Advanced statistics: developing a formal model of emergency department census and defining operational efficiency.

BACKGROUND Emergency department (ED) crowding has been a frequent topic of investigation, but it is a concept without an objective definition. This has limited the scope of research and progress toward the development of consistent and meaningful operational responses. OBJECTIVES To develop a straightforward model of ED census that incorporates concepts of ED crowding, daily patient surge, throughput time, and operational efficiency. METHODS Using 2005-2006 patient encounter data at a Level 1 urban trauma center, a set of three stylized facts describing daily patterns of ED census was observed. These facts guided the development of a formal, mathematical model of ED census. Using this model, a metric of ED operational efficiency and a forecast of ED census were developed. RESULTS The three stylized facts of daily ED census were 1) ED census is cyclical, 2) ED census exhibits an input-output relationship, and 3) unexpected shocks have long-lasting effects. These were represented by a three-equation system. This system was solved for the following expression, Census(t) = A(.) + B(.) cos(vT + epsilon) + a(e(t)), that captured the time path of ED census. Using nonlinear estimation, the parameters of this expression were estimated and a forecasting tool was developed. CONCLUSIONS 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.

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