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. 2024 Dec 27;18(1):e010778. doi: 10.1161/CIRCOUTCOMES.123.010778

Referral Networks, Racial Inequity, and Hospital Quality for Open Heart Surgery

C Ben Gibson 1, Cheryl L Damberg 1, Jose J Escarce 2, Shiyuan Zhang 1, Megan S Schuler 1, Luke J Matthews 1, Ioana Popescu 1,2,✉
PMCID: PMC11745697  NIHMSID: NIHMS2035501  PMID: 39727033

Abstract

BACKGROUND:

Differences in the quality of hospitals where Black and White patients receive coronary artery bypass grafting (CABG) surgery have been documented. We examined the contributions of physician networks to the gap.

METHODS:

This was a cross-sectional study of all Medicare fee-for-service Black and White patients undergoing elective CABG during 2017 to 2019; the primary care physicians and cardiologists treating them for 12 months before surgery (the patients’ physician network); and CABG-performing hospitals within 100 miles of each patient. We measured the strength of ties between treating physicians and hospitals as the number of shared prior CABG patients (24 months before surgery). Conditional logit models assessed the relationship between race, prior physician-hospital ties, and receiving CABG at hospitals with minimum versus the median-above-minimum mortality difference, while accounting for home-to-hospital distances.

RESULTS:

The study included 76 376 patients; 5.1% were Blackpatients. Black and White patients were admitted to similar mortality hospitals (3.1% versus 3.1%; P=0.07), but Black patients lived closer to lower-mortality hospitals than White patients (mean hospital mortality within median travel distance, 2.5% versus 2.7%; P<0.001). Black patients were treated less often at the lowest-mortality hospitals overall and within the median travel distance (10.5% versus 13.9% and 37.4% versus 45.1%; P<0.001 for both). In conditional logit models, the Black-White risk ratio of using hospitals with median versus lowest mortality was 1.02 ([95% CI, 0.98–1.06]; P=0.18) in models including only race and hospital mortality; 1.07 ([95% CI, 1.01–1.13]; P<0.001) in models adding home-to-hospital distances; and 1.06 ([95% CI, 0.96–1.16]; P=0.11) in models also accounting for physician-hospital ties.

CONCLUSIONS:

Despite the improvement of previously described disparities in the quality of hospitals treating Black and White patients, Black patients remain less likely to undergo CABG at their lowest available mortality hospitals, possibly due to suboptimal physician referrals.

Keywords: aged, cardiologists, hospitals, Medicare, networks, referral

WHAT IS KNOWN

  • Black-White disparities in the treatment and outcomes of elective coronary artery bypass grafting surgery have been documented.

  • These disparities are due in part to differences in the quality of hospitals where Black and White patients receive surgery.

WHAT THE STUDY ADDS

  • Different from prior research, this national study of Medicare fee-for-service coronary artery bypass grafting surgery recipients found that, on average, Black and White patients were treated at hospitals with similar 30-day mortality.

  • Black patients had lower-mortality hospitals closer to them, but physician referral networks before surgery contributed to White patients receiving coronary artery bypass at better hospitals.

  • While the apparent closing of the Black-White gap in high-quality hospital use for coronary artery bypass is encouraging, Black patients remain less likely to receive treatment at their best available hospitals possibly due to suboptimal physician-hospital referrals.

Prior research has shown that Black patients who undergo elective coronary artery bypass grafting (CABG) surgery have higher mortality, more frequent complications, and higher readmission rates compared with White patients.1–4 These outcome differences may be due in part to differences in the quality of hospitals where Black and White patients receive CABG.3,5,6 However, the relative contributions of patient, health care system, and local contextual factors to these differences are not well understood. In particular, physician-hospital referral networks may play an important role and may be more amenable to intervention within the health care system.

Studies have shown that Black and White patients are treated by primary care physicians (PCPs) with different access to hospitals and specialty services7,8 In turn, differences in PCPs may contribute to differences in the quality of cardiac surgeons for Black and White patients undergoing CABG.9 Recent work using social network analysis has shown that cardiac care specialists in hospital areas with large minoritized populations are more isolated in their networks, with potential negative consequences for care coordination and quality.10 Other social network analysis work has quantified the segregation of cardiac care networks within health care markets11 and across CABG provider teams within the same hospital, where it was associated with higher Black-White mortality gaps.12 Altogether, this body of evidence suggests that Black and White patients use different physician referral networks for CABG, but how much these networks contribute to differences in the quality of hospitals where patients undergo surgery remains unclear.

