Mathematical Modeling of the Impact of Hospital Occupancy : When Do Dwindling Hospital Beds Cause ED Gridlock?

Objectives. The time emergency department (ED) patients spend from presentation to admittance is known as their length of stay (LOS). This study aimed to quantify the inpatient occupancy rate (InptOcc)/ED LOS relationship and develop a methodology for identifying resource-allocation triggers using InptOcc-LOS association-curve inflection points. Methods. This study was conducted over 200 consecutive days at a 700-bed hospital with an annual ED census of approximately 50,000 using multivariate spline (piecewise) regression to model the InptOcc/LOS relationship while adjusting for confounding covariates. Nonlinear modeling was used to assess for InptOcc/LOS associations and determine the inflection point where InptOcc profoundly impacted LOS. Results. At lower InptOcc, there was no association. Once InptOcc reached ≥88%, there was a strong InptOcc/LOS association; each 1% InptOcc increase predicted a 16-minute (95% CI, 12–20 minutes) LOS prolongation, while the confounder-adjusted analysis showed each 1% InptOcc increase >89% precipitating a 13-minute (95% CI, 10–16 minutes) LOS prolongation. Conclusions. The study hospital’s InptOcc was a significant predictor of prolonged ED LOS beyond the identified inflection point. Spline regression analysis identified a clear inflection point in the InptOcc-LOS curve that potentially identified a point at which to optimize inpatient bed availability to prevent increased costs of prolonged LOS.