Tactical Increases in Operating Room Block Time Based on ... · Section Editor: Franklin Dexter Tactical Increases in Operating Room Block Time Based on Financial Data and Market

Economics, Education, and PolicySection Editor: Franklin Dexter

Tactical Increases in Operating Room Block Time Basedon Financial Data and Market Growth Estimates fromData Envelopment Analysis

Liam O’Neill, PhD*

Franklin Dexter, MD, PhD†

BACKGROUND: Data envelopment analysis (DEA) is an established technique thathospitals and anesthesia groups can use to understand their potential to growdifferent specialties of inpatient surgery. Often related decisions such as recruit-ment of new physicians are made promptly. A practical challenge in using DEA inpractice for this application has been the time to obtain access to and preprocessdischarge data from states.METHODS: A case study is presented to show how results of DEA are linked tofinancial analysis for purposes of deciding which surgical specialties should beprovided more resources and institutional support, including the allocation ofadditional operating room (OR) block time on a tactical (1 yr) time course. Statedischarge abstract databases were used to study how to perform and present theDEA using data from websites of the United States’ (US) Healthcare Cost andUtilization Project (HCUPNet) and Census Bureau (American FactFinder).RESULTS: DEA was performed without state discharge data by using census datawith federal surgical rates adjusted for age and gender. Validity was assessedbased on multiple criteria, including: satisfaction of statistical assumptions, facevalidity of results for hospitals, differentiation between efficient and inefficienthospitals on other measures of how much surgery is done, and correlation ofestimates of each hospital’s potential to grow the workload of each of eightspecialties with estimates obtained using unrelated statistical methods.CONCLUSIONS: A hospital can choose specialties to target for expanded OR capacitybased on its financial data, its caseloads for specific specialties, the caseloads fromhospitals previously examined, and surgical rates from federal census data.(Anesth Analg 2007;104:355–68)

Data envelopment analysis (DEA) is a techniquethat hospitals and anesthesia groups can use tounderstand their potential to grow different special-ties of inpatient surgery (Table 1). Rather thanrecruit another vascular surgeon and then wait tosee if workload increases, a hospital can determinebeforehand whether there is potential for market

growth in vascular surgery. Previous papers havedescribed the methodology, focusing sequentiallyon establishing: validity (1), usefulness for severalapplications (2), and presentation of results (3).Those three papers describe how to benchmark eachspecialty’s surgical caseload at a study hospitalrelative to caseloads at all other hospitals in thestudy hospital’s state.

In the current paper, we consider a hospital atwhich surgical workload had increased progressivelyover 7 yr. However, during the next 7 yr, inpatientsurgical workload had not increased. Outpatient sur-gery had declined, as competing facilities were openedby physicians. Efforts to maintain workload included theallocation of large amounts of operating room (OR)block time. The hope had been to have sufficient excessof revenues to variable costs (i.e., contribution margin) tooffset the large capital and fixed staffing costs. Theseefforts were failing, resulting in a more precarious finan-cial condition. The question asked by the administratorsand anesthesiologists was whether there were specialtiesto target for short-term institutional support to promotegrowth. Such surgical specialties would need to haveboth market growth potential and a relatively highcontribution margin.

From the *Department of Health Management and Policy,University of North Texas, Fort Worth, Texas; and †Division ofManagement Consulting, Departments of Anesthesia and HealthManagement and Policy, University of Iowa, Iowa City, Iowa.

Accepted for publication October 26, 2006.Some of this material was presented at the Institute for Opera-

tions Research and Management Science annual meetings in SanFrancisco, CA, November 16, 2005, and in Pittsburgh, PA onNovember 7, 2006.

Financial disclosure: FD is Director of the Division of ManagementConsulting of the University of Iowa. He receives no funds personallyother than his salary from the State of Iowa, including no travelexpenses or honorarium, and has tenure with no incentive program.

Address correspondence and reprint requests to Franklin Dex-ter, Division of Management Consulting, Department of Anesthesia,University of Iowa, Iowa City, IA 52242. Address e-mail to [email protected].

Copyright © 2007 International Anesthesia Research SocietyDOI: 10.1213/01.ane.0000253092.04322.23

Vol. 104, No. 2, February 2007 355

The limiting factor to answering such a questionscientifically is neither the financial analysis nor theDEA. Every hospital that bills Medicare and knows itsimplant costs has the needed financial data (4). Per-forming the financial analysis in Excel takes 1–2 h withappropriate software. Performing the DEA itself takesabout 30 min.

The challenge has been the time and effort requiredto obtain and process a new set of state dischargeabstract data to obtain an abstract of the hospitaliza-tion of each patient undergoing one of the studiedprocedures at every hospital in the state. First, ap-proval is obtained from the hospital’s state for thedata, which (appropriately) involves multiple forms.Second, the data need to be cleaned, as the quality offields varies among states. These time-consumingsteps can make the DEA seem impractical.

Instead of using state discharge abstract data tomeasure the actual rates at which specific procedureswere performed, the analysis could potentially bebased on estimates derived from readily-availablenational data. For example, the age- and gender-adjusted rate of lung lobectomy in the United States(US) can be obtained in about 10 min from the websiteof the US Agency for Healthcare Research and QualityHealthcare Cost and Utilization Project’s data ware-house (http://hcup.ahrq.gov/) (5). The same applies tothe other common procedures listed in Table 1. Inaddition, the population by age and gender can bedetermined for all US counties from the Census Bu-reau’s website (http://factfinder.census.gov/). Multi-plying the rate times the population might besufficient to determine how much surgery is likelybeing done on residents living near a hospital.

In this paper, we develop such a process that relieson data available from Federal websites. We apply it

to the study hospital and its financial data. We use sixdifferent criteria to validate the process, and in theprocess further explore the underpinnings of usingDEA to guide selective increases in allocations of ORblock time.

CASE STUDYThe case study is presented here in lieu of a

separate Background section. The Validation sectionfollows, as it relies on an understanding of the DEAmaterial in the Case Study section.

None of the steps in this case study is new, otherthan the automatic identification of surgeon specialty,later. We list the specific steps taken for the specifichospital studied. Readers who would be performingthe financial analyses and/or the DEA will need torefer to the referenced papers for step-by-step meth-odologies and equations.

Figure 1 shows the overall contribution margin perOR hour for each surgeon from the study hospitalover 1 yr, along with the 95% confidence intervals (6).The patients included underwent outpatient surgeryor were admitted on the day of their elective surgery(4,6,10). Among these 11,496 cases, 6.2% were of aprocedure listed in Table 1. Only elective surgery wasstudied, because a hospital can alter its elective work-load through tactical decisions, while changes in ur-gent surgery involve longer-term strategic planning.