The current study sought to assess the specific contributions of physician referral networks to disparities in the quality of hospitals, where Black and White fee-for-service aged Medicare patients undergo elective CABG (ie, excluding urgent procedures for which physician referrals may have played a lesser role). The study framework was informed by hospital choice models,13,14 which posit that patients and their physicians, given specific needs and preferences, choose particular hospitals over reasonably available alternatives based on geographic availability and a host of hospital-level attributes. For the current study, we used the Medicare-published 30-day CABG mortality measure as the key hospital attribute, because it is a highly significant outcome available to both physicians and patients. The study further builds on the existing hospital choice framework by investigating the specific contributions of physician networks through their preexisting relationships with CABG-performing hospitals. We conceptualized physician networks as the totality of PCPs and cardiologists treating study patients for 12 months before CABG surgery. We excluded cardiothoracic surgeons as they are hospital-based, and surgeon and hospital choices are tightly interconnected for this high-risk complex procedure.15

Methods

Data Sharing Statement

This study was approved by the Institutional Review Board. Due to the retrospective nature of this study, the requirement for informed consent was waived. The sponsors of this study were not involved in data analysis and article preparation. Because of a strict Data Use Agreement with the Centers for Medicare and Medicaid Services (CMS), requests to access the dataset from qualified researchers trained in human subject confidentiality protocols may be sent to the CMS.

Data Sources and Study Cohort

We used Medicare enrollment and inpatient files to identify all Black and White fee-for-service Medicare patients undergoing isolated CABG surgery during 2017 to 2019 (ie, the index patients) and the hospitals where they were treated. We excluded patients potentially undergoing urgent CABG (eg, due to myocardial infarction or after failed percutaneous coronary intervention) and patients undergoing CABG in association with other procedures, such as valve replacement or repair, due to likely different hospital referral patterns driven by the underlying procedure complexity. We also excluded patients younger than 66 years or without continuous Medicare enrollment during the prior 12 months, to ensure data completeness.

We used the Medicare Carrier and Outpatient files to identify all PCPs and cardiologists who submitted claims for services provided to study patients during the 12 months before CABG surgery. We then used Medicare inpatient files to identify other CABG patients for whom these physicians also submitted claims during the 24 months before the index patients’ surgery, and the hospitals, where the surgery was performed. We used these data to map physicians’ prior hospital ties, which, in turn, served to operationalize physician-hospital relationships as a factor contributing to patients’ hospital choices.

We obtained risk-standardized 30-day hospital-level CABG mortality (the study’s key hospital attribute) and hospital location coordinates (to assess geographic availability) from the 2017 to 2019 CMS Hospital Compare files.

Ascertaining Physician-Hospital Networks for Study Patients and Measuring the Strength of Physician-Hospital Ties

For each study patient, we defined a physician-hospital network as all PCPs and cardiologists providing care during the 12 months before CABG surgery and all CABG-performing hospitals reasonably available to the patient. Hospitals reasonably available were defined as all hospitals within a 100-mile radius of the patients’ residential zip code. We then ascertained preexisting ties between each physician and CABG-performing hospitals in a patient’s physician-hospital network via shared prior patients with CABG. Specifically, for each patient, the strength of preexisting physician-hospital ties was determined by the number of CABG patients shared between the full network of treating physicians and each network hospital over the 24 months before the study patient’s CABG hospitalization. Figure 1 is a visual representation of the physician-hospital network ties mapping process.

Figure 1.

Figure 1.

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Algorithm to identify primary care physician (PCP) and cardiologist physician networks before coronary artery bypass grafting (CABG) surgery and assess the strength of their ties to CABG-performing hospitals: an example. In the depicted scenario, CABG-performing hospitals A to E are all available within 100 miles of index patient 5’s zip code of residence. Patient 5’s treating physician is ascertained based on claims for services provided to the patient during the 12 months before hospitalization for CABG surgery. Prior patients 1 to 4 are other patients with CABG for whom this physician also submitted claims during the 24 months before patient 5’s surgery. These patients had CABG at hospitals A and C. The strength of the physician’s relationship with patient 5’s hospitals is then given by the number of patients previously shared by the physician with each hospital. Shared patients are then summed across all physicians in patient 5’s network (ie, all PCPs and cardiologists providing care to patient 5 during the 12 months before surgery) for each hospital available to patient 5.

