Influence of parameter uncertainty on the tardiness of the start of a surgical case following a preceding surgical case performed by a different surgeon

Abstract

Background: To-follow surgeons suffer from tardiness of start times due to preceding surgical cases in operating rooms (OR) taking longer than scheduled. Preceding cases take longer than their expected (mean) time not only because of process variability (e.g., different surgical first assist) but parameter uncertainty (e.g., surgeon has not previously performed the procedure at the hospital). Uncommon combinations of scheduled procedures occur frequently. We quantified Bayesian methods’ mitigation of the effect of parameter uncertainty on tardiness at a hospital. Methods: There were N = 7361 pairs of first and second cases of the day of different surgeons performed in the same OR and with the same sequence as that assigned as of 7 P.M. the day before surgery. For each pair, random OR times for the first case were generated from the posterior distribution incorporating surgical suite, year, estimated OR time from the surgeon and scheduler, and historical OR times, classified by combination of surgeon and scheduled procedure(s). Results: The cases of a second surgeon that followed a preceding case with 0–3 historical OR times accounted for 21.1% (SE 1.2%) of the total tardiness and 17.1% (SE 0.9%) of cases. The pairwise ratios of total tardiness to cases equaled 1.233 (95% confidence interval 1.203–1.263). The calculations were repeated for cases with no historical data. The pairwise ratios averaged 1.223, not significantly different (P = 0.35). Conclusions: Without using a Bayesian method, instead of 21% of tardiness attributable to cases with few data, it would be nearly 100%. Therefore, the results predict the value of using a Bayesian method for estimating OR times at hospitals with case scheduled of uncommon procedures. Bayesian methods can be implemented with a spreadsheet (e.g., Excel worksheet) or a database table updated annually.