Figure 2 shows the successive exclusion of special-ties for consideration of targeted growth throughincreases in OR allocations. The steps were describedpreviously (10). Each surgeon is used as a surrogatefor his or her specialty. Only increases in OR alloca-tions are considered, because reductions rarely aremandated via tactical mechanisms. If a decision were

Table 1. Description of the Data Envelopment Analysis Model

Outputs—Numbers of hospital discharges including the listedprocedures, obtained from the corresponding CCS or DRG (1)

Specialty for which listed procedures are a reliablesurrogate (1,2) for the �inpatient workload�

AAA Abdominal aortic aneurysm resection Vascular surgeryCABG Coronary artery bypass graft Cardiac surgeryColorectal Colorectal resection General surgeryCraniotomy Craniotomy, not for trauma Neurological surgeryHip replacement Hip replacement OrthopedicsHysterectomy Hysterectomy GynecologyLung resection Lung resection General thoracic surgeryNephrectomy Nephrectomy UrologyInputsBeds Staffed acute and intensive care beds at the hospitalCounty Estimated total hospital charges for the above eight procedures performed on residents of

hospitalsRegion County and region, normalized by the land square miles of hospital’s county and regionSurgeons Surgeons who performed at least three cases of any one of the above eight procedures at the

hospitalTech Number of nine high technology services (2) offered at the hospital (e.g., solid organ

transplantation)CCS represents Clinical Classifications’ Software. The corresponding International Classification of Diseases Version 9 Clinical Modification procedure codes are available at the US Agency forHealthcare Research and Quality’s website http://www.hcup-us.ahrq.gov/toolssoftware/ccs/ccsfactsheet.jsp (accessed 10/11/05) (5). DRG represents Diagnosis Related Groups. Craniotomy,not for trauma, in adults was obtained from the hospital discharges for US federal DRG 1 or 2. The outputs and inputs are as previously published, except that County and Region were obtainedfrom US federal data warehouses. The charges for use in calculating these two variables were year 2003 surgical charges. At the time of the analysis, 2003 was the most recent year of hospitaldata available from the federal website. The year is likely irrelevant, because charges are used only to provide the average relative resource use for the different procedures listed above (1,2).

356 Estimating OR Market Growth Potential ANESTHESIA & ANALGESIA

made to reduce a specific program, the hospital likelywould allow the number of subspecialty surgeons todecrease through attrition. As the subspecialty’s ORworkload declines gradually, progressively less ORtime would be allocated to reduce expected under-utilized OR time (11).

First, surgeons (specialties) with below averagecontribution margin per OR hour were excluded fromconsideration of being allocated more block time thanneeded for their existing cases (10). The reason is that,instead, some or all of the additional OR time could beused as general purpose overflow for specialties thathave filled their allocated OR time (12,13) and havemore cases to perform (14,15). Both surgeons withbelow and above average contribution margin per ORhour would have access to that overflow OR time.Thus, the natural expansion of specialties into theoverflow time would result in the cases scheduled intooverflow OR time having approximately the averagecontribution margin per OR hour. If much less extraOR time is available versus the expected growth in useof OR time by surgeons (specialties) with high contri-bution margins per OR hour, some surgeons withabove average contribution margins may also be ex-cluded from additional allocations. The Appendix ofRef. (10) gives the equations for calculating the thresh-old value to use.

Second, among the remaining surgeons (special-ties), those with �2 h a week of cases were excludedfrom further consideration (10).

Third, the hospital administrators’ and anesthesi-ologists’ judgment was that virtually all of the outpa-tient cases would be lost for those surgeons who hadinvested in a physician-owned ambulatory surgerycenter. For all of these surgeons, once their outpatientcases were excluded, their remaining cases repre-sented �2 h per week of cases. Thus those surgeons(specialties) were excluded (10).

Fourth, intensive care unit (ICU), postanesthesiacare unit, and hospital ward beds were considered.There were no reports of cancellations due to limitedcapacity. Thus, these were not considered constraintsin the analysis, which differs from the analyses pub-lished for two other hospitals (10,16). In addition,there were no reports of variability among days of theweek in the numbers of admissions to ICUs or wardsafter elective (scheduled) surgery causing disruptionof the admission of nonsurgical patients from emer-gency departments (17). Therefore, variability amongdays of the week also was not considered, unlikeanalyses published for other hospitals (18,19).

Fifth, those surgeons (specialties) with wide confi-dence intervals in estimated contribution margin perOR hour from Figure 1 were identified in Figure 2 (6).The confidence intervals are useful to identify sur-geons (specialties) for which outlier patients couldcause spurious tactical decisions (9). All such surgeonshad been excluded from previous steps. Thus, theuncertainty was not considered in the analysis (9).

The functional specialties of the remaining sur-geons in Figure 2 were identified. Each outpatient visitor hospitalization with surgery had a primary Inter-national Classifications of Diseases Clinical Modifica-tion 9 procedure code (ICD-9-CM). The correspondingClinical Classifications Software (CCS) code was ob-tained for each ICD-9-CM from the federal websitelisted in the legend of Table 1. Thus, there was oneCCS for each case. The most common CCS code wasobtained for each surgeon. Specialty was determinedbased on the most common CCS. There was noambiguity for any surgeon. For example, the twocardiac surgeons in Figure 2 both had “Coronaryartery bypass graft” as the most common CCS; thethree general surgeons had “Cholecystectomy andcommon duct exploration;” the five gynecologists had“Hysterectomy, abdominal and vaginal;” and the foururologists had “Procedures on the urethra.”

The next step in the process of allocating increasesin OR block times while considering the financialimplications was to estimate potential for growth inOR workload (10).

Figure 3 shows a graphical representation of aProductivity Ratio calculated by the DEA. The variablesare listed in Table 1. Refs. (3) and (20) give thecorresponding equations. The values along the axes

Figure 1. Contribution margin per operating room (OR) hourfor the 87 surgeons. Circles show each surgeon’s ratio ofmean contribution margin among all of the surgeon’s pa-tients to mean OR hours among all of the surgeon’s patients.Each ratio is identical to the ratio of the surgeon’s overallcontribution margin to overall use of OR time. The horizon-tal bars are 95% upper and lower confidence intervals for theratios, calculated using Fieller’s method (6–8). The periodstudied was February 2004 through January 2005. Some ofthe ratios have wide confidence intervals because the sur-geons performed few cases. Some are wide because thesurgeons performed different types of procedures withwidely different contribution margins (9).

Vol. 104, No. 2, February 2007 © 2007 International Anesthesia Research Society 357

are the annual numbers of Colorectal discharges andstaffed acute care hospital Beds.

Hospital discharges with a Colorectal CCS proce-dure are plotted, because the discharges are propor-tional to the total workload of general surgery (1,2).The other seven surgical procedures used to representtheir specialties are given in Table 1. Appendix 1 ofRef. (1) reviews other potential procedures and whythey were not used.

