The choice of employment arrangement in the market for hospitalist services.

1. Introduction

Hospitalists specialize in the management of patients who are hospitalized and provide continuity of hospital care from admission to discharge. Clinical studies show that hospitalists reduce average length of stay and contain cost without compromising quality of care (Meltzer et al. 2002). By closely monitoring patients and coordinating the flow of information, they limit the number of unnecessary tests and procedures, help reduce medical errors, and help in the formulation of practice guidelines (Meltzer 2001a; Wachter and Goldman 2002). Since hospitalists were first introduced as a "new breed of physicians" in 1996, the number of physicians specializing in hospital medicine in the United States has grown beyond 11,000 (Kralovec et al. 2006), with future projected growth to 20,000, about the number of cardiologists in the United States (Wachter 2004b).

For physician groups, hospitalists are attractive in that they enable the referring physicians to delegate the hospital-based component of their patients' medical care. In turn, for hospitals, the ability to manage utilization and thereby contain cost without compromising the quality of care makes hospitalists an attractive proposition. In response to these diverse incentives, a variety of employment arrangements for hospitalists has emerged. These include hospitalist-only groups, the integration of hospitalists into multispecialty groups, and the development of hospital-based hospitalist programs in both teaching and nonteaching facilities.

While the growing number of hospitalists is beyond dispute, to date no study has examined the underlying economic forces responsible for the diversity in employment arrangements. This is especially important because the prevailing employment model in a given market may affect the optimality of reimbursement rates set by a regulator or payer organization. To the extent that rate-setting agencies ignore the endogeneity of employment arrangements, under current legal statutes reimbursement levels may fail to achieve their intended allocation goals.

In this paper, we provide the first systematic analysis of how the differing motives of primary care groups and hospitals for the adoption of hospitalists are reconciled, how the strategic interaction between these two players may give rise to multiple equilibria, and how trends in hospitalization rates and fixed setup costs may explain gradual shifts in the predominant employment arrangements.

2. The Incentives to Employ Hospitalists Directly

Hospitalists, regardless of who employs them, are the liaison between primary care physicians and hospitals and confer benefits to both parties. Yet hospitals and primary care physicians weigh differently the various dimensions of a hospitalist's performance. While primary care physicians want hospitalists to focus solely on ensuring high quality of inpatient care, even if it raises the cost of treatment (which is borne by the hospital), hospitals want hospitalists to strike a balance between the cost of treatment and its quality. Thus, either party can capture important additional benefits if it employs the hospitalists that it uses itself rather than contracting with hospitalists employed by another party. By employing them directly, the hiring party can overcome constraints on fee splitting, enabling it to share with its hospitalists the cost savings they generate for the employer and, thus, achieve greater cost reductions than if it bought services from outside hospitalists.

As long as the costs of setting up its own hospitalist program are not too high, each party will prefer to employ and use its own hospitalists. While hospitals can refuse to allow hospitalists who they do not employ themselves, primary care physicians can refuse to send their patients to a hospital that refuses to admit their hospitalists. As will be shown in the model here, this conflict implies that the relative bargaining power of each party plays a key role in determining which employment arrangement prevails in a given market. It also implies that the prevailing employment arrangement may be inefficient if kickbacks are ruled out.

Figure 1 sketches the three most salient employment arrangements for hospitalists: employed by hospitals (forward integration), employed by physician groups (backward integration), and self-employed through hospitalist-only groups ("freestanding"/no integration).

[FIGURE 1 OMITTED]

Table 1 shows the distribution of hospitalist employment arrangements in hospitals in 2003 and 2004. The figures are based on the American Hospital Association's (AHA's) annual surveys of hospitals in 2003 and 2004, the first two years for which information about hospitalist use and employment arrangement is publicly available.

Hospitals using hospitalists employed by a hospital or university comprised the largest group in both years, followed by hospitals whose hospitalists were employed by a hospitalist-only group and those whose hospitalists were employed by a physician group. Overall, in both survey years, over 90% of hospitals in which hospitalists provided care used one of these three employment arrangements.

Growth was not uniform across employment arrangements. The number of hospitals that employed hospitalists themselves grew by 13%, the number of hospitals using hospitalists employed by physician groups grew by 34%, and the number of hospitals using self-employed hospitalists grew by 24%.

Table 2 shows results from the 2003 Productivity and Compensation Survey of hospitalist groups conducted by the Society of Hospital Medicine (SHM), the largest professional association of hospitalists in the United States.

