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Statistical Power Analysis to Estimate How Many Months of Data Are Required to Identify Operating Room Staffing Solutions to Reduce Labor Costs and Increase Productivity

Epstein, Richard H., MD*; Dexter, Franklin, MD, PhD

doi: 10.1097/00000539-200203000-00029
ANESTHETIC PHARMACOLOGY: Research Report
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We performed a statistical power analysis to determine how many historical data are needed for optimal operating room (OR) management decision making. The work applies to hospitals that provide service for all of its surgeons’ elective cases on whatever workday the surgeons and patients choose. The hospital and anesthesia group adjust OR staffing and patient scheduling to care for the patients while minimizing OR staffing costs and maximizing labor productivity. Two years of data were obtained from a seven-OR surgical suite. The data were repeatedly split into training and testing datasets. The optimal staffing solution was calculated for each training dataset to maximize the efficiency of OR time usage and was then applied to the corresponding testing dataset. Training datasets ranged in size from 30 to 270 consecutive workdays. With 30 workdays of data, the statistical method identified staffing solutions that had an average of 35% decreased costs and 27% increased productivity as compared to the existing staffing plan. There was no significant improvement in performance with more than 210 workdays (10 mo) of data. With 30 workdays of OR or anesthesia group data, the optimization method can significantly reduce staffing costs and increase productivity compared with existing staffing. When applied routinely for adjusting staffing (e.g., on a quarterly basis), 9 to 12 mo of data should be used.

*Department of Anesthesiology, Jefferson Medical College, and Medical Data Applications, Ltd.; and †Division of Management Consulting, Department of Anesthesia, University of Iowa, Iowa City, Iowa

Medical Data Applications, Ltd., developed and markets the CalculatOR™ software that performed the analysis described in this article.

October 29, 2001.

Address correspondence and reprint requests to Franklin Dexter, Division of Management Consulting, Department of Anesthesia, University of Iowa College of Medicine, Iowa City, IA 52242. Address e-mail to Franklin-Dexter@UIowa.edu.

Hospitals and anesthesia groups need to do a better job at adjusting operating room (OR) staffing and patient scheduling on a long-term basis (e.g., quarterly) to care for their patients efficiently (1–4). Currently, managers generally rely on ad hoc estimates and OR data analysis to determine how many people to have working in surgical suites. A statistical method to maximize the efficiency of OR time usage, reduce OR and anesthesia group staffing costs, and increase labor productivity has been developed (1–4). In eight of nine surgical suites where the statistical method was applied, staffing costs were significantly less than for the staffing being used by the managers (2).

The statistical method is applicable to facilities at which the surgeons and patients choose the dates of elective surgery and the facility cares for all of its surgeons’ patients. The method works by using the following data from each elective case: surgical group, location (OR number), start time, and end time. In this context, the “surgical group” comprises several surgeons who share allocated OR time (e.g., orthopedic surgery). The data can be obtained from the surgical suite’s OR information system, an electronic anesthesia patient record, the hospital’s billing system, or the anesthesia group’s billing data. The statistical method determines how many staffed ORs should be available each day for each surgical group and, for each of these ORs, how long the staff should be scheduled to work (e.g., 8, 10, or 13 h) (2). For example, a staffing solution for a cardiac surgery group on Mondays might be two ORs, one with staff scheduled to work 8 h and the other for 13 h. The number of ORs staffed determines the number of first-case-of-the-day starts, but not the total number of hours of cases that the surgeons can book, because the facility’s mission is to ensure that all patients receive care (2).

What is unknown is how many historical data are necessary or ideal to make appropriate decisions regarding OR staffing with the statistical method. In the previous study (2), 2 yr of data was used because that was what was available for analysis. It is not known whether the statistical method can perform equally or nearly as well with fewer data. Because many surgical suites have less than 2 yr of data, and because collecting this much information prospectively would delay the implementation of an improved staffing solution, shortening the period of data collection may be beneficial. In addition, when applied routinely (e.g., quarterly) to reevaluate OR nursing or anesthesia staffing, reducing the period of data collection would permit the statistical method to better respond to long-term trends in workload (5,6). For these reasons, in this study, we performed a statistical power analysis to answer the question.

