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Hospital mergers and referrals in the United States: patient steering or integrated delivery of care?

Many tertiary care hospitals (acquirers ) acquire non-tertiary care hospitals (targets), and some of these mergers lead to a significant increase in referrals from the target to the acquirer. This study examines the hospitals' motives for integration and for increasing referrals using hospital discharge data from the Pittsburgh area. I develop and estimate a model of referral choice based on a reputation mechanism. The results suggest that low- or average-quality acquirers exploit their targets' monopoly power to steer patients to the acquirers. Distinguished acquirers, on the other hand, seem to have motives other than patient steering, including the integrated delivery of care.

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Since the 1990s, there have been many hospital merger cases in which a tertiary care hospital that provides specialized care (the acquirer) acquires a non-tertiary care hospital that does not offer such services (the target). (1) Several media reports note that mergers of this type could lead to an increase in referrals from the target to the acquirer (Bernstein 1996; Brown 2001). Because the number of tertiary care hospitals is limited, patients typically present themselves first at their local non-tertiary care hospital for diagnosis; patients then are referred to a tertiary care hospital when necessary. This makes referrals from hospitals not offering the service an important path for specialized services. (2) This is especially the case for cardiac surgery, as only a limited number of hospitals offer this service and the major source of admission is physician referrals (Mukamel, Weimer, and Mushlin 2006). Huckman (2006) reported that acquirers on average experience an increase in cardiac surgery admissions from the target's primary market. On the other hand, Nakamura, Capps, and Dranove (2007) found that in the majority of cases, there appears to be no change in referrals to the acquirers, although some acquisitions do lead to a significant increase in referrals for cardiac surgery as well as other specialized services.

This paper studies why some mergers are more successful in increasing cardiac referrals than others and, more importantly, what motivates this type of merger and the subsequent increase in referrals. The health economics literature offers two hypotheses that have completely different welfare and policy implications. The theory of transaction costs asserts that integration could enable the merging parties to resolve internal agency problems and to make relation-specific investments (Grossman and Hart 1986; Klein, Crawford, and Alchian 1978; Williamson 1979, 1985). Accordingly, hospital acquisitions could facilitate not only economies of scale and scope, but also joint investments in quality improvement and cost reduction--that

is, the integrated delivery of care (Burns and Pauly 2002). If this were the case, integration could produce an increase in referrals to the acquirers. Nevertheless, a completely different motivation is also possible. While referral laws prohibit hospitals from paying physicians for their referrals, the laws also exempt certain forms of payment between hospitals and their affiliated physicians. Thus, hospital acquisition can be used as a loophole for providing monetary or nonmonetary rewards to physicians who give referrals--a practice known as patient steering. While the integration of hospitals might not affect physicians' decisions regarding whether to refer a patient to a tertiary care hospital, hospitals could shift referral volume from nonaffiliated hospitals to affiliated hospitals. (3)

Because health care providers are imperfect agents for patients, a reputation mechanism plays a central role in disciplining health care providers. Consider a physician at a nontertiary care hospital choosing where to refer her patients for tertiary care. Suppose the non-tertiary care hospital is affiliated with a tertiary care hospital and that the physician is paid for referrals made to the acquirer hospital. What would prevent the physician from referring all patients to the acquirer, provided that she is an imperfect agent of her patients? Since she is partially altruistic, her utility decreases if she refers a patient to a hospital that is not the best choice for the patient in terms of quality and traveling costs. Moreover, she also could have a selfish reason for not referring all patients to the acquirer. If a patient referred to the acquirer later learned that this was not the best choice for that patient and shared this information with others through word of mouth or popular ratings, the physician could suffer a loss of reputation and decreased demand for her services.

To examine how the reputation mechanism affects the incentives of referring hospitals, I develop a model in which hospital care is an experience good and patients' preferences for referring hospitals are affected by the average utility experienced by prior patients. (4) The model predicts that competitive pressure reduces agency problems by increasing the effectiveness of reputation as a disciplinary mechanism. Because patients experience firsthand the quality of the hospital to which they are referred, making referrals for motives other than patient welfare could hurt the referring hospital's overall reputation. Accordingly, if referrals increase due to patient steering, the increase would be greater when the target faced less competition.

I estimate a multinomial logit model of referral choice for cardiac surgery using hospital discharge data from the Pittsburgh area. The majority of acquisitions led to a significant increase in referrals. In addition, I find that a merger involving a non-tertiary care hospital facing little competition led to a greater increase in referrals. This finding is consistent with the patient-steering hypothesis. On the other hand, there is one notable exception. My sample includes three tertiary care hospitals that are renowned for high-quality care and are affiliated with a number of non-tertiary care hospitals. These high-quality acquirers were much less likely to have increased referrals from the targets compared to other acquirers, and target hospitals facing little competitive pressure were less likely to refer patients to these high-quality acquirers. My findings indicate that boosting referrals by acquiring a non-tertiary care hospital in an uncompetitive market is a much more attractive strategy for low- and average-quality tertiary care hospitals than for their high-quality counterparts. Thus, hospital acquisition could result in a shift of patient volume from higher-quality hospitals to lower-quality hospitals. Such a shift could have serious negative effects on patient welfare.

Background

In the 1990s, the integration of tertiary and non-tertiary care hospitals increased (Huckman 2006; Nakamura, Capps, and Dranove 2007), as did mergers between hospitals and physician practice groups (Ciliberto 2006; Cuellar and Gertler 2005). In the health economics literature, these types of mergers are referred to as vertical integrations (Ciliberto 2006; Ciliberto and Dranove 2005; Cuellar and Gertler 2005; Gal-Or 1999; Gaynor 2005; Huckman 2006; Nakamura, Capps, and Dranove 2007), and similar motives are hypothesized for both. Thus, I review previous literature on hospital-physician integration as well as on hospital mergers.

