Care Fragmentation Predicts 90-Day Durable Ventricular Assist Device Outcomes

ABSTRACT

Objectives: To examine whether fragmentation of care is associated with worse in-hospital and 90-day outcomes following durable ventricular assist device (VAD) implant.

Study Design: Cohort study.

Methods: This study was conducted using Medicare claims linked to the Society of Thoracic Surgeons (STS) Interagency Registry for Mechanically Assisted Circulatory Support (Intermacs) among patients undergoing VAD implant between July 2009 and April 2017. Medicare data were used to measure fragmentation of the multidisciplinary care delivery network for the treating hospital, based on providers’ history of shared patients within the previous year. STS Intermacs data were used for risk adjustment and outcomes ascertainment. Hospitals were sorted into terciles based on the degree of network fragmentation, measured as the mean number of links separating providers in the network. Multivariable regression was used to associate network fragmentation with 90-day death or infection risk.

Results: The cohort included 5159 patients who underwent VAD implant, with 11.2% dying and 27.6% experiencing an infection within 90 days after implant. After adjustment, a 1-unit increase in network fragmentation was associated with an increase of 0.179 in the probability of in-hospital infection and an increase of 0.183 in the probability of 90-day infection (both P < .05). Similar results were observed in models of the numbers of in-hospital and 90-day infections. Network fragmentation was predictive of the probability of 90-day mortality, although this relationship was not significant after adjustment.

Conclusions: Care delivery network fragmentation is associated with higher in-hospital and 90-day infection rates following durable VAD implant. These networks may serve as novel targets for enhancing outcomes for patients undergoing VAD implant.

Am J Manag Care. 2022;28(12):e444-e451. https://doi.org/10.37765/ajmc.2022.89280

Takeaway Points

The structure of care delivery networks may serve as novel targets for improving outcomes, especially for high-risk patients.

• Fragmentation of care delivery poses considerable challenges for patients with advanced heart failure.
• We examined whether fragmentation of care is associated with worse in-hospital and 90-day outcomes following durable ventricular assist device (VAD) implant.
• Fragmentation in care delivery networks was associated with higher in-hospital and 90-day infection rates following durable VAD implant.

Durable ventricular assist devices (VADs) provide lifesaving benefit for patients with advanced heart failure refractory to guideline-directed medical care. However, patients undergoing VAD implant are at substantial risk of infections that significantly increase morbidity and affect survival.^1-4 Further, the risk of infection is particularly important in this patient population because it limits expansion of VAD therapy to the considerably larger patient population with less advanced heart failure, who might otherwise derive benefit.

Although few studies have examined the factors that may contribute to hospital-level differences in postimplant VAD infections, recent health care policy reforms have targeted, in part, fragmentation in care delivery within and across episodes and clinical settings.

Fragmentation of care delivery poses considerable challenges for patients with advanced heart failure given the frequent association with other complex comorbidities that benefit from integrated care delivery. Prior to admission for VAD implant, disease management and care optimization require coordination (eg, communication and information exchange) among providers to accomplish collaborative tasks, including patient selection, timing of implant, hemodynamic optimization, and nutritional assessment across multiple provider specialties. Administrative claims have previously been used to map care delivery networks for patients undergoing inpatient surgical procedures. As an example, within the setting of coronary artery bypass grafting (CABG), health systems whose providers work more closely together around episodes of care had lower rates of emergency department visits, readmissions, and mortality.⁵ Similar network analyses have not been applied to more complex surgical populations requiring more intensive care coordination and communication, nor have they leveraged clinically informed data sets for risk adjustment and outcomes ascertainment.

This study tests the hypothesis that within-hospital care delivery network fragmentation is positively associated with post–VAD implant 90-day infections and mortality. To address this hypothesis, fragmentation in each care delivery network was measured at the hospital-year level, using the mean number of links separating providers in the network, or “average path length,” an established structural measure from network science, and subsequently associated with 90-day post–VAD implant outcomes.

