P017: Does a busy day predict another busy day? A time-series analysis of multi-centre emergency department volumes

Introduction: Variations of patient volumes in the ED according to days of the week and month of the year are well-established. Anecdotally, ED volumes follow ‘waves’ that correlate with previous days. Time-series models have traditionally been used in econometrics to develop financial models, but have been adapted in other fields, such as health informatics. This study uses a time-series approach to assess whether these impressions are valid. Methods: The daily volume of patients presenting to four emergency departments (ED) at the Nova Scotia Health Authority from Jan 2010 to May 2015 were analyzed to assess for the effect of previous volumes on future volumes. Parameters were selected using the auto-correlation (ACF) and partial auto-correlation functions (PACF) for a Seasonal Auto-regressive Integrated Moving Average (SARIMA) model. The Box-Jenkins statistic was assessed for model suitability. To assess for accuracy, a forecast of the model was evaluated with a year of volumes set aside for testing. Results: The EDs saw an average of 365.1 patients per day, with a minimum of 188 patients and a maximum of 479. The increasing trend in volumes consistent with the increasing number of ED presentations nation-wide was detrended using linear regression. There was a significant correlation in ACF with the previous day (ρ1 = 0.297). A seasonal, periodic trend was seen weekly. Significant correlations occurred annually (ρ365 = 0.279) and at 29 days (ρ29 = 0.339), consistent with the lunar cycle. A seasonal model was postulated incorporating an auto-regressive (AR) coefficient, and a moving average (MA) coefficient for the previous day’s volume. An AR and MA seasonal coefficient were each incorporated using the weekly period. When using the model on the test data, the model predicted 4 more patient presentations on average than the true value, with 90% of the values within 37 presentations of the true volume. The Box-Jenkins statistic was non-significant, indicating no problems with model specification. Conclusion: The volume of patients presenting to an ED system is correlated with that of the previous day. A weekly seasonal variation was confirmed. Auto-correlations also occur annually and possibly associated with the lunar cycle. Previous ED volumes may be useful in forecasting patient volumes. The time-series approach may discover further ways to predict ED volumes.