Table of Contents
Advances in Emergency Medicine
Volume 2014 (2014), Article ID 904807, 5 pages
Research Article

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

University of Oklahoma College of Medicine and Hillcrest Medical Center, Tulsa, OK 74135, USA

Received 24 April 2014; Revised 25 June 2014; Accepted 25 June 2014; Published 15 July 2014

Academic Editor: Angelo P. Giardino

Copyright © 2014 Lori Whelan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.