METHODS

This study involved the secondary analysis of 2 data sources: (1) Medicare claims (through data use agreement 2019-54083 between the University of Michigan and the Research Data Assistance Center) and (2) Society of Thoracic Surgeons (STS) Interagency Registry for Mechanically Assisted Circulatory Support (Intermacs) data (provided by its Data Coordinating Center at the University of Alabama to the University of Michigan through permission from the National Heart, Lung, and Blood Institute for the purposes of data set linkage). Informed consent for registrant participation in STS Intermacs was required until Protocol v4.0 (February 27, 2014). Details for hospital and patient linkages between these data sets have been previously reported.⁶

The study sample (eAppendix Figure 1 [eAppendix available at ajmc.com]) included 5159 patients undergoing primary durable VAD implant with an FDA-approved device between July 2009 and April 2017. Medicare suppression rules were enforced and represented in data tables with dashes.⁷ Patients with Medicare Advantage and those not enrolled in Medicare parts A or B for the duration of 180 days prior to index admission and 365 days after VAD implant were excluded. Only patients in the STS Intermacs database were included in the analysis.

Use of these data was approved by Michigan Medicine’s Institutional Review Board.

Measuring Care Delivery Network Fragmentation

The structure of care delivery networks associated with VAD-implanting hospitals was mapped using Medicare claims, which have been widely used in past research on physician networks.^5,8-10 Informed by prior published series,¹¹ all fee-for-service Medicare beneficiaries undergoing durable VAD implant were identified within each hospital and for each year. A unique network was constructed for each patient’s case, by first identifying all providers who billed for the focal patient within the episode of care, defined as a window beginning 180 days preceding hospital admission (for VAD implant) and extending until 180 days post discharge. This approach determines the full set of “nodes” that appear in that patient’s care delivery network. Then, the existing relationships among those providers, or the “edges,” are determined by examining all other common patients whom the providers treated (and billed for) in the 1 year prior to the focal patient’s admission for VAD implant. In other words, a relationship between any pair of providers would exist only if, in the last year, they had at least 1 other patient in common.

Networks were defined to include only the following providers (given their involvement in VAD care): anesthesiologists, VAD-implanting cardiac surgeons, non–VAD-implanting cardiac surgeons, cardiologists, critical care specialists, nurse practitioners, and physician assistants.

Fragmentation in care delivery networks was measured using the average path length.^12,13 A path is a series of steps (“links”) that must be traversed for 1 node in the network (eg, provider) to reach another node. For example, in eAppendix Figure 2A, there is 1 link between providers A and B, 2 links between providers A and C, and 3 links between providers A and D. The average path length is thus dependent on the connections between all pairs of nodes, with the average path length in eAppendix Figure 2B calculated as 1.33 and in eAppendix Figure 2C (containing an additional connection) as 1.17 links. Providers are only directly linked (ie, have a path distance of 1) if they have previously collaborated in the provision of care for the same shared patient; however, providers can be indirectly linked through the collaborators of their collaborators. As such, this measure is most well known as underpinning the “small world” and related “6 degrees of separation” phenomena.^13-15

In networks where the average number of links separating network members is longer (ie, where fragmentation is greater), information diffuses more slowly and less accurately, whereas in networks where the average number of links is shorter (ie, less fragmentation), information diffuses more quickly and more accurately.^13,16 VAD hospital-level measures of fragmentation were recomputed for each beneficiary to account for dynamic changes in network structures (eg, providers entering or leaving a network, new relationships being formed). Thus, 2 patients undergoing durable VAD implant at the same hospital, but even a few days apart, may have distinct values of fragmentation. eAppendix Figure 3 shows care delivery networks at 2 hospitals. Despite having nearly identical number of providers (84 for hospital A, 82 for hospital B), their fragmentation differs (hospital A fragmentation: 1.25; hospital B fragmentation: 1.67).

Clinical Outcomes

There were 2 primary outcomes. First, postoperative infections (incidence) and number of infections were assessed using the STS Intermacs registry’s definition for Infection Adverse Event (eAppendix Text 1). Rates of infections were estimated through 90 days following implant, as the risk of infection is greatest within this time frame.¹⁷ Second, postimplant mortality was assessed through 90 days following implant.

