A generic method for evaluating crowding in the emergency department

Andreas Halgreen Eiset, Mogens Erlandsen, Anders Brøns Møllekær, Julie Mackenhauer, Hans Kirkegaard

Crowding in the emergency department (ED) has been studied intensively using complicated non-generic methods that may prove difficult to implement in a clinical setting. This study sought to develop a generic method to describe and analyse crowding from measurements readily available in the ED and to test the developed method empirically in a clinical setting. We conceptualised a model with ED patient flow divided into separate queues identified by timestamps for predetermined events. With temporal resolution of 30 min, queue lengths were computed as Q(t + 1) = Q(t) + A(t) - D(t), with A(t) = number of arrivals, D(t) = number of departures and t = time interval. Maximum queue lengths for each shift of each day were found and risks of crowding computed. All tests were performed using non-parametric methods. The method was applied in the ED of Aarhus University Hospital, Denmark utilising an open cohort design with prospectively collected data from a one-year observation period. By employing the timestamps already assigned to the patients while in the ED, a generic queuing model can be computed from which crowding can be described and analysed in detail. Depending on availability of data, the model can be extended to include several queues increasing the level of information. When applying the method empirically, 41,693 patients were included. The studied ED had a high risk of bed occupancy rising above 100 % during day and evening shift, especially on weekdays. Further, a 'carry over' effect was shown between shifts and days. The presented method offers an easy and generic way to get detailed insight into the dynamics of crowding in an ED.