Differences in survey format of each group may explain the proportional discrepancy between the AHA data and the SHM data. The AHA survey asked U.S. hospitals whether they used and employed hospitalists, while the SHM surveyed hospitalist groups directly. As many hospitalist-only groups serve multiple hospitals, they will appear multiple times in the AHA survey yet only once in the SHM survey. As such, the AHA data probably overestimate the share of this group relative to the SHM. On the other hand, programs run by hospitals should align one to one from AHA to SHM. A second difference is that the AHA survey includes the bulk of U.S. hospitals, while the SHM survey had an approximate 30% response rate and, as such, is likely to overstate the share of well-established hospital-based hospitalist programs relative to freestanding hospitalists groups.

Economic theory predicts that if hospitalists are uniformly engaged in a specific set of tasks, the health care system will converge to a single, cost-minimizing employment arrangement. In this light, the diversity of employment arrangements is puzzling. Despite the importance of the choice of employment arrangement for realizing the efficiency gains promised by the hospitalist movement, this question has received scant attention in the literature.

Apart from teaching duties for hospitalists who are employed by academic health centers, hospitalists are engaged in similar tasks across all employment arrangements. We conjecture that differences in transaction costs, perhaps reflected in the legal status of advantageous financial and contractual arrangements, account for the emergence of various employment models. These transaction costs hinder the parties involved in the continuum of care from sharing the efficiency gains. As a result, we would expect the direct employment by the hospital or physician groups to prevail over independent employment whenever the efficiency gains of the former exceed those of the latter.

Primary care physicians must make two types of decisions. The first decision is whether to delegate inpatient care to hospitalists, balancing gains from specializing in office-based patient care against the potential discontinuity of care that the introduction of hospitalists creates. This handoff, at the point of the patient's transfer from the referring physician's office to the hospital, can lead to a loss of patient-specific information that might be relevant for optimizing the person's medical care in the hospital (Sox 2001). If they decide to use hospitalists, the second decision that primary care physicians must make is whether to employ them directly, balancing the fixed setup cost of employing hospitalists against the savings due to smoother continuity of care. Hospitalists that are directly employed by primary care groups will maintain close contact with the patient's primary care physicians, who convey to the hospitalist their knowledge of the patient's medical history and treatment preferences. Hospitalists employed directly by primary care physicians are more likely to use the hospital's resources in accordance with their employer's objectives.

The growing infrequency and the higher severity of the typical hospitalization have made hospital work less attractive for office-based clinicians (Meltzer 2001b). A decline in time spent in the hospital by primary care physicians lowers their return to investing in skills necessary for inpatient care. When hospital-based care becomes an "economically inefficient use of their own time" (Wachter 2004a), perhaps because of long travel times to the hospital yet similar reimbursement rates for office and hospital care, primary care physicians have an incentive to delegate this component of the patient's medical care to hospitalists. Moreover, primary care physician groups may prefer to employ or contract directly with hospitalists because it may give them better control over the hospitalist's priorities in treating the referring group members' hospitalized patients. Compared to direct employment by the hospital, this arrangement may mitigate the possible loss of knowledge about the patient's medical history and treatment preferences, which might be particularly acute for older patients.

When primary care physicians rarely supervise their patients' care in the hospital, it lowers the hospital's ability to interface with them, manage their patients' utilization, introduce them to new technologies, trust their familiarity with the hospital infrastructure and staff, and reduce medical errors. By and large, hospitals prefer to have physicians committed to inpatient care, and their ultimate choice is whether to set up a hospitalist program. By employing hospitalists directly, hospitals can reward hospitalists easily and legally for the cost savings, improvements in outcomes, and patient satisfaction ratings and thereby align the hospitalists' objectives with those of the hospital. This alignment may be particularly important when the hospital chooses to manage costly medical technologies whose use can be monitored and controlled by hospitalists. It might be argued that hospitalists represent the latest generation of utilization management. (1) In fact, compared to personnel expected to follow guideline-based utilization management, hospitalists enjoy greater discretion to vary treatment parameters in line with the hospital's global cost containment and quality-of-care objectives.

Direct employment by either a hospital or a primary care group may provide both the employer and the hospitalists with convenient access to a contractual agreement that allows them to share the gains from applied hospital medicine. While the fact that primary care physicians spend less time performing inpatient tasks makes hospitalists more attractive to both primary care physicians and hospitals, it is less informative for answering the question of who should employ them and what their primary goals under each employment arrangement would be.