Beds are plotted, because they are a surrogate forthe size and the market visibility of the hospital, asrelevant for marketing to potential patients (21). Bedswere defined as the number of staffed acute care bedsas reported in the annual survey of the AmericanHospital Association. Neither surgical beds nor ORswere used, because it is the number of acute care bedsthat predicts the market visibility of a hospital (21).

The other two surrogates used for market visibility arethe number of Surgeons and high-Technology services(Table 1). Hospitals with larger market visibility gen-erally perform more surgery.

The filled square in Figure 3 shows the studyhospital. Open circles are used to show Colorectaldischarges and Beds for hospitals in Iowa and Penn-sylvania. The study hospital sent its data of Table 1,excluding the County and Region variables. Theselatter variables are the focus of the Validation section,later. They are estimates of the amount of surgeryperformed at any hospital on residents of the countyand region.

DEA selects automatically those outputs and inputsin Table 1 for the study hospital to appear as efficientas possible at producing surgery. A virtual, bench-mark hospital is created simultaneously by DEA andshown as a triangle in Figure 3. The productivity ratiofor Colorectal discharges to Beds is the ratio of theslopes of the two lines in Figure 3. Because the line forthe study hospital is above the line for its benchmarkhospital, the study hospital is performing more gen-eral surgery than expected, based on its physical sizeand visibility.

Table 2 shows the productivity ratios for all com-binations of outputs from Table 1 to inputs from Table1 expressed as percentage differences from the corre-sponding benchmark hospital. For example, from Fig-ure 3, the Colorectal surgery per Beds of the studyhospital was approximately 20% higher than that ofthe benchmark hospital. The value of the productivityratio in the corresponding column and row of Table 2is 20%.

Table 2 shows that CABG and Hysterectomy werethe outputs chosen automatically by DEA to make thestudy hospital appear as efficient as possible. Theinputs selected by DEA were Beds, County, Region, andTechnology. The combinations of these selected outputsand inputs are listed in bold italic. The efficiency scoreof the hospital equals approximately 2.0, where 2.0 �200% � 100% plus the listed bold italic values. The

Figure 2. Successive exclusion of surgeons(specialties) for consideration of targetedgrowth. The contribution margins per op-erating room (OR) hour along the horizon-tal axis are the same as those listed alongthe vertical axis of Figure 1. Progressiveexclusion of surgeons (specialties) from leftto right in the figure and from bottom totop in the legend match the First, Second,and so forth in the Case Study section of thepaper.

Figure 3. Graphical representation of one of the productivityratios in Table 2. The variables of Colorectal discharges andhospital Beds are defined in Table 1. The study hospital,located in the southern US, is shown with a square. Dataenvelopment analysis uses all of the hospitals, shown bycircles, to choose automatically those outputs and inputsthat make a hospital appear as efficient as possible. Thevirtual, benchmark hospital is created simultaneously, andis shown by a triangle. The productivity ratio equals thepercentage difference of the slope of the line for the studyhospital versus the slope of the line for the benchmarkhospital.


study hospital produced 2.0 as much surgery as thebest other hospitals could if they had the same condi-tions (inputs).

Because DEA selected which outputs and inputs tocompare based on making the study hospital appearas efficient as possible, the efficiency score of 2.0represents a best-case scenario. The result is based onthe premise that the managers have been focusingextra resources on those outputs that would make thehospital as efficient as possible at producing surgery.For example, more OR block time may have beenallocated tactically to those specialties that the man-agers forecasted could grow and use it. Letting DEAselectively choose outputs to study makes sense, asthe analysis then reflects the ability of a hospital tofocus on the specialties for which the hospital canproduce a lot of surgery. A specialty orthopedichospital may be very efficient, yet will perform poorlyat producing thoracic surgery.

The selection of inputs by DEA identifies the bottle-necks to doing more surgery at the hospital. Ref. (2)presents these concepts graphically. However, thegraphs are limited to one input and one or twooutputs, whereas the productivity ratios of Table 2show multiple dimensions simultaneously. The equa-tions for the super-efficient DEA model that were usedto create Table 2 are given in Refs. (2) and (3).

Some of the values in Table 2 are negative. Thestudy hospital had relatively weak market capture forthese outputs: AAA for vascular surgery, Craniotomyfor neurological surgery, and Hip Replacement for

orthopedic surgery. Readers interested in how thetable was produced using DEA should refer to Ref. (3).

Table 3 lists the four hospitals contributing to thevirtual, benchmark hospital. The same weight fromthe second column of Table 3 is applied to all proce-dures (third through 10th columns) at each of thehospitals (listed as A–D). The selection of the hospitalscontributing to the benchmark and their weights are adirect consequence of the selection of outputs andinputs to make the study hospital appear as efficientas possible (2).

A gap is the number of additional cases of each typeof procedure that the hospital can be producing basedon the hospital’s performance relative to its bench-mark hospital. The gap is expressed in Table 3 as apercentage of the current number of cases. A negativegap infers that more cases are being done than ex-pected from the benchmark hospital. A positive gapshows the potential of the study hospital to increase itsworkload for the specialty. The positive gaps areshown in bold italic in Table 3. Graphical representa-tions of the steps to compute gaps can be found in Ref.(2). Relevant equations are in Ref. (3).

Table 3 (last row) shows that the study hospital hasthe potential to capture more of its local market forAAA (vascular), Craniotomy (neurological), and Hipreplacement (orthopedic) surgery, but not more of thespecialties named in Figure 2: cardiac, general, gyne-cological, or urological surgery. For those specialties,the hospital is already doing as much as the best of

Table 2. Productivity Ratios for the Study Hospital

AAA CABG Colorectal CraniotomyHip

replacement HysterectomyLung

resection NephrectomyBeds �70 100 20 �50 �30 100 30 40County �70 100 20 �50 �30 100 30 40Region �70 100 20 �50 �30 100 30 40Surgeons �80 60 0 �60 �40 60 0 20Tech. �70 100 20 �50 �30 100 30 40Values given are percentage values. Abbreviations for the outputs (columns) and inputs (rows) are given in Table 1. For example, Surgeons refers to the total number of surgeons at each hospitalas is relevant to market visibility, not the number of surgeons for each of the columns in this Table 2 (1,2). Data envelopment analysis chooses automatically outputs and inputs to make thestudy hospital appear as efficient as possible. The combinations of these selected outputs and inputs are listed in bold italic. The equations for the calculations used to produce the Table aregiven in Ref. (3). The so-called super-efficient data envelopment analysis model was used (1,3). The software used for the linear programming was the Premium version of Solver, the add-infrom Frontline Systems (Incline Village, NV) that came with Microsoft Office Excel 2003 (Redmond, WA). The productivity ratios were rounded to the nearest 10% to make the interpretation easier.

