Advanced Statistics: Developing a Formal Model of Emergency Department Census and Defining Operational Efficiency

Abstract

The basic pattern of ED census can be represented by a straightforward expression. This expression can be quickly adapted to a variety of inquiries regarding ED crowding, daily surge, and operational efficiency.

From Model to Forecasting: A Multicenter Study in Emergency Departments

“…This is also important because new models of emergency crowding have been developed using a mathematical model of the incoming flow (patient visits). 7 Numerous authors have already become interested in the prediction of patient visits in EDs, [8][9][10][11][12][13][14][15] as well as in walk-in clinics, 6,[16][17][18] mainly using calendar variables in multiple linear regression models. 19 These methods examine correlations between patient visits and a number of independent determinants, mostly calendar variables.…”

Modeling Complex Systems: Gaining Valid Insights and Avoiding Mathematical Delusions

“…This latter behavior is commonly termed external or independent validation and is particularly important in the development of clinical decision rules and models used to predict patient outcomes. 15,16 In summary, in both the studies of Greineder et al 11 and Flottemesch et al 12 the modeling strategy yields insights into system behaviors that might otherwise remain hidden. I can easily envision the initiation of a clinical trial targeting patients with sepsis in the ED, utilizing surface cell markers and a design that fails to consider the impact of cell degradation with storage, only to find that the resulting false-positive assays were a limiting and crippling factor after trial completion.…”

“…Thus, the model has value as a forecasting tool and as a method to consider ''what if'' scenarios. 12 The value of this model, however, or at least the likelihood it will be used by others, might be limited by its level of mathematical complexity. This would be unfortunate, given the importance of having a common, quantitative language with which to describe and study ED efficiency and crowding.…”

“…In addition, the authors used three separate data sets so that initial model development and estimation, model testing and revision of parameters, and final model evaluation could all occur without having any data be used more than once. 12 The resulting mathematical expression has two distinct values. First, it yields insights in the meanings of both ED ''efficiency'' and ''crowding.''…”

“…In the study by Flottemesch et al, 12 the authors created a mathematical model that predicts the dynamic behavior of emergency department census, allowing an explicit link between easily observable characteristics (e.g., current census, timing, and number of patient arrivals) and important underlying characteristics (e.g., efficiency, degree of crowding, ability to recover from upward transient fluctuations in patient arrivals). The approach taken here was not simulation; rather, they combined preexisting knowledge regarding patterns in ED census (called ''stylized'' facts by the authors) with empirical observations regarding the dynamics specific to a particular ED (that define key model parameters) to yield a mathematical expression that gives new insights into the relationships between directly observed and nonobserved ED characteristics and allows the prediction of future behavior, including the effects of fluctuations in patient arrivals beyond the normal, expected daily and seasonal cycles.…”