Independent of which employment arrangement will ultimately be utilized, setting up and coordinating a new hospitalist program entails fixed costs. These may be financed by providers or insurers who stand to gain financially from the cost savings of such an institution. At present, pressure from managed care organizations provides an additional impetus for both hospitals and physician groups to use hospitalists. Although cost savings are a major concern of hospitals as well, the other primary motives for a hospital-initiated program are convenience for their physician staff, improved care of unassigned patients, and improvements in hospital safety and quality (Pham et al. 2005).

As with all physicians, there are three basic means through which hospitalists may be paid: salary, according to productivity only, or via a combination of both. The SHM data indicate that hospital-employed and academic practices are most likely to be directly salaried, while physicians in hospitalist-only groups are more than five times more likely to be paid on a purely productivity-based scheme than the national average. Perhaps because of their greater use of productivity-based compensation methods, such private groups have been shown to have the highest median collections, encounter rates, and consultation rates. Academic hospitalist institutions, on the other hand, most commonly salaried, have the lowest median collections, encounter rates, and consultations of all despite evidence indicating they may offer a more complex range of services.

Regarding the savings that hospital medicine programs ultimately realize, the wide and expanding body of literature is in conflict: Some analyses reveal legitimate cost savings over primary care physician inpatient care, while some find no such significant changes (Coffman and Rundall 2005). In comparing employment arrangements to one another, however, the data available are more limited. Halasyamani et al. (2005) compared private hospital medicine groups and academic hospitalists against a common control group of community primary care physician inpatient data. The result was that academic hospitalists effected larger savings (20% decrease in length of stay, 10% decrease in adjusted costs) than did the private practitioners (8% decrease in length of stay, 6% decrease in adjusted costs). Feasible arguments for this are either that the hospital-employed groups had more financial incentive alignment for cost saving, through cost sharing with their hospitals (or similar mechanisms), or that the academic hospitalists were more proficiently integrated into the hospital infrastructure through which they were employed, allowing for greater streamlining of care. As to quality, the two test groups showed statistically insignificant differences in 30-day readmission rates as well as both in-hospital and 30-day mortality levels.

3. The Model

In this section, we present a model to derive the conditions under which the various employment arrangements emerge. We conceptualize the market for hospitalist services as a noncooperative game, in which two players--the hospital and the primary care physician group--choose whether to employ hospitalists directly by comparing the incremental profits of either choice.

We discuss the primary care physician and the hospital problems independently, assuming that hospitals and primary care physicians operate as separate profit-maximizing entities on the vertical care continuum. The values of the players' problems depend on the regulatory and technological constraints that they operate under as well as the opposing player's choice of action. For primary care physicians, the availability of inpatient-dedicated doctors obviates costly commutes to and from the hospital and investment in hospital-specific knowledge. In turn, the ability of hospitalists to manage the utilization of inpatient services makes them an attractive proposition for hospitals. Once the payoff functions have been derived, players choose simultaneously but independently whether to employ hospitalists themselves. The set of equilibria is characterized as a function of points in the parameter space. We derive how changes in two key parameters--a decline in the frequency of hospitalizations and a decline in players' cost of setting up a hospitalist program--will affect the distribution of employment arrangements. The section concludes with a discussion of three extensions to the model: the emergence of hospitalist-only groups, third-party mandates of hospitalist use, and the role of vertically integrated health care systems.

The Primary Care Physician's Problem

Each primary care physician must decide how much time to allocate to seeing patients in the office and seeing patients in the hospital. Let [R.sub.O] and [R.sub.H] denote the reimbursement per patient seen in the office and in the hospital, respectively. We normalize total work time to 1 and let s denote the fraction of time allocated to hospital care, so that the fraction of time allocated to office work is 1 - s. Let the number of patients seen in either setting, K(s) and K(1 - s), be an increasing convex function of the time allocated to that setting: K'(*) > 0, K"(*) > 0, K(0) = 0. Thus, as in Rosen (1983), K(*) exhibits increasing returns to specialization, reflecting learning economies inherent in specialization by site of care, as well as fixed cost elements of acquiring site-specific human capital and commuting to that site of care.

If managing a patient's hospital care is more highly reimbursed than a patient's office visit, [R.sub.H] > [R.sub.O], all other things equal, physicians will want to allocate all their time to hospital care. But the physician himself can at most see as many of his patients in the hospital, K(s), as he referred to the hospital, [mu] x K(1 - s), where [mu] is the fraction of patients seen in the office and required to be transferred to the hospital. (2) Formally,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

This optimization problem is shown in Figure 2.