Table 3. Gaps in the Number of Cases of Each Procedure Type at the Study Hospital

Weight AAA CABG Colorectal CraniotomyHip


resection Nephrectomy

Study Hospital 14 756 186 32 179 459 47 44Hospital A 0.64 31 244 143 57 263 210 26 23Hospital B 0.07 52 270 120 35 147 171 48 27Hospital C 0.13 53 671 156 62 160 276 31 24Hospital D 0.20 85 577 156 115 274 235 62 53Benchmark (weighted

combination)48 382 152 70 255 232 37 30

Difference (gap) 34 �374 �34 38 76 �227 �10 �14% difference (gap) 240 �49 �18 119 42 �49 �22 �31

The % is the number of additional cases of each type of procedure that the study hospital can be producing based on the hospital’s performance relative to its benchmark hospital. Abbreviationsfor the outputs (columns) are given in Table 1. The equation for the weights in the second column is Eq. (13) of Ref. (3), with the weights being the ratios of the � to the � in that equation.Without rounding, the sum of the weights equals 1.042. For the super-efficient data envelopment analysis model, as we used, the sum of weights is not constrained to equal 1.0. Although inreference (3) we arbitrarily set the negative differences equal to 0, we did not do so in this Table 3 or in Table 7. The �49% equals 100% � (1/1.96 � 1). Where 1.96 is the effective score,rounded to 2.0 in the text of the paper.


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any other combination of hospitals (i.e., as much as thevirtual, benchmark hospital).

Table 4 shows a sensitivity analysis. DEA wasrepeated four times, each with exclusion of one of thefour hospitals contributing to the virtual, benchmarkhospital. In each circumstance, the gaps were less thanzero for cardiac surgery, gynecology, and generalsurgery. This increases our confidence in the resultsfrom Table 3.

After combining the results of Figure 2 and Table 3,there were four surgeons remaining, representingthree specialties. These surgeons are labeled as “Tar-get” in Figure 2.

One surgeon did spine cases and had an aboveaverage contribution margin per OR hour. However,his five colleagues, also doing mostly spinal surgery,had overall contribution margins per OR hour thatwere significantly less than average. The surgicalgroup had divided the cases among themselves withunequal distributions by procedure and payer. Thehospital administrators’ judgment was that allocatingadditional OR time and other resources for spinalsurgery would not achieve more patients of the pre-ferred type. Doing more spinal cases would result inless cash for future investments, not more.

The hospital’s two pain physicians and one plasticsurgeon represented the final three “Target” surgeonsin Figure 2. The decision was made to evaluateexpansion in these two specialties by communicationwith those surgeons and their referring physicians.

The preceding material reviewed DEA and showedhow results of DEA are linked to a financial analysisfor purposes of deciding which specialties should beprovided more resources and institutional support,specifically additional OR block time.

VALIDATIONThe case study is novel, because DEA was per-

formed without hospital discharge abstract data fromthe study hospital’s state. The data used were financialdata from the study hospital, input and output valuesfor the study hospital (Table 1), data from other stateswith accessible data (1,2), and federal websites. Theremainder of our paper evaluates the validity of this

process, including a direct comparison of results ofDEA using state discharge data versus federal data.

Validation was performed with the same years ofdata that were used for our previous studies of DEAapplied to surgery so that we could compare our newfindings to these prior results. The PennsylvaniaHealth Care Cost Containment Council’s 1998 dataincluded all patients discharged during 1998 from anon-Federal Pennsylvania hospital (1). The corre-sponding data for Iowa were the 2001 discharges fromthe Iowa Hospital Association (2,3).

Hospitals for which DEA would not be useful wereexcluded (1), based on two criteria.

First, hospitals were excluded that have fewer than200 beds. Such hospitals perform too few inpatientcases. For example, in Iowa, no hospital with �200beds performed (2) Craniotomy or Nephrectomy andonly one such hospital performed CABG or Lungresection. Note that this exclusion of hospitals refersonly to the hospital’s use as benchmarks. When statedischarge abstract data are used to estimate the Countyand Region variables, all hospitals in the state are usedfor that purpose.

Second, hospitals were excluded that are located incounties with populations exceeding 1 million. Hospi-tals in large metropolitan areas (e.g., Philadelphia andPittsburgh) have an unlimited supply of potentialpatients. Their challenges to growth are competition,marketing, and high fixed costs (e.g., real estate).

Figure 4 shows how DEA was performed using USfederal data instead of discharge abstract data fromthe state of the study hospital. The federal data wasobtained from public websites. The US federal dataare from nonfederal short-term, general, and otherspecialty hospitals, just like the hospitals in the statedischarge abstract databases. The steps in Figure 4 areconsidered below.

We developed the methodology of Figure 4 toovercome the practical limitations of the DEA dis-cussed in the Introduction. Only the County andRegion variables from Table 1 were changed. We willestablish that the change does not reduce the validityof DEA (1) by showing a statistically significant, albeitmodest, increase in validity of DEA results.

Table 4. Sensitivity of Gaps in the Study Hospital’s Procedures to Inclusion of each Hospital Contributing to the Benchmark

Excluded hospitalAdditional

hospital(s) added? AAA CABG Colorectal CraniotomyHip


resection Nephrectomy

None 240 �49 �18 119 42 �49 �22 �31Hospital A Yes 276 �53 �19 10 3 �47 2 �38Hospital B Yes 226 �50 �16 122 47 �47 �24 �32Hospital C Yes 233 �50 �16 107 44 �45 �20 �31Hospital D No 248 �51 �19 70 21 �50 �15 �37

Values given are percentage values. The four hospitals originally contributing to the benchmark are listed on the left (Table 3). The selection of the benchmark hospitals and their weights area direct consequence of the selection of outputs and inputs to make the study hospital appear as efficient as possible. The gap is the ratio of the difference to the current number of cases.A negative gap infers that more cases are being done than expected from the benchmark hospital(s). A positive gap shows the potential of the study hospital to increase its workload for thespecialty. When Hospital D was excluded, there were only three hospitals contributing to the benchmark (Table 3). When Hospital A, B, or C was excluded, other hospitals were added. The Tableshows that the magnitude of the gaps in neurological, orthopedic, and thoracic surgery are sensitive to the inclusion of Hospital A. The Results in the case study describe how these sensitivitieshave no impact on management decisions. Hospital A is in a small city in Iowa. The hospital had the same technology index as the study hospital, performing all types of care except transplant.Otherwise, Hospital A had fewer beds, surgeons, county surgical charges per square mile, and region surgical charges per square mile. Nevertheless, it performed more AAA, craniotomies, andhip replacements than the study hospital.


The Region of a hospital refers to the surgicalcharges for residents of the county of the hospital andof the counties contiguous to the county of the hospital(Table 1). The charges are used to provide the averagerelative resource use for the eight different proceduresstudied (Table 1) (1,2). When data are obtained from astate inpatient database, surgical procedures per-formed on residents who travel outside the state for

care are not included. The use of federal website dataovercomes this limitation.