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Methods

Staffing cost was calculated as the sum of the staffed OR hours and the relative cost of working late (an “overtime ratio”) multiplied by the overutilized hours (OR hours exceeding the regularly scheduled OR hours). This overtime ratio included not just the direct cost of overtime (1.5) but also an incremental factor (0.25) for the indirect costs resulting from employee dissatisfaction, recruiting expenses to replace those who leave, and surgeon and patient frustration in working late from cases not being completed until late in the day (2,3). For example, if an OR nursing and anesthesia team were scheduled to work 8 h and instead worked 9 h, then the staffing cost would be 9.75 h, where 9.75 = (8 regular hours) + 1.75 × (1 overutilized hour). The unit of staffing costs can be converted to dollars by multiplying the result by the average cost per regularly scheduled hour for the nursing and anesthesia staff in an OR.

Productivity was calculated by taking the total hours of elective cases, including turnover times, and then dividing by the staffing cost. Continuing the example, productivity would equal 92%, where 92% = (9 h of cases) ÷ (staffing cost of 9.75 h).

Underutilized OR hours were the hours of OR time before the end of the regularly scheduled hours during which there was neither a case nor a turnover time. If on a given day a given surgical group had no underutilized hours and no overutilized hours, then the budgeted OR time was used as efficiently as possible (1,4).

Two years of data (507 workdays) were available from a seven-OR, community, multiple-specialty surgical suite. The manager’s staffing at this surgical suite and the optimal staffing solution were reported previously in table 2 of Dexter et al. (2).

The total hours of elective cases (from the time of patient entrance into an OR until his or her exit from the OR) and turnover times were calculated (6) for each surgical group on each day (1,4) of the week. We considered the optimal staffing solution for each surgical group on each day of the week to be that which minimized the inefficiency of the use of OR time, as measured by the sum of the underutilized hours and the overtime ratio multiplied by the overutilized hours (1,4). We found this optimal staffing solution by considering all possible staffing solutions (2,7), starting with 0 h and progressively increasing the staffed hours until additional increases in the staffed hours caused this value to increase. We considered all possible mixtures of 8-, 10-, and 13.3-h shifts. If providing 0 h to a group resulted in the more efficient use of OR time (1,4) than providing the minimum of one OR for 8 h, then no OR was assigned to that surgical group for that day. All such groups were combined into an “other” group. The solution for the “other” group was then calculated. At least one OR was allocated for “other” groups for at least 8 h each day of the week.

Calculations were performed with Microsoft Access 97 and Excel 2000 (Redmond, WA).

For the statistical power analysis, we divided the 507 workdays of data into two subsets. The first subsets of data (training datasets) were used to identify potential staffing solutions. These solutions were then tested on the remaining workdays of data (testing datasets). The training datasets ranged in size from 30 to 270 consecutive workdays, with an incremental value of 30 workdays. The first day of each training dataset was chosen at random.

We used each training dataset to identify the staffing solution that minimized the sum of underutilized hours and the overtime ratio multiplied by overutilized hours (1,4). The performance of the staffing solution was then evaluated by applying it to the corresponding testing dataset. For example, if the training dataset included workdays 100 to 189, then the testing dataset included workdays 1 to 99 and workdays 190 to 507. The staffing cost and productivity were calculated and reported compared with the values achieved by applying the actual staffing at the surgical suite to the testing dataset.

This process of splitting the data into 2 was then repeated 99 times for each of the 9 different training dataset lengths. Confidence intervals were calculated with Student’s t-test for the means of the results of the 100 analyses.

In addition to staffing cost and productivity, we also analyzed the variability among testing datasets in the hours of OR time planned for surgical groups on each day of the week. For example, a hospital might plan 8, 10, or 13.3 h for a surgical group on a Monday, depending on the randomly selected training dataset. We used those combinations of surgical group and day of the week, including the “other” group, that were assigned at least 8 h of staffing for all 100 repetitions of the analysis. The variability among testing datasets in allocated OR hours was measured by the coefficient of variation of staffed hours among the 100 repetitions for each of these 17 combinations of surgical group and day of the week.

