A Bayesian framework for describing and predicting the stochastic demand of home care patients

Home care providers are complex structures which include medical, paramedical and social services delivered to patients at their domicile. High randomness affects the service delivery, mainly in terms of unplanned changes in patients' conditions, which make the amount of required visits highly uncertain. Hence, each reliable and robust resource planning should include the estimation of the future demand for visits from the assisted patients. In this paper, we propose a Bayesian framework to represent the patients' demand evolution along with the time and to predict it in future periods. Patients' demand evolution is described by means of a generalized linear mixed model, whose posterior densities of parameters are obtained through Markov chain Monte Carlo simulation. Moreover, prediction of patients' demands is given in terms of their posterior predictive probabilities. In the literature, the stochastic description of home care patients' demand is only marginally addressed and no Bayesian approaches exist to the best of our knowledge. Results from the application to a relevant real case show the applicability of the proposed model in the practice and validate the approach, since parameter densities in accordance to clinical evidences and low prediction errors are found.