Title:
Comparison of methods for measuring crowding and its effects on length of stay in the emergency department.

Abstract:
This consensus conference presentation article focuses on methods of measuring crowding. The authors compare daily versus hourly measures, static versus dynamic measures, and the use of linear or logistic regression models versus survival analysis models to estimate the effect of crowding on an outcome.
Emergency department (ED) visit data were used to measure crowding and completion of waiting room time, treatment time, and boarding time for all patients treated and released or admitted to a single ED during 2010 (excluding patients who left without being seen). Crowding was characterized according to total ED census. First, total ED census on a daily and hourly basis throughout the 1-year study period was measured, and the ratios of daily and hourly census to the ED's median daily and hourly census were computed. Second, the person-based ED visit data set was transposed to person-period data. Multiple records per patient were created, whereby each record represented a consecutive 15-minute interval during each patient's ED length of stay (LOS). The variation in crowding measured statically (i.e., crowding at arrival or mean crowding throughout the shift in which the patient arrived) or dynamically (every 15 minutes throughout each patient's ED LOS) were compared. Within each phase of care, the authors divided each individual crowding value by the median crowding value of all 15-minute intervals to create a time-varying ED census ratio. For the two static measures, the ratio between each patient's ED census at arrival and the overall median ED census at arrival was computed, as well as the ratio between the mean shift ED census (based on the shift in which the patient arrived) and the study ED's overall mean shift ED census. Finally, the effect of crowding on the probability of completing different phases of emergency care was compared when estimated using a log-linear regression model versus a discrete time survival analysis model.
During the 1-year study period, for 9% of the hours, total ED census was at least 50% greater than the median hourly census (median, 36). In contrast, on none of the days was total ED census at least 50% greater than the median daily census (median, 161). ED census at arrival and time-varying ED census yielded greater variation in crowding exposure compared to mean shift census for all three phases of emergency care. When estimating the effect of crowding on the completion of care, the discrete time survival analysis model fit the observed data better than the log-linear regression models. The discrete time survival analysis model also determined that the effect of crowding on care completion varied during patients' ED LOS.
Crowding measured at the daily level will mask much of the variation in crowding that occurs within a 24-hour period. ED census at arrival demonstrated similar variation in crowding exposure as time-varying ED census. Discrete time survival analysis is a more appropriate approach for estimating the effect of crowding on an outcome.