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Large Variability in the Diversity of Physiologically Complex Surgical Procedures Exists Nationwide Among All Hospitals Including Among Large Teaching Hospitals

Dexter, Franklin MD, PhD*; Epstein, Richard H. MD; Thenuwara, Kokila MBBS, MD, MME; Lubarsky, David A. MD, MBA§

doi: 10.1213/ANE.0000000000002634
Healthcare Economics, Policy, and Organization: Original Clinical Research Report
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BACKGROUND: Multiple previous studies have shown that having a large diversity of procedures has a substantial impact on quality management of hospital surgical suites. At hospitals with substantial diversity, unless sophisticated statistical methods suitable for rare events are used, anesthesiologists working in surgical suites will have inaccurate predictions of surgical blood usage, case durations, cost accounting and price transparency, times remaining in late running cases, and use of intraoperative equipment. What is unknown is whether large diversity is a feature of only a few very unique set of hospitals nationwide (eg, the largest hospitals in each state or province).

METHODS: The 2013 United States Nationwide Readmissions Database was used to study heterogeneity among 1981 hospitals in their diversities of physiologically complex surgical procedures (ie, the procedure codes). The diversity of surgical procedures performed at each hospital was quantified using a summary measure, the number of different physiologically complex surgical procedures commonly performed at the hospital (ie, 1/Herfindahl).

RESULTS: A total of 53.9% of all hospitals commonly performed <10 physiologically complex procedures (lower 99% confidence limit [CL], 51.3%). A total of 14.2% (lower 99% CL, 12.4%) of hospitals had >3-fold larger diversity (ie, >30 commonly performed physiologically complex procedures). Larger hospitals had greater diversity than the small- and medium-sized hospitals (P < .0001). Teaching hospitals had greater diversity than did the rural and urban nonteaching hospitals (P < .0001). A total of 80.0% of the 170 large teaching hospitals commonly performed >30 procedures (lower 99% CL, 71.9% of hospitals). However, there was considerable variability among the large teaching hospitals in their diversity (interquartile range of the numbers of commonly performed physiologically complex procedures = 19.3; lower 99% CL, 12.8 procedures).

CONCLUSIONS: The diversity of procedures represents a substantive differentiator among hospitals. Thus, the usefulness of statistical methods for operating room management should be expected to be heterogeneous among hospitals. Our results also show that “large teaching hospital” alone is an insufficient description for accurate prediction of the extent to which a hospital sustains the operational and financial consequences of performing a wide diversity of surgical procedures. Future research can evaluate the extent to which hospitals with very large diversity are indispensable in their catchment area.

From the *Division of Management Consulting, Department of Anesthesia, University of Iowa, Iowa City, Iowa

Department of Anesthesiology, Perioperative Medicine and Pain Management, University of Miami, Miami, Florida

Department of Anesthesia, University of Iowa, Iowa City, Iowa

§Department of Anesthesiology, Perioperative Medicine and Pain Management, University of Miami Health System, Miami, Florida.

Published ahead of print November 22, 2017.

Accepted for publication October 3, 2017.

Funding: Departmental.

The authors declare no conflicts of interest.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s website.

The Division of Management Consulting, Department of Anesthesia, University of Iowa, performs the calculations described in the Introduction and Discussion of this article. F.D. receives no funds personally other than his salary and allowable expense reimbursements from the University of Iowa and has tenure with no incentive program. He and his family have no financial holdings in any company related to his work, other than indirectly through mutual funds for retirement. Income from the Division’s consulting work is used to fund Division research.

Reprints will not be available from the authors.

Address correspondence to Franklin Dexter, MD, PhD, Division of Management Consulting, Department of Anesthesia, University of Iowa, 200 Hawkins Dr, 6 JCP, Iowa City, IA 52242. Address e-mail to Franklin-Dexter@UIowa.edu.

Multiple previous studies have shown that having a large diversity of procedures has a substantial impact on quality management of hospital surgical suites. At hospitals with substantial diversity, unless validated statistical methods suitable for rare events are used, anesthesiologists will have inaccurate predictions of surgical blood usage, case durations, cost accounting and price transparency, times remaining in late running cases, and use of intraoperative equipment.1–12 What is unknown is whether large diversity is a feature of only a few very unique set of hospitals nationwide (eg, the largest hospitals in each state or province).

