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Statistical Analysis of Postanesthesia Care Unit Staffing at a Surgical Suite with Frequent Delays in Admission from the Operating Room—A Case Study

Dexter, Franklin MD, PhD; Epstein, Richard H. MD*,; Penning, Donald H. MS, MD

doi: 10.1097/00000539-200104000-00029
Case Report: Case Report
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Department of Anesthesia, University of Iowa, Iowa City, Iowa; the *Department of Anesthesia, Jefferson Medical College, Philadelphia, Pennsylvania; and the †Department of Anesthesia, Sunnybrook and Women’s Health Sciences Centre, and Department of Anesthesia, University of Toronto, Toronto, Canada

This project was funded by Sunnybrook and Women’s Health Sciences Centre, Toronto, Canada, and Wayne State University, Department of Anesthesiology, Detroit, Michigan.

December 21, 2000.

Franklin Dexter is employed by the University of Iowa, in part as a consultant to anesthesia groups, companies, and hospitals. Richard Epstein is President of Medical Data Applications, Ltd., which developed the CalculatOR™software.

Address correspondence to Franklin Dexter, Division of Management Consulting, Department of Anesthesia, University of Iowa, Iowa City, IA 52242. Address e-mail to franklin-dexter@uiowa.edu.

IMPLICATIONS: The statistical method can identify postanesthesia care unit staffing solutions to match operating room caseload with significantly fewer staffed hours than the staffing solution developed by practicing post anesthesia care unit managers. CalculatOR™ can complete the analysis sufficiently quickly (overnight) on a personal computer as to be practical.

At some surgical suites, if each nurse in the postanesthesia care unit (PACU) is caring for as many patients as staffing standards permit (typically two), then patients remain in their operating rooms (ORs) until PACU nurses become available to care for them. Surgical suite staffing costs increase if patients frequently remain in the OR resulting in overtime to finish the day’s scheduled cases.

In this case study, we describe PACU staffing at a surgical suite in which on more than half of the workdays at least one patient waited in their OR for an opening in the PACU. We applied a statistical method we previously developed for analysis of weekend staffing requirements (1) to determine the method of scheduling the existing nurses, without increasing staffing hours, so as to minimize the percentage of workdays with patients waiting in their ORs, and the minimum number of additional PACU nursing hours that would be needed to satisfy the hospital’s objective to decrease this rate to 5% of days or less.

We knew that the statistical method would identify the least expensive PACU staffing solution (1). However, we did not know whether the statistical method would provide for significantly fewer workdays with patients waiting in their ORs than the staffing solution being used by the PACU nursing managers based on their experience. We also did not know whether the statistical method could identify a staffing solution that was more accurate than the PACU nursing managers’ proposed staffing solution at achieving the hospital’s objective of having the minimum number of PACU nursing hours required for the percentage of workdays with patients waiting in their ORs to be 5% of days or less. Finally, our case study provided information into whether the statistical method can run sufficiently quickly on a personal computer as to be useful in practice.

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Methods

The statistical method generates a staffing solution using three types of data: 1) historical data on the numbers of patients who would be in the PACU at each workday hour if patients had not had to wait for admission into the PACU, 2) the percentage of days for which the surgical suite was willing to accept having at least one patient being delayed in their admission into the PACU, and 3) the duration and start times of the shifts that the PACU nurses considered to be desirable. Analysis of perioperative staffing focuses on the percentages of days with adequate staffing, not hours with adequate staffing, because the adequacy of staffing among days is statistically independent whereas the adequacy of staffing among hours on the same day is correlated (1,2).

Each of the possible staffing solutions evaluated by the statistical method (1) was a different combination of 14 different 8-h and 10-h shifts. We considered every 8 and 10-h shift starting at 8 am or later and ending at 11 pm or earlier (i.e., 8 am to 4 pm, 9 am to 5 pm, 3 pm to 11 pm, 8 am to 6 pm, 9 am to 7 pm, and 1 pm to 11 pm). This gave 14 different shifts.

