Forecasting daily admissions to an emergency department considering single and multiple seasonal patterns

Abstract

When dealing with several years of daily data, such as the number of daily admissions to a hospital's emergency department (ED), how complex does it get to forecast into the future? With that in mind, this study has two main goals: to explore the differences between several methodologies, considering both single and multiple-seasonal patterns; and to select the most suitable model for the administration of a Portuguese hospital to use while managing their ED. To that end, we first considered the data as a time series with a single weekly seasonal pattern. We then modelled the data using time series regression, linear regression with autoregressive integrated moving average (ARIMA) errors, seasonal ARIMA and exponential smoothing techniques. Second, the data was set to be a time series with weekly and annual seasonal patterns. Then, using Fourier terms, we applied time series regression, linear regression with ARIMA errors and trigonometric exponential smoothing state space models with Box–Cox transformation, ARMA errors, Trend and Seasonal components (TBATS) for the analysis. After selecting the best-fitting models using the Akaike Information Criteria (AIC) values, we forecasted into the future and compared the results using both training and test datasets’ root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) values. The time series regression model based on seasonal variables and a weekly seasonal pattern gives the best results. However, we decided to use linear regression with ARIMA errors, seasonal variables, and both weekly and annual seasonal patterns. This produces similar results but allows for the annual seasonality to be considered, which is useful when more data is added.