We use a case study to investigate how to answer three common questions regarding hospital market capture for elective inpatient surgery.
(i) The hospital studied in this paper performs 40% of the neurosurgery and 25% of the inpatient urology surgery in its rural state. Workloads for those specialties are more than twice that of the next largest workload hospitals. In contrast, the hospital performs 9% of its state’s cardiac surgery and has a workload half that of the hospital with the largest cardiac workload. The cardiac surgeons want more operating room (OR) time, faster turnovers, and capital investment for minimally invasive equipment. Controlling for the distance patients would need to travel for care, would increasing capacity likely increase cardiac surgery workload by a financially important amount?
(ii) The study hospital has fewer thoracic surgery hospitalizations than for any other surgical specialty. The Chief of Surgery asks the Chief of Anesthesia about support for recruiting another thoracic surgeon. Is the current inpatient workload for thoracic surgery (121 lung resections) large or small compared with those of orthopedics (213 hip replacements), urology (132 nephrectomies), and cardiac surgery (304 coronary artery bypass grafts, CABG)?
(iii) The study hospital’s busiest specialty by discharges is orthopedics. The anesthesia group may recruit another anesthesiologist who is subspecialty trained in regional anesthesia. However, a decrease in orthopedic workload would likely cause frustration and disrupt the anesthesiology group. How sensitive is the study hospital’s orthopedic workload to changes in decision making at nearby competing hospitals?
In this paper, we apply the technique of data envelopment analysis (DEA) to measure market capture of elective inpatient surgery for all hospitals in a state (see Methods for description and Appendix for equations). Market capture is predicted by DEA, applied to hospital discharge data, using both the relationships between input model variables and overall surgical workload and the correlations among different specialties’ workloads (1 1
Methods
Outputs Studied
Discharge data from one United States (US) rural state were studied for the 115 non-federal hospitals that performed at least 10 cases of at least one of the eight studied procedures in 2001 (Table 1 ). The rationale and validation for using the studied procedures was described previously (1
Table 1:
The number of hospital discharges for craniotomy in adults, not for trauma, was determined by counting discharge abstracts with Centers for Medicare and Medicaid Services’ (CMS) Diagnosis Related Groups’ (DRG) value of one (FY00–01 and FY01–02).
The number of hospital discharges for the other seven procedures was determined using the six International Classification of Diseases, Ninth Revision, Clinical Modification (ICD-9-CM) procedure codes in each discharge abstract. The combinations of ICD-9-CM procedure codes encompassing each studied procedure were derived from the Agency for Healthcare Research and Quality’s (AHRQ) Clinical Classifications Software aggregation of ICD-9-CM (1
Inputs Studied
The five input variables examined were as previously validated (1 2–4
“Beds” were defined as the number of staffed acute care beds as reported in the annual survey of the American Hospital Association. We did not use surgical beds or ORs because it is the number of acute care beds that predicts hospital visibility and the number of discharges (2
“Surgeons” was measured as the number of physicians at the hospital admitting at least three patients undergoing one of the eight studied procedures, as listed in the discharge abstract.
“Technology” was measured as the number of the following services provided by the hospital: ORs (every hospital studied had this), cardiac catheterization, cardiac surgery, shock-wave urological lithotripsy, megavoltage radiation therapy, magnetic resonance imaging, organ transplantation, neonatal intensive care, and trauma care (5,6
“Weighted county discharges” were calculated by taking, for the residents of each county, the sum of the number of each of the studied procedures multiplied by the corresponding DRG weight of the procedure. The weight used was the modal DRG weight among all discharges in the state with that procedure (1 Table 1 . The modal DRG weight for colorectal resection was 3.4 and for hysterectomy was 0.8. Thus, the weighted county discharges would be 15.2, where 15.2 = 4 × 3.4 + 2 × 0.8.
“Contiguous county surgical discharges” were measured as for county demand, except that the geographic area included the hospital’s county and those counties sharing a common border with the hospital’s county.
Calculating Gaps in Procedure Caseloads Using DEA
DEA is not analogous to multivariate regression with eight dependent (output) variables and five independent variables. To visualize DEA, we use an example with just one output and one input. We make the distinction throughout the Methods between DEA and regression, as many readers may have experience with regression. That experience does not apply to the methodology we used.
