Abstract
Background:
Evidence of higher hospital volume being associated with improved outcomes for patients undergoing total knee replacement (TKR) is mostly based on arbitrary distribution-based thresholds.
Objective:
We aimed to define outcomes-based volume thresholds using data from a national database.
Research Design:
The Stratum Specific Likelihood Ratio (SSLR) method was applied to the MedPAR Limited Data Set inpatient data from 2010-2015 to derive outcome-based categories by calculating the likelihood of an adverse event within each stratum.
Subjects:
Medicare patients who had undergone primary TKR between 2010 and 2015.
Measures:
Surgical and TKR specific complications occurring within the index hospitalization and all-cause readmission within 90 days were considered adverse events. We derived an average annual TKR case volume for each hospital, and applied the SSLR method to determine volume categories indicative of a similar likelihood of 90-day post-operative complications. Hierarchical multivariable logistic regression with a random intercept for hospital nested within study year and adjusted for patient and hospital characteristics was performed to determine if these volume thresholds were still associated with the odds of 90-day readmission for complications after adjustment.
Results:
SSLR analysis yielded four hospital volume categories based on likelihood of 90-day post-operative complications: 1-31 (low), 32-127 (medium), 128-248 (high), and 429+ (very high) TKRs performed per year. The results of the hierarchical multivariable logistic regression showed significantly increased odds of 90-day complications at lower volume categories. Sensitivity analyses confirmed our main findings.
Conclusions:
This study is the first to provide national-level volume categories that are evidence-based. Publicizing these thresholds may enhance quality measures available to patients, providers, and payors.
Introduction:
Total knee replacement (TKR), one of the most effective surgical procedures, aims to alleviate debilitating knee pain and improve function.1 More than one million procedures are performed in the US each year, and utilization is expected to increase rapidly in the next decade.2 Given the significant impact of TKR hospitalization and rehabilitation costs on third-party payors and large employers, they have explored numerous strategies to perform this procedure efficiently. With mounting evidence showing that higher TKR hospital volume is associated with lower complication rates, several large employers have contracted with some of the highest volume hospitals to perform TKR for their employees, even if it meant flying them out to that hospital for care.3
While it is easy to flag the highest volume hospitals in the nation, thresholds for high volume hospitals have been inconsistent in the literature.4–9 For example, while Katz et al. identified 25 TKRs/year as the first threshold for higher volume,4 Anis et al. defined that first threshold as 250 TKRs/year.9 This variability is largely the result of determining these thresholds a priori either arbitrarily or using a distribution-based definition (e.g., tertiles or quartiles). With ample evidence proving a volume-outcome relationship, and to overcome this inconsistency, Wilson and colleagues aimed to identify volume thresholds based on a change in outcomes. They applied the Stratum Specific Likelihood Ratio (SSLR) method to the New York State-wide database to derive outcome-based categories.5 In simple terms, the SSLR method determines the threshold for higher volume hospitals based on a significant improvement in patient outcomes.5 While innovative, Wilson’s work was criticized for being limited to data from one state. To overcome these limitations, we applied the SSLR method to national data and derived outcomes-based hospital volume thresholds for TKR.
Methods:
Data Source:
After obtaining approval from our institutional review board, we identified patients undergoing primary TKR from the Medicare Provider Analysis and Review (MedPAR) 100% Inpatient Limited Dataset (LDS), a national administrative database containing patient-level data on all inpatient hospital discharges from Medicare beneficiaries. TKR patients were identified from January 1, 2010 to September 30, 2015 using ICD-9-CM (81.54) procedure codes and from October 1, 2015 to December 31, 2015 using ICD-10-CM procedure codes (0SRC, 0SRD, 0SRT, 0SRU, 0SRV, 0SRW, 0QRB, 0QRC, 0QRD, 0QRF).10 Hospital characteristics by study year (teaching status, hospital ownership, rural or urban status) were identified from the American Hospital Association yearly surveys.