[FIGURE 2 OMITTED]

The solid V-shaped line shows the objective function [R.sub.o]K(1 - s) + [R.sub.H]K(S), where, without loss of generality, [R.sub.O] is normalized to 1. The objective function is the sum of K(1 - s) [equivalent to] [R.sub.O]K(1 - s), represented by the downward-sloping solid line, and [R.sub.H]K(s), represented by the upward-sloping broken line, which in turn is a multiple of K(s), represented by the upward-sloping solid line.

The intersection of K(s) and [mu] x K(1 - s), represented by the downward-sloping broken line, defines the highest value of s, denoted [s.sub.max], that still satisfies the constraint; that is, [s.sub.max] solves K(s) = [mu] x K(1 - s). If K(*) is homogeneous of degree t > 0, [mu] x K(1 - s) = K([[mu].sup.1/t](1 - s)) and

[s.sub.max]([mu]) = [[mu].sup.1/t]/1 + [[mu].sup.1/t]' (2)

where [s.sub.max] [member of] [0,0.5] is the maximum fraction of time that the primary care physician can spend on inpatient care for a given referral rate [mu]. Note that, from Equation 2, [S.sub.max]([mu]) is increasing in [mu], [s.sub.max](0) = 0, and [s.sub.max](1) = 0.5. (3)

As both K(s) and K(1 - s) are convex in s, so is the objective function, implying that a corner solution will obtain, that is, [s.sup.*] [member of] {0,[s.sub.max]}. As a consequence of increasing returns to time spent in either setting, the primary care physician will either refer all his hospital-bound patients to a hospitalist, K(0) = 0, or refer none, K([s.sub.max]) [equivalent to] [mu] x K(1 - [s.sub.max]). (4) In Figure 2,

[R.sub.O] x K(1) + [R.sub.H] x K(0) > [R.sub.O] x K(1 - [s.sub.max]) + [R.sub.H] x K([s.sub.max]) = K(1 - [s.sub.max])[[R.sub.O] + [mu] x [R.sub.H]],

that [s.sup.*] = 0. That is, the physician will specialize in office-based care and will want to use a hospitalist to cover inpatient care.

From the figure, it is also apparent that an increase in [R.sub.H] relative to [R.sub.O] will pivot the objective function upward, while an increase in g will truncate it at a higher value for [s.sub.max]. Both make it more likely that the solution is [s.sup.*] = [s.sub.max]; that is, the physician will cover both the office-based and the hospital-based portion of his patients' care.

Primary care physicians develop a long-term relationship with their patients: They are familiar with the patients' medical history and possess other idiosyncratic, patient-specific information pertinent to the patient's optimal treatment. This information may be lost when the patient is handed off to a hospitalist. Let C([E.sub.p]) denote the cost to the primary care physician of handing off a patient to a hospitalist, where [E.sub.p] = 1 if the primary care physician decides to employ hospitalists directly and [E.sub.p] = 0 otherwise. This cost represents the time spent conveying critical information from the primary care physician to the hospitalist, investing in specific relationship and network formation. We posit that potential deficiencies in the hospital-based portion of a patient's care arising from the discontinuity of care can be reduced when hospitalists are employed directly by the primary care clinic: 0 < C(1) < C(0). Hospitalists who are directly employed by primary care physicians build greater levels of relationship-specific capital than hospitalists who work independently of primary care physicians: They enjoy better access to patient information, communicate more closely with physicians in their group, and have greater incentives to provide postdischarge feedback. Therefore, when primary care clinics must decide whether to employ hospitalists directly, they will balance improvements in the continuity of care of a typical patient, C(0)-C(1), against fixed setup costs, [F.sup.p].

Once the costs of handing off patients to hospitalists and of employing hospitalists directly are included, physicians will choose to specialize in office-based care when

K(1) x ([R.sub.O] - [mu] x C([[??].sub.p])) - [[??].sub.p] x [F.sub.p] [greater than or equal to] K(1 - [s.sub.max]) x ([R.sub.O] + [mu] x [R.sub.H]), (3)

where [[??].sub.p] [member of] {0,1} represents the profit-maximizing choice by primary care physicians to employ hospitalists themselves:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Rearranging Equation 3, we can express the condition for specialization in office-based care as follows:

[R.sub.O][K(1) - K(1 - [s.sub.max])] [greater than or equal to] [R.sub.H] x [mu] x K(1 - [s.sub.max] + K(1) x [mu] x C([[??].sub.p] + [[??].sub.p] x [F.sub.p]. (4)

Equation 4 expresses the decision problem of a primary care physician who has been providing patient care both in the office and in the hospital and who now contemplates specializing in office-based care only.