Figure 1 shows the number of CABG discharges at each hospital in the state plotted versus the weighted surgical discharges among patients from each hospital’s county. The least squares regression line gives the average increase in the output (CABG per year) for each unit increase in the input (county weighted discharges). In contrast, DEA’s efficient frontier is composed of the collection of hospitals providing for the maximum increase in the output achievable for a given level of input (1 Appendix ).
Figure 1.:
Coronary artery bypass graft surgery (CABG) discharges at each hospital in the studied state versus the weighted surgical discharges among patients from each hospital’s county. The regression line gives the average increase in the output (CABG per year) for each unit increase in the input (county weighted discharges). Data Envelopment Analysis (DEA)’s efficient frontier yields the maximum achievable increase in the output for each unit increase in the input. The study hospital S happens to define the efficient frontier. Every other hospital is inefficient versus this benchmark hospital, including the hospital performing the most CABG per year (Inefficient I).
The study hospital S defines the efficient frontier. Every other hospital is inefficient versus this benchmark hospital, including the hospital performing the most CABG per year (Inefficient I ). Because hospital I is above the regression line, hospital I performs more CABG than expected. Still, in this example with one output and input, it is inefficient at market capture for surgery relative to the benchmark hospital. DEA identified inefficiency that was missed by regression.
We next envision DEA using the same input but with two outputs: craniotomy and nephrectomy (Fig. 2 ). To present this graphically in two dimensions we divide each hospital’s procedure count by the weighted discharges among patients from the hospital’s county. We show data for 9 of the 10 hospitals in the state with at least 10 discharges for both procedures. The study hospital is the one excluded. We label three hospitals A, B, and I.
Figure 2.:
Data Envelopment Analysis (DEA) with one input and two outputs. The input is weighted surgical discharges among patients from each hospital’s county. The outputs are caseloads of craniotomy and nephrectomy. This is shown as procedure count divided by weighted discharges among patients from the hospital’s county. Data are plotted for 9 of the 10 hospitals with at least 10 discharges for both procedures. The study hospital is the one excluded. Hospital I is an inefficient hospital in Figure 2, just as it was in
Figure 1 . The point I’ is the projection of the point I onto the efficient frontier. Interpretation of I’ is given in Methods.
Hospital I is an inefficient hospital in Figure 2 . We project point I onto the efficient frontier, thereby obtaining a point on the figure labeled I’, representing a virtual hospital. The efficiency score for hospital I equals the distance between (0,0) and the point on the figure labeled I divided by the distance between (0,0) and point on the figure labeled I’. This ratio equals 0.30. Hospital I has 30% efficiency for surgical market capture versus its benchmark hospitals A and B. The efficiency score represents differences among hospitals in all procedures simultaneously (Appendix ).
Figure 2 also shows relative caseloads of nephrectomies and craniotomies. Points I and I’ have the same ratio of nephrectomies to craniotomies. The projection of point I onto the efficient frontier (i.e., point I’) falls between the benchmark hospitals A and B. The efficient frontier line between A and B defines the range of best practice for the ratios of caseloads for nephrectomy and craniotomy. Hospital I is equally inefficient at market capture of both nephrectomies and craniotomies.
Figure 3 uses the same hospitals as Figure 2 but considers a different inefficient hospital C, which performs equal numbers of nephrectomies and craniotomies. The efficient frontier between A and B shows that best practice is more craniotomies performed than nephrectomies. Thus, hospital C has a relative lack of craniotomies. The gap in craniotomies per weighted discharge equals the distance between point C’ and point A multiplied by hospital C’s efficiency score. The efficiency equals 32%, the distance between (0,0) and point C divided by the distance between (0,0) and point C’. Figure 4 shows the efficient frontier of Figure 3 multiplied by 0.32, contracted to the scale of Hospital C.
Figure 3.:
Gap in craniotomies per weighted discharge equals the distance between point C’ and point A multiplied by hospital C’s efficiency score. The data are as in
Figure 2 . The efficient frontier between points A and B shows that best practice is more craniotomies performed than nephrectomies. Thus, hospital C has a relative lack of craniotomies.
