^{1}Although the direct effect of reducing turnover times on revenue is negligible at many hospitals,

^{1}indirect effects on revenue may be large. Long turnover times frustrate anesthesiologists and surgeons waiting to provide patient care,

^{2}may reduce professional satisfaction, and may reduce surgical workload if surgeons have a choice of facilities at which to do their cases. In addition, the perception of prolonged turnover times by surgeons, anesthesiologists, and administrators can result in substantial organizational costs resulting from multiple meetings and assessments of workflow. We evaluated the validity and usefulness of comparing (benchmarking) mean turnover times, without the use of confidence intervals, among hospitals.

^{3,4}Interventions to reduce prolonged turnovers can involve changing work hours of existing staff or the use of additional personnel. For example, between consecutive abdominal aortic aneurysm resections, an additional housekeeper can be assigned to help clean while an additional nurse assists anesthesia providers in preparing necessary intravenous fluids and supplies. If money were available for personnel who usually work elsewhere to be available part-time for the surgical suite, the time of day for them to be available should be when most prolonged turnovers occur. We describe and validate a statistical method to estimate the percentage of turnover times that are prolonged and that occur at specified hours of the day. The period of the day for which this percentage is the largest should be targeted for managerial improvement. We investigated whether this period can differ from the hours of the day with the largest percentage of turnovers that are prolonged.

#### Materials and Methods

^{5}

##### Comparing (Benchmarking) Mean Turnover Times among Hospitals

^{1}Even for academic, tertiary surgical suites with reputations for slow turnover times, 90 min is more than 3 SDs longer than the mean (see Results). OR allocation and staffing analyses must consider nonsequential case scheduling, whereas benchmarking studies assess cleanup and setup times (including associated patient events, such as transport to the OR). Turnover times longer than a cut point (

*e.g.*, 90 min at tertiary surgical suite or 60 min at freestanding, outpatient facility) often are set equal to the cut point for purposes of OR allocation and staffing

^{1}but are excluded for purposes of benchmarking. For example, suppose that the first elective case of the day ended at 9 am, and the second started at 2 pm. The calculated turnover time was 5 h. For purposes of assessing the impact of turnover times on OR allocation and staffing,

^{1}a value of 90 min could be used. For purposes of benchmarking in this article, we exclude large outliers such as the 5-h value. We do not know what portion of the 5-h period represented cleanup and setup. In contrast to the calculation of mean turnover time, no turnovers were excluded when determining the percentage of turnovers that were prolonged and occurred at an hour of the day. Calculation of the percentages was robust to the influence of outliers, unlike the calculation of the sample mean. The influences of both cleanup/setup times and nonsequential case scheduling are quantified in the percentages of turnovers that are prolonged. Managers must be able to compare the percentages to staffing by hour of the day, because anesthesia providers are experiencing long periods between patient care and revenue.

*P*values were calculated using exact methods. Sample mean turnover times from 29 other hospital surgical suites in the United States were used for comparison.

##### Four-step Statistical Method to Analyze Prolonged Turnovers

*versus*a shorter period, because otherwise there are hours of the day with no observed prolonged turnovers. We used thirteen 4-week periods (

*i.e.*, 1 yr) when analyzing data from the two study hospitals and evaluated using between five and nineteen 4-week periods using Monte-Carlo simulation (below).

Fig. 1 Image Tools |
Fig. 2 Image Tools |
Table 3 Image Tools |

^{2}(0.95,2n)/2m per 4-week period.

^{6}For example, at Hospitals A and B, turnovers were studied for the 16 h of the day between 7 am and 11 pm. For 8 and 14 h of the day, respectively, the mean number of prolonged turnovers was at least two every 4 weeks (figs. 1 and 2).

*t*distribution to calculate lower and upper confidence limits of the proportion. Maintain an overall 0.05 type I error rate by using a Bonferroni correction based on the number of comparisons.

^{7}The number of comparisons (in this fourth step) equals the number of hours of the day for which the lower 95% confidence bound for the mean number of prolonged turnovers during a 4-week period (from the second step) was at least 2. This requirement was necessary for the proportions to be estimated reliably (see Discussion).

##### Validity and Usefulness of the Statistical Method to Analyze Prolonged Turnovers

*i.e.*, thirteen 4-week periods). From just a few 4-week periods, we could make an estimation error when we use the sample estimate as an estimate of the population proportion. To investigate fewer (5ā12) and larger (14ā19) numbers of 4-week periods, we used a realistic discrete-event simulation of a 15-OR surgical suite (appendix). Simulation provided a known and unchanging mean turnover time for 1.3 million days. Different subsets of the data were analyzed statistically.