The left-hand side of Equation 4 shows the marginal benefit of specializing in office-based care: It is the monetary value of the increase in the number of patients that the physician can see in the office now. It represents the gains from specialization in office care, including eliminating travel time to and from the hospital, eliminating the need for extensive personal acquaintance and institutional knowledge required for coordinating care in the hospital, and using this time instead to improve productivity of office care or spending more time to see patients in the office.

The right-hand side of Equation 4 shows the marginal cost of specializing in office-based care. The first term, [R.sub.H] x [mu] K(1 - [s.sub.max]), measures the opportunity cost of specialization: It is the monetary value of hospital-based patient care that the primary care physician foregoes by specializing. The second term, K(1) x [mu] x C([[??].sub.p]), measures the additional cost that the primary care physician now incurs because he is handing off patients designated for hospital care to a hospitalist. As explained previously, this cost includes the time spent conveying patient-specific treatment-relevant information to the hospitalist. The third term, [[??].sub.p] x [F.sub.p], represents the primary care physician's cost of using hospitalists if he decides to employ them himself ([[??].sub.p] = 1).

In separate work, we show that primary care physicians, pediatricians, and family practitioners operate in an environment where both the rate of referring patients to the hospital, [mu], and the reimbursement for hospital-based care relative to office-based care, [R.sub.H]/[R.sub.O], are low (David and Helmchen 2006). Consistent with Equation 4, physicians in these specialties rely on hospitalists, while specialists with relatively high values for [mu] and [R.sub.H] / [R.sub.O], such as cardiologists, gastroenterologists, and endocrinologists, tend to retain the hospital-based portion of patient care.

Specializing in office care is feasible only if another physician assumes the hospital-based portion of a patient's care. The emergence of hospital medicine allows those physicians who provide office-based care only to delegate the management of their patients' hospital care to hospitalists. (5)

As noted in the introduction, to ensure that their patients are supervised by hospitalists in the hospital, primary care physicians can avail themselves of three different options: They can hire hospitalists themselves (backward integration), they can send their patients to hospitals that employ hospitalists themselves (forward integration), or they can contract with a freestanding group of hospitalists (entrepreneurial model).

Let [B.sub.p] denote the benefit per patient to the primary care physician of employing a hospitalist directly (not including fixed set up costs). This represents the savings in travel time to and from the hospital as well as the other gains of possibly higher quality of inpatient care minus the price that the primary care physician must pay the hospitalist per patient:

[B.sub.p] = K(1) x ([R.sub.O] - [mu]C(1)) - K(1 - [s.sub.max]([mu])) x ([R.sub.O] + [mu] x [R.sub.H). (5)

Alternatively, under either the forward-integration or the entrepreneurial model, the primary care physician can use hospitalists without incurring the fixed cost of direct employment. In this case, however, we posit that the hospitalists that assume the care of patients sent to them by primary care physicians enjoy less access to patient information, communicate less closely with the primary care physicians, and have fewer incentives to provide postdischarge feedback than if they were employed directly by the primary care physicians. Let [[beta]sub.p] denote the multiplier for using hospitalists that are not directly employed by the primary care physicians:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

The values of [B.sub.p] and [[beta].sub.p] defined in Equations 5 and 6, respectively, as well as [F.sub.p], will be used next to derive the primary care physician's payoff as a function of his own and the hospital's decision to employ hospitalists. Once the analogous values have been derived for the hospital, these functions are used to derive the set of equilibria for a variety of points in the parameter space.

The Hospital's Problem

Hospitals stand to gain from inpatient-dedicated physicians, even if they do not employ them directly. These physicians familiarize themselves with the inpatient setting, understand the organizational barriers and structure, and form close professional relations with specialists, technicians, nurses, and other hospital personnel.

For each patient, the hospital receives a prospective payment D and incurs a cost C, which decreases with the fraction of time s that the physician supervising the patient's inpatient-care episode spends on hospital care. When s < 1, the physician is a primary care physician who spends 1 - s on office-based care; when s = 1, the physician is a hospitalist. C also decreases with the physician's effort level, e [member of] {0,1}. In other words, the hospital's gains are partitioned into returns from having physicians dedicated to inpatient care, s, and benefits from employing them directly, which allows the hospital to affect the physician's effort level, e. The hospital's profit per patient is

[pi] [equivalent to] D - C(e, s), with [partial derivative][pi]/[partial derivative]e > 0, [partial derivative][pi]/[partial derivative]s > 0.