Figure 4.:
Efficient frontier of
Figure 3 multiplied by 0.32, contracted to the scale of hospital C. Hospital C’s gap in craniotomies expressed on a per county weighted discharge basis equals the distance between point C and point A’. Hospital C’s gap in craniotomies equals (C to A’) multiplied by hospital C’s county’s weighted discharges.
In Figure 4 , A’ equals 32% of A and B’ equals 32% of B. Hospital C’s gap in craniotomies expressed on a per county weighted discharge basis equals the distance between point C and point A’. Thus, hospital C’s gap in craniotomies equals (C to A’) multiplied by hospital C’s county’s weighted discharges.
In a short-term, 1-yr period, hospitals I and C are unlikely to change their overall efficiency of market capture for surgery substantively, as that would involve increasing all outputs. However, hospital C has the potential for simpler interventions such as recruiting another neurosurgeon. The DEA estimates the potential increase in craniotomies from publicly available state and provincial data. Thus, the DEA results are both relevant and available not just to physicians and administrators at hospital C but at other hospitals in proximity to hospital C. Their neurosurgical workloads are at risk for short-term strategic decisions by Hospital C. The gaps provide this information (Appendix ).
If a hospital does not perform a given procedure, by definition it has a gap in that procedure. This result is of no value to the hospital, as obviously it decided to not do the procedure. In addition, such gap values should not count toward the at-risk caseload for that procedure at other hospitals. Doing otherwise would neglect the expensive fixed costs and long set-up time required to add a surgical specialty at a hospital. Consequently, we apply thresholds for the analysis (1
Using Figures 2 through 4 , we showed how to calculate gaps for inefficient hospitals. We use the analogous method, known as the super-efficient model, to calculate gaps for the efficient hospitals (1,5,7 1
Applying DEA to Each Hospital
DEA determines the efficiency and gaps of each hospital using the data from the other 114 hospitals. Thus, the methods described above were performed 115 times. This is unlike least-squares regression that is applied only once to all hospitals and estimates the same parameters for all hospitals. The DEA was performed using the Solver tool in Excel.
When the DEA is scaled from the few dimensions of the figures to eight outputs and five inputs, the efficiency score for market capture of surgery contains a numerator and a denominator.
The denominator of the efficiency score is a linear combination of the five input variables. In Figures 1 through 4 , the weights equaled zero for all inputs but county weighted discharges. In reality, some hospitals’ efficiency scores are maximized by having all five weights non-zero. DEA automatically assigns each hospital the unique set of weights that maximizes its efficiency score. DEA thereby models physicians’ and administrators’ strategic decision-making based on the hospital’s local marketplace, including the characteristics and number of nearby hospitals. For example, hospital I appears to be inefficient in Figures 2 and 3 because those figures use the weights chosen by DEA for study hospital S, with the only non-zero input weight being for county weighted discharges. Provided administrators and physicians at hospital I make strategic decisions based on maximizing market capture, then hospital I is efficient (Fig. 5 ). Hospital I competes effectively with the other three large hospitals in its city by offering the maximum high-tech services.
Figure 5.:
Data Envelopment Analysis (DEA) for Hospital I in Figures 1and 2. Hospital I’s DEA model includes one input: the number of high-tech services. Unlike in this figure, Hospital I appears to be inefficient in
Figure 2 and 3 , because those figures use the weights chosen by DEA for study hospital S.
The numerator of the efficiency score is a linear combination of the caseload of each of the eight studied procedures. DEA assigns each hospital the unique set of weights that maximizes its efficiency score. DEA thereby models physicians’ and administrators’ preferential focus on those surgical specialties at which the hospital excels. Even if a hospital does not perform a procedure, the hospital may still be efficient by capturing the surgical market for the procedures it does perform.
Interpreting Caseload for the Eight Common Procedures
Interpretation of gap values depends on the correlation between caseloads of the studied procedures and workloads of the surgical specialties. Alternative measures for the latter include sums of hospital discharges and of resource-intensity weights. Caseloads for the eight procedures were highly correlated to their specialties’ inpatient workloads in Pennsylvania (1 Table 1 ). A linear combination of the 8 studied procedures accounted for 99% of the variance among the 115 hospitals in weighted discharges for the studied specialties.