Hospital inpatient discharge data exclude patients undergoing ambulatory (outpatient) surgery; this is by definition. Consequently, analyses of diversity using only hospital discharge data generally are limited to physiologically complex procedures (eg, defined as >7 American Society of Anesthesiologists base units).13–16 For example, the partition between 7 and 8 base units excludes International Classification of Diseases version 9 Clinical Modification (ICD-9-CM) code 51.23 “laparoscopic cholecystectomy” but includes 57.71 “radical cystectomy” and 52.7 “radical pancreaticoduodenectomy” (“Whipple procedure”). For example, 2 physiologically complex procedures performed frequently are ICD-9-CM 39.50 “angioplasty of other noncoronary vessel(s)” and 03.09 “other exploration and decompression of spinal cord.” Physiologically complex procedures are performed only in hospitals, as compared with free-standing ambulatory surgery centers.

The diversity of surgical procedures performed at a hospital can be quantified using a summary measure, the number of procedures commonly performed at the hospital.17 For calculation, the “number of procedures” refers to the total number of different codes observed among all discharges meeting inclusion criteria at each hospital (eg, ICD-9-CM code 36.15 “single internal mammary-coronary artery bypass”). The relative proportion of procedures of each code is calculated for each hospital.17 The sum of the squares of the proportions is each hospital’s Herfindahl index.17 The Herfindahl index equals the probability that any 2 procedures selected at random, with replacement, from a list of all procedures performed at the hospital have the same code. The inverse of the Herfindahl is an index referred to as the “number of procedures of each code performed commonly” at the hospital.17 The procedures (ie, codes) common at one hospital often differ from those at other hospitals. Each increase in the number of different procedures performed can be associated, in a monotonic fashion, with an increase in the inverse of the Herfindahl.17–20 There are several tutorials online about this measure of diversity.21–24 A recent Statistical Grand Rounds showed how very well the measure of diversity differentiated among hospitals in Iowa.17 As examples, a large teaching25 hospital performed 4584 of the studied procedures in a year, of 274 different physiologically complex procedure codes; 78.1 procedures were performed commonly (standard error [SE], 1.8; Figure 1, far left). A small non-teaching25 hospital performed 97 of the studied procedures that year, of 5 different physiologically complex procedure codes; 2.0 procedures were performed commonly (SE, 0.2; Figure 1, far right). For brevity, subsequently throughout the article, when we use the word “procedure” (or “procedures”), we mean the surgical procedure as specified by its unique code, not the number of cases with the procedure code that were performed at the hospital.

Figure 1.

Figure 1.

What differentiated the largest teaching25 hospital in Iowa from the other hospitals in the state for the care of adult patients was the hospital’s diversity of physiologically complex procedures.15,16 In the current article, we evaluate the generalizability of that finding nationwide.

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METHODS

We used the 2013 Nationwide Readmissions Database subject to the required data use agreement.26 The database was purchased from the US Healthcare Cost and Utilization Project of the US Agency for Healthcare Research and Quality.27

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Specific Hypotheses

Hypothesis 1.

Previous epidemiological studies revealed that most facilities commonly perform <10 procedures, both nonphysiologically complex and physiologically complex.17,28 We formulated the following hypothesis:

Most (ie, >50%) acute care hospitals in the United States commonly perform <10 physiologically complex surgical procedures.

The comparator of “<10 procedures” is based on data from the state of Iowa, where 116 of 117 hospitals commonly performed <6 inpatient and outpatient procedures among pediatric patients 2 years and younger.17 This comparator is based also on US national data. Among hospitals and ambulatory facilities submitting data to the American Society of Anesthesiologists’ National Anesthesia Clinical Outcomes Registry, the mean (SE) number of inpatient and outpatient procedures commonly performed at each facility was 13.59 (0.12), with median 10.728; in the current study, we limited consideration to inpatient procedures. Hypothesis 1 matters for large teaching25 hospitals because it means that the chances are in favor (ie, relative risk >1) that other acute care hospitals in the catchment region will have lesser diversity.

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Hypotheses 2 and 3.

In contrast to the majority of hospitals, a large teaching25 hospital in Iowa was found to perform commonly approximately 3 times as many different procedures, among pediatric patients, as any of the other 116 hospitals in the state.17 Approximately 8% of hospitals in the United States are large teaching25 hospitals. Among patients of all ages, the large teaching25 hospital in Iowa commonly performed more than 3 times as many anesthesia procedures as the average facility nationwide.29 Multiplying 3 times the 10 physiologically complex procedures from hypothesis 1 gave 30 procedures. We formulated 2 hypotheses that the previous results for the large teaching25 hospital in Iowa would hold nationwide when applied to physiologically complex procedures:

Hypothesis 2: At least 5% of acute care hospitals in the United States commonly perform >30 physiologically complex surgical procedures (ie, large diversity).