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Results

Using 30 workdays of data, the statistical method identified staffing solutions that had an average of 35% lower staffing costs (95% confidence interval, 34% to 36%) and 27% higher staff productivity (95% confidence interval, 26% to 28%) than the existing staffing plans (Fig. 1). The productivity achieved by the statistical method was 80.5% ± 0.3% (se). Increasing the number of workdays of data beyond 180 did not significantly improve performance at increasing productivity (P > 0.05) (Fig. 2). Increasing the number of workdays from 30 to 210 days decreased the coefficient of variation (P < 0.05), but further increases in the size of the training dataset did not significantly reduce the coefficient of variation in hours of OR time planned for each surgical group (Fig. 3).

Figure 1

Figure 1

Figure 2

Figure 2

Figure 3

Figure 3

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Discussion

The statistical method can identify staffing solutions with significantly lower staffing costs and higher productivity with 30 workdays of OR or anesthesia group data (Fig. 1). However, performance improves with increasing amounts of historical data up to 210 workdays, or 10 months of calendar time (Figs. 2 and 3). We therefore recommend that, when the OR or anesthesia group managers apply the statistical method to readjust staffing occasionally (e.g., on a quarterly basis), 9 to 12 months of data be used.

The reason for using a year or less of data routinely, even when more are available, is that the statistical method does not incorporate statistical corrections for trends and seasonality (1,2,4). Therefore, using the briefest data period possible is advantageous.

The results of the power analysis suggest that the statistical method will apply to many surgical suites (1–5), not just to the nine previously published (2). The reason is that only one year of historical data is needed. The average number of outpatient surgery cases performed with an anesthesia provider each day in the United States per 10,000 population does not vary systematically month to month on an 11-month basis (5). However, the statistical method applies only to surgical suites that take care of all of its surgeons’ patients and at which the surgeons and patients choose the day of surgery. This scheduling strategy is common, in part because it applies to surgical suites where patient scheduling is restricted to regularly scheduled hours, cases are not canceled on the day of surgery for nonmedical reasons, and surgeons routinely underestimate scheduled case durations to fit them into the allocated hours.

Previously published recommendations for forecasting OR workload for surgical groups’ OR time allocations recommended that 11 months of historical data be used (6,8). That study differed from this one in that the mission of the surgical suites considered was to care for all of the surgeons’ patients within a reasonable (four-week) period (6), rather than to take care of the surgeons’ patients on whatever workdays the patients and surgeons choose. The previous result (6) probably also applies to surgical suites that plan a limited number of hours of OR time for elective cases and then allocate OR time to surgical groups on the basis of utilization or financial measures such as contribution margin (revenue minus hospital variable costs) (5,9,10). These scheduling goals differ from the one considered in this article (2). Of note, a statistical power analysis was also previously performed for surgical suites that aim to allocate OR time to individual surgeons on the basis of their adjusted utilizations (i.e., including turnover times) or patients’ waiting times (11). Decades of data can be needed to estimate caseload accurately (11), probably explaining some surgical suites’ practical difficulties in using OR utilizations for OR time allocations.

The statistical method minimizes the sum of underutilized hours and the overtime ratio multiplied by the overutilized hours. This represents the efficiency of use of OR time (1,4). Maximizing the efficiency of the use of OR time is not identical to minimizing staffing costs, nor is it identical to maximizing labor productivity. We chose to maximize the efficiency of OR time utilization per se for several reasons. This is what Strum et al. (1,4) previously did, and we followed suit (2). The strategy applies regardless of how staff are paid; maximizing the efficiency of use of OR time is inherently “good.” This strategy provides for a very simple probabilistic interpretation permitting extensive, well developed mathematical theory to be applied to interpreting results. Finally, and most important, the practical differences in the staffing solutions are very small in comparison to the impact of rounding OR time allocations to the nearest allowable increment of hours (i.e., 0, 8, 10, etc.) (12). The performance and data requirements required to maximize OR efficiency will, of course, be superior to that which we report in this paper (Figs. 1, 2). We deliberately studied the end points showing the worst possible performance of the statistical method.

In summary, by using a statistical method that maximizes the efficiency of use of OR block time, OR allocations made with 30 workdays of data can reduce staffing costs and increase productivity. Routine adjustments to OR allocations would be made with 9–12 months of data.

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References

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© 2002 International Anesthesia Research Society