Figure 5 shows, for each county in Iowa andPennsylvania, the ratio of the weighted surgicalcharges of its region’s residents to that of just its ownresidents. The data were obtained just from the statedatabases. The ratios before normalization are alllarger than 1.0, because each county’s region includesthe county. The ratios were significantly less forcounties contiguous to a state border (Mann–WhitneyP � 0.0002, n � 166 counties). The ratios were less forborder counties, because their numerators were un-derestimates of actual regional surgical charges. Infact, if a county’s region were homogeneous, round,and equally straddling two states, then the Regionvariable estimated using data from one state wouldbe half its true value. The lower panel of Figure 5shows that normalizing the County and Region sur-gical charges by land square miles successfullyeliminated the bias (P � 0.58). The land square milesof each county comes from the US census bureauwebsite (Fig. 4).

Figure 6 shows calculated percentage differences forcounty surgical charges per square mile estimated usingthe federal websites versus state databases. As predicted,charges were significantly larger when estimated usingfederal data versus state data (Wilcoxon’s signed ranktest P � 0.0001, n � 166 counties). Differences weresignificantly larger for border counties than for nonbor-der counties (Mann–Whitney P � 0.001).

Not all border counties have the same chance of itsresidents leaving the state for surgery. During the 2000US Census, the place of work was determined for asample of workers 16 yr and older residing in eachcounty. If many residents of a county commuted

Figure 4. Steps to perform the data envelopmentanalysis using United States (US) federal datawarehouses. The US Census Bureau’s website ishttp://factfinder.census.gov/. HCUPNet is thewebsite of the US Agency for Healthcare Re-search and Quality Healthcare Cost and Utiliza-tion Project’s data warehouse (http://hcup.ahrq.gov/) (5). Data obtained from the websitesare indicated by boxes with dots. The boxes indouble lines are calculated quantities.

Figure 5. Ratio of the weighted surgical charges of eachcounty’s region’s residents to that of the charges of just thecounty’s residents, as obtained fro m the state databases.Each data point is for a county in Iowa or Pennsylvania (n �166). When calculating surgical charges for residents, thesurgery could have been performed in any hospital in itsstate. The upper panel shows that the statistical distributionsof the ratios differ significantly before normalization by landsquare miles (Mann–Whitney P � 0.0002). The lower panelshows that the statistical distribution of the ratios do notdiffer after normalization (Mann–Whitney P � 0.58).


out-of-state for work, that would suggest economicactivity (including healthcare) outside the state, butclose to the border. Each increase in the percentage ofcounty residents working outside the state was asso-ciated with an increase in the difference in countysurgical charges per square mile estimated using thefederal websites versus the state inpatient databases(Spearman’s P � 0.0001).

The preceding results for Figure 6 are consistent with thehypothesis that state inpatient databases can underestimatesurgical rates for counties close to borders. Results shouldbe similar, but less significant, by region. The lower panelsshow that our findings matched this hypothesis.

Table 5 shows that the inaccuracies in estimatingthe County and Region variables for hospitals in bordercounties may have influenced results of DEA for more

Figure 6. Calculated percentage differences for county surgical charges per square mile estimated using the federal websitesversus state databases.

Table 5. Influence of Hospitals in Border Counties on Results of the Data Envelopment Analysis (DEA)

Percentages ofthe 74 hospitals studied

Hospital is in county that is coincident to the state border 41� � � or selected at least one benchmark hospital(s) that is in a county that is

coincident to the state border using � � �Original DEA model based on state data 85DEA model with normalization by land square miles and based on state data 88DEA model with normalization by land square miles and based on state and

federal data88

Hospital is in region that is coincident to the state border 79� � � or selected at least one benchmark hospital(s) that is in a region coincident

to the state border using � � �Original DEA model based on state data 92DEA model with normalization by land square miles and based on state data 93DEA model with normalization by land square miles and based on state and

federal data92

The 74 hospitals studied are the hospitals in Iowa and Pennsylvania with at least 200 beds and located in a county with a population of less than 1 million people (i.e., not in Philadelphiaor Pittsburgh). For readers with a background in DEA, a hospital was considered to be selected if its � weight from the envelopment form was at least 0.0001. The corresponding equationsare the final three in the Appendix of Ref. (2) or the first three in Ref. (3).


than 90% of hospitals. More than three quarters ofhospitals in Iowa and Pennsylvania with at least 200Beds are in a region coincident to a state border.However, even that result understates the effect. Ahospital that is located neither in a border county norin a region coincident to a state border may choose atleast one benchmark hospital that is located near astate border.

Although Figures 5 and 6 and Table 5 suggestbenefits of using federal data for the DEA, the use offederal data should be balanced against methodologi-cal concerns. Figure 4 shows that the County andRegion variables are estimated by multiplying eachcounty’s population for 10 combinations of age andgender by the corresponding age and gender adjustednational surgical rates. The federal surgical rates willbe biased estimators for the surgical rates of theresidents of some counties.

The assumption of homogeneity of surgical ratesamong counties may have a small effect on results ofthe DEA. What affects the DEA is the hospital surgicalworkload, determined by numbers of patients, not therates. The County and Region variables depend on theproduct of population and rate for each of the proce-dures. Among the 166 counties, the populations var-ied 340-fold and the population densities 1100-fold.Among the 45 counties with at least one of the

hospitals studied using DEA, populations varied 41-fold and the population densities 71-fold. Variationsin surgical rates were much smaller (e.g., 1.6-fold forColectomy and 3.6-fold for Hysterectomy, when limitedto benign disease for which there is high variation inpractice) (22). Thus, variation in population amongcounties is so large that variation in surgical rates mayhave a negligible impact on variation in the Countyand Region variables among counties. We addressedthis issue by reestablishing the validity of DEA usingthe revised methodology of Figure 4.

The six criteria applied previously to validate DEAwere repeated.

