Predicting patient arrivals to an accident and emergency department

To characterise and forecast daily patient arrivals into an accident and emergency (A&E) department based on previous arrivals data.

Arrivals between 1 April 2002 and 31 March 2007 to a busy case study A&E department were allocated to one of two arrival streams (walk-in or ambulance) by mode of arrival and then aggregated by day. Using the first 4 years of patient arrival data as a "training" set, a structural time series (ST) model was fitted to characterise each arrival stream. These models were used to forecast walk-in and ambulance arrivals for 1-7 days ahead and then compared with the observed arrivals given by the remaining 1 year of "unseen" data.

Walk-in arrivals exhibited a strong 7-day (weekly) seasonality, with ambulance arrivals showing a distinct but much weaker 7-day seasonality. The model forecasts for walk-in arrivals showed reasonable predictive power (r = 0.6205). However, the ambulance arrivals were harder to characterise (r = 0.2951).

The two separate arrival streams exhibit different statistical characteristics and so require separate time series models. It was only possible to accurately characterise and forecast walk-in arrivals; however, these model forecasts will still assist hospital managers at the case study hospital to best use the resources available and anticipate periods of high demand since walk-in arrivals account for the majority of arrivals into the A&E department.