Forecasting Waiting Time to Treatment for Emergency Department Patients

Problem definition. The current systems of reporting waiting time to patients in public emergency departments (EDs) has largely relied on rolling average or median estimators which have limited accuracy. This paper proposes to use the statistical learning algorithms that significantly improve waiting time forecasts. Practical Relevance. Generating and using a large set of queueing and service flow variables, we provide evidence of the improvement in waiting time accuracy and reduction in prediction errors. In addition to the mean squared prediction error (MSPE) and mean absolute prediction error (MAPE), we advocate to use the percentage of underpredicted observations as patients are more concerned when the actual waiting time exceeds the time forecast rather than vice versa. Provision of the accurate waiting time also helps to improve satisfaction of ED patients. Methodology. The use of the statistical learning methods (ridge, LASSO, random forest) is motivated by their advantages in exploring data connections in flexible ways, identifying relevant predictors, and preventing overfitting of the data. We also use quantile regression to generate time forecasts which may better address the patient's asymmetric perception of underpredicted and overpredicted ED waiting times. Results. We find robust evidence that the proposed estimators significantly outperform the commonly implemented rolling average. Using queueing and service flow variables together with information on diurnal fluctuations, quantile regression outperforms the best rolling average by 18% with respect to MSPE and reduces by 42% the number of patients with large underpredicted waiting times. Managerial implications. By reporting more accurate waiting times, hospitals may enjoy higher patient satisfaction. We show that to increase the predictive accuracy, a hospital ED may decide to provide predictions to patients registered only during the daytime when the ED operates at full capacity translating to more predictive service rates and the demand for treatments.