Division of Management Consulting, Department of Anesthesia, University of Iowa, 200 Hawkins Drive, 6JCP, Iowa City, IA 52242, USA.
Anesth Analg. 2013 Jul;117(1):205-10. doi: 10.1213/ANE.0b013e318291d388. Epub 2013 Jun 3.
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.
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.
(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).
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.
病例持续时间的概率估计对于手术当天及之前的几个决策很重要，包括在手术室日程安排中填补或防止出现空缺，以及比较使用特殊设备的手术室和未使用特殊设备的手术室之间的病例持续时间，以防止资源冲突。贝叶斯方法使用外科医生估计的手术室时间和历史数据的加权组合来预测下一个相同组合的病例的中位数持续时间。使用类似程序的数据估计该预测周围的过程变异性（即变异系数）。贝叶斯方法依赖于一个参数 τ，该参数指定计划估计与特定数量的历史数据中位数中包含的信息之间的等效性。
在美国 3 家学术医院获得了多项手术和外科医生的手术室入口到出口的时间（“病例持续时间”）。开发了一种新的估计参数 τ 的方法。
（1）该方法可靠且具有内容有效性、收敛有效性、同时有效性和结构有效性。（2）按手术程序分层时，计划持续时间与实际持续时间之间的 Somer's D 相关系数较小（0.05-0.14），但在所有病例和手术程序中汇总时较大（0.58-0.78）。这种相关模式与使用历史持续时间中位数（或平均值）时的模式相匹配。因此，计划持续时间和历史数据在估计未来病例的中位数持续时间方面基本上是可互换的。（3）大多数病例（79%-88%）要么历史持续时间很少（0-2），以至于贝叶斯估计主要受计划持续时间的影响，要么历史持续时间很多（>10），以至于贝叶斯估计主要受历史持续时间的影响。因此，计划持续时间与历史数据之间的平衡对大多数病例的结果几乎没有影响。（4）平均绝对预测误差对参数的广泛范围（例如，1-10）不敏感。这意味着 τ 不需要为给定的医院进行计算，而是可以设置为任何合理的值（例如 5）。
了解病例持续时间的贝叶斯方法的性能很重要，因为持续时间的变异性对手术前一天和手术当天的适当管理决策有很大影响。这些决策都需要使用计划持续时间和历史数据。重要的不是 τ 的选择，而是使用贝叶斯方法量化变异性并将其用于管理决策。