The fraction of time devoted to hospital care by primary care physicians who manage care for their hospitalized patients is [s.sub.max]([mu]) = [[mu].sup.1/t][1 + [[mu].sup.1/t]] [member of] [0,0.5]. Assume that in this case the hospital cannot exercise efficient utilization management or induce the primary care physicians to exert cost-cutting effort, so that e = 0, and the hospital's profit per patient is

D - C(0, [s.sub.max]([mu])).

If inpatients are managed by hospitalists, s = 1. If these hospitalists are not employed by the hospital, the hospital cannot induce them to exert additional effort, so that e = 0, and the hospital's profit per patient is

D - C(0,1).

As [s.sub.max]([mu]) < 1, the hospital's expected benefit of using hospitalists, denoted [[beta].sub.H][B.sub.H], is

[[beta].sub.H][B.sub.H] [equivalent to] N x [C(0, [s.sub.max]([mu]))- C(0,1)],

where N is the number of inpatient admissions. From the assumption that C is decreasing in s, [[beta].sub.H][B.sub.H] > 0; that is, ceteris paribus, hospitals prefer to use hospitalists.

When would hospitals employ hospitalists directly? While hospitals are reimbursed according to prospective payment schedules, primary care physicians or hospitalists employed by them are paid according to a fee-for-service payment schedule. And while hospitals have incentives to discharge patients more quickly, primary care physicians do not. In fact, by keeping sick patients in the hospital, physicians shift their treatment costs to the hospital and away from their private practice. By sharing the surplus generated from cost containment, the incentives of hospitals and hospitalists can be aligned. If hospitalists are employed by the hospital, they can be induced to economize on tests and procedures, adhere to utilization protocols, and decrease length of stay by focusing on throughput management and discharge orientation. At the same time, the hospital-employers incur the fixed cost of setting up a hospitalist program, denoted [F.sub.H].

We posit that [F.sub.H] represents the cost of setting up a system that monitors the realized cost per patient and thereby allows the hospital to detect performance differences between hospitalists. Let w denote a bonus per patient managed that the hospital pays its hospitalists on top of their regular wage. If the hospital wants to induce the hospitalist to exert effort level e = 1, its minimum cost per patient, inclusive of the bonus, is found by solving

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where U(*) is the hospitalist's utility function, which is increasing and concave in w and decreasing in e, and [U.bar] is the hospitalist's reservation utility that reflects his outside opportunities. (6)

As the objective function is increasing in w, either the participation or the incentive compatibility constraints will be binding:

U([w.sup.*](C(1,1)),1) [equivalent to] max{[U.bar],U([w.sup.*](C(0,1)),0)},

which implicitly defines the bonus necessary to induce e = 1. (7)

Let

[B.sub.H] [equivalent to] N x [C(0, [s.sub.max]([mu])) - {C(1,1) + [w.sup.*](C(1,1))}] (7)

denote the cost savings, gross of the fixed cost [F.sub.H] of setting up the hospitalist program, if the hospital uses a hospitalist that it employs directly.

We can define 13, as the multiplier that represents the hospital's cost savings of using another party's hospitalists relative to using its own hospitalists:

[[beta].sub.H] = [[beta].sub.H][B.sub.H]/[B.sub.H] = [C(0, [s.sub.max]([mu])) - C(0,1)]/[C(0, [s.sub.max]([mu])) - {C(1,1) + [w.sup.*](C(1,1))}]. (8)

Similar to the primary care physician problem, [B.sub.H], [[beta].sub.H], and [F.sub.H] will be used to characterize the hospital's benefits and costs of using hospitalists.

Equilibrium

When the primary care physician group decides whether to employ hospitalists, it takes into account the possibility that the hospital employs its own hospitalists and vice versa. We conceptualize the simultaneous employment decisions by the two players as a noncooperative game in which each player chooses whether to employ his own hospitalists to maximize his payoff for a given choice by the other player. Let P([E.sub.p], [E.sub.H]) and H([E.sub.p], [E.sub.H]) denote the primary care physician and the hospital's payoff for the action pair ([E.sub.p], [E.sub.H]), where, in analogy to the definition of [E.sub.p], [E.sub.H] = 1 if the hospital decides to employ hospitalists directly and [E.sub.H] = 0 otherwise.