Key Variables

Beyond prior physician-hospital ties, key study variables included patient race, hospital mortality, and home-to-hospital distance. We defined race as non-Hispanic Black or White based on the Research Triangle Institute variable, which is available in the Medicare enrollment file, has good specificity for the 2 race categories, and is currently used by CMS in health care disparities reporting.16 We used the CMS publicly reported 30-day risk-standardized mortality following CABG as a measure of hospital quality. We measured the straight-line (Euclidian) distance between the centroids of patients’ zip code of residence and hospital longitude and latitude as a proxy for home-to-hospital distance. While straight-line distances may underestimate travel (eg, in large metro areas), they are well correlated with actual travel times.17,18

Additional variables included age, sex, and an indicator for Medicaid dual eligibility (as a proxy for low-income) obtained from the enrollment files, and a comorbidity score representing the weighted sum of comorbidities recorded during patients’ hospitalization, ascertained from ICD-10 secondary diagnostic codes and calculated following published methods.19,20 Because variation in hospital use may be associated with sociodemographic and clinical characteristics,14,21,22 we used these variables to conduct subanalyses of the relationship between race and the quality of the hospitals where they received surgery.

Analytical Approach

Descriptive analyses included comparisons of Black and White patient with CABG characteristics, the characteristics of admitting hospitals and those available to the patients, and the characteristics of the physician networks treating them. We used the t test, Kruskal-Wallis nonparametric test, and χ2 test, as appropriate for each comparison.

To examine the relationship between patient race, hospital mortality, and preexisting physician-hospital network ties, we used a conditional logit regression (McFadden) model.23 In this model, the probability that a patient uses a particular hospital is a function of the characteristics of all hospitals reasonably available to that patient (ie, a patient’s hospital choice set). We explicitly accounted for the characteristics of the admitting hospital (eg, mortality) as well as those of hospitals geographically available but not used. Patient race was interacted with hospital characteristics to assess whether the effects of these characteristics on the likelihood of using a particular hospital differed by race.

We modeled the probability that a patient uses a particular hospital as a function of hospital mortality, home-to-hospital distances for all CABG-performing hospitals within 100 miles of the patients’ zip code of residence, and the strength of preexisting physician-hospital network ties. We specified the hospital mortality variable as the difference between the mortality of each hospital in a patient’s choice set and the lowest available hospital mortality in that set. To control for distance decay effects, we used a binary indicator variable for the closest hospital and a set of indicator variables for incremental distance categories (ie, within 2 miles of the closest hospital, 2 to 5, 5 to 10, 10 to 20, 20 to 30, 30 to 40, 40 to 50, and >50 miles from the closest hospital). Due to its skewed distribution, the strength of ties between patients’ physician networks and hospitals was modeled as a log count.

Models were estimated for the entire cohort and for high-risk and vulnerable subgroups, including aged >75 years, female sex, Medicaid dual eligibility, and having a comorbidity score in the upper tercile of the cohort distribution. Main analyses measured hospital ties for the full referral path (including PCPs and cardiologists). We also conducted sensitivity analyses using cardiologist-only hospital ties, as cardiologists represent the linchpin of the CABG referral path.

Predicted Probability of Receiving Care at Hospitals With Increasing Mortality for Black and White Medicare Patients Undergoing CABG

We used the conditional logit model coefficients to estimate the probability of using hospitals with increasing mortality for Black and White patients and to calculate the Black-White risk ratio of using hospitals with median versus lowest mortality available in each patient’s hospital choice set. We calculated these probabilities based on (1) the mortality of available hospitals, (2) further adjusting for home-to-hospital distances, and (3) further adjusting for the strength of ties between physician networks and hospitals.

All analyses were performed using base R and the survival, fields, and raster packages.

Results

Descriptive Data

The study sample included 76 376 Medicare patients with CABG; 5.1% were Black. Black patients were younger (72.1 versus 73.9 years), more often female (42.3% versus 24.4%), and dually Medicare-Medicaid eligible (25.4% versus 6.6%), and they had higher baseline comorbidity scores (10.5 versus 8.84). Substantially more Black patients lived in the South (66.0% versus 46.3%) and fewer in the West (4.8% versus 12.4%) compared with White patients.

