction of new patient flows following hospital reconfiguration. A UK based case study of small residential areas and hospitals in North East London and Essex is presented within the context of a review of emergency hospital siting in London.