In this game, deciding to employ one's own hospitalists involves incurring the nonrecoverable fixed cost. For some action pairs, the players' preferred actions are incompatible with each other. For instance, when both the primary care physician and the hospital decide to employ their own hospitalists, (1,1), both will want to use their own hospitalists. To determine who will eventually treat (and bill) the inpatient population, we introduce an index of the hospital's bargaining power, [[theta].sub.H], where [[theta].sub.H] = 1 means that the hospital decides whose hospitalists will be allowed to treat the inpatient population and [[theta].sub.H] = 0 means that the physician group decides whose hospitalists will be used and if any hospitalists will be used at all. The two players, their two possible actions, and their payoffs are represented in Figure 3.

[FIGURE 3 OMITTED]

When [[theta].sub.H] = 0, different parameter values will give rise to different (sets of) equilibria, as shown in Table 3.

Recall that [[beta].sub.p], [B.sub.p], [[beta].sub.H], and [B.sub.H] are all functions of [mu], the fraction of patients seen in the office and required to be transferred to the hospital, so that the possible equilibria can be depicted for different combinations of ([F.sub.p], [F.sub.H], [mu]). For simplicity, [F.sub.p] = [F.sub.H] = F is assumed in Figure 4.

[FIGURE 4 OMITTED]

When [[theta].sub.H] = 0, primary care physicians can compel the hospital to allow them to manage their inpatients themselves or to accept the hospitalists that they employ themselves. As the figure shows, for very low values of [mu], the fixed cost of employing hospitalists, F, likely exceeds the benefit [B.sub.p] for primary care physicians, deterring them from employing hospitalists themselves. Instead, any use of hospitalists in this market will depend on the hospital's benefit [B.sub.H] relative to its fixed cost F.

As [mu] increases, the benefit [B.sub.p] increases. The reason is that the primary care physician's opportunity cost of employing hospitalists, K(1 - [s.sub.max]) x ([R.sub.O] + [mu] x [R.sub.H]), decreases, as the larger [mu] makes it optimal to shift more time to inpatient care, which in turn reduces the gains from specialization in either setting. For a given fixed cost, the greater benefit makes it more profitable for the primary care physician to employ hospitalists. As the hospital has no bargaining power and, therefore, must accept the primary care physicians' use of their own hospitalists, the hospital most commonly will not find it profitable to set up its own hospitalist program.

If fixed costs are larger than the incremental value of moving from using hospitalists to employing them ([F.sub.p] > (1 - [[beta].sub.p])[B.sub.p]), two equilibria are possible:

1. As before, (1,0) may prevail. If the primary care physicians have decided to employ their own hospitalists, they can compel the hospital to accept these to manage their inpatients at the exclusion of any hospitalists that might be employed by the hospital. As a result, the hospital would not be able to raise its revenue beyond [[beta].sub.H][B.sub.H] if it set up its own program.

2. Alternatively, (0,1) may prevail. When [F.sub.p] > (1 - [[beta].sub.p])[B.sub.p] and given that the hospital has decided to employ its own hospitalists, the additional revenue that the primary care physicians could earn by setting up their own program and compelling the hospital to accept their own hospitalists, (1 - [[beta].sub.p])[B.sub.p], is less than the setup cost, [F.sub.p].

The ability of some hospitals to force primary care physicians to hand off their patients to the hospital's hospitalists ([[theta].sub.H] = 1) has received more attention than some primary care physicians' ability to bypass a facility's hospital medicine program ([[theta].sub.H] = 0).

The obligation to use a hospital's own inpatient physicians has been met with opposition by many primary care physicians. Some are apprehensive about the adverse effects on the continuity of their patients' care and their own practical liabilities affected by hospital-mandated hospitalist use and have brought legal action to reinstate voluntary admissions procedures (Maguire 1999), often reversing hospital policy. Many primary care physicians remain unconvinced that the continued diffusion of the hospitalist model will ultimately benefit their practice or save costs to the system as a whole.

When [[theta].sub.H] = 1, the set of possible equilibria is given by Table 4. Under the assumption [F.sub.p] = [F.sub.H] = F, these equilibria are shown in Figure 5.

[FIGURE 5 OMITTED]

When [[theta].sub.H] = 1, the condition that the use of hospitalists be less profitable for primary care physicians than managing inpatients themselves, [[beta].sub.p][B.sub.p] < 0, is no longer binding, and we may observe hospital-employed hospitalists, (0,1), in areas where none would be used if [[theta].sub.H] = 0, (0,0). Although the primary care physicians would prefer to treat their hospitalized patients themselves, in this case the hospital can require them to use its hospitalists.