Overall, the 30-day CABG-specific mortality for study hospitals ranged from 1.2% to 8.5%. Table 1 presents the characteristics of hospitals available to and used by Black and White Medicare patients with CABG. The median distance from patients’ homes to admitting hospitals (median travel distance) was 15.0 miles for the study sample and significantly lower for Black versus White patients (9.8 miles versus 15.3 miles for Black versus White patients). Black and White patients underwent CABG surgery at hospitals with similar mortality (mean, 3.1% versus 3.1%; P=0.07). However, the lowest available hospital mortality was somewhat lower for Black versus White patients, both within the entire hospital choice set (mean, 1.9% versus 2.0%; P<0.001) and within the median distance to admitting hospitals (mean, 2.5% versus 2.7%; P<0.001). Black patients also lived closer to the closest CABG-performing hospital (median distance 5.6 versus 10.0 miles; P<0.001) and the lowest-mortality hospital within their choice set (median distance, 53.5 versus 56.4 miles; P<0.001). The better geographic availability of lower-mortality hospitals is also illustrated in Figure S1, which shows the distribution of the mean (1.a) and lowest available (1.b) mortality for Black and White patients’ hospital choice sets.

Table 1.

Characteristics of Hospitals Available To and Used by Black and White Medicare Patients Undergoing CABG Surgery During 2017–2019

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Despite better geographic proximity, Black patients were treated less often at the lowest-mortality hospitals both within the choice set (10.5% versus 13.9%; P<0.001) and within median travel distance (37.4% versus 45.1%; P<0.001). Finally, Black patients also had higher-mortality hospitals in the choice set and within median travel distance (mean 5.2 versus 5.0 and 3.8 versus 3.6, respectively; P<0.001 for both), but were treated at these highest mortality hospitals less often than White patients (6.2% versus 7.7% within the choice set and 33.0% versus 39.8% within median distance; P<0.001 for both).

Table 2 shows the characteristics of both full (PCP and cardiology) and cardiology-only physician-hospital networks treating Black and White patients during the 12 months before CABG surgery. Full networks treating Black patients had slightly lower percentages of cardiologists (50.4% versus 51.1%; P=0.007) but similar 5-year CABG volumes (120 versus 120; P=0.89) compared with networks treating White patients. Median numbers of prior unique hospital relationships (4 versus 4) were also similar, although the distribution of these unique relationships differed for full physician networks of Black versus White patients at the first (Q1) and third (Q3) quartiles (2 versus 3 for Q1 and 5 versus 6 for Q3; P<0.001). Finally, cardiologist-only networks for Black patients had somewhat lower prior CABG volumes than corresponding networks for White patients (79 versus 88; P<0.001), while the distributions of unique hospital ties for these networks were similar.

Table 2.

Characteristics of PCP and Cardiologist Networks Treating Black and White Fee-for-Service Medicare Patients for the 12 Months Before Undergoing CABG Surgery

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Regression Results

Results for the conditional logit model estimations using the full (PCP and cardiologist) physician-hospital networks are presented in Table 3. These results show that, as expected, both Black and White Medicare patients were more likely to undergo surgery at the closest CABG-performing hospital, but this effect was significantly stronger for Black patients. The likelihood of being treated at a particular hospital decreased with increasing home-to-hospital distance and hospital mortality; effects were similar for Black and White patients.

Table 3.

The Effects of Distance, Hospital Mortality, and Full (Primary Care and Cardiologist) Physician-Hospital Network Ties on Racial Differences in Hospital Use for CABG Surgery: Conditional Logit Model Coefficients, Standard Errors, and Statistical Significance

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The preexisting strength of physician-hospital network ties was positively and strongly associated with hospital use. However, physician-hospital ties had relatively weaker effects on admitting hospitals for Black versus White patients (P=0.02), meaning that Black patients were relatively less likely to receive surgery at particular hospitals based on physicians’ prior hospital ties than White patients were.

Results of models employing cardiologist-only hospital network ties (Table S1) and high-risk group subanalyses (Table S2) showed a similar direction of findings, although in some cases they did not reach statistical significance due to small subsample size.