Patient Characteristics

Both STS Intermacs and Medicare claims data were used to describe patient and clinical characteristics. STS Intermacs data (eAppendix Text 1) were used to evaluate preoperative factors commonly used for risk adjustment.

Medicare claims were used to enumerate the number and type of providers involved in the care of VAD within 1 year prior to admission to receive the VAD implant. The American Hospital Association file was used to identify teaching hospitals and the number of intensive care unit beds per hospital, and the Dartmouth Atlas of Healthcare was used to identify population-based resource utilization measures.

Statistical Analysis

Kruskal-Wallis tests were performed for continuous variables; χ² tests were performed for categorical variables in Table 1 and Table 2. The P values shown in Table 2 are from global tests. Multivariable regression models were developed to evaluate whether fragmentation within VAD hospitals was associated with in-hospital and 90-day postimplant outcomes. To facilitate computation in models with many fixed effects (eg, surgeon, year, hospital), linear probability models were used for estimating the probability of mortality and infection. Models using a logit specification (eAppendix Table 1A and eAppendix Table 1B) yielded similar results. Poisson pseudo–maximum likelihood regression was used for estimating the number of infections. In all regressions, important patient (eg, socioeconomic factors, comorbidities), hospital, and network confounders were adjusted for, with implant year and hospital additionally included as fixed effects. Selection of patient-level confounders was informed by the most recent STS Intermacs annual report¹⁸ (the model predictors are relatively consistent over time).^17,19 Hospital-network level factors were measured based on shared VAD patients within the hospital between the admission date of the focal patient and the 1 year preceding the admission date. All models were estimated with robust SEs.

A dominance analysis was conducted to decompose (using the R²) the contribution of the 3 groups of predictors (patient, hospital, network) for each outcome.

Several secondary analyses were conducted to evaluate the robustness of the primary findings. First, to ensure that any findings based on hospital-level network properties were not driven by spurious relationships, network measures were recomputed by focusing only on ties among each beneficiary’s immediate care team. Second, more conservative supplemental specification was conducted to include fixed effects for each beneficiary’s VAD surgeon. Third, primary analyses were recomputed to restrict to hospitals performing at least 10 VAD procedures over the study period.

Statistical analyses were conducted using StataMP version 16.1 (StataCorp). All tests were 2-sided (α = 0.05). To facilitate interpretation, descriptive statistics for hospitals are presented according to terciles of care delivery network fragmentation. The main results and conclusions, however, are based on the regression models, in which care delivery network fragmentation is measured on a continuous scale.

RESULTS

Hospital Characteristics Associated With Care Delivery Network Fragmentation

The demographics of the 5159 patients (129 hospitals) receiving a durable VAD implant are presented in Table 1. The median (IQR) number of VAD implants performed at each hospital was 34 (15-56). For the care of each VAD patient, the provider network was composed of a median (IQR) of 87.2 (55.6-119.6) providers, with cardiologists (median [IQR], 50.1 [29.7-69.1]) being the most commonly involved. Hospitals had a median (IQR) of 22 (12-31) intensive care unit beds, and 89% of the sample were academic hospitals.

Relative to low-fragmentation hospitals (eAppendix Table 2), hospitals with high care delivery network fragmentation had greater median (IQR) VAD volume (66 [47-85] vs 11 [6-16]; P < .001), more involved providers at the median (128.4 [103.9-186.0] vs 41.9 [31.1-56.9]; P < .001), and more intensive care unit beds at the median (27 [16-38] vs 16 [10-22]; P = .001).

Patient Characteristics Associated With Care Delivery Network Fragmentation

With few exceptions, patient characteristics were similar across terciles of fragmentation (Table 2). White patients represented the majority of the sample (73.7%) and the second largest group was Black patients (20.6%). Centers in the low-fragmentation tercile had the highest proportion of White patients (80.3%) relative to other races, whereas centers in the medium-fragmentation tercile had the lowest proportion of White patients (69.2%). Relative to patients operated on at low-fragmentation hospitals, patients at hospitals with high care delivery network fragmentation were more likely to have a history of cardiac surgery (44.8% vs 36.8%; P < .001) and to undergo concomitant surgery (43.9% vs 33.1%; P < .001). Patients at high-fragmentation hospitals were also more likely than those at low-fragmentation hospitals to have been transferred from an acute care hospital (26.6% vs 16.9%; P < .001).

