Modeling the Behavior of Patients Who Leave the Emergency Department Without Being Seen by a Physician

Abstract

Abandonment in queues has long been recognized as having a significant impact on system performance. Nevertheless, our empirical understanding of the key drivers for abandonment, particularly in observable systems, is limited. Most models of abandonment assume that it occurs after a length of time sampled from an exogenous distribution, with no dependence on the system. However, discrete-event simulation, a commonly used tool for decision making in service systems, permits much more complex (and hence accurate) models of abandonment than those simply based on time in system. To better inform our understanding of abandonment and guide our modeling of this behavior, we study three operational drivers of abandonment, namely, waiting time, queue-length, and service rate. Using operational data from a hospital emergency department, we show that all three factors affect a patient’s propensity for leaving the waiting area without being seen by a physician (LWBS). Further, these factors interact with each other in a non-linear fashion. We examine the shape of the hazard function for LWBS behavior. A constant hazard function, which is equivalent to an exponential patience distribution, is commonly assumed for abandonment, but is not an accurate model for such systems. However, the Weibull distribution, particularly when parameterized by appropriate covariates, does provide a good .t. We use these findings together with a numerical study to make recommendations for simulating LWBS behavior.