The statistical method (1) was implemented in the software application CalculatOR™. CalculatOR™ (Medical Data Applications, Ltd., Jenkintown, PA) was written to evaluate each of these different permutations of shifts sufficiently quickly as to be practical. For example, the algorithm skips permutations of shifts that only differ in the order in which the shifts are considered. Also, between 8 am and 11 pm there was usually at least one patient. In that national (American Society of Perianesthesia Nursing) standards require that two nurses be present at all times when a patient is in the PACU, all combinations of shifts with zero or one nurse present at any time of the workday were excluded from consideration.

The program determined the number of PACU nurses that would have been required at each hour of each workday such that no nurse would have cared for more than two patients. If during any hour of the 8 am to 11 pm workday a proposed staffing solution would not have provided adequate staffing (i.e., to have prevented a patient from waiting in the OR for a PACU opening, at least one nurse would have had to care for more than two patients), then the day in question was counted as being staffed inadequately by that proposed staffing solution. If the number of understaffed days exceeded a cutoff value, then that staffing solution was discarded as unacceptable. The cutoff value equaled the lower 95% distribution-free confidence bound on the number of workdays for which a proposed staffing solution could have provided an inadequate number of PACU nurses during at least 1 h while maintaining the prescribed (5%) level of future risk that the group accepted in being understaffed. This means that the staffing solution would allow, at most, one future day in 20 when not enough nurses are available to care for the patients as soon as they are ready to be transported from an OR to the PACU. For each staffing solution providing adequate coverage, the total number of daily staffed hours was calculated. From among all the staffing solutions that satisfied the risk criterion, the recommended staffing solution was selected from the ones with the least number of daily staff hours.

We also performed the analysis several more times using incrementally larger risks of being understaffed until we identified the minimum risk for which the total required nursing hours was no more than the current number of staffed hours. We then applied the sign test to compare the percentage of workdays with patients waiting in their ORs using the statistical method’s staffing solution versus the staffing solution in use by the PACU nursing managers. This current staffing was developed empirically by the PACU nursing managers based on their experience in working at the PACU and their efforts to match PACU staffing to OR workload.

The specific phase I PACU under consideration was a tertiary surgical suite with a mixture of outpatient, inpatient, and same day admit cases. Many of the cases were of complex procedures with extensive PACU nursing workload. One year of data was available from the PACU. In that these data were available previously to the PACU nursing managers, our analysis focused on the potential value of the statistical analysis of the data, not the data itself.

We excluded weekends, federal holidays, a “slow down” period between Christmas and New Year’s, and another “slow down” period during school spring break week. This left 232 work days for analysis, during which 6,851 patients received care in the PACU. Even if no patient had been delayed in their entry into the PACU under consideration, there would never have been more than 20 patients in the PACU simultaneously (i.e., the maximum number of PACU nurses needed simultaneously was 10 or less). The computer program therefore evaluated (14 + 1)10 different permutations of shifts, which is approximately 580 billion.

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Results

CalculatOR™ performed the computations described in this paper in slightly under seven hours on a 233 MHz Pentium microprocessor with 64 MB RAM running Windows NT 4.0 (i.e., it did not take weeks or months of computation time).

At the current clinical staffing level (72 h between 8 am and 11 pm), on 56% ± 2% (se) of the days at least one patient waited in the OR for admission into the PACU. Using the statistical analysis, we identified a staffing solution with the same number of actual daily PACU nursing hours that would have resulted in significantly fewer (24% ± 1%, P < 10-10) days having been understaffed. This value of 24% provided for an upper 95% confidence bound for 28% of future days having patients wait for PACU admission. To achieve the improved service level, three of the four nurses currently working 10 am to 6 pm would need to change their shifts to 8 AM to 4 pm, 11 AM to 7 pm, and 2 pm to 10 pm, respectively.

If the staffing solution developed empirically by the PACU nursing managers (requiring 24 additional staffed hours per day) had been used, then 10% ± 2% of the days would have been understaffed. This value of 10% provided for an upper 95% confidence bound for 14% of future days having patients wait for PACU admission.