Outcomes (overall and stratified by terciles of fragmentation) are displayed in Table 3 and eAppendix Table 3. In-hospital mortality varied significantly by tercile (event frequency is suppressed according to Medicare rules). In-hospital infection rates occurred among 19.2% of patients (mean [SD] infections, 1.6 [1.1]), although rates were higher at high- vs low-fragmentation hospitals (20.3% vs 16.4%; P = .051). Overall, 11.2% of patients died within 90 days of implant, with mortality rates similar across terciles (11.0% vs 11.5%; P = .818). Infections within 90 days of implant occurred among 27.6% of patients (mean [SD] infections, 1.6 [1.1]), with the infection rates marginally higher at high-fragmentation hospitals (28.9% vs 25.2%; P = .051).

Care Delivery Network Stability Over Time

Across terciles, there was no statistically significant trend in the structure of the care delivery network over time (P = .346). However, statistically significant time trends within terciles were observed, specifically for the medium- and high-fragmentation groups (coefficient = 0.013; P < .001; and coefficient = 0.003; P = .002, respectively; both coefficients indicate the estimated change in fragmentation/year). Thus, among hospitals that already have higher care delivery network fragmentation, the distance between providers in the network is continuing to increase over time (Figure 1).

Multivariable Results

Results of crude and multivariable modeling for both in-hospital and 90-day outcomes are displayed in eAppendix Table 4A and eAppendix Table 4B, respectively. With regard to in-hospital outcomes (Figure 2A), fragmentation was not significantly associated with mortality in crude (model 1: coefficient = –0.009; P = .364) or risk-adjusted (model 3: coefficient = –0.010; P = .387) analyses. However, fragmentation was significantly and positively associated with (1) the risk of developing any infection (model 6: coefficient = 0.179; P = .002)—every 1-unit (ie, 1 “link”) increase in care delivery network fragmentation is associated with an increase of 0.179 in the probability of infection—and (2) the number of infections (model 9: coefficient = 1.113; P = .006)—every 1-unit increase in care delivery network fragmentation is associated with an increase in the number of infections by a factor of exp(1.11) = 3.04. These in-hospital findings regarding infections were qualitatively similar for 90-day outcomes (Figure 2B). Although care delivery network fragmentation was significantly associated with the risk of 90-day mortality (model 10: coefficient = 0.114; P = .003), this relationship was not robust to the inclusion of controls. Across outcomes, network properties are more predictive than hospital characteristics (volume) (eAppendix Figure 4). The predictive power of network properties was comparable in magnitude with those of patient demographics and clinical indicators. The findings were qualitatively similar when decomposing the adjusted R².

The results of additional analyses support these primary results. Specifically, the findings are similar when evaluating relationships only among the immediate care team of the focal beneficiary (eAppendix Table 5), when excluding low-volume hospitals (eAppendix Table 6), and when including surgeon fixed effects (eAppendix Table 7).

DISCUSSION

Analyses of care delivery networks using administrative claims provide a unique lens into how care is delivered across providers and disparate clinical settings.^5,9,10,20-22 This study is among the largest evaluation of care delivery networks (1) involving the merging of clinical registry data with administrative claims to ascertain clinically relevant outcomes and (2) among patients with advanced heart failure, a chronic disease that requires intensive provider and institutional health care services. In this current analysis, hospitals with higher care delivery network fragmentation were more often academic institutions that conducted more VAD procedures and had worse associated risk-adjusted clinical outcomes (eg, higher infection rates).

This study is also among the first to report a significant association between intrahospital variation in care delivery networks and postimplant durable VAD outcomes, specifically postimplant infections, a major driver of post-VAD morbidity. Previously, Hollingsworth and colleagues used network analysis to assess the role of physician teamwork (eg, clustering coefficient) and outcomes⁵ among 251,630 Medicare beneficiaries receiving CABG surgery.

