Value of a scheduled duration quantified in terms of equivalent numbers of historical cases.

BACKGROUND

Probabilistic estimates of case duration are important for several decisions on and soon before the day of surgery, including filling or preventing a hole in the operating room schedule, and comparing the durations of cases between operating rooms with and without use of specialized equipment to prevent resource conflicts. Bayesian methods use a weighted combination of the surgeon's estimated operating room time and historical data as a prediction for the median duration of the next case of the same combination. Process variability around that prediction (i.e., the coefficient of variation) is estimated using data from similar procedures. A Bayesian method relies on a parameter, τ, that specifies the equivalence between the scheduled estimate and the information contained in the median of a certain number of historical data.

METHODS

Times from operating room entrance to exit ("case duration") were obtained for multiple procedures and surgeons at 3 U.S. academic hospitals. A new method for estimating the parameter τ was developed.

RESULTS

(1) The method is reliable and has content, convergent, concurrent, and construct validity. (2) The magnitudes of the Somer's D correlations between scheduled and actual durations are small when stratified by procedure (0.05-0.14), but substantial when pooled among all cases and procedures (0.58-0.78). This pattern of correlations matches that when medians (or means) of historical durations are used. Thus, scheduled durations and historical data are essentially interchangeable for estimating the median duration of a future case. (3) Most cases (79%-88%) either have so few historical durations (0-2) that the Bayesian estimate is influenced principally by the scheduled duration, or so many historical durations (>10) that the Bayesian estimate is influenced principally by the historical durations. Thus, the balance between the scheduled duration versus historical data has little influence on results for most cases. (4) Mean absolute predictive errors are insensitive to a wide range of values (e.g., 1-10) for the parameter. The implication is that τ does not routinely need to be calculated for a given hospital, but can be set to any reasonable value (e.g., 5).

CONCLUSIONS

Understanding performance of Bayesian methods for case duration is important because variability in durations has a large influence on appropriate management decisions the working day before and on the day of surgery. Both scheduled durations and historical data need to be used for these decisions. What matters is not the choice of τ but quantifying the variability using the Bayesian method and using it in managerial decisions.