Forecasting arrivals and occupancy levels in an emergency department

This is a sequel to Whitt and Zhang (2017), in which we developed an aggregate stochastic model of an emergency department (ED) based on the publicly available data from the large 1000-bed Rambam Hospital in Haifa, Israel, from 2004–7, associated with the patient flow analysis by Armony et al. (2015). Here we focus on forecasting future daily arrival totals and predicting hourly occupancy levels in real time, given recent history (previous arrival and departure times of all patients) and useful exogenous variables. For the arrival forecasting, we divide the dataset into an initial training set for fitting the models and a final test set to evaluate the performance. By using 200 weeks of data instead of the previous 25, we identify (i) long-term trends in both the arrival process and the length-of-stay distributions and (ii) dependence among successive daily arrival totals, which were undetectable before. From several forecasting methods, including artificial neural network models, we find that a seasonal autoregressive integrated moving average with exogenous (holiday and temperature) regressors (SARIMAX) time-series model is most effective. We then combine our previous ED model with the arrival prediction to create a real-time predictor for the future ED occupancy levels.