Health systems whose physicians had more collaborative experience together achieved more favorable 60-day outcomes. The present study advances this literature by leveraging STS Intermacs clinical data for risk adjustment and outcomes ascertainment. Hospitals with lower network fragmentation had better risk-adjusted short-term and mid-term outcomes with respect to post–VAD implant infections.

In numerous contexts, including cardiovascular surgery, greater network fragmentation has been found to negatively affect outcomes and other forms of performance by limiting the ability of teams to effectively coordinate. Fragmented networks are associated with slower transfer of knowledge and information and with less collaborative experience among team members. Consequently, greater network fragmentation among providers is likely to have a negative impact on outcomes in contexts such as VAD care, where patient status is complex and effective treatment requires care coordination across multiple settings and specialties.

These findings have implications for reducing VAD-associated morbidity. Provider collaboration within 1 year prior to admission is a significant predictor of 90-day postimplant outcomes. Ongoing payment reform efforts may provide a pathway for evaluating the effectiveness of enhancing novel, informal care delivery networks. Funk and colleagues, using Medicare claims, estimated that enhancing informal integration among Medicare CABG episodes may result in $130.5 million in savings attributed to reduced readmissions.²⁰ Future work should also evaluate the role of benchmarking low- vs high-performing institutions as defined in part by their care delivery network properties.

Our results complement findings on the patient-provider relationship, which has been shown in prior work to affect outcomes, including mortality among patients with heart failure. Future research may benefit from jointly considering both patient-provider and provider-provider relationships, including the possibility of interactive effects.

Limitations

Several limitations exist in the present study. First, although it did not include all durable VADs implanted in the United States, this study includes nearly all FDA-approved devices implanted for commercial use, and Medicare beneficiaries represent on average 47.6% of a hospital’s total STS Intermacs implants.⁶ Second, although the network measures used do not capture all the providers involved in caring for patients undergoing VAD implant nor all methods of communication, this study leverages published approaches for inferring provider (physician and allied health professional) relationships.²³ Third, although confounding may persist, commonly cited patient-level factors and hospital variation were accounted for through multivariable modeling. Fourth, although it captured all surgeons implanting FDA-approved durable VADs, this study may be limited in statistical power to advance the evaluation of VAD surgeon centrality. Fifth, although these data reflect experiences through July 2017, this cohort represents the largest and most contemporaneous experience evaluating care delivery networks associated with VAD implant. Sixth, this study reports significant and robust associations between fragmentation and infection, but not fragmentation and mortality. The inability to detect a relationship with mortality suggests that mortality in the VAD context is driven more by patient characteristics or technical factors than by the quality of collaboration among team members. Alternatively, the lack of an association may also be due to insufficient statistical power (ie, small sample size) with respect to the number of deaths relative to the number of infections that occur following VAD implantation. Although the present study is unable to distinguish definitively among these possible explanations, they serve as a useful direction for subsequent research.

CONCLUSIONS

This study documents important variations in intrahospital provider care fragmentation for patients undergoing durable VAD implant. Patients receiving care at hospitals with less care delivery network fragmentation have lower adjusted risks of both in-hospital and 90-day postimplant infection. Given these findings, future work may consider interventions targeting preimplant provider care fragmentation as a novel approach for enhancing VAD outcomes. 

Author Affiliations: Department of Strategic Management and Entrepreneurship, Carlson School of Management, University of Minnesota (RJF), Minneapolis, MN; Department of Cardiac Surgery, Michigan Medicine, University of Michigan (FDP, HH, LC, DSL), Ann Arbor, MI; Department of Biostatistics, School of Public Health, University of Michigan (MZ, GY), Ann Arbor, MI; Now with Renmin University of China (GY), Beijing, China; Division of Infectious Diseases, Department of Medicine, Michigan Medicine (PNM), Ann Arbor, MI; Mixed Methods Program, Department of Family Medicine, University of Michigan (PPC), Ann Arbor, MI; Strategy, Ethics, and Entrepreneurship, Darden School of Business, University of Virginia (KDK), Charlottesville, VA.

