Enhancing the forecast accuracy of the daily number of patients arrivals in emergency department by hybrid ARIMAX-ANN algorithm

Accurate forecasting of daily arrivals in Emergency Departments (ED) is crucial for healthcare providers. This study incorporates a variety of factors, including meteorological and calendar influences, into the forecasting of ED patient arrivals. Due to the complex linear and nonlinear associations these factors have with ED arrivals, two hybrid algorithms were developing to enhance forecasting accuracy. These algorithms combine Auto-Regressive Integrated Moving Average (ARIMA) with Artificial Neural Network (ANN) methodologies, leveraging their strengths in handling linear and nonlinear relationships in patient arrival data. The first hybrid algorithm utilizes an ANN model with inputs comprising ARIMA-fitted values of the time series, ANN-fitted values of the ARIMA residuals, and ANN-fitted values of the time series, excluding nonlinear input features from ARIMA. The second hybrid approach combines ARIMA and ANN forecast values of the time series. Robust performance metrics were employ to validate the effectiveness of these hybrid algorithms, allowing for a clear comparison with standalone ARIMA, ANN, LSTM, and GLM forecasts at short, intermediate, long, and overall horizons. The overall accuracy indices for ARIMA, ANN, hybrid1, hybrid2, LSTM and GLM algorithms are RMSE = 37.43, 44.33, 39.33, 33.82, 55.53 and 34.96; ME = −16.38, 22.08, 13.93, 2.85, −36.24 and 5.65; SMAPE = 5.32, 6.57, 6.00, 5.18, 8.27, and 4.62, respectively. The hybrid2 algorithm demonstrates superior performance across short, intermediate, and overall horizons, while the ARIMAX model excels in long horizons characterized by low volatility. Although hybrid1 and ANN exhibit similar overall accuracy, the hybrid2 algorithm enhances accuracy indices specifically in the intermediate horizon, which is marked by high volatility. These findings significantly improve the predictive capabilities of existing algorithms and provide valuable insights for strategic decision-making in managing patient flow in emergency departments.