1. DEA chooses for a study hospital the collectionof outputs and inputs that make the study hos-pital appear as efficient as possible. If there is atleast one other hospital that produces more ofthe selected outputs with the selected inputs,then the study hospital is inefficient. Each hos-pital is compared to all other hospitals. Thisprocess is presented graphically in Ref. (2). Effi-cient and inefficient hospitals should differ sig-nificantly on other measures that would indicaterelatively large production of surgery (1). Forexample, surgeons would be more likely to prac-tice exclusively at an efficient hospital. That may

Table 6. Validity of the Three Methods of Data Envelopment Analysis Assessed Using Differences Between the Efficient andInefficient Pennsylvania Hospitals

Characteristic

Efficienthospitals (N � 25)

(median � quartiledeviation or %)

Inefficienthospitals (N � 28)

(median � quartiledeviation or %) P-value

Significant differences support validity of the DEA, with all three methods of DEA giving the same resultsMarket share among its

surgeons90% � 11% 64% � 15% 0.003

Affiliations per surgeon 1.4 � 0.2 1.8 � 0.2 0.002Nonsignificant differences support validity of the DEA, with all three methods of DEA giving same results

Beds 275 � 109 263 � 50 0.226Technology 5 � 2 5 � 1 0.500Surgeons 70 � 30 58 � 22 0.310Border county? 44% 46% 0.999Rural county? 24% 14% 0.488Teaching hospital? 20% 11% 0.453

Nonsignificant differences support validity of the DEA, with each of the three DEA methods specified by the rowCounty

PA data $ 82 � $47 (million) $ 95 � $41 (million) 0.383PA data, per square mile $125 � $56 (thousand) $142 � $97 (thousand) 0.345US data, per square mile $131 � 47 (thousand) $157 � $110 (thousand) 0.254

Region (i.e., county and contiguous counties)PA data $568 � $386 (million) $687 � $277 (million) 0.187PA data, per square mile $ 98 � $70 (thousand) $151 � $103 (thousand) 0.154US data, per square mile $103 � $78 (thousand) $149 � $115 (thousand) 0.175

DEA stands for “Data Envelopment Analysis”. The three methods of DEA were: (i) State of Pennsylvania (PA) data without normalizing County and Region by land square miles, (ii) State of PAdata with normalization of County and Region by land square miles, and (iii) federal and PA data with normalization of County and Region by land square miles. The five inputs used in the DEAand their units are given in Table 1. The “Market share among the surgeons” had a numerator of the number of the eight studied procedures that were performed at a given hospital and adenominator of the number of such procedures performed at all hospitals by the hospital’s surgeons. The “Affiliations per surgeon” was defined as the number of hospitals at which the surgeonperformed at least one of the eight, studied, procedures. Exact P-values for the continuous variables were calculated using the Wilcoxon–Mann–Whitney test (StatXact-7, Cytel Software Corporation,Cambridge, MA). P-values for discrete variables were obtained using Fisher’s exact test.


be because the OR management helps the sur-geons get more surgery done or because eachsurgeon doing most of her cases at the hospitalresults in each surgeon filling an OR on the daysshe operates. Regardless of the reason why,Table 6 shows that these results hold for Penn-sylvania, the state with the ancillary data (1).

2. There should not be statistically significant dif-ferences in input variables between efficient andinefficient hospitals (1). For example, efficienthospitals should not have more beds than inef-ficient hospitals. This is known in the DEAliterature as the mathematical assumption ofconstant returns-to-scale. Table 6 shows that thiscondition holds.

3. Efficient and inefficient hospitals should match oninput variables excluded from the DEA model.Previously, reasonable additional inputs for whichdifferences were appropriately shown to be absentwere binary variables: (a) whether a hospital was ateaching hospital and (b) whether a hospital waslocated in a rural county (1). Table 6 shows thatthese two conditions hold. Table 6 also shows thathospitals in border counties were, appropriately,not more or less likely to be efficient.

4. A gap is the number of additional cases of a typeof procedure that the hospital can be producingbased on the hospital’s performance relative toits benchmark hospital. Calculated gaps in eachhospital’s cases for each type of procedureshould be correlated to estimates obtained usingunrelated statistical methods. A nonlinear re-gression method was applied to Pennsylvaniadata (1). Table 7 shows that this condition holds.

As a further test, calculated gaps should haveface validity. There is no gold standard to whicha person can mentally compare a gap when it is

zero or positively valued for a hospital perform-ing the procedure (i.e., when the gap is useful).The DEA addresses a problem for which there isno other developed methodology. On the otherhand, if a hospital hardly performs a procedure,the gap value should not be negative and non-negligible. Thresholds used for a hospital“hardly performing a procedure” were fewerthan 10 discharges per year of AAA, Craniotomy,Lung resection, or Nephrectomy, and fewer than 20discharges per year of CABG, Colorectal resection,Hip replacement, and Hysterectomy (1). Among the85 combinations of hospital-procedure belowthe threshold (1), all gaps were ��1.5 cases forthe three methods of DEA.

5. Table 1 lists the eight outputs, measured by thenumber of cases of each procedure at each hos-pital. For each procedure, the number of cases ata hospital is positively correlated with otherestimates of surgical workload for the proce-dure’s specialty (1,2). The objective of DEA is notto estimate how many more lung resections per secan be expected to be done at the hospital, butthe potential increase in thoracic surgery. Thesecorrelations are unaffected by the changes to theDEA methodology of Figure 4.

For example, among the 74 hospitals studied(Table 5), the eight Spearman’s rank correlationcoefficients are all at least 0.89 between thenumber of cases of each procedure and the sumof the Diagnosis Related Groups’ weights for alldischarges of its specialty. The Spearman’s cor-relation is 0.98 between the sum of the eightstudied procedures and the sum of dischargesfor the eight studied specialties.

6. The methods of presenting DEA results for asingle hospital are shown in Figure 3 and Tables

Table 7. Validity of the Three Methods of Data Envelopment Analysis Based on Positive Spearman Rank Correlations Between Gapsin the Procedures and Estimates from Nonlinear Regressions of Hospital’s Deficits in Those Procedures

Procedure

PA dataPA data, normalizing by

land square milesUS data, normalizing by

land square miles Hospitalsabove

threshold(N)

Correlationcoefficient

One-sidedP-value


One-sidedP-value


One-sidedP-value

AAA 0.376 0.010 0.368 0.010 0.344 0.014 39CABG 0.753 �0.001 0.785 �0.001 0.780 �0.001 27Colorectal 0.553 �0.001 0.627 �0.001 0.556 �0.001 52Craniotomy 0.433 0.008 0.516 0.001 0.470 0.004 32Hip replacement 0.632 �0.001 0.609 �0.001 0.640 �0.001 53Hysterectomy 0.684 �0.001 0.740 �0.001 0.759 �0.001 53Lung resection 0.563 �0.001 0.421 0.004 0.449 �0.001 40Nephrectomy 0.484 0.002 0.412 0.006 0.434 0.002 37Full procedure names and descriptions are given in Table 1. There are N � 53 Pennsylvania hospitals. Hospitals excluded for each procedure were those “hardly performing a procedure,” definedas fewer than 10 discharges per year of AAA, Craniotomy, Lung resection, or Nephrectomy, and fewer than 20 discharges per year of CABG, Colorectal resection, Hip replacement, andHysterectomy (1). The nonlinear regression effectively considered the hospital’s potential elective surgical workload for each procedure to be proportional to the number of age and gender adjustedhospital admissions (1). The three methods of Data Envelopment Analysis (DEA) were: (i) State of Pennsylvania (PA) data without normalizing County and Region by land square miles, (ii) Stateof PA data with normalization of County and Region by land square miles, and (iii) federal and PA data with normalization of County and Region by land square miles. Rank correlations wereused to compare the residuals of the nonlinear regression to the gaps of the three methods of DEA. Rank correlations were used, because there was: (i) absence of a theoretical argument fora linear relationship, (ii) skewed data, and (iii) multiple zero values for gaps. The P-values were calculated using Monte–Carlo simulation to an accuracy of within 0.0001 (StatXact-7). The P-valuesare one-sided as only positive correlation would support the validity of the DEA.