Integration of this type cannot be fully explained by the horizontal merger model because the merging parties produce complementary rather than supplementary goods. This is probably why it is called vertical, although the merging parties do not have a buyer-seller relationship prior to the merger, making double marginalization irrelevant (Gaynor 2005). Gal-Or (1999) raised the theoretical possibility that hospital and physician alliances gain collective bargaining power over managed care organizations. However, the empirical evidence regarding the effect of hospital-physician integration on hospital prices is mixed (Ciliberto and Dranove 2005; Cuellar and Gertler 2005; Gaynor 2005). In addition, studies by Town and Vistnes (2001) and Capps, Dranove, and Satterthwaite (2003) imply that hospital mergers have a limited effect on prices unless the consolidating hospitals are direct competitors in the local market. (5)

Integration could enable the merging parties to exploit economies of scale and scope by eliminating redundant treatment or medical examination via the sharing of medical records and the development of a unified information system. Additionally, better communication among physicians at the merging hospitals or among acquired physicians and other hospital staff may lead to better coordinated care (Gillies et al. 1993; Shortell et al. 1996). However, past empirical studies have found little evidence of efficiency gains (Cueller and Gertler 2005; Huckman 2006; Madison 2004a, 2004b). Some studies have found little support for quality improvement (Huckman 2006; Madison 2004a). (6) Others have reported that particular types of consolidations result in a small but statistically significant reduction in the mortality rate (Cueller and Gertler 2005; Madison 2004b). Still, it can be argued that it might take a long time before hospitals can enjoy gains in efficiency and quality from integrated delivery of care. In addition, whether integration is motivated by the opportunity for integrated delivery of care and whether gains actually accrue from it are different issues. This study focuses on the former, whereas the aforementioned studies examine the latter.

Integration also could be an effective strategy for attracting physician referrals. Burns and Wholey (1992) showed that physician convenience is an important determinant of hospital choice. This finding suggests that physicians have a significant influence on the choice of a hospital. Cuellar and Gertler (2005) found that hospitals tend to have an increased case volume after they integrate with physicians. Huckman (2006) reported that, on average, hospitals offering cardiac surgery experience an increase in referrals after acquiring hospitals that do not offer the service. Nakamura, Capps, and Dranove (2007) found similar effects for a wide range of tertiary care services, although they also noted that the magnitude of the change varies greatly by merger] Nevertheless, I know of no study that has examined whether the patient-steering hypothesis alone can explain integration motives and the increase in referrals.

Legal restraints prohibit hospitals from buying referrals from physicians. The 1972 Anti-Kickback Law imposes both criminal and civil penalties on any physician who knowingly and willfully solicits or receives any remuneration for referring Medicare or Medicaid patients) The 1995 Stark Physician Self-Referral Law prohibits physicians from referring Medicare or Medicaid patients to hospitals with which they have financial relationships, regardless of the intent of the parties. (9) However, both of the aforementioned statutes permit certain forms of payment from a hospital to affiliated physicians (Hubbell, Mauro, and Moar 2006; Hyman 2001; Morrison 2000).

Model of Referral Choice

In this section, I develop a theoretical model in which non-tertiary care hospitals refer patients to tertiary care hospitals for advanced treatment. In the model, hospital care is an experience good, and patients' preferences for a non-tertiary care hospital depend on the average utility of patients who used the hospital in the previous period. (10) Non-tertiary care hospitals are assumed to consider the effect of patients' satisfaction on future demand and profit when making referrals. I show that when demand for a non-tertiary care hospital is more responsive to a prior user's experience, the hospital places greater weight on patients' preferences in choosing referral destinations.

There are i = 1, ..., I patients, j = 1, ..., J nontertiary care hospitals, and k = 1, ..., K tertiary care hospitals. There are two periods, at the beginning of which each patient chooses one non-tertiary care hospital. (11) With a certain probability, the physicians at the non-tertiary care hospital find that the patient needs a referral for advanced treatment at a tertiary care hospital. (12) For simplicity, I assume that tertiary care hospitals do not provide nontertiary care and that all patients start at nontertiary care hospitals. (13) Non-tertiary care hospitals earn a fixed profit margin per admission. (14) After referrals are made, the patients experience the quality of the referred tertiary care hospitals. At the end of the first period, the average utility of patients at each non-tertiary care hospital becomes common knowledge. When patients choose non-tertiary care hospitals at the beginning of the second period, they consider the average utility of the patients in the first period.

Patients

Let [V.sup.i.sub.jk] denote patient i's utility when she is referred from non-tertiary care hospital j to tertiary care hospital k. I assume that [V.sup.i.sub.jk] is the sum of a deterministic and a random component. The deterministic component is derived from the observable characteristics of patients, non-tertiary care hospitals, and tertiary care hospitals. The random component is determined by factors that are unobservable to the econometrician. I assume that the random component is observable to patient i and to the referring hospital when a referral is made.

Similarly, let [W.sup.i.sub.jt] be patient i's utility when she chooses non-tertiary care hospital j in period t. I assume that [W.sup.i.sub.jt] is the sum of a deterministic component [w.sup.i.sub.jt] and a random component that follows the extreme value distribution. The expression [w.sup.i.sub.jt] is determined by the observable characteristics of patients and hospitals, while the random component is determined by factors that are unobservable to the econometrician. The random component is observable to patient i at the beginning of period t, but no one knows the value of the random component before period t starts. Because the random component follows the extreme value distribution, [s.sup.i.sub.j], the expected probability that patient i chooses non-tertiary care hospital j in period 2, can be written as follows:

[s.sup.i.sub.j] = exp ([w.sup.i.sub.j2])/[J.summation over (j' = 1)] ex[ (w.sup.i.sub.j'2]). (1)

The choice of non-tertiary care hospitals by patients in the second period is affected by the average utility of the patients who chose the non-tertiary care hospitals in the first period. This specification reflects not only that there could be publicly available hospital ratings based on popular votes but also that word of mouth could play an important role in hospital choice (Dafny and Dranove 2008). For simplicity, I assume that each patient's utility depends only on her own experience at the referral destination.

Non-Tertiary Care Hospitals

I assume that non-tertiary care hospitals are partially altruistic, such that when they refer their patients in the first period, they choose the referral destinations to maximize the weighted sum of three factors: the referred patients welfare [W.sup.i.sub.jk], physician convenience (or non-monetary utility), and the expected profit over the two periods. When a nontertiary care hospital is integrated with a tertiary care hospital, the non-tertiary care hospital is assumed to consider the joint profit of both hospitals. Let [M.sup.i.sub.jk] be the financial or non-monetary gains for target hospital j from referring patient i to acquirer k. (15) Independent hospitals have no consideration for the income of any tertiary care hospitals.

