title: Explanation for the near-constant mean time remaining in surgical cases exceeding their estimated duration, necessary for appropriate display on electronic white boards.
abstract: BACKGROUND
  Consider a case that has been ongoing for longer than the scheduled duration. The anesthesiologist estimates that there is 1 hour remaining. Forty-five minutes later the case has not yet finished, and closure has not yet started. We showed previously that the mean (expected) time remaining is approximately 1 hour, not 15 minutes. The relationship is a direct mathematical consequence of the log-normal probability distributions of operating room (OR) case durations. We test the hypothesis that, with an accurate probabilistic model, until closure begins the estimated mean time remaining would be the mean time from the start of closure to OR exit.
  
  
  METHODS
  Among the 311,940 OR cases in a 7-year time series from 1 hospital, there were 3962 cases for which (1) there had been previously at least 30 cases of the same combination of scheduled procedure(s), surgeon, and type of anesthetic and (2) the actual OR time exceeded the 0.9 quantile of case duration before the case started. A Bayesian statistical method was used to calculate the mean (expected) minutes remaining in the case at the 0.9 quantile. The estimate was compared with the actual minutes from the time of the start of closure until the patient exited the OR.
  
  
  RESULTS
  The mean ± standard error of the pairwise difference was 0.2 ± 0.4 minutes. The Bayesian estimate for the 0.9 quantile was exceeded by 10.2% ± 0.01% of cases (i.e., very close to the desired 10.0% rate).
  
  
  CONCLUSIONS
  If a case is taking longer than the expected (scheduled) duration, closure has not yet started, and someone in the OR is asked how much time the case likely has remaining, the value recorded on a clipboard for viewing later should be the estimated time remaining (e.g., "1 hour") not an end time (e.g., "5:15 pm"). Electronic whiteboard displays should not show that the estimated time remaining in the case is less than the mean time from start of closure to OR exit. Similarly, if closure has started, the expected time remaining that is displayed should not be longer than the mean time from closure to OR exit. Finally, our results match previous reports that, before a case starts, statistical methods can reliably be used to assist in decisions involving the longest amount of time that cases may take (e.g., conflict checking for resources, filling holes in the OR schedule, and preventing holes in the schedule).
authors.affiliation: Department of Anesthesiology, Vanderbilt University Medical Center, Nashville, TN, USA.
authors.forename: Vikram
authors.initials: V
authors.lastname: Tiwari
authors.forename: Franklin
authors.initials: F
authors.lastname: Dexter
authors.forename: Brian S
authors.initials: BS
authors.lastname: Rothman
authors.forename: Jesse M
authors.initials: JM
authors.lastname: Ehrenfeld
authors.forename: Richard H
authors.initials: RH
authors.lastname: Epstein
mesh_terms: D001071:Appointments and Schedules; D001499:Bayes Theorem; D017598:Efficiency, Organizational; D006801:Humans; D017146:Models, Organizational; D015233:Models, Statistical; D009870:Operating Room Information Systems / Q000458:organization & administration* / Q000706:statistics & numerical data; D009873:Operating Rooms / Q000458:organization & administration* / Q000706:statistics & numerical data; D010561:Personnel Staffing and Scheduling / Q000458:organization & administration* / Q000706:statistics & numerical data; D010562:Personnel Staffing and Scheduling Information Systems / Q000458:organization & administration* / Q000706:statistics & numerical data; D011336:Probability; D013997:Time Factors; D017748:Time Management / Q000458:organization & administration*; D016526:Workload / Q000706:statistics & numerical data