Hypothesis 3: Most (ie, >50%) large teaching25 hospitals commonly perform >30 physiologically complex surgical procedures (ie, large diversity).

If hypotheses 2 and 3 were accepted, the findings would be important because large diversity has substantial operational and financial consequences.1–7 Furthermore, large teaching25 hospitals can be perceived as having different operational and financial performance because of the presence of trainees. However, the presence of trainees may not be the cause of differences in performance but, rather, the diversity of performed procedures.

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Hypotheses 4–6.

There have been several studies from the large teaching25 hospital in Iowa quantifying the diversity of its surgical procedures and the consequences of this diversity.15–17,29–31 There was also a study from a large teaching hospital in Philadelphia.25,32 We found no other related studies.a Consequently, we framed our final hypotheses, with the magnitude tested being that of hypothesis 1:

(Hypothesis 4) Increased hospital size is associated with a greater diversity of physiologically complex surgical procedures, and (hypothesis 5) teaching status is associated with greater diversity, but (hypothesis 6) there is substantive variability (interquartile range ≥10 common procedures) among large teaching25 hospitals in their diversity of surgical procedures.

If hypotheses 4–6 were accepted, the implication would be that “large teaching hospital”25 would be an insufficient description for accurate prediction of the extent to which a hospital sustains the operational and financial consequences of performing a wide diversity of surgical procedures. In other words, hospital bed count and teaching status would be inaccurate surrogates for knowing the diversity of performed procedures at the hospital.

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Database Used

The Nationwide Readmissions Database included 14,325,172 discharges from 2006 nonfederal, acute care hospitals33,34 located within 21 US states35 (ie, this was not a sample of discharges, as was provided in the National Inpatient Sample). These states represented 49.3% of the US population and 49.1% of US hospital discharges.36 We excluded 25 hospitals that were inferred to be pediatric hospitals based on most of their discharges comprising patients younger than 18 years. The remaining population was 13,163,635 medical and surgical discharges of adult patients from N = 1981 hospitals.

The physiologically complex procedures were defined as including procedure(s) with ICD-9-CM codes corresponding to the Current Procedural Terminology codes to which the American Society of Anesthesiologists had assigned >7 Relative Value Guide base units.15,16 However, for a few ICD-9-CM codes, especially vascular procedures, the same code could be applied to different anatomical locations, making the code insufficient to determine physiological complexity.16 Furthermore, due to technological improvements in surgical care, some of these procedures may not have been limited to inpatient surgery. An example of a physiologically complex procedure with potentially some missing cases was total hip replacement (81.51), assigned 8 base units. The mean nationwide length of stay in 2013 for the 96% of these discharges without “major complications or comorbidities” was 3.02 days. We addressed both issues by adding the criterion that the patient’s discharge diagnosis-related group (DRG) needed to have a mean nationwide length of stay at least 4.00 days for the discharge to be included in the study. The mean national length of stay in 2013 for each DRG was obtained from the National Inpatient Sample using HCUPnet.37 Once the ≥4.00-day criterion was applied, the most common physiologically complex procedure nationwide28 was ICD-9-CM 36.15, “single internal mammary-coronary artery bypass” (Supplemental Digital Content, Table A, http://links.lww.com/AA/C134). Many of those patients were categorized as having DRG 236, which has a mean length of stay of 6.3 days; each of the other 5 DRG’s for “coronary bypass” had longer mean length of stays.