Predicted Probabilities and Black-White Risk Ratios of Receiving Care at Hospitals With Increasing Mortality

Figure 2 illustrates the change in predicted probabilities of being treated at particular hospitals for Black and White patients with CABG, given each patient’s hospital choice set and increasing hospital mortality. Figure 2A used coefficients from models based solely on the mortality of hospitals in each patient’s choice set, shows that the probability of being treated at a particular hospital decreased as hospital mortality increased for both Black and White patients, and the Black-White difference was not significant. Figure 2B, based on models that also accounted for distances between patients’ residential zip codes and hospitals in the choice set, shows that White patients were significantly less likely than Black patients to receive care at a particular hospital as hospital mortality increased. Because Figure 2B already accounts for differences in geographic access, it suggests that nongeographic factors contribute to White patients receiving care at lower-mortality hospitals. Figure 2C, based on models that further accounted for the effects of physician-hospital networks, shows that the probability of receiving care at hospitals with higher-than the best available mortality increased relative to Figure 2B for both Black and White patients, while the difference in probabilities became nonsignificant (possibly due to less precise estimates for Black probabilities related to the relatively smaller Black sample size or its higher heterogeneity). Taken together, Figure 2B and 2C suggest that physician network effects contributed to treatment at lower-mortality hospitals for both Black and White patients, but these effects were more pronounced among White patients.

Figure 2.

Figure 2.

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Predicted probabilities of receiving care at hospitals with increasing mortality for Black and White Medicare patients undergoing coronary artery bypass grafting (CABG) in 2017 to 2019. A, probabilities are based on available hospital mortality. B, probabilities are based on hospital mortality and home-to-hospital distances. C, probabilities are based on hospital mortality, distances and physician network hospital relationships.

To further illustrate the differences in the mortality of hospitals, where Black and White patients received care, we used the model coefficients to also calculate the Black-White risk ratio of being treated at the hospital with the median above minimum mortality difference versus the minimum mortality hospital within the choice set. These risk ratios were 1.02 ([95% CI, 0.8–1.06]; P=0.18) in models only accounting for the mortality of available hospitals, 1.07 ([95% CI, 1.01–1.13]; P<0.001) in models also accounting for distance to available hospitals, and 1.06 ([95% CI, 0.96–1.16]; P=0.11) in models that further accounted for the strength of physician-hospital ties.

Discussion

In this contemporary cohort of Medicare patients with CABG, we found that Black and White patients received surgery, on average, at hospitals with similar mortality. Further, the probability of being treated at a particular hospital decreased with increasing hospital mortality for both Black and White patients. However, given their better geographic proximity to low-mortality hospitals, Black patients were expected to be treated at lower-mortality hospitals more often than White patients. Instead, Black patients were treated at these hospitals less often, partly due to differences in physician-hospital referral networks. Finally, physician networks seem to have a stronger influence on where White patients receive CABG compared with Black patients.

The finding that Black and White patients underwent elective CABG at hospitals of similar quality (as reflected by the hospital mortality measure) is notable, encouraging, and stands apart from prior research showing large Black-White disparities in high-quality hospital use for this common cardiac procedure.3,5,6,24 There are substantial differences, however, between this study and prior research. Previous findings of disparities are based on older data or other types of measures (eg, composite quality measures,5 Society of Thoracic Surgons data on a limited number of hospitals,3 or more imprecise measures of hospital quality for cardiac care).8 In contrast, the current study includes the majority (89%) of CABG-performing hospitals in the United States and is based on data collected after the CMS first published 30-day CABG mortality rates in the context of national pay-for-performance programs. Thus, it is possible that the reporting and reimbursement policies leading to national improvements in outcomes for CABG surgery25 may have also contributed to reductions in Black-White disparities.

Despite closing the gap in the quality of hospitals used, Medicare Black patients remained more likely than White patients to receive elective CABG at the nearest hospitals and less likely to receive CABG at the best (lowest mortality) hospitals available within a reasonable distance. Given that Black patients continue to suffer worse CABG outcomes,1 and that patients with CABG fare significantly better at high-quality hospitals,26 optimizing the use of the best available hospitals may help reduce the Black-White gap in CABG outcomes.