All non-tertiary care hospitals earn a fixed profit margin of [tau] per patient in the second period, and [rho] is the discount rate for the

profit in the next period. Thus, the discounted value of hospital j's expected profit in period 2, evaluated by hospital j at the beginning of period 1, is [rho][tau] [l.summation over (i=1) [s.sup.i.j]. As described earlier, [s.sup.i.sub.j] is a function of [w.sup.i.sub.j2], and [w.sup.i.sub.j2] is a function of the average utility of patients who were referred from hospital j to tertiary care hospitals in the first period. Accordingly, the utility level of each patient at the referral destination affects the profit of the referring hospital in period 2. Specifically, based on the first-order Taylor expansion, the incremental change in the discounted expected profit when hospital j refers patient i to tertiary care hospital k in period 1 can be approximated by [beta] [rho][tau] [V.sup.i.sub.jk] 1/[N.sub.j][l.summation over (i'=1)] [s.sup.i'.sub.j0] (1 - [s.sup.i'.sub.j0]) where [beta] is a constant, [N.sub.j] is the number of patients who were referred from hospital j in period 1, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] See Nakamura (2006) for the details of the derivation.

Let me denote 1/[N.sub.j] [I.summation over (i'=1)] [s.sup.i'.sub.j0] (1 - [s.sup.i'.sub.j0] as RD[E.sub.j], which represents the responsiveness of demand for non-tertiary care hospital j to a patient's experience. The payoff of non-tertiary care hospital j from referring patient i to tertiary care hospital k in period 1 is specified as follows:

[[mu].sup.i.sub.jk] = [V.sup.i.sub.jk] ([[alpha].sub.j] + [beta][rho][tau] RD[E.sub.j) + [Z.sub.jk] + [M.sup.i.sub.jk] + [Aff.sub.jk]. (2)

The altruism parameter [[alpha].sub.j] is a measure of the importance that hospital j places on patients' preferences independent of reputation effects. [Z.sub.jk] is the referring physician's non-monetary utility when a patient is referred to tertiary care hospital k from hospital j. [Aff.sub.jk] is an indicator variable that takes the value of one if hospital j is affiliated with hospital k and zero otherwise. Hospital j chooses the tertiary care hospital with the highest payoff as the referral destination for patient i.

Measure of the Responsiveness of Demand

The model shows that non-tertiary care hospital j places a greater emphasis on patients' preferences when RD[E.sub.j] is large. The term RD[E.sub.j] represents the responsiveness of demand for hospital j to a patient's experience, and it approximates the marginal change in demand for j given an increase in the quality of one patient's experience at j. It also can be regarded as the elasticity of demand with respect to quality. (16) This formula relies on the assumption that demand for non-tertiary care hospitals can be treated as a logit model. When the hospital market is more competitive, a change in reputation has a greater effect on hospital demand because it is easier for patients to avoid hospitals with bad reputations. Thus, RD[E.sub.j] can be thought of as a measure of the competitive pressure faced by hospital j.

In the literature on hospital competition, the Herfindahl-Hirschman index is commonly used as a measure of competition, wherein the geographical area defines the market. An important assumption underlying the index is that all firms in the same market are homogenous and face the same degree of competition. In the hospital market, this assumption might be unrealistic. Hospitals are vertically differentiated in terms of their quality of care and range of service offerings. As a result, hospitals in the same market could face different degrees of competition, depending on their service offerings and quality of care. The use of RDE allows one to avoid this problem.

Empirical Specification

Based on the theoretical model described in the previous section, I develop a referral choice model for coronary artery bypass graft surgery (CABG) and percutaneous transluminal coronary angioplasty (PTCA) using hospital discharge records from Pennsylvania for the years 1997 and 2002. (17) I treat hospitals offering CABG/PTCA as tertiary care hospitals and the other short-term general hospitals as non-tertiary care hospitals, and study referrals from the latter to the former. When tertiary care hospitals are affiliated with non-tertiary care hospitals, I refer to the former as acquirers, and when non-tertiary care hospitals are affiliated with tertiary care hospitals, I refer to the former as targets. Thus, all of the acquirers and none of the targets offer CABG/PTCA, and some tertiary care hospitals and some non-tertiary care hospitals are independent (i.e., they are neither acquirers nor targets). In the remaining portion of this section, I explain the empirical specification of the model and discuss the identifying assumptions.

Cardiac Surgery (CABG/PTCA)

Inter-hospital referrals are common for cardiac surgery cases because only a small fraction of hospitals offer CABG/PTCA. While some patients undergo CABG/PTCA immediately after suffering heart attacks, others undergo CABG/PTCA on an elective basis. The patients who have elective surgery typically have initial symptoms of ischemic heart disease, such as chest pain or shortness of breath, and they present themselves at their local hospitals. If the hospitals do not offer cardiac surgery, the patients are referred to more technologically advanced hospitals. This paper studies the referral choice for such patients.

There are several reasons why hospitals particularly benefit from attracting referrals for CABG/PTCA. First, cardiac surgery is known for its high profit margins (Huckman 2006). Second, empirical work suggests that CABG/PTCA is associated with learning by doing. (18) Provided that quality improves and cost decreases in correlation with the experience of the medical staff, hospitals can establish dominant positions in their local markets by performing a greater number of surgeries.

Referral Choice

In this subsection, I describe empirical specifications of equation 2. The altruism parameter [[alpha].sub.j] could vary with the ownership status of non-tertiary care hospitals. However, all of the hospitals studied here are nonprofit, so I assume that [[alpha].sub.j] = [alpha] for all j = 1, ...., J [V.sup.i.sub.jk], which is patient i s utility when referred to tertiary care hospital k from non-tertiary care hospital j, is specified as a linear function of the travel time from patient i's home to hospital k [T.sup.i.sub.k], the square of [T.sup.i.sub.k], the quality of hospital k as commonly perceived by all patients, and an independently and identically distributed (i.i.d.) random variable [[epsilon].sup.isub.k].

The common quality of hospital k is specified as a linear function of a hospital specific effect [H.sub.k], the indicator variable [Aff.sub.jk] (which takes the value of one if hospital j is affiliated with hospital k and zero otherwise), and [Aff.sub.jk][High.sub.k] where [High.sub.k] is a dummy variable that takes the value of one if hospital k is regarded as being among the top hospitals in the region and zero otherwise. Because hospital quality is difficult to measure (Carey and Burgess 1999; Geweke, Gowrisankaran, and Town 2003), I use hospital-specific effects [H.sub.k] to account for quality differences among hospitals. (19) I allow hospital-specific quality to depend on the organizational relationships between the referring hospital and the tertiary care hospital because if integration leads to better coordination of care, referrals from the target to the acquirer would benefit the patients. I also allow the effect of the alliance on the quality of care to depend on whether the acquirer is a high-quality hospital.

