An Exact, Order-Statistic Approach to Predicting Phase I Recovery Closing Time in an Ambulatory Surgery Center to Provide Advance Notification to Anesthesiologists

BACKGROUND:Anesthesiologists vary in their desired balance between clinical workload, compensation, and personal time. Interventions that allow clinicians to individualize their work commitments have been associated with improved employee satisfaction. However, such flexibility relies on knowing when clinical responsibilities are likely to end on a given day. Without accurate predictions of when they expect to finish, clinicians cannot reliably individualize their scheduling decisions. METHODS:We performed a retrospective observational study of daily times at which the final patient left the Phase I recovery over a multi-year period at an ambulatory surgery center. Using rolling historical windows, exact percentile-based prediction limits were calculated from prior observed days. Prediction limits are predefined upper bounds for future daily observations. For each window, the prediction limit was computed as the exact order statistic corresponding to the selected percentile of the makespan, avoiding parametric assumptions about the underlying distribution. A pragmatic rolling window size was selected based on the stability of the prediction limit. Predictions with lower day-to-day variation were expected to be more useful for clinicians' day-to-day planning. RESULTS:Accuracy of exact percentile prediction limits was similar across candidate window sizes, ranging from 5 to 100 days, with observed exceedance rates remaining close to the nominal 20% level for the 80th-percentile prediction limit. The coefficient of variation of estimates decreased with increasing window size before approaching a gradual plateau, with little additional reduction in variability beyond 60 workdays. A 60-workday window provided stable 80th-percentile prediction limits while preserving the expected exceedance rate, where 80% means expected to be exceeded at most 1 day out of 5. Application of this approach to a separate synthetic log-normal dataset demonstrated comparable accuracy and variability behavior across window sizes. Example application was made to a single-specialty orthopedic hospital. CONCLUSIONS:A rolling, distribution-free prediction method based on exact order statistics provides stable and interpretable estimates of when the Phase I recovery is likely to close and the last anesthesiologist can leave for the day. Using a 60-workday historical window, this approach preserves expected upper-tail exceedance behavior while reducing day-to-day variability of the prediction limit. Such estimates enable anesthesiologists to better anticipate late work and align their daily scheduling decisions with more data-based predictions of when their workday is likely to end.