#### Results

##### Comparing (Benchmarking) Mean Turnover Times among Hospitals

*P*< 10

^{ā4}). When the average turnover was calculated for each workday, there was significant correlation from one daily average to the next daily average (

*P*= 0.04, n = 254 workdays). When the average turnover was calculated for each week, there was significant correlation from one week to the next week (

*P*= 0.03, n = 52 weeks). Averaging over 4-week periods was sufficient to eliminate this autocorrelation (

*P*= 0.58, n = 13). The sample mean Ā± SD of turnovers averaged over 4-week periods was 37 Ā± 1 min (n = 13). Because the distribution of the average turnover times during 4-week periods was consistent with a normal distribution (Lilliefors test,

*P*= 0.91), parametric confidence intervals were calculated. Using the SD of 1 min and the n of 13, the width of the 95% confidence interval for the mean implied by the Student

*t*distribution was less than 1 min.

*P*< 10

^{ā4}). There was no correlation among daily averages (

*P*= 0.80, n = 252 workdays). The mean Ā± SD of turnovers averaged by workday was 36 Ā± 4 min (n = 252). The distribution of the mean turnovers by day was consistent with a normal distribution by the Lilliefors test (

*P*= 0.58). Using the SD of 4 min and the n of 252, the width of the 95% confidence interval for the mean was again less than 1 min.

##### Turnovers and/or Delays That Are Prolonged at Specified Hours

*i.e.*, 1 yr) of data, the type I error rate was accurate to within 0.5% (table 2).

*#*to represent number and

*turn*to represent turnovers, the proportion of turnovers that were prolonged and that occurred during the

*t*th hour

*P*< 10

^{ā4}by Kruskal-Wallis for both hospitals). However, there were few turnovers near the end of the workday at the two hospitals (table 3). That was why the prolonged turnovers later in the workday were readily observable. The percentage of turnovers that were prolonged and that occurred during each hour of the day peaked at both hospitals during the 1-hr period starting at 1 pm (figs. 1 and 2). This timing does not suggest causes such as lunch breaks, the ending of procedures lasting all morning, or something special in the middle of the day being the cause of most prolonged turnovers occurring in the middle of the day at the two hospitals. If so, the percentage of turnovers at each hour that were prolonged would have also peaked in the middle of the day. Prolonged turnovers occurred predominantly in the middle of the day at the two hospitals because that was when most turnovers occurred (table 3).

#### Discussion

*i.e.*, < 1 min) as to be unneeded.

##### Choosing the Number of Hours of the Day to Analyze

*i.e.*, the mean is 2), there is a 21% chance that at least two of the five 4-week periods contain no prolonged turnovers. Such zero values violate assumptions of a normal distribution for the proportions, making the confidence intervals for the turnovers inaccurate.

##### Correlations among Successive Turnovers

*t*test could not validly be applied to individual observations of turnover times. Individual turnovers could not be pooled naively into two groups: before and after intervention. These results were expected, matching findings for OR staffing costs,

^{1,8}ORs in use at different times of the day,

^{9}and OR workload for purposes of OR allocation.

^{5}A simple and valid solution is simply to pool data, in this instance turnover times, by 4-week period.

^{1,5,8,9}

##### Limitations

*t*distribution could not have been used to calculate the confidence intervals.

^{10,11}However, it does affect the measured turnover times for each service as would be used for benchmarking. A potential solution to this problem is to exclude turnovers between cases performed by different services. However, because the validity of doing so likely varies among surgical suites, we think that validation for each suite would depend on performing the analysis without and with exclusion. Still, a method to do the latter has not yet been developed.

*e.g.*, more staff) depend on the hour of the day.

#### Conclusion

##### Appendix

^{12}using ARENA version 7.01 (Rockwell Software, Sewickley, PA) was used to represent the random flow of patients from ORs through the postanesthesia care unit. Each of the 65,000 workdays was simulated independently of all other workdays.

^{13}Services with brief, moderate, and long durations were assigned mean scheduled durations of 1.0, 2.0, or 3.0 h, respectively, with a common SD of the logarithm of case duration in hours equal to 0.725.

^{13}After calculation, the scheduled durations were bounded between 0.3 and 1.9 h for the 1-h service, between 0.6 and 3.9 h for the 2-h service, and between 0.9 and 5.9 h for the 3-h service. Durations were rounded up to the nearest 5 min. Turnover times were generated randomly from a log-normal distribution with a mean Ā± SD of 0.50 Ā± 0.25 h. The 90th, 95th, and 99th percentiles were 0.8, 1.0, and 1.3 h, respectively. The time exceeded the mean by at least 15 min (

*i.e.*, were āprolongedā by our choice used in the figures) for 13% of turnovers.

^{14ā16}In addition, 1% of cases were cancelled at random, resulting in unused OR time.

^{17}Cited Here...