A Bayesian Approach to Prediction Using the Gravity Model, with an Application to Patient Flow Modeling

This paper investigates the potential for estimation and prediction by Bayesian methods of hospitalization flows classified by place of residence and hospital site. The focus is especially with respect to emergency (unplanned) admissions to hospitals. The need for strategic modeling and forecasting arises since the structure of U.K. emergency service provision is subject to changes involving site closures or changes in bed numbers. The gravity model, reflecting patient demand, hospital supply, and distance effects has been applied to patient flows, but generally in a situation of unchanged destination states. It may be modified, however, in accordance with major changes in hospital service structure, to include access effects (the interplay of supply and distance) and temporal variation in its parameters. Therefore, prediction may be applied to a “new” situation defined, for example, by closures of entire hospital sites. The modeling approach used may be adapted to other flow models where destinations may be added or eliminated (for example, trade‐area models). A case study involves a sector of London subject to such a restructuring following the U.K. government's 1997–98 review of London's emergency services.