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Statistical Methods

Several different inferential methods of analyses were used. Tests of single proportions to 50.0% (hypothesis 1 and 3, “most”) and to 5.0% (hypothesis 2) were performed using 1-sided binomial tests. For example, if 123 of the 1981 hospitals (ie, 6.21%) commonly performed >30 physiologically complex procedures, we would conclude that in general at least 5.0% of hospitals do so, because 123 of 1981 results in (a) the 1-sided comparison with 5.0% having P = .0094 and (b) the 99% lower confidence limit (CL) of 5.01% slightly exceeding 5.0%. The CLs of the proportions were calculated using the conservative nonparametric Clopper–Pearson method; they are 1 sided, matching the hypotheses. Effects of the database’s 3 teaching status categories25 and 3 hospital size categories25 on the number of common procedures were tested using the Kruskal–Wallis test (hypotheses 4 and 5). Dunn’s method was used for the corresponding, reported, post hoc pairwise comparisons. The CL and the P value for the interquartile ranges of the number of common procedures (hypothesis 6) were calculated asymptotically.38

No statistical power analysis was planned a priori because the population size studied, 1981 different acute care nonpediatric hospitals in the United States, was finite. However, we knew that previous studies successfully detected significant (P < .0001) differences in the diversity of physiologically complex procedures among hospitals in 1 US state using 6 months of data.15,17 In the current study, we had corresponding data for 21 states and 12 months of data.

For our 6 hypotheses, we treated P < .01 as statistically significant and correspondingly report 99% CL.

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RESULTS

Figures 1 and 2 show that the diversity of procedures represents a substantive differentiator among hospitals.39,40Figures 1 and 3 show the probability distributions of the diversity of procedures among all hospitals and among the large teaching25 hospitals, respectively. In the Appendix are results showing convergent validity of the use of the number of physiologically complex procedures commonly performed as the study end point.

Figure 2.

Figure 2.

The median number of commonly performed physiologically complex procedures was 8.1. There were 53.9% of the hospitals with <10.0 physiologically complex procedures commonly performed (lower 99% CL, 51.3%; Figure 1). Hypothesis 1 was accepted based on P = .0002 for comparison to 50%.

The threshold of 30 commonly performed physiologically complex procedures represented >3 times the median surgical diversity (8.1 procedures). There were 14.2% of the hospitals with such large (>30.0) diversity (lower 99% CL, 12.4%). Hypothesis 2 was accepted based on P < .0001 for comparison to 5%.

Approximately half (48.4%) of the hospitals with a large diversity of physiologically complex procedures were classified as large teaching25 hospitals. In addition, 80.0% of the 170 large teaching25 hospitals had large diversity (lower 99% CL, 71.9%; Figure 3). Hypothesis 3 was accepted based on P < .0001 for comparison to 50%.

Figure 3.

Figure 3.

Table.

Table.

Larger hospitals had a greater diversity of physiologically complex procedures than did the small- and medium-sized hospitals (Table). Since both P < .0001, hypothesis 4 was accepted. In addition, teaching25 hospitals had greater diversity than did the rural and urban non-teaching25 hospitals (Table). Since both P < .0001, hypothesis 5 was accepted. However, there was considerable variability among the large teaching25 hospitals in their numbers of commonly performed physiologically complex procedures (interquartile range, 19.3 procedures; lower 99% CL, 12.8 procedures; Figure 3). Since P = .0001 for the test of the interquartile range compared with 10.0 procedures, hypothesis 6 was accepted.

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DISCUSSION

Implications of Study’s Results for Hospitals With Large Diversity

More than 12.4% of hospitals had >3 times the median diversity (hypothesis 2). Such large diversity was a characteristic of most large teaching25 hospitals (hypothesis 3). This finding is important because diversity substantially influences processes related to assessment of hospital quality, including prediction of surgical blood usage, case durations, cost and price transparency, times remaining in late running cases, and intraoperative equipment use.1–12 These hospitals should expect that state and provincial interventions and management policies based on standardization would often not apply or lack benefit. These hospitals should expect also that their operational processes to measure quality and reduce costs would need to be suitable for many different procedures (eg, not procedure-specific clinical pathways and standardization, but interventions such as having all patients undergo preoperative evaluation including care coordination). Operating room directors and anesthesiologists should understand that this is not because their hospital is large or because it has resident training programs, but rather because of the diversity of its procedures.

We previously showed that hospitals can develop internal business processes to perform efficiently, even when the number of physiologically complex procedures is so large that many are rarely encountered.31 In a DRG-type reimbursement system, as used in the United States and Australia,41 discharge of patients sooner than the mean length of stay nationwide results in greater contribution margin (ie, current or future reimbursement minus variable costs). The mean difference in days is economically relevant, being proportional to the total number of hospital days reimbursed by a DRG-based system in excess of the total number of hospital days that the hospital actually provides.42 The extra money (margin) is proportional to the mean difference in days. Rare physiologically complex procedures have DRGs with long mean lengths of stay.31 Consequently, rare procedures have greater opportunities for large mean differences in days (ie, large increase in hospital margin).43 For example, a 10% reduction in mean length of stay from 4.0 days is 0.4 days, while a 10% reduction from a mean of 10.0 days is a full day. As hypothesized, rare procedures (ie, those related to large diversity) were observed in practice to have substantively greater contribution margins per hour of operating room time.31 Our results of the current study are important because a hospital not recognizing its unique diversity may focus on targeting for growth the few nationally common procedures, even though such common procedures generally are less beneficial financially and are already performed by other nearby hospitals.15,16,30