2–4. These methods need to be obtained from themathematics of DEA without making additionalassumptions (3). This condition was satisfiedpreviously (3) and is unaffected by the changesto the DEA methodology outlined in Figure 4.

Finally, the validity of changes to the DEA method-ology can be evaluated by considering pair-wise differ-ences in efficiency scores between different DEA models.Making small changes to the methodology withoutchanging the sample size should not affect the efficiencyscores for most hospitals (i.e., the medians should beunaffected). The top half of Table 8 shows that thisprediction holds.

Previously we tried unsuccessfully to pool dataamong states (2). The county sizes had been different.Now, County and Region are normalized by landsquare miles. Federal data are used to compensate forborder effects. Hospitals are limited to those withenough Beds for DEA to be relevant, eliminatingmultiple small hospitals in Iowa.

Pooling hospitals among states should result insmall but statistically significant reductions in themedian efficiency scores, because each hospital is nowbeing compared to a broader population of potentialbenchmark hospitals (23). The bottom half of Table 8shows that this prediction holds.

Increasing the sample size can only result in de-clines in efficiency scores (23). For the few hospitalswith large declines in efficiency scores, qualitativeassessments should indicate that the changes likelyrepresent improvements in accuracy. Strikingly, thetwo hospitals with the largest declines were the hos-pitals with the two highest original scores: 7.75–1.37and 6.96–4.22. This observation further supports thevalidity of pooling hospitals between states. As thenumber of hospitals increases, the likelihood of en-countering another similar hospital that is close tobeing as efficient as possible at producing surgery alsoincreases (23). The two biggest outliers were reignedin by the changes to the methodology. The incremen-tal effect of adding an additional hospital tends to

decrease as the sample size increases (23). None of theother declines in efficiency scores exceeded 0.6.

The hospital with the largest decline was referred toas Example Hospital C in Ref. (1). Its unique featurewas that although its county had the smallest popu-lation and amount of surgery among its residents, thehospital’s Craniotomy caseload was the third most andCABG caseload was the seventh most among hospitalsin Pennsylvania. We used this hospital to highlightthat market visibility (Beds, Surgeons, and Technology)need not be an important cause of limitations on thecapture of the surgical market (1). In the currentpaper, the decline in the hospital’s efficiency scoreoccurred as a result of normalization by land squaremiles. The hospital’s county not only had the smallestpopulation and weighted surgical charges, but wasalso the county with the smallest land square miles.Even though the analysis continues to show the hos-pital is unique, the original results were likely inflated.This finding supports the face validity of the modifi-cation of the DEA methodology shown in Figure 4.

The hospital with the second largest decline in itsefficiency score was the study hospital in Refs. (2) and(3). As described previously, the input chosen to makethe hospital appear as efficient as possible was itsCounty weighted surgical charges, just as for thepreceding hospital. The productivity ratios presentedin Ref. (3) showed that although the hospital’s gapsequaled zero for all outputs in the original model, thehospital was relatively weak in orthopedics (Hip re-placement). The second weakest specialty was cardiacsurgery (CABG). We used that finding to highlight theusefulness of examining the productivity ratios (3). Inthe current paper, the decline in the hospital’s effi-ciency score resulted from the consolidation of databetween states. The reason was that this Iowa hospitalwas now being compared to the Pennsylvania hospitalin the preceding paragraph, with its strength in CABG.The result was a slight gap for the Iowa hospital inCABG (23 cases) and Hip replacement (25 cases). Theseresults, too, seem reasonable.

Table 8. Pair-wise Differences in Efficiency Scores for Hospitals Among Different Data Envelopment Analysis Models

Modification ofmethodology State

Original medianefficiency score Median change P-value

Nonsignificant median changes in efficiency scores support validity of the modification of methodologyNormalizing county

and region by landsquare miles

Iowa 1.265 (N � 21) �0.007 0.855Pennsylvania 0.985 (N � 53) 0.007 0.627Both 1.102 (N � 74) 0.006 0.647

Normalizing andusing US data

Iowa �0.064 0.241Pennsylvania 0.010 0.106Both 0.005 0.559

Significant median changes of predicted magnitude support validity of the modification of methodologyPooling data from

Iowa andPennsylvania

Iowa �0.094 0.026Pennsylvania �0.061 �0.001Both �0.067 �0.001

The Wilcoxon’s signed rank test was used. P-values are exact (StatXact-7).


DISCUSSIONWe applied and validated new methods for using

DEA to judge the ability of a hospital to performadditional inpatient surgery for specific specialties.We then applied the DEA to a hospital in a differentstate to assess decisions related to tactical selectiveincreases in OR block time. The results were presentedin reverse order to emphasize the practicality of themethod for a real hospital and to avoid a separatebackground section with hypothetical examples.

The ability to use federal website data to assessCounty and Region surgical workload makes DEA resultsbroadly practical and accessible for OR managers. Eachhospital wanting to assess its inpatient surgical work-load can compare itself to other hospitals that havepreviously been examined. As each hospital benefits, itcontributes its own data, making DEA that much moreinformative to the next hospital, and so forth.

Although the use of federal website data increasesthe validity of DEA by a statistically significantamount, the increase is modest. We believe that theincrease in validity is of importance only to the extentthat it is very strong evidence that the validity was notdiminished (i.e., the benefit of the new method is thatit is easier to perform).

Our use of DEA is unique in evaluating hospitalperformance (24). Almost all previous studies of hos-pital efficiency using DEA have been analyses of datafrom multiple hospitals to assess health systems andpolicy (24). A few studies have applied DEA to datafrom individual organizations to support managerialdecision-making within the organization (e.g., physi-cians within a large medical group). In contrast, ourfocus has been the application of DEA to data frommultiple hospitals to support managerial decision-making within a single hospital (1–3).

