Bayesian prediction of emergency department wait time

Increasingly, many hospitals are attempting to provide more accurate information about Emergency Department (ED) wait time to their patients. Estimation of ED wait time usually depends on what is known about the patient and also the status of the ED at the time of presentation. We provide a model for estimating ED wait time for prospective low acuity patients accessing information online prior to arrival. Little is known about the prospective patient and their condition. We develop a Bayesian quantile regression approach to provide an estimated wait time range for prospective patients. Our proposed approach incorporates a priori information in government statistics and elicited expert opinion. This methodology is compared to frequentist quantile regression and Bayesian quantile regression with non-informative priors. The test set includes 1, 024 low acuity presentations, of which 457 (44%) are Category 3, 425 (41%) are Category 4 and 160 (15%) are Category 5. On the Huber loss metric, the proposed method performs best on the test data for both median and 90th percentile prediction compared to non-informative Bayesian quantile regression and frequentist quantile regression. We obtain a benefit in the estimation of model coefficients due to the value contributed by a priori information in the form of elicited expert guesses guided by government wait time statistics. The use of such informative priors offers a beneficial approach to ED wait time prediction with demonstrable potential to improve wait time quantile estimates.