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Implications of Study’s Results Implemented by Calculating Diversity Using Local Data

We used a large sample to understand the diversity of physiologically complex surgical procedures within hospitals. Our results for hypothesis 1 show that most hospitals commonly performed few physiologically complex procedures. The implication is that their limited diversity can be quantified and used for strategic planning.

Our results show that studies of clinical, financial, and/or operational dependent variables that treat size25 and/or teaching status25 as independent variables can miss an important causal factor, namely, diversity. There is considerable variability of diversity even among large teaching25 hospitals. Thus, our hypotheses 4–6 show that administrators and policy analysts should not assume that an individual large teaching25 hospital performs a large diversity of procedures (Figure 3). Rather, diversity needs to be measured.28 Health service investigators need to measure each hospital’s diversity and control for the variability of diversity among hospitals when performing comparative studies.

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Limitations

In our experience, nearly every strategic analysis requires adjustments based on the available data (eg, using whatever classification system the country, state, or province uses for its hospital discharge data).16,31 We did so by limiting consideration to patients with discharge DRGs that included a national average length of stay of at least 4.0 days. Because of these limitations, we restricted our conclusions to those that were likely generalizable (see Appendix). This was feasible because we achieved narrow confidence intervals by using a sample size of discharges relevant to a population size of half the United States.

Our results likely were biased toward underestimating the variability in diversity among hospitals. The procedures in the 2013 database were classified using ICD-9-CM. The ICD-9-CM has many procedures pooled into generic “other” categories, a consequence of its lower level of granularity. The ICD-9-CM classification was replaced as of October 2015 by a different classification system, International Classification of Diseases, 10th Revision, Procedure Coding System. While ICD-9-CM has 2373 unique surgical (“major therapeutic”) procedures, the International Classification of Diseases, 10th Revision, Procedure Coding System has 49,730.44–46

Our results also were likely biased toward underestimating the diversity of procedures, per se. We studied physiologically complex surgery in the current study because those procedures differentiated the largest teaching25 hospital in the State of Iowa from other hospitals in the state for the care of adult patients.15,16 At that hospital, 18% of surgical anesthetics, inpatient or outpatient, are physiologically complex.29 Physiologically complex surgery is inpatient surgery. For cost accounting of hospitalizations, the unique combination of procedures that each patient undergoes matters, because each procedure contributes to costs.18,46,47 Creating combinations reduces the relative incidence of procedures that are common nationwide (Supplemental Digital Content, Table A, http://links.lww.com/AA/C134). In addition, some hospitals have large diversity among their nonphysiologically complex procedures.28,29 At the average hospital in the state of Texas, 93% of the observed combinations of procedures were performed at most once per month at the hospital.46 In addition, 54% of the surgical discharges and 68% of the hospital costs were for procedures performed at most once per month at the hospital.46,47

Finally, our study was limited to the analysis of 1 year of data. A decade of data would provide insight into the effect of policy on longitudinal changes in the diversity of procedures.

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CONCLUSIONS

The diversity of procedures represents a substantive differentiator among hospitals. The unique diversity of physiologically complex surgical procedures performed by some US large teaching25 hospitals can be quantified. “Large teaching hospital” alone is an insufficient description for accurate prediction of the extent to which a hospital sustains the operational and financial consequences of performing a wide diversity of surgical procedures. Controlling for diversity should be considered when making some comparisons among hospitals. When working at hospitals with large diversity, substantial operational benefit can be expected when using statistical methods designed for rare procedures (eg, predicting case durations and forecasting blood transfusion). Future research can evaluate the extent to which hospitals with very large diversity are indispensable in their catchment area and how diversity influences hospitals’ rate of growth.

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APPENDIX

The results in this Appendix show convergent validity of the use of the number of physiologically complex procedures commonly performed as the study end point. Rank correlations among statistics were tested using the Spearman rank correlation coefficient, with asymptotic P values (StatXact-11; Cytel, Cambridge, MA).