To find hospitals that provide an exceptionally high quality of care, I use three different measures: hospital rankings by U.S. News & Worm Report, the number of cardiac surgeries performed, and the number of cardiac surgery patients from outside the county. Assuming that practice makes perfect, the surgical volume of a hospital reflects the experience of its medical staff and thus its quality. Additionally, provided that severely ill patients are more willing to travel for better quality care, hospitals that attract greater numbers of such patients are more likely to be superior in terms of their quality of care. Among the tertiary care hospitals in my data set, three--the University of Pittsburgh Medical Center (UPMC) Presbyterian, UPMC Shadyside, and Allegheny General Hospital--were far superior to others with these criteria, so I define them as high-quality hospitals.

I specify [Z.sub.jk], physicians' non-monetary utility from referring a patient from non-tertiary care hospital j to tertiary care hospital k, as a linear function of a hospital-specific effect D[H.sub.k], (20) the travel time from hospital j to hospital k D[T.sub.jk], the square of D[T.sub.jk], and an i.i.d. random variable [[zeta].sub.jk]. (21) Because I lack a good measure of the (non-monetary) attractiveness of the tertiary care hospitals for the referring physicians, I use hospital-specific effects D[H.sub.k] to account for differences among hospitals in terms of their accessibility and amenity for the referring physicians. (22)

The financial gain for target hospital j from referring patient i to acquirer k, [M.sup.i.sub.jk], is specified as a linear function of the characteristics of patient i, the nature of the affiliation, and the dummy variable indicating whether hospital k is among the top hospitals [High.sub.k]. To control for patient characteristics, I include [Old.sup.i], a dummy variable indicating whether the patient is at least 80 years old, and P[I.sup.i], a dummy variable equal to one if the patient is covered under a private fee-for-service insurance plan. The coefficient of [Old.sup.i] measures whether targets selectively refer healthier patients to the acquirers, and the coefficient of P[I.sup.i] indicates whether targets selectively refer better insured patients to the acquirers. To account for the nature of the affiliation, I include First [Yr.sub.jk], a dummy variable indicating whether the referral is made within one year of the acquisition, and [Loose.sub.jk], a dummy variable that takes the value of one if non-tertiary care hospital j has an organizational relationship with tertiary care hospital k and is not owned by hospital k. (23) This specification allows the effect of integration on referrals to vary with the time after acquisition and the degree of organizational integration.

If the incremental cost of treating a patient decreases with surgical volume at the hospital, the average profit margin will be higher for high-quality (and thus high-volume) hospitals. On the other hand, high-quality acquirers are likely to face capacity constraints due to their own popularity. Specifically, Bazzoli et al. (2003) reported that some tertiary care hospitals occasionally face capacity problems in their highly renowned heart programs. Likewise, Ho (2009) estimated that the majority of "star" hospitals (i.e., hospitals particularly attractive to patients) face capacity constraints. Therefore, the sign of the coefficient of [Aff.sub.jk] [High.sub.k] depends on whether the former or the latter effects dominate.

Since I cannot observe the true value of RD[E.sub.j], I use its estimate. Let RD[E.sup.est.sub.j] be the estimated value of RD[E.sub.j], and let [[phi].sub.j] be the error in the estimation. It can be shown that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [[lambda].sub.1], [[lambda].sub.2], [[kappa].sub.1], [[kappa].sub.2], [[delta].sub.1], [[delta].sub.2],.., [[delta].sub.5], [upsilon], and [omega] are some parameters, and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Assuming that [[zeta].sup.i.sub.jk] is i.i.d. extreme-value distributed, equation 3 can be estimated as a standard multinomial logit model. Nakamura (2006) explains the derivation of equation 3 and discusses the identifying assumptions. The definitions of the explanatory variables are provided in Table 1.

Measure of the Responsiveness of Demand

I assume that the demand for non-tertiary care hospitals from patients who could need cardiac surgery is well represented by the choice of hospitals for acute myocardial infarction (AMI) or heart attack treatment. I estimate a multinomial logit model of hospital choice for AMI treatment where the explanatory variables are hospital-specific effects and the travel time between the patient's home and the hospital. Based on the estimated parameters, I compute RD[E.sup.est], the measure of the responsiveness of the demand to a patient's experience. See Nakamura (2006) for details of the estimation procedure.

Assumptions About the Referring Hospital

Since I cannot observe the specific hospital from which each patient is referred, I include three different assumptions about the referring non-tertiary care hospital and estimate the model separately for each assumption. First, there are some cases in which a patient had cardiac catheterization (for diagnostic purposes) at a hospital that did not offer CABG/PTCA and the patient then went on to have CABG/PTCA at another hospital. I assume that these patients were referred from the first hospital to the second (Assumption 1). Second, when a patient who had cardiac surgery at a tertiary care hospital is highly likely to go to a specific non-tertiary care hospital for AMI treatment, I assume that the patient was referred from that non-tertiary care hospital (Assumption 2). Based on the estimated model of hospital choice for AMI treatment, I calculate the probability of choosing each non-tertiary care hospital for each patient who has had cardiac surgery. (24) If the probability exceeds 50%, then I assume that the patient was referred from the non-tertiary care hospital. (25) Third, if a CABG/ PTCA patient's home is within a five-minute drive from a non-tertiary care hospital, I assume that the patient was referred from that hospital (Assumption 3). (26)

Data

I use 1997 and 2002 hospital discharge data from hospitals in Regions 1 and 3, which I obtained from the Pennsylvania Health Care Cost Containment Council (PHC4). (27) Regions 1 and 3 cover the southwest area of Pennsylvania surrounding Pittsburgh. (28) The discharge data contain every case of CABG/PTCA, cardiac catheterization, and AMI. The variables include the admitting hospital, the procedure performed, and the patient's age, sex, residential zip code, and diagnoses, as well as patient identifiers that link patients across records. The information on hospital acquisitions comes from Irvin Levin Associates and from local newspaper articles. Information on the location and other characteristics of hospitals in the area was obtained from the American Hospital Association's (AHA) annual survey and from the PHC4. The travel time was obtained using the driving hours calculator provided on the Mapquest.com web site.

Following definitions used in the AHA survey, I treat a hospital as offering CABG/PTCA if it performed at least 20 CABG/PTCAs during the year. I limit my analysis to non-tertiary care hospitals included under Assumption 1, so that the scope of the analysis is the same across the three assumptions. Non-tertiary care hospitals included in the analysis are called "referring hospitals." I also limit my analysis to the patients whose hospital choice was unaffected by considerations related to insurance provider networks. Thus, I only include patients covered under Medicare, Blue Cross, and commercial indemnity insurance plans, excluding patients covered under Medicare health maintenance organization (HMO) and Blue Cross managed care plans. I also exclude patients younger than age 50 and those who had cardiac surgery with a primary diagnosis of AMI, as they account for a small percentage of patients and could have different hospital preferences.

