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The Problem of Emergency Department Overcrowding: Agent-Based Simulation and Test by Questionnaire


The Problem of Emergency Department Overcrowding: Agent-Based Simulation and Test by Questionnaire Roger A. McCain PhD, Richard Hamilton, M.D. Frank Linnehan PhD – PowerPoint PPT presentation

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Title: The Problem of Emergency Department Overcrowding: Agent-Based Simulation and Test by Questionnaire

The Problem of Emergency Department Overcrowding
Agent-Based Simulation and Test by Questionnaire
  • Roger A. McCain PhD,
  • Richard Hamilton, M.D.
  • Frank Linnehan PhD

For presentation to Artificial Economics 2011
  • The Seventh Conference,
  • The Hague, Sept. 1-2

The Problem
  • Overcrowding of hospital emergency departments is
    a recognized problem in the U. S. A.
  • Patients seek healthcare in the Emergency
    Department for a variety of reasons.
  • a portion have an acute emergency
  • a portion seeks care because of lack of an
    acceptable alternative.
  • Drawing on noncooperative game theory, we argue
    that ED overcrowding is the equilibrium state of
    the current health care system.

  • One generally accepted solution to ED
    overcrowding and congestion is to in- crease
  • If the game theory hypothesis is correct, then
    increasing capacity will merely reproduce the
    crowding problem on a larger scale.

Our Study
  • We address this issue by means of
  • Examples from noncooperative game theory
  • Agent-based simulations
  • The scale is larger
  • Boundely rational learning is incorporated
  • A Questionnaire Study
  • The agent-based simulations and the questionnaire
    study are coordinated.

A Small-Scale Example
This is an anticoordination game, and presents
special problems for a learning model.
At a Slightly Larger Scale
  • The patients arrive in a random order.
  • This determines the patients place in line.
  • Average waiting time is proportional to the place
    in line.
  • Being one place further back in the line reduces
    this satisfaction by two
  • The alternative to the ED provides a satisfaction
    level of five.

Noncooperative Solution
  • This game has a large number of solutions.
  • All are defined by the same condition, however
    just six choose the ED while the other four
    choose their alternative.

  • In a real case, we would expect
  • Just as in the two-person anticoordination game,
    equilibrium requires some agents to choose
    different strategies even if they themselves do
    not differ.
  • When the strategies are modes of service, the
    number choosing the different services in
    equilibrium will be such that the different
    services yield the same benefits, in expected
    value terms.
  • The equilibrium is not efficient, in general.

  • To further extend the model and allow for 1) much
    larger numbers of potential pa- tients, 2)
    heterogeneity of health states, experience, and
    expectation, 3) boundedly rational learning, and
    4) initialization effects, dynamic adjustment and
    transients, we undertook agent-based computer

Agents Are Patients
  • For these simulations, the agents are potential
    patients, while the ED is not a player in the
    game but a mechanism that mediates the
    interaction of the agents.
  • It is assumed that (at each iteration of the
    simulation) agents are randomly sorted into four
    health states.

Health States
  • Agents in states 1 and 3 have health concerns
    such that treatment in the ED offers a higher
    benefit than the alternative in the absence of
  • For agents in state 2, there is a health concern
    such that treatment through the alternative mode
    offers higher expected benefit than treatment by
    the ED, even in the absence of congestion.
  • Others have no need for health care.

Some Details 1
  • In the simulations, there are 10,000 agents, and
    at each iteration they are sorted into health
    states such that about 60 will seek health care
    from one source or another.
  • Each agent makes the decision based on an
    expected benefit variable, with a normally
    distributed pseudorandom error.
  • Qualification For technical reasons having to do
    with the trial-and-error learning process, at
    least 5 of those agents who seek health care
    choose the Emergency Department regardless of
    their expectations.

Some Details 2
  • After all these decisions have been registered,
    the congestion of the emergency department is
    computed by comparing its capacity parameter to
    the number of users.
  • Congestion exists only when the number of users
    is greater than capacity
  • The experiences for all agents who choose the ED
    are then computed on the basis of congestion
    together with the parameters of their specific
    health states, with a pseudorandom variate to
    capture the uncertainty inherent in medical

Some Details 3
  • Numerical indicators of experience are roughly
    calibrated to the five-point Likert scale used in
    the questionnaire survey reported below.
  • Expected benefits are then updated.
  • The updating formula is the Koyck lag formula,
    Et aXt-1 (1-a)Et-1.
  • For the simulations reported a 1/2.