Predicting DEA Results Using Less Than Full Information
An administrator may want to predict DEA results without the full analysis to get less information but with less effort. We evaluated the equivalency of DEA results by progressively simplifying the model for Pennsylvania (1
A hospital may not have ready access to its state’s or provinces’ hospital discharge data, and want to avoid purchasing the data. An analyst who has worked with data from one state may want to apply it to a hospital in another state to get quick, “close enough,” answers. We assessed the efficiency of Pennsylvania hospitals using a jackknife method, in which each studied Pennsylvania hospital (1
Results
The study hospital’s efficiency score was maximized using one input (county weighted discharges) and two outputs (nephrectomy and craniotomy). Figure 6 shows Figures 2 through 4 plus the study hospital S.
Figure 6.:
Study hospital’s efficiency score was maximized using one input and two outputs. The input was weighted surgical discharges among patients from each hospital’s county. The outputs were the counts of nephrectomies and craniotomies. Figure 6 reveals that the study hospital S is significantly more efficient than all other hospitals for these output-input combinations.
The binding constraint on the study hospital’s market capture was the number of weighted discharges among people living in the hospital’s county. This makes intuitive sense because its hospital beds are 100% of maximum (i.e., more than any other hospital in the state), surgeons 75% of maximum, technology index 100% of maximum, and region weighted discharges 63% of maximum, whereas county weighted discharges are only 18% of maximum. This answers the first question in the Introduction. Although the hospital’s cardiac surgery workload is half that of hospital I with the largest workload, on a per county weighted discharge basis the study hospital is efficient (Fig. 1 ). Already the percentages of patients having surgery at the study hospital that were not from the hospital’s county were 98% for nephrectomy and 94% for craniotomy and CABG. Neither adding OR time, reducing turnovers, nor buying more equipment is likely to increase cardiac surgery workload substantively.
The second question in the Introduction is answered by the finding of zero gaps for all procedures. The thoracic surgeons are doing as much surgery as expected based on the hospital’s visibility in the marketplace and its county’s and region’s weighted discharges.
There is another hospital in the study hospital’s county (Table 2 ). That hospital is also efficient at market capture for elective inpatient surgery, has zero gaps for the eight studied procedures, and has county weighted discharges as its binding constraint on surgical workload. Aligning hospital discharge and Census 2000 data, county weighted discharges may be relatively small because the county’s population is 30% of maximum and weighted discharges on a per capita basis is 38% of maximum.
Table 2:
The study hospital’s county has the smallest per capita population of Medicare eligible patients of all counties in the state. If 2 hospitals have equal market visibility, but 1 is 10 miles further away from the residence of a Medicare beneficiary, the odds are <50% that the patient will choose the hospital that is further away (4
The third question in the Introduction is answered by reviewing gaps of hospitals with market areas for orthopedics that overlap with the market area of the study hospital (Table 2 ). The study hospital’s orthopedic workload is highly sensitive to changes in decision making at nearby competing hospitals. For example, in counties contiguous to the study hospital’s county, one of the six hospitals puts surgical workload at the study hospital at risk. That hospital’s gap in orthopedic surgery equals 40% of the current orthopedic workload at the study hospital. In the broader market area, gaps of other hospitals total 124% of the current orthopedic workload at the study hospital.
Performing DEA for hospitals in the market area of the study hospital reveals which specialties’ workloads at the study hospital are relatively secure from other hospitals’ short-term strategic decisions. Those specialties are vascular, cardiac, and neurological surgery (Table 2 ). Workloads in thoracic and urological surgery are potentially sensitive to decisions by one hospital. Workloads of gynecological surgery at the study hospital may be highly at risk.
Predicting DEA Results Using Less Than Full Information
For the study hospital, the sole input variable was county weighted discharges. However, trying to simplify the DEA analysis process by including just population values from the US Census resulted in four of eight procedure’s gaps being incorrect. This was because the benchmark hospitals changed. Similarly, erroneous results were obtained for 21% of the hospitals in the rural state (Table 3 ).