The list of hospital systems and their member hospitals is presented in Table 2. (29) Non-tertiary care hospitals are excluded if they do not appear to have referred any patients after cardiac catheterization. (30) As a result, there are nine targets (including St. Clair) with five acquirers in 1997 and 11 targets with 10 acquirers in 2002. In addition, there are nine independent referring hospitals and eight independent tertiary care hospitals in 1997, and five independent referring hospitals and seven independent tertiary care hospitals in 2002. (31) Many targets have multiple acquirers, and many acquirers have multiple targets. As a result, there are 22 possible combinations of targets and acquirers in 1997, and there are 28 such combinations in 2002. (32) This feature of the data permits me to analyze the acquirers to which a target increases referrals and the targets from which an acquirer receives increased referrals. Table 3 shows the number of each type of hospital in my sample.

I treat the data set as a pooled cross-section wherein the unit of observation is an admission to a hospital. Table 4 shows the summary statistics for the patient characteristics, the characteristics of the hospitals chosen for CABG/PTCA, and the characteristics of the presumptive referring hospitals under each

assumption. The statistics regarding the chosen and referring hospitals' characteristics are calculated at the patient level. The numbers are largely similar across assumptions. The vast majority of patients are Medicare beneficiaries, and more than half of them have their surgeries at a high-quality hospital. (33) Table 5 summarizes the characteristics of the tertiary care hospitals included in the analysis. (34) High-quality acquirers are all teaching hospitals and have a much greater surgical volume than other tertiary care hospitals, but the numbers are largely similar between other acquirers and non-acquirers.

Results

I estimate the parameters in the models described earlier using maximum likelihood. (35) The estimation results for AMI patients are presented and discussed in Nakamura (2006). (36) The summary statistics of RD[E.sup.est] for the referring hospitals are presented in Table 6. While independent referring hospitals have larger RDEs on average than target hospitals, the variance is large for both independent hospitals and targets. This considerable variation in RD[E.sup.est] enables the comparison of referral patterns based on the competitive pressure faced by the referring hospitals.

Table 7 shows the results of the multinomial logit estimation of referral choice, where the outcome is the tertiary care hospital chosen for a cardiac surgery. (37) The signs and statistical significance of the estimated coefficients are largely similar regardless of the assumptions about the referring hospitals. Exceptions include the estimated coefficients for the first six variables: DT, [DT.sup.2], T, [T.sup.2], RD[E.sup.est] x T, and RD[E.sup.est] x [T.sup.2]. This discrepancy could arise because only patients who live close to non-tertiary care hospitals are selected under Assumptions 2 and 3, with the patient's traveling time and the referring physician's traveling time thus highly correlated under these assumptions. Under Assumptions 1 and 2, the referring physician's traveling time has a negative effect on the probability of referral. (38)

The coefficient of Aff is positive and significant under any of the assumptions about the referring hospitals. The coefficient of Aff x Loose is negative under all of the assumptions and is statistically significant under Assumption 1. Likewise, the coefficient of Aff x First Yr is negative under all of the assumptions and is statistically significant under Assumption 1. These results indicate that target hospitals tend to refer patients to tertiary care hospitals with which they have organizational relationships and that it takes time for such effects to become noticeable. In addition, the effect of affiliation seems smaller when the acquirer does not own the target.

The coefficient of Aff x Old is not significant under any of the assumptions concerning the referring hospitals. The coefficient of Aff x PI is positive and significant under Assumption 1. These results are largely consistent with the findings of Nakamura, Capps, and Dranove (2007) that some target hospitals selectively refer patients with more remunerative insurance to their acquirers, but do not select patients based on the severity of illness.

The coefficient of Aff x High is negative and significant under all of the assumptions about the referring hospitals, implying that highly renowned acquirer hospitals are less aggressive in attracting referrals from their target hospitals. The coefficient of Aff x RDE is negative under all of the assumptions about the referring hospitals and is statistically significant under Assumption 1. This finding indicates that when the acquirers are not among the top hospitals, targets with demand that is more responsive to a patient's experience are less likely to refer their patients to the acquirers. On the other hand, the coefficient of Aff x RDE x High is positive and significant under all of the assumptions about the referring hospitals. (39) In addition, it is greater in magnitude than the coefficient of Aff x RDE. Thus, competitive pressure as experienced by the target is positively associated with the probability of referrals to the distinguished acquirers.

Based on the theoretical model described previously, I interpret my findings as follows. When the acquirer's quality of care is not superior, increased referrals help the acquirer to increase profits and accumulate surgical volume. However, patients do not benefit from being referred from the target to the acquirer. Thus, target hospitals facing highly responsive demand avoid referring patients to their acquirers when there are better alternatives for patients. In contrast, targets facing unresponsive demand do not lose future customers even if they have a bad reputation, so they steer patients to their acquirers. The three distinguished acquirers are much less aggressive in attracting referrals from targets, probably because they face capacity constraints similar to those of other highly renowned hospitals (Bazzoli et al. 2003; Ho 2009). In addition, competitive pressure on the target increases referrals to the acquirer. Clearly, the patient-steering hypothesis does not apply to these distinguished acquirers.

Conclusion and Discussion

This paper investigates why referrals increase when tertiary care hospitals acquire non-tertiary care hospitals. My findings suggest that mergers could reduce patient welfare if low-quality tertiary care hospitals acquire non-tertiary care hospitals that face little competitive pressure. In such cases, referrals from the target to the acquirer are likely to increase, both because the targets do not need to worry about the reputation consequences of referring patients to low-quality hospitals and because the acquirers desperately need to attract referrals. As a result, patients would be steered from high-quality hospitals to hospitals of lower quality. Additionally, this type of acquisition would result in a shift of surgical volume from higher-volume hospitals to lower-volume hospitals, and could hinder higher-volume hospitals from accumulating surgical volume and exploiting volume-out-come effects. Nevertheless, there is one notable exception. Hospital acquisitions by distinguished tertiary care hospitals appear to be motivated by objectives other than increasing referrals.

In terms of policy implications, it is worth noting that it would be unrealistic to attempt to completely prevent hospitals from providing monetary and nonmonetary incentives to affiliated physicians to attract referrals. Likewise, it might be difficult to detect and prohibit only "bad" acquisitions that lead to undesirable patient steering. Additionally, it might be unrealistic to reduce primary and secondary care physicians' influence over hospital choice for specialized care because these physicians often have better knowledge on local hospitals and their patients' medical needs than their patients do. Their influence would remain--or even increase in the future--if physician specialties become more fragmented as medicine advances, and accordingly, if the quality of care depends more critically on matching the patient's specific medical needs and the physician's specialized skills.

