title: Advanced statistics: developing a formal model of emergency department census and defining operational efficiency.
abstract: 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.
  
  
  OBJECTIVE
  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.
authors.affiliation: HealthPartners Research Foundation, Minneapolis, MN, USA. thomas.j.flottemesch@healthpartners.com
authors.forename: Thomas J
authors.initials: TJ
authors.lastname: Flottemesch
authors.forename: Bradley D
authors.initials: BD
authors.lastname: Gordon
authors.forename: Spencer S
authors.initials: SS
authors.lastname: Jones
mesh_terms: D019352:Censuses; D003441:Crowding; D017598:Efficiency, Organizational; D004636:Emergency Service, Hospital / Q000458:organization & administration*; D006801:Humans; D015233:Models, Statistical; D010360:Patient Transfer / Q000458:organization & administration; D013997:Time Factors; D014193:Trauma Centers; D014505:Urban Population