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Evaluation of time-series models for forecasting demand for emergency health care services

Díaz-Hierro J, Martín Martín JJ, Vilches Arenas A, López Del Amo González MP, Patón Arévalo JM, Varo González C

Empresa Pública de Emergencias Sanitarias, Málaga, Spain. 2Universidad de Granada, España. 3Universidad de Sevilla, Spain. 4Investigador independiente, Spain.

Objective: To evaluate a combined set of 6 time-series models for improving the
management of short-term calls for emergency health services.
Methods: The demand for emergency health services in the province of Malaga was
analyzed between 2004 and 2008. Using standard software, we constructed and
evaluated 3 decomposition models and 3 econometric models. The models considered
summer months and atypical values, influenza cases, and number of overnight
admissions as the exogenous inputs. We compared the models using the usual
econometric tests, such as the root mean square error (RMSE), the mean absolute
percentage error (MAPE), and the maximum absolute percentage error (MaxAPE)
among others.
Results: The models had MAPEs under 5%. Autoregressive integrated moving average
(ARIMA) modeling with intervention had the lowest RMSE. Harmonic analysis had the
smallest difference between the MAPE and MaxAPE. In the validation phase, ARIMA with
intervention had the poorest fit, and harmonic analysis and ARIMA with exogenous
input had the best fits.
Conclusions: A forecast of the demand for emergency calls can be generated using 2
models simultaneously to improve short-term planning. Decomposition models and
ARIMA with intervention warn of unexpected changes, whereas ARIMA or other models
with exogenous inputs and harmony component analysis can introduce alternative
planning scenarios, improve our understanding of demand, and facilitate decisionmaking.
Implementing these models with standard software decreases the cost of this
approach in emergency services.

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