Cohort inclusion and exclusion criteria followed a modified version of the criteria from the 2014 CMS Measure.11 Fee-for-service patients with an eligible index admission were included if they were 65 years of age or older at the time of surgery, were not enrolled in Medicare due to disability or end stage renal disease, and had available Medicare Part A data in the month of discharge and 90 days following surgery. Exclusion criteria included having surgery performed outside the US, undergoing concurrent TKR revision, and having primary discharge diagnoses of mechanical complications or malignant neoplasm. Patients were also excluded if they were transferred from another acute care facility or skilled nursing facility, were discharged from the hospital against medical advice, and those with more than two TKR procedures coded during index hospitalization. Finally, patients were excluded if dates of TKR, death, and/or admission being temporally misaligned (Figure 1).
Figure 1:
Data exclusion criteria for Medicare patient records who underwent primary total knee replacement during the study period from 2010 – 2015.
Footnote: *Underwent a concurrent TKR revision during same hospitalization, primary diagnosis of mechanical complications or malignant neoplasm, transfer from acute care facility or skilled nursing facility, discharged AMA, more than two TKR coded during same hospitalization, underwent surgery in US territory, Medicare Part A data unavailable within 90 days post-surgery, temporal misalignment of death, surgery, or discharge dates.
Primary Outcome:
We used the SSLR method to generate hospital volume categories based on complications within 90 days of receiving surgery. Following the methodology used by Wilson et al., we included 22 possible complications that were both specific to TKR and general to surgical procedures (Table 1, Supplemental Digital Content).5 Where applicable, complications were identified following the 2014 CMS Measure Methodology for assessing complications in TKR and total hip arthroplasty.11
Statistical analysis:
Originally described by Peirce and Cornell in 1993 for diagnostic testing, SSLR analysis determines the optimum number of cut points to approximate the Area Under the Receiver Operating Curve (AUROC) derived by maximum likelihood.12 In the context of volume-outcomes research, a SSLR indicates how much more or less likely a specific outcome is for individuals within a specific volume stratum. The approach used by Peirce and Cornell identifies cut points where the risk of adverse events drops most abruptly, allowing for identification of volume strata with a similar likelihood of an outcome.5, 12
Hospitals were stratified by annual case volume, where each distinct case volume was considered its own stratum. To create strata adjusted for all years of data, we derived the average annual TKR case volume for each hospital by dividing the total number of TKR performed at that hospital during the study period by the number of years the hospital was present in the data. A likelihood ratio was then calculated for each stratum based on the total number of adverse events occurring in that stratum. For this study, a complication within 90 days of surgery was considered an adverse event, and a surgery resulting in no complications was considered a normal event. The 95% confidence intervals were constructed for each stratum likelihood, then iteratively checked. If two neighboring intervals overlapped, the two strata were then merged to form a new stratum. The process was repeated until all 95% confidence intervals were non-overlapping.
Hierarchical multivariable logistic regression with a random intercept for hospitals was performed to determine if the volume thresholds identified by SSLR were still associated with distinct odds of 90-day complications after adjustment for patient and hospital characteristics. To account for potential changes in hospital characteristics over time, the model was parametrized to nest hospitals within study years. The model was adjusted for age, race, sex, teaching status, hospital ownership, rural or urban status, and 31 Elixhauser comorbidities.13, 14 SSLR analysis was performed using Excel 2021 (Microsoft) and R Statistical Software v.4.1.2 (R Core team 2021). Multivariate analyses were performed using SAS 9.4 (SAS Institute, Cary, NC).
Sensitivity analysis:
Sensitivity analyses were conducted by repeating the SSLR and multivariate analyses excluding complications flagged as Present On Admission (POA) in the primary study cohort when developing the SSLR thresholds, thus excluding potential existing conditions not related to surgery, and by excluding complications not included in the CMS TKR/THR Complication Measure methodology. These analyses were chosen to examine how SSLR volume categories may vary depending on changes to the cohort used to identify complications. Sensitivity analyses were also conducted with correlated standard errors for hospitals nested within years.
