Probabilistic Forecasting of Patient Waiting Times in an Emergency Department

Problem definition: We study the estimation of the probability distribution of individual patient waiting times in an emergency department (ED). Whereas it is known that waiting-time estimates can help improve patients’ overall satisfaction and prevent abandonment, existing methods focus on point forecasts, thereby completely ignoring the underlying uncertainty. Communicating only a point forecast to patients can be uninformative and potentially misleading. Methodology/results: We use the machine learning approach of quantile regression forest to produce probabilistic forecasts. Using a large patient-level data set, we extract the following categories of predictor variables: (1) calendar effects, (2) demographics, (3) staff count, (4) ED workload resulting from patient volumes, and (5) the severity of the patient condition. Our feature-rich modeling allows for dynamic updating and refinement of waiting-time estimates as patient- and ED-specific information (e.g., patient condition, ED congestion levels) is revealed during the waiting process. The proposed approach generates more accurate probabilistic and point forecasts when compared with methods proposed in the literature for modeling waiting times and rolling average benchmarks typically used in practice. Managerial implications: By providing personalized probabilistic forecasts, our approach gives low-acuity patients and first responders a more comprehensive picture of the possible waiting trajectory and provides more reliable inputs to inform prescriptive modeling of ED operations. We demonstrate that publishing probabilistic waiting-time estimates can inform patients and ambulance staff in selecting an ED from a network of EDs, which can lead to a more uniform spread of patient load across the network. Aspects relating to communicating forecast uncertainty to patients and implementing this methodology in practice are also discussed. For emergency healthcare service providers, probabilistic waiting-time estimates could assist in ambulance routing, staff allocation, and managing patient flow, which could facilitate efficient operations and cost savings and aid in better patient care and outcomes. Supplemental Material: The online supplement is available at https://doi.org/10.1287/msom.2023.1210 .