Our case study addressed one application of DEA:long-term (1 yr) tactical allocation of additional ORblock time (10). We previously used the hospital in thelast paragraph of the Validation section to show othersimilar applications. That hospital performed 40% ofthe neurosurgery and 25% of the inpatient urologicsurgery in Iowa (2). Discharges in those specialtieswere twice that of the next highest hospitals. Incontrast, the hospital performed 9% of Iowa’s cardiacsurgery. Its cardiac workload was half that of thehighest volume hospital. One question asked at thehospital was whether cardiac surgery could be in-creased by the overlapping finishing of a case in oneOR with the induction of the next patient in anotherOR to reduce turnover times. Another question askedwas whether capital investment for minimally inva-sive equipment could prompt additional referral ofpatients resulting in growth in cardiac surgery. Thecurrent paper shows that may be caseload could havebeen increased by a negligible two CABG patients permonth. The limiting factor was, and still is, a lack ofelderly patients living near the hospital. This example

shows how DEA can be of value to anesthesia groupsin recruitment decisions. DEA can also be useful forOR managers and surgical services committees withdiscretion in how increases in operational budgets areallocated and how capital purchases are chosen.

The case study shows that we are making progressat understanding the steps and issues in improvingdecision-making for allocating additional OR timetactically. Figures 1–4 show that decision-makers arevery unlikely to know whether a haphazard alterna-tive method of analysis is giving an answer that is“close enough” without also doing formal, coupledfinancial and market growth (DEA) analyses. Ourinterpretation is strengthened by the fact that simpleversions of these analyses were sufficient for ourstudy hospital. Administrators at the hospital happenednot to need to consider limited ICU beds (16), uncer-tainty in estimated contribution margins per OR hour(6,9), expert estimates of market growth potential (10), orthe competitive effects of other hospitals (2,25). Havinglearned what it takes to model surgical demand appro-priately (Fig. 4), we are skeptical that intuition alone cancome close to getting the correct answer.

An appropriate alternative to performing a math-ematical analysis to assist in the tactical decision is notto make a tactical decision. Instead of reserving addi-tional OR time for a few targeted specialties, the extraOR time would be used as overflow. The overflow ORtime is used by specialties that have filled theirallocated OR time (12,13) and have more cases toperform (14,15). Over many months, the service thatconsistently uses the overflow OR time would havesome of the overflow OR time allocated to them(13,15). Essentially, the allocation of OR time to spe-cific services is being limited to the shorter-termoperational stage. An advantage to this “wait and see”approach is that experienced managers generally pre-fer to postpone making decisions when having tochoose among alternatives that require trade-offs (26).Some readers may want to refer to the case studies ofthe current paper and of a prior paper (10) as evidencethat deferring tactical decisions can be a good choice.

In the case study (Fig. 1), consideration of incrementalrevenue was limited to hospital reimbursement. How-ever, also including professional reimbursement in theanalysis can provide insight into differences in perspec-tive between hospital and physicians (27). In addition, oralternatively, an intangible value can be added for eachadditional patient of desired types (e.g., cancer patientreceiving care at a cancer hospital or cardiac patient at ahospital making the strategic decision to focus on cardiaccare). The incremental revenue may even be zero for allpatients other than those targeted by a public ministry.However, the latter is increasingly uncommon as morecountries migrate to prospective payment based onDiagnosis Related Groups (28).

The hospital studied in our paper was private.Nonetheless, the linkage of financial analysis withDEA for purposes of tactical increases in allocated OR


time can be useful for public hospitals. Unless everypurchase request by every surgeon, and every requestfor salary support for new surgeons is satisfied, thehospital makes tactical decisions based in part onfinancial criteria. The allocation of additional OR timetactically is a budgetary decision, just like the pur-chase of new expensive OR equipment to care for anew population of patients.

A finding of the study hospital was unusual. Spe-cialties with some of the highest hospital contributionmargins per OR hour were those doing outpatientsurgery (e.g., pain medicine) (Fig. 2). The findingreinforces that contribution margin per OR hour re-sults by specialty differ markedly among facilities (27).Usually, the highest values are for specialties withsubstantial inpatient surgery (4,16,29). Specialties withlonger average lengths of stays can have higher con-tribution margins per OR hour, because such patientsoffer more opportunities for discharge of patients afew days sooner than average (27). To explain finan-cial analysis results for individual surgeons (special-ties), we use the difference between each inpatient’shospital length of stay and the national average lengthof stay for all patients with the same Diagnosis RelatedGroups (27,30).

For the studied hospital, data on contribution marginper OR hour (Figs. 1 and 2) did not need to be combinedmathematically with estimates of potential marketgrowth. If they had, we would have used equation (19)in Ref. (10). A question that administrators and surgeonstypically ask is what happens if more OR time wereallocated tactically to a specialty and they do not use it.The OR time that would otherwise be under-utilizedwould be released for services that have filled theirallocated OR time and still have more cases to schedule(13,14,31). The important implication is that there ismarked mitigation of the financial risk of inaccuracy inresults from DEA (10).

Although the method of performing DEA usingFigure 4 enables rapid decisions for some problems,the approach seems limited for determining the causeof a gap value. For example, Tables 2–4 show that thehospital in the case study had a weakness in vascularsurgery. This was no surprise, considering that thehospital had only one vascular surgeon. What wasunknown was the potential financial return fromperforming more vascular surgery. Nevertheless, ifthe hospital had recruited another vascular surgeon,would the gap have been reduced or would twosurgeons be doing the same relatively small numbersof cases? Those questions can be addressed by consid-ering the impact of competing hospitals on the studyhospital (2,25) and by studying the types of vascularprocedures performed at the study hospital and theirdifferentiation from that of competing hospitals(32,33). Both assessments rely on the state data that webypassed by following the methodology outlined inFigure 4. Thus, state discharge data provide informa-tion useful to individual hospitals that cannot be

completely replaced by federal data. Such uses of thestate data are not affected by the issues of the bordercounties considered in Figures 5 and 6.

Finally, DEA is limited to the assessment of workloadat hospitals, which may not be relevant to medicalpractices. If an anesthesia group practices at two nearbyhospitals, both with gaps in a specialty, the actions takenby the hospitals to address the gaps may be irrelevant tothe group, since the numbers of patients at the twohospitals combined could remain unchanged.

ACKNOWLEDGMENTSThe authors thank Ruth Wachtel, PhD MBA, for her

thoughtful review of our paper.

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ERRATUMIn the February 2007 issue of Anesthesia & Analgesia, in the article by O’Neill and Dexter, “Tactical Increasesin Operating Room Block Time Based on Financial Data and Market Growth Estimates from DataEnvelopment Analysis” (Anesth Analg 2007;104:355–68), there are two errors in the footnote to Table 3 onpage 359. The first sentence of the caption starts: “The % is the number of additional cases” which shouldbe “The gap is the number of additional cases.” The second line has “with the weights being the ratios ofthe � to �”, which should be “with the weights being the ratios of the � to �.” The publisher regrets the error.

630 Volume Therapy and Sepsis ANESTHESIA & ANALGESIA

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Tactical Increases in Operating Room Block Time Based on ... · Section Editor: Franklin Dexter Tactical Increases in Operating Room Block Time Based on Financial Data and Market