While extant research documents that Black and White patients are treated by different physicians and hospitals,7,8,27 the role of physician networks in hospital use disparities has not been previously quantified. The current study sheds new light on this role by showing that physician networks contribute to being treated at lower-mortality hospitals for both Black and White patients; however, this effect is stronger for White versus Black patients. This finding highlights potentially suboptimal referral networks for Black versus White patients and may have several explanations and corresponding implications for policy and interventions. Organizational factors such as hospital credentialing processes and health system affiliations could lead to differences in high-quality hospital access for physicians treating Black and White patients, albeit these factors are understudied. Further, physicians may not be aware of, or may distrust, data-driven published hospital quality measures and instead rely on personal networks, reputation-based assessments, and patient preferences when making hospital referrals.15,28 Moreover, for procedures such as CABG, referring physicians consider the quality of referral surgeons over that of hospitals when making referral decisions.15,29 Thus, effective interventions need to consider both physician access to high-quality hospitals and physician improved awareness and acceptance of hospital quality measures.

The study also shows that differences in the quality of hospitals, where Black and White patients receive care remain even after accounting for geographic access and physician-hospital network effects, and the probability of using higher-mortality hospitals increases in the absence of favorable network effects for both Black and White patients. This particular finding suggests that other factors also influence hospital use decisions, overall and for Black and White patients differently. First, social determinants of health exacerbated by structural racism (eg, income-related difficulties, lack of transportation, or the need for nearby support to assist with transitions of care) likely play a role in patients’ decisions about which hospitals to use.30–32 Second, differences in patient beliefs, attitudes, and preferences may counteract the favorable effects of referral networks. For Black patients, these factors may be represented by high levels of historical mistrust in particular health care institutions which have historically perpetuated systemic racism, preferences for hospitals supportive of the community,33–35 or preferences for racially concordant care, which are known to improve outcomes for minoritized racial/ethnic groups.36,37 Moreover, like their physicians, patients may not consider published hospital quality measures when referral decisions are made except in areas with overall poor quality of care,38 trusting their and their peers’ experiences instead.39 This may be particularly true for minoritized and other vulnerable populations.40

Several limitations to the current study should be noted. First, analyses focused on Black and White aged fee-for-service Medicare beneficiaries. While this presents an advantage due to access to a national sample of CABG hospitals and patients unrestricted by insurance, hospital use disparities and the effects of physician networks of different magnitude may be observed for younger populations, patients of other races/ethnicities, or those with Medicare managed care, private insurance, or uninsured. Future work to describe the role of referral networks for these populations is key to crafting all-encompassing national and local policies. Second, we measured hospital quality using the risk-adjusted hospital-level CABG mortality measure published by CMS. Disparities may have various magnitudes and be impacted differently by physician networks for other important outcomes such as postoperative CABG complications.

Despite its limitations, the current study highlights the important and divergent roles played by geographic proximity and physician-hospital networks in where Black and White patients receive CABG and provides the framework and tools to expand this inquiry to other populations and outcomes. Based on literature5,41,42 showing racial gaps in treatment at high-quality hospitals for other major conditions and procedures, our findings may be part of a larger population problem. While we offer several explanations for the differences observed regarding physician network effects, more in-depth work is needed to understand the relative role of each of these explanations and craft effective interventions. Such interventions may focus on increasing public awareness of hospital quality measures and physician buy-in, and addressing persistent structural racism barriers by improving the quality of hospitals serving Black patients, improving access to specialists and hospitals for physicians treating Black patients, and regaining patients’ trust in medical institutions.

Article Information

Sources of Funding

The study was funded by grants from the National Institutes of Health (National Heart, Lung, and Blood Institute, R01HL148420) and the Agency for Healthcare Research and Quality (1U19HS024067-01).

Disclosures

None.

Supplemental Material

Tables S1 and S2

Figure S1

Supplementary Material

hcq-18-e010778-s001.pdf (100.9KB, pdf)
hcq-18-e010778-s002.pdf (125.8KB, pdf)
hcq-18-e010778-s003.pdf (141.1KB, pdf)

Nonstandard Abbreviations and Acronyms

CABG
coronary artery bypass grafting
CMS
Centers for Medicare and Medicaid Services
PCP
primary care physician

For Sources of Funding and Disclosures, see page 67.

Contributor Information

Jose J. Escarce, Email: JEscarce@mednet.ucla.edu.

Shiyuan Zhang, Email: Szhang@rand.org.

Luke J. Matthews, Email: lmatthew@rand.org.

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hcq-18-e010778-s001.pdf (100.9KB, pdf)
hcq-18-e010778-s002.pdf (125.8KB, pdf)
hcq-18-e010778-s003.pdf (141.1KB, pdf)

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