A Representative Simulation
A Complication
  • These agents form their expectations as to the
    benefit from ED care on the basis of their own
    past experience plus an error.
  • Those who choose the ED are the ones who most
    overestimate the benefits of the ED.
  • This is shown by the upper black line.
  • Nevertheless experienced benefit from the ED
    converges to the experienced benefit of the

Why this Wrinkle?
  • It is crucial that the agents learn only from
    their own experience. In an anticoordination game
    imitative learning will not converge to a Nash
  • An early version of the simulations had no
  • The questionnaire study indicated that the
    average ED patient was disappointed.
  • The experience-plus-error model retrodicts that

More Simulations
  • For this study 18 distinct simulations were
  • Two simulations were run using each of 9 random
    number seeds.
  • For one series of 9 simulations the capacity of
    the Emergency Department was set at 500, while
    for others it was set at 1000.
  • The simulations were run for 200 iterations.
  • The next slide shows the recorded Emergency
    Department congestion for the 18 simulations run.

Reported Experience Type 1
Reported Experience Type 2
Number of Users
Conclusions from the Simulations 1
  1. As in the small-N models, an equilibrium or
    stable state corresponds to congestion sufficient
    to reduce the benefits of users of the ED to
    approximate equal- ity with the benefits from
    alternative service
  2. In these simulations with a large but finite
    number of agents and boundedly rational learning,
    the approximation to Emergency Department
    Overcrowdiing to the alternative benefit may not
    be perfect and may vary somewhat with parameters
    and initialization, so that

Conclusions from the Simulations 2
  1. An expansion of ED capacity can result in some
    slight improvement in congestion and patient
    experience, despite very substantial
    deterioration of the experience due to
    congestion, and finally
  2. these results are uniform and predictable over
    simulations with a wide range of differing random
    inputs and detailed evolution.

Questionnaire 1
  • A telephone survey was conducted of patients who
    visited the emergency department of the hospital
    of the Drexel University School of Medicine.
  • These telephone surveys were conducted by an
    independent research group who were given a list
    of all patients who had visited the ED during
    summer, 2007.
  • Names and telephone numbers were randomly chosen
    from this list to complete 301 interviews.

Questionnaire 2
  • Eight survey items were used to assess patient
  • Quantity of care,
  • Promptness of care.
  • Administrative staff effectiveness
  • Medical staff capability
  • Personal Care

6. Staff Time Spent 7. Overall Quality of
Care 8. Overall Satisfaction
Questionnaire 3
  • A five point, Likert- type response scale was
    used for each item, ranging from 1 Very
    satisfied to 5 Very dissatisfied.
  • The same facets of satisfaction were also used to
    assess the patients expected experience in the ED
    and the patients expected experience with an
    alternative mode of care

Questionnaire 4
  • Paired t-tests were used to assess differences in
    satisfaction levels between what the patients
    experienced at the ED and expected satisfaction
    with the alternative (Table 3), as well as the
    difference in the expected and experienced
    satisfaction with the ED.

Concluding Summary 1
  • The project reported in this paper was highly
    interdisciplinary, drawing ideas and techniques
    from several sources. There are novel
    contributions for each.
  • For health care policy, we have specified,
    tested, and verified a Nash equilibrium
    hypothesis of the cause and nature of emergency
    room overcrowding. This hypothesis implies that
    increasing emergency room capacity may have
    little or no impact on overcrowding, in the
    absence of important changes in access to the
    alternative modes of medical care.

Concluding Summary 2
  • For game theory, we have provided an example of
    testing a game-theoretic equilibrium model by
    questionnaire methods, using a realistically
    scaled agent-based computer simulation with
    boundedly rational learning to extend the
    insights of two- and small N-person game models
    to generate hypotheses for the survey.

Concluding Summary 3
  • For questionnaire methods, we have provided an
    example of application to hypotheses from game
    theory and some evidence of the importance and
    consequences of heterogeneity, and the
    possibility of modeling heterogeneity explicitly
    by means of agent-based computer simulation.
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