Table 3:
Hospital characteristics alone require less processing of hospital discharge data. For the rural state, 6% of hospitals would get erroneous results. As a comparison, 15% would be erroneous for the studied Pennsylvania hospitals (Table 3 ).
Each hospital can readily obtain its own data from internal sources. Its gap could be calculated using data from hospitals in other states or provinces. The DEA automatically finds similar hospitals. However, the performance was very poor in that erroneous results were obtained for 98% of hospitals (Table 3 ).
Discussion
We previously showed the validity of using DEA to determine by how much hospitals can increase elective inpatient surgical workloads for each specialty (1
The case study shows that DEA may be of value to heads of anesthesia groups in recruitment decisions. The DEA may also be useful for OR managers and surgical services committees, with discretion in how increases in operational budgets are allocated and how capital purchases are chosen. Equivalently, the method provides analysis that may be useful for presenting the rationale for increases in operational budgets and/or capital purchases to a hospital’s larger budget committee.
A foundation to applying DEA to estimate market capture for inpatient surgery is the automatic evaluation of the correlations in different specialties’ workloads (Appendix ). The fundamental reason why the DEA works (1
Data need to be obtained from the studied state or province (Table 3 ). All the studied input variables need to be included in the DEA. There does not appear to be a simplification to doing the full analysis.
As found previously (1 Table 1 ). Caseload is a reliable surrogate for inpatient surgical workload. Perfect correlations should not be expected because the workload of a specialty is poorly defined, incomplete, and prone to measurement error. This is why we apply DEA to procedure counts (1
Similar analyses can be applied to any state, region, or organization that collects discharge data. In 2003, 30 states participated in data collection for the State Inpatient Databases as part of AHRQ’s Healthcare Cost and Utilization Project. However, only a few states record outpatient surgery, and some that do so focus only on specific populations such as children. Although we foresee no theoretical reason why the DEA model would not work for freestanding ambulatory surgery centers, because of these data limitations, the DEA can only be applied, currently, to assess inpatient surgery.
In the previous article (1
When a gap is positive, there is potential for the hospital to increase the specialty’s workload. That does not mean that increasing workload would benefit the hospital financially. In practice, the opposite may occur. In addition, there may not be sufficient operational capacity to recruit another surgeon. These issues should be considered when interpreting DEA results. Doing so is not limiting because financial assessment for different surgical specialties, including consideration of capacity constraints, is well developed (8
Political issues may prevent direct reduction of workload in a given subspecialty, even though the contribution margin per OR hour is much less for that subspecialty versus other subspecialties that are eager for more resources. In that situation, having the subspecialty’s workload being at risk from another hospital may be a blessing for administrators. Workload at risk is not necessarily disadvantageous.
The need for considering DEA results with a simultaneous financial analysis does not apply to professional groups making hiring decisions. The danger to them is in recruiting physicians and staff without achieving an increased workload. The gaps alone address this problem. The alternative approach is to perform a retrospective analysis (e.g., using the previous 48 weeks of surgical specialties’ OR workloads) (9 10
Appendix: Equations to Perform DEA Using Excel Solver Tool
We use the following notation. There are n hospitals, k = 1, 2,…, n, each producing p surgical procedures, p = 1, 2,…, 8. The outputs (i.e., number of discharges) for the rth procedure at the kth hospital equals Y r,k , r = 1,…, p . There are m input factors that determine a hospital’s potential elective surgical workload, with m = 5 for this study. The ith strategic (input) factor at the kth hospital equals X i,k , i = 1,…, m. The efficiency score of the kth hospital is 1/φk . Slacks in the outputs and inputs for the kth hospital are represented by
and
respectively. Gaps in the outputs are represented by
Using linear programming, solve (1,7
subject to constraints:
and
The estimate of the efficient frontier is the piecewise linear convex combination of all hospitals with efficiency scores 1/φk ≥ 1.
Equations 1 through 3 can be shown to be identical to:
subject to constraints:
The above equations are derived from the Output-Oriented CCR DEA model (12
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