Results:
Over the study period, 1,402,240 Medicare patients underwent TKR in 3,841 hospitals. Characteristics of the study cohort included 63.4% female, 5.2% Black, and 1.1% Hispanic. The mean age was 73.0 (5.9) years. Hospital annual volume ranged from 1 to 2171 TKRs/year. Over the study period, 41,463 patients (2.96%) had a complication within 90 days of undergoing TKR. (Table 1) The most frequent TKR-specific complications were mechanical complications (n = 4514, 0.32%) and infection (n = 303, 0.02%). The most frequent general complications were pneumonia (n = 8351, 0.60%) and urinary complications (n = 6887, 0.49%) (Table 2).
Table 1.
Patient characteristics by 90 day complications status
| No complications within 90 days n (%) = 1,360,777 (97.04) | 90 Day Complication n (%) = 41,463(2.96) | Overall N = 1,402,240 | |
|---|---|---|---|
| Volume Category, n (%) | |||
| 1-31 (low) | 114626 (8.4) | 4934 (11.9) | 119560 (8.5) |
| 32-127 (medium) | 526747 (38.7) | 17087 (41.2) | 623634 (44.5) |
| 128-428 (high) | 606724 (44.6) | 16910 (40.8) | 543834 (38.8) |
| 429+ (very high) | 112668 (8.3) | 2532 (6.1) | 115200 (8.2) |
| Gender, n (%) | |||
| Male | 495087 (36.4) | 18485 (44.6) | 513572 (36.6) |
| Female | 865690 (63.6) | 22978 (55.4) | 888668 (63.4) |
| Race, n (%) | |||
| White | 1232905 (90.6) | 37333 (90.0) | 1270238 (90.6) |
| Black | 70207 (5.2) | 2372 (5.8) | 72579 (5.2) |
| Asian | 12233 (0.9) | 425 (1.0) | 12658 (0.9) |
| Hispanic | 15027 (1.1) | 468 (1.1) | 15495 (1.1) |
| North American Native | 5591 (0.4) | 156 (0.4) | 5747 (0.4) |
| Unknown/Other | 24814 (1.8) | 709 (1.7) | 25523 (1.8) |
| Age, mean (SD) | 73.0 (5.9) | 74.0 (6.2) | 73.0 (5.92) |
| Comorbidities, n (%) | |||
| AIDS | 160 (0.01) | 5 (0.01) | 165 (0.01) |
| Alcohol Abuse | 8467 (0.6) | 458 (1.1) | 8252 (0.6) |
| Deficiency Anemias | 153104 (11.3) | 6454 (15.6) | 159558 (11.4) |
| Arthritis | 56176 (4.1) | 1662 (4.0) | 57838 (4.1) |
| Blood Loss | 15463(1.1) | 652 (1.6) | 16115 (1.2) |
| Congestive Heart Failure | 39635 (2.9) | 3325 (8.0) | 42960 (3.1) |
| Chronic Lung Disease | 188635 (13.9) | 7358 (17.7) | 195993 (14.0) |
| Coagulopathy | 30626 (2.3) | 1863 (4.5) | 32489 (2.3) |
| Depression | 146692 (10.8) | 4684 (11.3) | 151376 (10.8) |
| Diabetes (uncomplicated) | 278846 (20.5) | 8696 (21.0) | 287542 (20.5) |
| Diabetes (complicated) | 23901 (1.8) | 1139 (2.8) | 25040 (1.8) |
| Drug Abuse | 3100 (0.2) | 116 (0.3) | 3216 (0.2) |
| Hypertension | 988940 (72.7) | 29177 (70.4) | 1018117 (72.6) |
| Hypothyroidism | 246627 (18.1) | 6951 (16.8) | 253578 (18.1) |
| Liver Disease | 9399 (0.7) | 373 (0.9) | 9772 (0.7) |
| Fluid and Electrolyte Disorders | 114062 (8.4) | 8407 (20.3) | 122469 (8.7) |
| Metastatic cancer | 959 (0.07) | 61 (0.2) | 1020 (0.07) |
| Other Neurological Disorders | 57830 (4.3) | 2491 (6.0) | 60321 (4.3) |
| Obesity | 231760 (17.0) | 7636 (18.4) | 239396 (17.1) |
| Paralysis | 2848 (0.2) | 406 (1.0) | 3254 (0.2) |
| Peripheral Vascular disease | 32991 (2.4) | 1712 (4.1) | 34703 (2.5) |
