Forecasting Models of Emergency Department Crowding

The authors investigated whether models using time series methods can generate accurate short-term forecasts of emergency department (ED) bed occupancy, using traditional historical averages models as comparison. From July 2005 through June 2006, retrospective hourly ED bed occupancy values were collected from three tertiary care hospitals. Three models of ED bed occupancy were developed for each site: 1) hourly historical average, 2) seasonal autoregressive integrated moving average (ARIMA), and 3) sinusoidal with an autoregression (AR)-structured error term. Goodness of fits were compared using log likelihood and Akaike's Information Criterion (AIC). The accuracies of 4- and 12-hour forecasts were evaluated by comparing model forecasts to actual observed bed occupancy with root mean square (RMS) error. Sensitivity of prediction errors to model training time was evaluated, as well. The seasonal ARIMA outperformed the historical average in complexity adjusted goodness of fit (AIC). Both AR-based models had significantly better forecast accuracy for the 4- and the 12-hour forecasts of ED bed occupancy (analysis of variance [ANOVA] p < 0.01), compared to the historical average. The AR-based models did not differ significantly from each other in their performance. Model prediction errors did not show appreciable sensitivity to model training times greater than 7 days. Both a sinusoidal model with AR-structured error term and a seasonal ARIMA model were found to robustly forecast ED bed occupancy 4 and 12 hours in advance at three different EDs, without needing data input beyond bed occupancy in the preceding hours.