Source of Funding: This project was supported by grant number R01HS026003 from the Agency for Healthcare Research and Quality. The content is solely the responsibility of the authors and does not necessarily represent the official views of the Agency for Healthcare Research and Quality. Support for The Michigan Society of Thoracic and Cardiovascular Surgeons Quality Collaborative (MSTCVS-QC) is provided by Blue Cross and Blue Shield of Michigan and Blue Care Network (BCBSM) as part of the BCBSM Value Partnerships program. Although BCBSM and MSTCVS-QC work collaboratively, the opinions, beliefs, and viewpoints expressed by the authors do not necessarily reflect the opinions, beliefs, and viewpoints of BCBSM or any of its employees.

Data for this study were provided, in part, by Intermacs, previously funded, in part, by the National Heart, Lung, and Blood Institute (NHLBI) of the National Institutes of Health under contract No. HHSN268201100025C. This study was undertaken prior to the acquisition of Intermacs by the Society of Thoracic Surgeons.

Author Disclosures: Dr Pagani is a member of the scientific advisory board of FineHeart, Inc; a member of the Data Safety Monitoring Board for Carmat, Inc; a member of the Data Safety Monitoring Board for the NHLBI PumpKIN clinical trial; and chair of the Society of Thoracic Surgeons Intermacs Task Force. Outside of this work, Dr Likosky receives funding from the Agency for Healthcare Research and Quality (for other grants) and the National Institutes of Health, receives partial salary support from BCBSM, and is a consultant to the American Society of ExtraCorporeal Technology. The remaining authors report no relationship or financial interest with any entity that would pose a conflict of interest with the subject matter of this article.

Authorship Information: Concept and design (RJF, FDP, PNM, PPC, KDK, DSL); acquisition of data (FDP, DSL); analysis and interpretation of data (RJF, FDP, HH, MZ, GY, PNM, KDK, DSL); drafting of the manuscript (RJF, PNM, PPC, LC, KDK, DSL); critical revision of the manuscript for important intellectual content (RJF, FDP, MZ, GY, PNM, PPC, LC, DSL); statistical analysis (RJF, HH, MZ, GY); provision of patients or study materials (FDP, DSL); obtaining funding (FDP, DSL); administrative, technical, or logistic support (FDP, HH, LC, DSL); and supervision (DSL).

Address Correspondence to: Russell J. Funk, PhD, Carlson School of Management, University of Minnesota, 321 19th Ave S, #3-354, Minneapolis, MN 55455. Email: rfunk@umn.edu.

REFERENCES

1. Milano CA, Rogers JG, Tatooles AJ, et al; ENDURANCE Investigators. HVAD: the ENDURANCE supplemental trial. JACC Heart Fail. 2018;6(9):792-802. doi:10.1016/j.jchf.2018.05.012

2. Rogers JG, Pagani FD, Tatooles AJ, et al. Intrapericardial left ventricular assist device for advanced heart failure. N Engl J Med. 2017;376(5):451-460. doi:10.1056/NEJMoa1602954

3. Mehra MR, Uriel N, Naka Y, et al; MOMENTUM 3 Investigators. A fully magnetically levitated left ventricular assist device — final report. N Engl J Med. 2019;380(17):1618-1627. doi:10.1056/NEJMoa1900486

4. Patel CB, Blue L, Cagliostro B, et al. Left ventricular assist systems and infection-related outcomes: a comprehensive analysis of the MOMENTUM 3 trial. J Heart Lung Transplant. 2020;39(8):774-781. doi:10.1016/j.healun.2020.03.002

5. Hollingsworth JM, Funk RJ, Garrison SA, et al. Association between physician teamwork and health system outcomes after coronary artery bypass grafting. Circ Cardiovasc Qual Outcomes. 2016;9(6):641-648. doi:10.1161/CIRCOUTCOMES.116.002714