| Psychoses | 20228 (1.5) | 881 (2.1) | 21109 (1.5) |
| Pulmonary Circulation disease | 11770 (0.9) | 5563 (13.4) | 17333 (1.2) |
| Renal Failure | 76253 (5.6) | 3915 (9.5) | 79168 (5.7) |
| Solid tumor, w/out metastasis | 7097 (0.5) | 267 (0.6) | 7364 (0.5) |
| Peptic ulcer disease w/bleeding | 504 (0.04) | 23 (0.06) | 527 (0.04) |
| Valvular disease | 59668 (4.4) | 2580 (6.2) | 62248 (4.4) |
| Weight loss | 3231 (0.2) | 598 (1.4) | 3829 (0.3) |
| Teaching Status, n (%) | |||
| Yes | 630792 (46.4) | 19877 (47.9) | 650669 (46.4) |
| No | 716403 (52.7) | 21243 (51.2) | 737646 (52.6) |
| Missing | 13582 (1.0) | 343 (0.83) | 13925 (1.0) |
| Urban Flag, n (%) | |||
| Yes | 1137296 (83.6) | 34047 (82.1) | 1171343 (83.5) |
| No | 209899 (15.4) | 7073 (17.1) | 216972 (15.5) |
| Missing | 13582 (1.0) | 343 (0.83) | 13925 (1.0) |
| Ownership, n (%) | |||
| Private - For profit | 234526 (17.2) | 6347 (15.3) | 240873 (17.2) |
| Private - Not for profit | 986103 (72.5) | 30523 (73.6) | 1016626 (72.5) |
| Public | 126566 (9.3) | 4250 (10.3) | 130816 (9.3) |
| Missing | 13582 (1.0) | 343 (0.83) | 13925 (1.0) |
Table 2.
Complications separated by TKR specific and general complications
| Complications | Total | Percent within patients with complications | Percent of all TKA | |
|---|---|---|---|---|
| TKA Specific | Mechanical complication | 4514 | 10.15% | 0.32% |
| Infection | 303 | 0.68% | 0.02% | |
| Knee Fracture | 198 | 0.45% | 0.01% | |
| Knee Dislocation | 129 | 0.29% | 0.01% | |
| General Surgical | Pneumonia | 8351 | 18.78% | 0.60% |
| Urinary complications | 6887 | 15.49% | 0.49% | |
| Ileus | 5841 | 13.14% | 0.42% | |
| Pulmonary Embolism | 5744 | 12.92% | 0.41% | |
| Respiratory complications | 5254 | 11.82% | 0.37% | |
| Digestive system complications | 4674 | 10.51% | 0.33% | |
| Acute myocardial infarction | 2654 | 5.97% | 0.19% | |
| Sepsis | 2308 | 5.19% | 0.16% | |
| Stroke | 1966 | 4.42% | 0.14% | |
| Peripheral Vascular | 1449 | 3.26% | 0.10% | |
| Nervous system complications | 805 | 1.81% | 0.06% | |
| Catheter associated UTI | 253 | 0.57% | 0.02% | |
| Major Bleed | 152 | 0.34% | 0.01% | |
| Retained Foreign Object | 89 | 0.20% | 0.01% | |
| Pressure Ulcer | 28 | 0.06% | 0.00% | |
| Vascular Catheter associated infection | 15 | 0.03% | 0.00% | |
| Air Embolism | 3 | 0.01% | 0.00% | |
| Blood Incompatibility | 1 | 0.00% | 0.00% | |
| Intracranial Injury Complication | 0 | 0.00% | 0.00% |
SSLR analysis identified three hospital volume thresholds based on the likelihood of 90-day complication: 32, 128, and 429 TKRs per year, producing four volume strata: 1-31 TKR (low-volume hospitals), 32-127 TKR (medium-volume hospitals), 128-428 (high-volume hospitals) and ≥ 429 TKR (high-volume hospitals). Of the study cohort, 8.5% of patients were in the low-volume category, 44.5% were in the medium-volume category, 38.8% were in the high-volume category, and 8.2% were in the very high-volume category. The AUROC was 0.58 (see Table 2, Supplemental Digital Content).