One possible solution would be to evaluate hospitals for the quality of the referrals made at the hospital. Hospital quality commonly is measured based on the outcomes of the patients who have been treated at only that one hospital. However, hospital evaluation could be based on outcomes for all patients who visited the hospital, including those who were referred or transferred to other hospitals. While caution should be exercised so as not to punish rural, nonspecialized hospitals for not having high-quality specialized hospitals nearby, monitoring changes in hospital quality measured in this way over time could prevent undesirable distortions in referral practice.

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Notes

This article is based on my thesis. I am grateful to my adviser, David Dranove, and the other members of my dissertation committee: Robert Porter, William Rogerson, and Mark Satterthwaite. I also thank Vivian Ho as well as seminar participants at Aoyama Gakuin, Massey, Northwestern, Tokyo, Tsukuba, and Western Ontario universities for their helpful comments. I am indebted to Cory Capps, who generously provided his codes for obtaining driving hours. I acknowledge generous financial support from the Sid Richardson Foundation while I was a Sid Richardson Scholar in Health Economics at the James A. Baker III Institute for Public Policy at Rice University. All errors are my own.

(1) These terminologies follow Huckman (2006) and Nakamura, Capps, and Dranove (2007).

(2) This paper studies referrals for procedures that the referrer cannot perform.

(3) I only consider the latter possibility, as it would be easier for target hospitals to change their referral destination than to change their criteria for making a referral, especially for major surgeries. Nevertheless, this is unlikely to affect the conclusions of the paper even if affiliations affect the propensity to refer.

(4) Folland (1985) categorized health care as an experience good. Brekke, Nuscheler, and Straume (2006) studied a model in which general practitioners refer patients to hospitals for secondary care and hospital care is an experience good.

(5) Because both tertiary and non-tertiary care hospitals provide nonspecialized services, their merger could be horizontal if the target were geographically close to the acquirer or to another hospital owned by the acquirer. Nevertheless, this is not the case with the majority of acquisitions in my sample.

(6) Huckman (2006) found that the statewide mortality for cardiac surgery did not improve after many hospitals in the state of New York offering cardiac surgery merged with hospitals that did not offer the service.

(7) Referrals might increase if both the target and the acquirer have increased numbers of managed care contracts. Nevertheless, Nakamura, Capps, and Dranove (2007) found increases in referrals for Medicare indemnity patients, thereby suggesting that there are other reasons for the increase.

(8) Anti-Kickback Law (42 U.S.C. [section] 1320a-7b(b)).

(9) Stark I/II (42 U.S.C. [section]1395nn; Social Security Act [section]1877 and [section]1903(s)).

(10) I assume that information regarding the overall quality of non-tertiary care hospitals is shared among patients through word of mouth or popular ratings. Dafny and Dranove (2008) found evidence for this "market-based learning."

(11) This assumption reflects the fact that high travel cost deters many patients from choosing tertiary care hospitals for an initial consultation, and thus few non-tertiary care hospitals directly compete with tertiary care hospitals. One specification (Assumption 2) in my estimation limits the sample to patients for whom there are no close tertiary care hospitals.

(12) Strictly speaking, the physicians at non-tertiary care hospitals refer patients, but I use the terms physicians at a non-tertiary care hospital and a non-tertiary care hospital interchangeably.

(13) In this section, a hospital that provides both non-tertiary and tertiary care is treated as two separate hospitals. In the estimation, I limit my analysis to referrals from hospitals not offering tertiary care services. Therefore, this assumption does not affect the analysis in subsequent sections.

(14) In reality, prices for managed care patients are determined in the negotiation between hospitals and insurers. Nevertheless, my analysis is not affected, as long as physicians take the prices as given when making referrals. In addition, net revenue from managed care payers accounted for less than one-third of the total hospital net revenue in Pennsylvania in 2002 (Pennsylvania Health Care Cost Containment Council 2003).

(15) Acquirer hospitals might use administrative pressure to attract referrals from target hospitals. For instance, a manager at a target might ask the physicians to justify referrals made to tertiary care hospitals other than the acquirer.

(16) For the reasons described in endnote 14, I assume that reputation has negligible effects on hospital prices and on the price elasticity of demand.

(17) I use the terms CABG/PTCA and cardiac surgery interchangeably. CABG and PTCA are competing technologies for the treatment of coronary artery disease (Bradford et al. 2001; Huckman 2006).

(18) There are a number of studies on the volume-outcome relationship in CABG/PTCA. For recent work on the subject, see Epstein et al. (2004) for PTCA and Hannan et al. (2003) for CABG.

(19) I allow [H.sub.k] to vary by year in the estimation.

(20) I allow D[H.sub.k] to vary by year in the estimation.

(21) Burns and Wholey (1992) found that physicians tend to refer patients to the hospitals that are close to their offices.

(22) Teruya (2004) reported that one hospital offers physicians free meals at a special cafeteria to attract referrals.

(23) In my data, some tertiary care hospitals and non-tertiary care hospitals are members of the same consortium of hospitals, although the relationship is not based on ownership. I treat them as having a loose relationship.

(24) The choice probability is summed over both tertiary and non-tertiary care hospitals. Patients who are likely to choose tertiary care hospitals for heart attack treatments are excluded from the analysis under Assumption 2.

(25) RD[E.sup.est.j] is calculated based on the estimated choice probabilities of all patients whose home is within a one-hour drive of hospital j. This limits the correlation between RD[E.sup.est] and a patient's estimated choice probability.

(26) Patients who bypassed non-tertiary care hospitals and went directly to tertiary care hospitals are likely to be excluded from the analysis under Assumptions 1 and 2. On the other hand, they might not be excluded under Assumption 3.

(27) The choice of area and time frame primarily reflects data availability. In addition, this area experienced numerous hospital acquisitions in the early 1990s (Burns et al. 2000).

(28) Region 1 includes the following counties: Allegheny, Armstrong, Beaver, Butler, Fayette, Greene, Washington, and Westmoreland. Region 3 includes Bedford, Blair, Cambria, Indiana, and Somerset.

(29) A hospital system is a group of hospitals under common ownership.

(30) A trivial explanation for why some mergers are more successful in increasing referrals than are others is that some target hospitals admit few patients who need cardiac referrals and thus do not have the ability to increase referrals. I exclude non-tertiary care hospitals not included under Assumption 1 from my sample to focus on other explanations, although this reduces the comparability of my results under Assumption 2 and Assumption 3 to those indicated in the previous literature.

