Forecasting daily counts of patient presentations in Australian emergency departments using statistical models with time-varying predictors

Objective: This research aimed to (i) assess the effects of time-varying predictors (day of the week, month, year, holiday, temperature) on daily ED presentations and (ii) compare the accuracy of five methods for forecasting ED presentations, including four statistical methods and a machine learning approach.

Methods: Predictors of ED presentations were assessed using generalised additive models (GAMs), generalised linear models, multiple linear regression models, seasonal autoregressive integrated moving average models and random forest. The accuracy of short-term (14 days), mid-term (30 days) and long-term (365 days) forecasts were compared using two measures of forecasting error.

Results: The data are the numbers of presentations to public hospital EDs in South-East Queensland, Australia, from 2009 to 2015. ED presentations are largely affected by year of presentation, and to a lesser extent by month, day of the week and holidays. Maximum daily temperature is also a significant predictor of ED presentations. Of the four statistical models considered, the GAM had the greatest forecasting accuracy, and produced consistent and coherent forecasts, likely due to its flexibility in modelling complex time-varying effects. The random forest machine learning approach had the lowest forecasting accuracy, likely due to overfitting the data.

Conclusions: Calendar and temperature variables, not previously considered in the Australian literature, were found to significantly impact ED presentations. This study also demonstrates the potential of GAMs as a dual explanatory and forecasting method for the modelling, and more accurate prediction, of ED presentations.