6. Liang Q, Ward S, Pagani FD, et al. Linkage of Medicare records to the Interagency Registry of Mechanically Assisted Circulatory Support. Ann Thorac Surgery. 2018;105(5):1397-1402. doi:10.1016/j.athoracsur.2017.11.044

7. CMS cell size suppression policy. Research Data Assistance Center. May 8, 2017. Accessed November 10, 2022. https://www.resdac.org/articles/cms-cell-size-suppression-policy

8. Hollingsworth JM, Funk RJ, Garrison SA, et al. Differences between physician social networks for cardiac surgery serving communities with high versus low proportions of black residents. Med Care. 2015;53(2):160-167. doi:10.1097/MLR.0000000000000291

9. Kim D, Funk RJ, Yan P, Nallamothu BK, Zaheer A, Hollingsworth JM. Informal clinical integration in Medicare accountable care organizations and mortality following coronary artery bypass graft surgery. Med Care. 2019;57(3):194-201. doi:10.1097/MLR.0000000000001052

10. Everson J, Funk RJ, Kaufman SR, et al. Repeated, close physician coronary artery bypass grafting teams associated with greater teamwork. Health Serv Res. 2018;53(2):1025-1041. doi:10.1111/1475-6773.12703

11. Onnela JP, O’Malley AJ, Keating NL, Landon BE. Comparison of physician networks constructed from thresholded ties versus shared clinical episodes. Appl Netw Sci. 2018;3(1):28. doi:10.1007/s41109-018-0084-1

12. Newman M. Networks. 2nd ed. Oxford University Press; 2018.

13. Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature. 1998;393(6684):440-442. doi:10.1038/30918

14. Dodds PS, Muhamad R, Watts DJ. An experimental study of search in global social networks. Science. 2003;301(5634):827-829. doi:10.1126/science.1081058

15. Travers J, Milgram S. An experimental study of the small world problem. In: Leinhardt S, ed. Social Networks: A Developing Paradigm. Elsevier; 1977:179-197.

16. Lazer D, Friedman A. The network structure of exploration and exploitation. Adm Sci Q. 2007;52(4):667-694. doi:10.2189/asqu.52.4.667

17. Kirklin JK, Pagani FD, Kormos RL, et al. Eighth annual INTERMACS report: special focus on framing the impact of adverse events. J Heart Lung Transplant. 2017;36(10):1080-1086. doi:10.1016/j.healun.2017.07.005

18. Kormos RL, Cowger J, Pagani FD, et al. The Society of Thoracic Surgeons Intermacs database annual report: evolving indications, outcomes, and scientific partnerships. J Heart Lung Transplant. 2019;38(2):114-126. doi:10.1016/j.healun.2018.11.013

19. Kirklin JK, Naftel DC, Pagani FD, et al. Seventh INTERMACS annual report: 15,000 patients and counting. J Heart Lung Transplant. 2015;34(12):1495-1504. doi:10.1016/j.healun.2015.10.003

20. Funk RJ, Owen-Smith J, Kaufman SA, Nallamothu BK, Hollingsworth JM. Association of informal clinical integration of physicians with cardiac surgery payments. JAMA Surg. 2018;153(5):446-453. doi:10.1001/jamasurg.2017.5150

21. Funk RJ, Owen-Smith J, Landon BE, Birkmeyer JD, Hollingsworth JM. Identifying natural alignments between ambulatory surgery centers and local health systems: building broader communities of surgical care. Med Care. 2017;55(2):e9-e15. doi:10.1097/MLR.0000000000000118

22. Hollingsworth JM, Funk RJ, Owen-Smith J, Landon BE, Hollenbeck BK, Birkmeyer JD. Assessing the reach of health reform to outpatient surgery with social network analysis. Ann Surg. 2015;261(3):468-472. doi:10.1097/SLA.0000000000000880

23. Barnett ML, Christakis NA, O’Malley J, Onnela JP, Keating NL, Landon BE. Physician patient-sharing networks and the cost and intensity of care in US hospitals. Med Care. 2012;50(2):152-160. doi:10.1097/MLR.0b013e31822dcef7