(31) The number of referring hospitals and tertiary care hospitals drastically changed between 1997 and 2002 because many hospitals started offering cardiac catheterization and CABG/PTCA.

(32) I treat hospitals participating in Pyramid Health as being affiliated with each other.

(33) The number of observations decreased between 1997 and 2002 because more patients were covered under HMOs and were thus excluded from the 2002 analysis.

(34) The average surgical volume declined from 1997 to 2002 due to the increase in hospitals offering CABG/PTCA.

(35) I used GAUSS codes by Train, Revelt, and Ruud (1999).

(36) In summary, the signs and statistical significance of the estimated coefficients are as expected. In particular, the results show that patient traveling hours are the most important determinant of hospital choice for AMI patients, especially older patients.

(37) Because RD[E.sup.est]s are calculated based on estimated parameters, the standard errors reported here could be underestimated. Ideally, I would like to correct for this, but I was not able to apply the method proposed in Murphy and Topel (1985) in a straightforward manner because RD[E.est]s are complicated functions of the estimated parameters. Using other measures of competition, such as the Herfindahl-Hirschman index, would result in the same problem, as they are also measured with an error and there is no way of correcting for the bias in the estimated covariance matrix.

(38) Another noticeable difference is that the magnitudes of the coefficients are much larger under Assumption 1 and that the coefficients of Aff x Loose, Aff x First Yr, Aff x PI and Aff x RDE are significant only under Assumption 1. These findings probably indicate that the referring hospitals for some patients are misidentified under Assumptions 2 and 3.

(39) Under Assumption 1, the coefficients of Aff and Aff x High have opposite signs and are close in magnitude, as are the coefficients of Aff x RDE and Aff x RDE x High. I performed the likelihood ratio test to analyze the statistical significance of the linear combinations of the coefficients. I rejected both null hypotheses at the 1% significance level under all of the assumptions concerning the referring hospitals.

Sayaka Nakamura, Ph.D., is an associate professor at the Graduate School of International Management, Yokohama City University. Address correspondence to Prof. Nakamura at 22-2 Seto, Kanazawaku, Yokohama, 236-0027, Japan. Emaik sayaka_n@yokohama-cu.ae.jp
Table 1. Definitions of explanatory variables

Variable        Definition

DT              Travel time between the referring
                hospital and tertiary care hospital

T               Travel time between the patient's home
                and tertiary care hospital

[RDE.sup.est]   Estimated responsiveness of demand for
                the referring hospital to a patient's
                experience

Aff             =1 if the tertiary care hospital is
                affiliated with the referring hospital;
                0 otherwise

Loose           =1 if the tertiary care hospital is
                loosely affiliated with the referring
                hospital; 0 otherwise

FirstYr         =1 if the tertiary care hospital became
                affiliated with the referring hospital
                within one year; 0 otherwise

Old             =1 if the patient is at least 80 years
                old; 0 otherwise

PI              =1 if the patient is privately insured;
                0 otherwise

High            =1 if the tertiary care hospital is high
                quality

Table 2. List of target and acquirer hospitals

Year          System                     Target hospitals

1997   AHERF                  Allegheny Valley
                              Canonsburg General
                              Forbes Regional

       Conemaugh              Meyersdale Community
                              Windber Hospital & Wheeling Clinic

       Mercy                  Mercy Providence
       UPMC                   Beaver Valley
                              Bedford
                              Braddock
                              McKeesport
                              South Side
                              St. Margaret

       Valley                 Sewickley Valley

       Western Penn           Suburban General

2002   Conemaugh              Meyersdale Community
                              Miners Hospital
                              Windber Medical Center

       St. Francis            Saint Francis Hospital--Cranberry

       Mercy                  Mercy Providence

       UPMC                   Bedford
                              Braddock
                              McKeesport
                              South Side
                              St. Margaret

       Valley                 Sewickley Valley

       Westmoreland           Frick

       West Penn Allegheny    Alle-Kiski (former Allegheny Valley)
                              Canonsburg General
                              Forbes Regional
                              Suburban General

Year          System                Acquirer hospitals

1997   AHERF                  Allegheny General

       Conemaugh              Conemaugh Valley Memorial

       Mercy                  Mercy Hospital of Pittsburgh
       UPMC                   Passavant
                              Shadyside
                              Presbyterian

       Valley                 Medical Center, Beaver

       Western Penn           Western Pennsylvania

2002   Conemaugh              Bon Secours Holy Family
                              Conemaugh Valley Memorial

       St. Francis            Saint Francis Medical Center

       Mercy                  Mercy Hospital of Pittsburgh

       UPMC                   Lee Regional
                              Passavant
                              Shadyside
                              Presbyterian

       Valley                 Medical Center, Beaver

       Westmoreland           Westmoreland Regional

       West Penn Allegheny    Allegheny General
                              Western Pennsylvania

Notes: Hospitals in boldface were included in the analysis. In 1997,
AHERF and Valley were loosely affiliated with each other through
Pyramid Health. St. Clair, a community care hospital in Pittsburgh,
was also a part of Pyramid Health. Pyramid Health was dissolved in
1998. In 2002, former AHERF and Western Penn hospitals formed West
Penn Allegheny.

Table 3. Number of referring and tertiary
care hospitals in the sample

                             1997     2002

Referring hospitals           18       16
Independent                    9       11
Target                         9        5
Loose                          4        0
First year                     8        0
Tertiary care hospitals       13       17
Independent                    8        7
Acquirer                       5       10
Loose                          2        0
First year                     5        0
High quality                   3        3

Note: All hospitals studied were secular nonprofit hospitals.