The number of commonly performed physiologically complex procedures (ie, 1/Herfindahl) was highly correlated with the number of physiologically complex procedures (r = 0.974) and number of discharges with at least 1 physiologically complex procedure (r = 0.955). Both Spearman correlations for these indicators of diversity had P < .0001. These studied 597,580 discharges were based on the criterion that the patient’s discharge DRG had a mean nationwide length of stay at least 4.00 days; see “Database Used” in Methods. As sensitivity analyses, we studied 2 additional criteria, which resulted in the exclusion of fewer cases. If a ≥3.00-day criterion had been used, then there would have been 973,725 discharges among patients undergoing a physiologically complex procedure. If this threshold had been used, nearly all patients undergoing total hip replacement (81.51) would have been included, not excluded as in our primary analysis (see Methods). The Spearman correlation between the number of commonly performed physiologically complex procedures and the number of discharges was r = 0.979. This result using the ≥3.00-day threshold compares with the r = 0.955 above using the ≥4.00-day threshold. If no criterion were placed on the DRG (ie, the inclusion criterion was only that the patient underwent a physiologically complex procedure), then there would have been 1,211,724 discharges studied (ie, approximately double the number used in our results). The Spearman correlation was still large: r = 0.980. Thus, the validity of our results was insensitive to the choice of the length of stay threshold applied to the physiologically complex procedures.

Among the 597,580 discharges with at least 1 physiologically complex procedure, most discharges had precisely 1 such procedure (57.58%; P < .0001 for the comparison to 50%). There were 26.89% of discharges with 2 procedures, 9.97% with 3 procedures, and 5.55% with 4 or greater procedures.

The hospitals commonly performing many (>10) physiologically complex procedures were in metropolitan areas (Figure 2).39,40

The variability in the numbers of commonly performed physiologically complex procedures among hospitals remained when analyzed using the corresponding Clinical Classifications Software (CCS) categorization of the included ICD-9-CM codes.48 Among all 1981 hospitals, the coefficients of variation were 111% by ICD-9-CM and 90% by CCS. The coefficients of quartile deviation were 91% by ICD-9-CM and 73% by CCS. Among the 170 teaching hospitals, the coefficients of variation were 33% by ICD-9-CM and 28% by CCS. The coefficients of quartile deviation were 23% by ICD-9-CM and 19% by CCS.

The numbers of commonly performed physiologically complex procedures reflected case mix or specialty when considered for all hospitals, but not among the large teaching hospitals (ie, institutions that would have all the specialties). Specifically, when analyzing all 1981 hospitals, the medians were 8.1 procedures by ICD-9-CM and 3.2 by CCS. These are reasonable numbers for specialties. Furthermore, by hospital, the 2 end points were highly correlated, Spearman r = 0.920. In contrast, among the large teaching hospitals, the medians were 40.8 procedures based on the ICD-9-CM (ie, too many to reflect specialty) versus 10.6 based on the CCS (ie, reasonably reflecting specialty). The rank correlation was much less than the rank correlation calculated using all hospitals, 0.493 (SE, 0.061; P < .0001) comparing the 2 rank correlations. Thus, the so-called species richness, being quantified using the numbers of physiologically complex procedures performed commonly, reflected for the large teaching hospitals diversity much larger than that of specialty.17,49

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DISCLOSURES

Name: Franklin Dexter, MD, PhD.

Contribution: This author helped design the study, obtain the data, analyze the data, and write and edit the manuscript.

Name: Richard H. Epstein, MD.

Contribution: This author helped design the study, obtain the data, analyze the data, and write and edit the manuscript.

Name: Kokila Thenuwara, MBBS, MD, MME.

Contribution: This author helped design the study and edit the manuscript.

Name: David A. Lubarsky, MD, MBA.

Contribution: This author helped write and edit the manuscript.

This manuscript was handled by: Nancy Borkowski, DBA, CPA, FACHE, FHFMA.

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FOOTNOTES

aPubMed search September 6, 2017: (“anesthesia procedures” or “anaesthesia procedures” or “surgical procedures” or “operative procedures” or “major therapeutic procedures”) and (“Herfindahl” or “diversity index” or “Shannon entropy”) not “Hirschman”, where “Hirschman” refers to the Herfindahl–Hirschman index for quantifying competition (ie, diversity of hospitals used rather than procedures within hospitals).

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