The results of the multivariable logistic regression showed significantly increased odds of 90-day complications at lower volume categories after adjusting for patient demographics. Compared to patients undergoing TKR at a very high-volume hospital, patients at high-volume (OR, 1.28 95% CI, [1.17, 1.41], medium-volume, (1.52, [1.39, 1.66]) and low-volume (2.05, [1.87, 2.26]) hospitals had increased odds of complication within 90 days of surgery (Figure 2 and Table 3). Full regression results are shown in Table 3 in the Supplemental Digital Content.
Figure 2:
Odds of 90-day readmission by hospital volume strata.
Footnote: Very high (429+) is the reference category.
Table 3.
Main and sensitivity analyses SSLR volume categories and odds ratios
| Analysis* | Low | Medium | High | |||
|---|---|---|---|---|---|---|
| Volume Category | Odds Ratio (95% CI) | Volume Category | Odds Ratio (95% CI) | Volume Category | Odds Ratio (95% CI) | |
| Main Analysis (Ref. 429+ TKR/year) | 1-31 | 2.05 (1.87, 2.26) | 32-127 | 1.52 (1.39, 1.66) | 128-428 | 1.28 (1.17, 1.41) |
| Sensitivity Analyses | ||||||
| Excluding POA**(Ref. 223+ TKR/year) | 1-40 | 1.71 (1.60, 1.82) | 41-90 | 1.44 (1.36, 1.53) | 91-222 | 1.221 (1.16, 1.29) |
| CMS specific§ (Ref. 364+ TKR/year) | 1-40 | 1.77 (1.53, 1.93) | 41-136 | 1.387 (1.28, 1.50) | 137-363 | 1.24 (1.14, 1.34) |
All regression analyses were adjusted for adjusted for age, race, sex, teaching status, hospital ownership, rural or urban status, and 31 Elixhauser comorbidities,
Refers to analysis conducted by excluding conditions POA when determining complications.
Refers to analysis conducted only on complications used in the CMS THA/TKA measure methodology.
When excluding conditions POA in determining presence of a complication, and when excluding complications not included in the CMS THR/TKR Complication Measure Methodology, SSLR yielded four volume categories (Table 3). These sensitivity analysis showed similar results to the main findings. Similar results were also observed when analysis accounted for correlated standard errors in the model. Full regression results are shown in Tables 4, 5, and 6 in the Supplemental Digital Content.
Discussion:
To determine nationally-derived, outcomes-based hospital volume thresholds for TKR, we used the SSLR method applied to the Medicare population undergoing TKR across hospitals in the United States. Using 90-day complication rates after TKR as our outcome, we established four outcomes-based TKR hospital volume thresholds, where higher volume was associated with better outcomes, even after adjusting for patient and hospital characteristics. Sensitivity analyses confirmed the robustness of our main results.