Table 4. Characteristics of patients, chosen hospitals, and
referring hospitals

                                             Assumption 1
                                         (catherization record)

                                          872 observations
                                          (319 from 2002)

                                         Mean           S.D.
Patient characteristics
  Female                                   .42            .49
  Age                                    72              8
  Expired when discharged                  .00            .00
  Medicare                                 .80            .40
  Blue Cross                               .16            .36
  Commercial                               .04            .20
  Hispanic                                 .00            .00
  Asian                                    .00            .00
  Black                                    .02            .15
  Race unknown                             .01            .10
Chosen hospitals' characteristics
  DT                                     29             15
  T                                      31             15
  High                                     .58            .49
  Aff                                      .45            .50
  Loose                                    .10            .29
  FirstYr                                  .07            .26
Referring hospitals' characteristics
  Teaching                                 .04            .19
  [RDE.sup.est]                            .67            .17
  UPMC (1997 and 2002)                     .38            .49
  Westmoreland (1997 and 2002)             .00            .06
  AHERF (1997 only)                        .12            .32
  Valley (1997 and 2002)                   .14            .35
  West Penn Allegheny (2002)               .03            .18

                                           Assumption 2
                                           (AMI demand)

                                         805 observations
                                         (309 from 2002)

                                         Mean           S.D.
Patient characteristics
  Female                                   .47            .50
  Age                                    73              8
  Expired when discharged                  .02            .14
  Medicare                                 .83            .37
  Blue Cross                               .15            .35
  Commercial                               .02            .14
  Hispanic                                 .00            .00
  Asian                                    .00            .00
  Black                                    .02            .15
  Race unknown                             .08            .28
Chosen hospitals' characteristics
  DT                                     37             15
  T                                      38             15
  High                                     .58            .50
  Aff                                      .29            .45
  Loose                                    .05            .22
  FirstYr                                  .06            .23
Referring hospitals' characteristics
  Teaching                                 .04            .20
  [RDE.sup.est]                            .55            .13
  UPMC (1997 and 2002)                     .25            .43
  Westmoreland (1997 and 2002)             .03            .17
  AHERF (1997 only)                        .10            .30
  Valley (1997 and 2002)                   .06            .24
  West Penn Allegheny (2002)               .11            .3l

                                          Assumption 3
                                           (location)

                                         1,003 observations
                                         (346 from 2002)

                                         Mean           S.D.
Patient characteristics
  Female                                   .41            .49
  Age                                    71              8
  Expired when discharged                  .02            .12
  Medicare                                 .80            .40
  Blue Cross                               .18            .38
  Commercial                               .03            .16
  Hispanic                                 .00            .00
  Asian                                    .00            .00
  Black                                    .04            .20
  Race unknown                             .07            .26
Chosen hospitals' characteristics
  DT                                     33             16
  T                                      33             16
  High                                     .54            .50
  Aff                                      .26            .44
  Loose                                    .04            .18
  FirstYr                                  .06            .23
Referring hospitals' characteristics
  Teaching                                 .04            .18
  [RDE.sup.est]                            .72            .19
  UPMC (1997 and 2002)                     .23            .42
  Westmoreland (1997 and 2002)             .02            .15
  AHERF (1997 only)                        .16            .37
  Valley (1997 and 2002)                   .05            .21
  West Penn Allegheny (2002)               .12            .33

Notes: See Table 1 for definitions of the variables for chosen
hospital's characteristics.

Statistics are based on the patient as a unit. Travel times are
expressed in minutes. S.D. = standard deviation.

Table 5. Characteristics of tertiary care hospitals included in the
analysis

                       High-quality acquirers    Other acquirers

                       Mean         S.D.         Mean         S.D.

1997

Number of hospitals       --         --            2           --
Number of CABG         1,110        248          517          405
Number of PTCA         1,954        960          695          578
Teaching                   1.00        .00          .33          .58

2002

Number of hospitals        3         --            7           --
Number of CABG           718        128          325          210
Number of PTCA         1,624        644          614          461
Teaching                   1.00       .00           .14          .38

                       Non-acquirers

                       Mean         S.D.

1997

Number of hospitals      9           --
Number of CABG         464          303
Number of PTCA         607          321
Teaching                  .29          .49

2002

Number of hospitals      7           --
Number of CABG         309           96
Number of PTCA         570          262
Teaching                  .29          .49

Note: All hospitals studied were secular nonprofit hospitals.
S.D. = standard deviation.

Table 6. Responsiveness of demand to patients' experiences for
referring hospitals included in the analysis

                       Number of
Hospital group         hospitals    Mean    S.D.    Minimum   Maximum

Independent                14        .52     .22      .25       .93
referring hospitals

Target hospitals           20        .68     .16      .43       .95

Note: S.D. = standard deviation.

Table 7. Estimated parameters for referral choice model

                                       Assumption 1
                                  (catherization record)

                                     872 observations
                                     (319 from 2002)

                                   Beta             S.D.

DT                                  -.147            .048
[DT.sup.2]                           .001            .001
T                                   -.146            .152
[T.sup.2]                           -.002            .002
[RDE.sup.est] x T                    .012            .197
[RDE.sup.est] x [T.sup.2]            .004            .003
Aff                                76.994          27.773
Aff x Loose                         -.877            .315
Aff x FirstYr                      -1.015            .285
Aff x Old                           -.148            .243
Aff x PI                             .476            .227
Aff x High                        -78.855          27.806
Aff x [RDE.sup.est]              -102.437          38.260
Aff x [RDE.sup.est] x High        107.181          38.269

                                      Assumption 2
                                      (AMI demand)

                                    805 observations
                                    (309 from 2002)

                                   Beta             S.D.

DT                                 -.495            .186
[DT.sup.2]                          .005            .002
T                                   .324            .307
[T.sup.2]                           .000            .004
[RDE.sup.est] x T                   .010            .454
[RDE.sup.est] x [T.sup.2]          -.011            .007
Aff                                5.585           1.638
Aff x Loose                        -.165            .495
Aff x FirstYr                      -.584            .328
Aff x Old                          -.012            .244
Aff x PI                           -.160            .309
Aff x High                        -8.275           1.977
Aff x [RDE.sup.est]               -4.222           2.724
Aff x [RDE.sup.est] x High         9.405           3.286

                                      Assumption 3
                                       (location)

                                    1,003 observations
                                     (346 from 2002)

                                   Beta             S.D.

DT                                 9.190           7.949
[DT.sup.2]                         -.107            .096
T                                 -8.805           7.953
[T.sup.2]                           .104            .096
[RDE.sup.est] x T                  -.927            .233
[RDE.sup.est] x [T.sup.2]           .007            .003
Aff                                3.566           1.739
Aff x Loose                         .303            .356
Aff x FirstYr                      -.255            .271
Aff x Old                           .257            .260
Aff x PI                            .272            .252
Aff x High                        -6.667           1.939
Aff x [RDE.sup.est]               -1.320           2.695
Aff x [RDE.sup.est] x High         6.635           2.951

Notes: See Table 1 for definitions of the explanatory variables.

The outcome is the tertiary care hospital chosen for a cardiac
surgery. S.D. = standard deviation.
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Author:Nakamura, Sayaka
Publication:Inquiry
Article Type:Statistical data
Geographic Code:1USA
Date:Sep 22, 2010
Words:10189
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