Real-time prediction of waiting time in the emergency department, using quantile regression

Emergency department (ED) waiting times can affect patient satisfaction and quality of care. We develop and validate a model that predicts an individual patient's median and 95th percentile waiting time by using only data available at triage.

From the existing ED information system, we extracted date and time of triage completion, start time of emergency physician consultation, and patient acuity category (1=most urgent, 3=least urgent). Quantile regression was applied for model development and parameter estimation by using visits from January 2011. We assessed absolute prediction error, defined as the median difference between the 50th percentile (median) predicted waiting time and actual waiting time, and the proportion of underestimated prediction, defined as the percentage of patients whose actual waiting time exceeded the 95th percentile prediction. The model was validated retrospectively with June 2010 data and prospectively with data from April to June 2011 after integration with the existing ED information system.

The derivation set included 13,200 ED visits; 903 (6.8%) were patient acuity category 1, 5,530 (41.9%) were patient acuity category 2, and 6,767 (51.3%) were patient acuity category 3. The median and 95th percentile waiting times were 17 and 57 minutes for patient acuity category 2 and 21 and 89 minutes for patient acuity category 3, respectively. The final model used predictors of patient acuity category, patient queue sizes, and flow rates only. In the retrospective validation, 5.9% of patient acuity category 2 and 5.4% of category 3 waiting times were underestimated. The median absolute prediction error was 11.9 minutes (interquantile range [IQR] 5.9 to 22.1 minutes) for patient acuity category 2 and 15.7 minutes (IQR 7.5 to 30.1 minutes) for category 3. In prospective validation, 4.3% of patient acuity category 2 and 5.8% of category 3 waiting times were underestimated. The median absolute prediction error was 9.2 minutes (IQR 4.4 to 15.1 minutes) for patient acuity category 2 and 12.9 minutes (IQR 6.5 to 22.5 minutes) for category 3.

Using only a few data elements available at triage, the model predicts individual patients' waiting time with good accuracy.