Our results confirmed prior volume-outcome relationships, demonstrating a significant decline in complication rates for each next highest stratum. Identified thresholds were similar to a priori thresholds at the lower end (slightly lower than the proposed Leapfrog criteria recommendation of 50 TKRs annually15) but differed significantly at the upper end (e.g., Katz et al. upper threshold (200) and Anis et al. threshold of 500).4,9 While these prior results may be close to what we found, they are prone to misclassifying hospitals into being low or high volume. This becomes important when these classifications serve as the basis for reimbursement, regionalization, or other policies. As such, our study provides an evidence-based means of classifying hospitals into high or low volume hospitals.
Although the thresholds established in this study are potentially relevant to all payors to help them vet providers, they are especially relevant to Medicare quality initiatives and reorganization. Medicare may use these thresholds to regionalize TKR care for enrollees to optimize their outcomes since similar Medicare regionalization policies for other procedures improved outcomes and reduced costs.16,17,18 Yet, it will be important to consider the implications of various cut points on TKR care. Regionalizing patients to the very high-volume hospitals would yield the lowest complication rates, but may significantly limit hospital choice, thus reducing access to care and potentially increasing patients’ travel and wait times. Moreover, due to wide geographic variation, regionalization of care policies may be region-specific and consider the costs and benefits associated with each cut point to optimize the region-specific gains from the regionalization of care.19
These outcomes-based volume thresholds may also have direct value for Medicare patients considering TKR. The hospital volume thresholds represent an additional metric that may enhance existing quality measures, such as CMS Hospital Compare, especially since prior studies have shown that the Hospital Compare website data may sometimes be misleading and could be enhanced.20 Exploring ways to present these data on the Hospital Compare’s website is needed to optimize their value for patients.
This study has several limitations. Since, only the Medicare population was included, complication rates may have been overestimated relative to the general TKR patient population.24 Case complexity was not available for study. Our thresholds were limited to 90-day post-operative complications, and did not consider other outcomes that are also important for TKR such as revision rates and functional outcomes. Though previous work found little difference in SSLR outcomes between 90 days and 2 years post-TKR, future work should re-examine these outcomes in greater detail at the national scale.5 The AUROC value of 0.58 was relatively low. Since Wilson et al. did not report their AUROC value, we cannot compare our findings to Wilson’s. However, we acknowledge that this AUROC value could suggest that hospital volume categories may not have a high accuracy for detecting complications after TKR. Finally, location-specific characteristics such as population and historical spending for TKA, which might affect the outcome of interest, were not included.
In conclusion, our study supports the use of SSLR as a promising method for future volume-outcome related research and provides evidence-based national-level hospital volume thresholds. These thresholds may be helpful to guide patients in choosing a hospital for their surgery, and payors and policymakers in making decisions about TKR care regionalization.
Supplementary Material
Table 1. List of all complication categories included in the study and the relevant ICD-9-CM and ICD-10-CM codes used to identify complications.
Table 2. Area under the receiver operating curve for the main analysis
Table 3. Adjusted odds ratios from multivariable logistic regression for the main analysis
Table 4. Adjusted odds ratios from sensitivity analysis excluding conditions present on admission.
Table 5. Adjusted odds ratios from sensitivity analysis using CMS specific complications.
Table 6. Adjusted odds ratios from sensitivity analysis using CMS specific complications and correlated standard errors.
Acknowledgments
This study was funded by a grant from the National Institute of Arthritis and Musculoskeletal and Skin Diseases (5R01AR078342-02) to the first author.
Footnotes
The authors have no conflicts of interest to declare.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Table 1. List of all complication categories included in the study and the relevant ICD-9-CM and ICD-10-CM codes used to identify complications.
Table 2. Area under the receiver operating curve for the main analysis
Table 3. Adjusted odds ratios from multivariable logistic regression for the main analysis
Table 4. Adjusted odds ratios from sensitivity analysis excluding conditions present on admission.
Table 5. Adjusted odds ratios from sensitivity analysis using CMS specific complications.
Table 6. Adjusted odds ratios from sensitivity analysis using CMS specific complications and correlated standard errors.