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

Abstract

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.