Using the year of data, the statistical analysis identified several different staffing solutions that would have resulted in 2.2% ± 1% understaffed days. All of these staffing solutions required 26 additional staffed hours per day compared to current staffing, 2 more hours per day than the staffing solution developed by PACU nurse managers. The value of 2.2% provided for an upper 95% confidence bound for 5% of future days having patients waiting for PACU admission. Because the statistical analysis considered the maximum number of patients present in the PACU each hour, this value was an overestimate of the actual risk of patients having to wait for PACU admission.

There was an inadequate sample size to assess daily variation statistically. Qualitative review of existing PACU workload and staffing did not show a systematic variation among days of the week (Table 1) (3).

Table 1

Table 1

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Discussion

In this case study, we showed that a statistical method previously developed for a different type of analysis, weekend staffing (1), can be used successfully to analyze PACU staffing. The statistical method can identify PACU staffing solutions which provide for significantly fewer workdays with patients waiting in their ORs than staffing solutions, with the same number of staffed hours, developed by PACU nursing managers based on their experience. The statistical method can identify staffing solutions that are more accurate than those proposed based on PACU nursing managers’ experience at achieving a hospital’s objective of having the minimum number of PACU nursing hours required for the percentage of workdays with patients waiting in their ORs to be 5% of days or less. Finally, the CalculatOR™ implementation of the statistical method can be completed on a personal computer for a relatively large PACU (98 staffed hours per workday) within a reasonable (<7 hours) amount of time, despite considering hundreds of billions of different staffing solutions.

The case we presented assumed that each nurse could not safely care for more than two PACU patients. The statistical method (1) can function with any staffing standard. Some patients may require 1:1 care. Patients’ acuities, expressed as an appropriate staffing ratio (4), can vary over time too. In that the analysis only considers staffing required for clinical care, additional staff are needed for breaks, lunches, education, continuing education, vacations, illnesses, etc.

We have previously described another method of statistical analysis of PACU staffing (2). However it does not apply to the problem described in this case study for two reasons. First, that method starts with the assumption that the nurses have chosen which shifts they want to work. It then asks how many nurses should work on each of those shifts so as to care for the patients while minimizing staffing costs. In contrast, the statistical method used in this paper determines the optimal distribution of shifts. Second, we developed the previous method (2) for PACUs that do not enforce patient staffing standards. At such surgical suites, when a case is finished in the OR, the OR nurses call and give report, and the patient is transported to the PACU–regardless of how busy the PACU already is. Because that study addressed a patient safety issue, statistical corrections were made for using multiple shifts. Consequently, many more days of data were required than used in this study. We did not make a statistical correction for multiple shifts in this study because the “penalty” in having the PACU being full was “only” economic. That is, if there are insufficient PACU nurses available to satisfy staffing standards, then the patient waits safely in their OR until a PACU nurse becomes available.

We focused on adjusting PACU staffing to maximize patient throughput in the surgical suite, not changing OR scheduling to fit PACU staffing. We recently analyzed this decision in detail and showed that adjusting PACU staffing to match the OR schedule can maximize surgeon convenience, surgical suite revenue, and anesthesia revenue, while minimizing how long patients wait for care (5).

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References

1. Dexter F, Macario A, Traub RD. Statistical method using operating room information system data to determine anesthetist weekend call requirements. AANA J 2000; 68: 21–6.
2. Dexter F, Rittenmeyer H. A statistical method for predicting postanesthesia care unit staffing needs. AORN J 1997; 65: 947–57.
3. O’Brien-Pallas L, Leatt P, Deber R, Till J. A comparison of workload estimates using three methods of patient classification. Can J Nurs Adm 1989; 2: 16–23.
4. Dexter F, Rittenmeyer H. Measuring productivity of the phase I postanesthesia care unit. J Perianesth Nurs 1997; 12: 7–11.
5. Dexter F, Traub RD. Sequencing cases in operating rooms— predicting whether one surgical case will last longer than another. Anesth Analg 2000; 90: 975–9.
© 2001 International Anesthesia Research Society