Forecasting Models of Emergency Department Crowding

Abstract

Objectives: 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.Methods: 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. Results: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.Conclusions: 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. ACADEMIC EMERGENCY MEDICINE 2009; 16:301-308 ª 2009 by the Society for Academic Emergency MedicineKeywords: crowding, forecasting, emergency service, hospital, operations research E mergency department (ED) overcrowding has become a significant problem throughout the United States, leading to possible increased health care costs, causing raised stress levels among staff and patients in EDs, and most importantly, adversely affecting patient outcomes. [1][2][3][4][5][6][7][8][9] One aspect of the problem is the difficulty of anticipating the timing and magnitude of overcrowded conditions. The ability to predict crowded conditions, especially hour by hour, could substantially impact ED operations. To this end, we evaluate how time series-based models perform in short-term forecasting of ED occupancy.Traditionally, ED operations directors have found historical averages to be reliable and accurate for longterm forecasts of ED behavior. For example, a director might use the average ED bed occupancy on Monday evenings at 21:00 over the past 2 years to determine how many staff should be working in the ED at that time. However, short-term forecasting of ED bed occupancy, such as might be useful for calling in additional staff or opening up hospital beds, is likely to need more accurate forecasting techniques.Several authors have looked to time series techniques, such ...

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