Purpose: The complexity of care within the hospital emergency department (ED) compounded with the multifaceted issues associated with excessive wait times lends itself well to systems analysis. The objective was to conduct a systematic literature review to identify and compare the types of systems analysis mathematical modeling techniques used to evaluate wait times in the hospital ED. Secondary objective was to describe strategies aimed at decreasing wait times.
Methods: Electronic databases Medline, Embase, Compendex, Inspec and Business Source Complete were searched from 2000 to 2009. The search was composed of two sections: mathematical modeling techniques and emergency medicine in a hospital setting. Studies were included if they analyzed data, typical daily arrival rates and patient demands and had a primary outcome related to wait times (i.e. length of stay, meeting benchmarks). The mathematical models were compared in the following categories: analytical or simulation, deterministic or stochastic, discrete or continuous, performance measures, level of data abstraction, capability of incorporating memory, capability of handling multiple resource constraints, computational and model building time, diagrams and software. Wait time reduction strategies were categorized into: scheduling, demand management, resource allocation, change in process times and other.
Results: Four different mathematical modeling techniques were identified in nineteen studies: discrete event simulation (DES) (n=14), discrete event simulation with optimization (n=1), system dynamics (n=2), and queuing model (n=2). DES may be preferable because of its characteristics and ability to model traits specific to the ED: stochastic to deal with uncertainty and variability (i.e. arrival rates), discrete (i.e. can measure percentiles, which is a common measurement governments use for benchmarking), can model multiple resource constraints simultaneously, and patient history influences trajectory in the model. Studies identified showed that: 1) Scheduling and altering the number of staff according to surges in patient demand were effective in decreasing wait times; 2) fast-tracking low acuity patients was effective in decreasing wait times, but only at the expense of high acuity patients; and 3) decreasing turnaround laboratory times or using point of care testing decreased wait times.
Conclusion: Each modeling technique has strengths and weaknesses and the choice between which model to use should be based on the objective and expected performance measure. DES was the most frequently used method because of its ability to model ED specific traits.
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