Time Series Forecasts of Emergency Department Patient Volume, Length of Stay, and Acuity

Abstract

Study hypothesis: Time series analysis can provide accurate predictions of emergency department volume, length of stay, and acuity. Design: Prospective stochastic time series modeling. Setting: A university teaching hospital. Interventions: All patients seen during two sequential years had time of arrival, discharge, and acuity recorded in a computer database. Time series variables were formed for patients arriving per hour, length of stay, and acuity. Prediction models were developed from the year 1 data and included five types: raw observations, moving averages, mean values with moving averages, seasonal indicators with moving averages, and auto-regressive integrated moving averages. Forecasts from each model were compared with observations from the first 25 weeks of year 2. Model accuracy was tested on residuals by autocorrelation functions, periodograms, linear regression, and confidence intervals of the variance. Results: There were 42,428 patients seen in year 1 and 44,926 in year 2. Large periodic variations in patient volume with time of day were found ( P < .00001). The models based on arithmetic means or seasonal indices with a single moving average term gave the most accurate forecasts and explained up to 42% of the variation present in the year 2 test series. No time series model explained more that 1% of the variation in length of stay or acuity. Conclusion: Time series analysis can provide powerful, accurate short-range forecasts of future ED volume. Simpler models performed best in this study. Time series forecasts of length of stay and patient acuity are not likely to contribute additional useful information for staffing and resource allocation decisions. [Tandberg D, Qualls C: Time series forecasts of emergency department patient volume, length of stay, and acuity. Ann Emerg Med February 1994;23:299-306.]