Predicting waiting time to treatment for emergency department patients

Background: 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 study proposes to use machine learning (ML) algorithms that significantly improve waiting time forecasts. Methods: By implementing ML algorithms and using a large set of queueing and service flow variables, we provide evidence of the improvement in waiting time predictions for low acuity ED patients assigned to the waiting room. In addition to the mean squared prediction error (MSPE) and mean absolute prediction error (MAPE), we advocate to use the percentage of underpredicted observations. The use of ML algorithms 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: Using queueing and service flow variables together with information on diurnal fluctuations, ML models outperform the best rolling average by over 20 % with respect to MSPE and quantile regression reduces the number of patients with large underpredicted waiting times by 42 %. Conclusion: We find robust evidence that the proposed estimators generate more accurate ED waiting time predictions than the rolling average. We also show that to increase the predictive accuracy further, a hospital ED may decide to provide predictions to patients registered only during the daytime when the ED operates at full capacity, thus translating to more predictive service rates and the demand for treatments.