Similarly, when [F.sub.H] < (1 - [[beta].sub.H])[B.sub.H], the hospital's dominant strategy is to employ its own hospitalists, and the lack of bargaining power on the part of primary care physicians makes it most profitable for them to abstain from employing their own hospitalists, resulting in (0,1) where (1,0) would hold if [[theta].sub.H] = 0.

Another way to interpret Figures 4 and 5 is by recognizing the secular trend of decreasing and F. The decrease in g over time represents the decrease in the number of hospitalized patients. Over time, it is likely that the fixed cost of setting up a hospitalist program declines as knowledge about the efficient design of such programs is disseminated and lessons from unsuccessful implementations are learned. The dotted line in Figure 5 represents such trend. A relatively high ([mu], F) pair is likely to lead to a (0,0) equilibrium in which hospitalists are not used (not desirable). As both g and F decrease, the use of hospitalists becomes more prevalent and employment arrangements will gradually switch from predominantly PCP-initiated to hospital-initiated models.

4. Discussion

In addition to primary care groups and hospitals, whose strategic interaction is the focus of the foregoing analysis, two other components of the health care chain may facilitate the adoption of hospital medicine: Hospitalists may choose to organize themselves as freestanding practice groups, effectively intermediating between primary care physicians and hospitals, while payer organizations may either attempt to compel the use of hospitalists or employ them directly. We discuss these two models in turn. Finally, we examine whether and how the conclusions of the analysis change if we relax the assumption that primary care groups and hospitals act independently of each other. This modification is particularly pertinent in the case of vertically integrated health care systems, in which hospitals and primary care physicians are contractually linked.

Hospitalist-Only Groups

In the previous analysis, hospitalists could be introduced into the health care continuum if either primary care physicians or hospitals hired them. In particular, if it was not profitable for at least one player to employ hospitalists, given the other player's choice, the model would predict that hospitalists would not be introduced; in other words, the equilibrium would be (0,0). This equilibrium nests a third option of adopting hospital medicine: Hospitalists can form freestanding hospitalist-only groups (the "entrepreneurial model").

Hospitalist-only groups are free to serve multiple primary care physician groups as well as multiple hospitals. As a result, hospitalists in a freestanding group are more likely to achieve the minimum efficient scale of inpatients under their supervision than hospitalists who serve only one primary care physician group or one hospital. Given this flexibility, self-employed hospitalists can reduce the variance of inpatients that they are called to manage at any given time. They may also diversify across different patient groups that are associated with individual primary care physician groups and hospitals. Insofar as these advantages translate into a greater net benefit, either by reducing the fixed set-up cost or by raising the benefit per inpatient served, than that achieved by primary care physicians- or hospital-employed hospitalists, self-employed hospitalists may find it profitable to enter the care continuum when neither primary care physicians nor hospitals would introduce them. When [F.sub.P] > [B.sub.P] for [[theta].sub.H] = 0 or [F.sub.H] > [B.sub.H] for [[theta].sub.H] = 1, the player with all the bargaining power has no interest in setting up his own hospitalist program, allowing hospitalist-only groups to emerge. These ranges are shown as shaded areas in Figures 4 and 5.

Third-Party Mandates of Hospitalist Use

The previous analysis was restricted to providers as the only parties who would introduce hospitalists. In practice, payers also have played a role in the rapid diffusion of hospitalists by mandating their use. Insurance companies may and have in the past refused reimbursement for inpatient care not given through hospital medicine programs. This practice, however, has recently declined in occurrence, hitting a "wall of protest" by reluctant primary care practitioners and concerned consumers, and many HMOs have found that "imposing mandatory models in individual hospitals can alienate local physicians and lead to disastrous results" (Maguire 1999). For instance, Smith, Westfall, and Nicholas (2002) documented a 1997 mandate by a regional HMO in Colorado for hospitalist usage that resulted in increased percase costs of care and lengths of stay. The relative infancy of the program may have negated the streamlining effects of hospitalists shown in other settings.

To the extent that payers aim to maximize the cost savings that hospitalists generate, they should insist that the efficient outcome be chosen, in other words, the action pair that maximizes the aggregate profit of primary care physicians and hospitals. From this perspective and insofar as they can compensate players for choosing an action that they would not choose otherwise, payers can overcome the potential inefficiencies inherent in the noncooperative nature of the way the employment decisions are reached in the absence of a third party.

As shown in Figure 5, a decline in [mu] and F will create incentives first for primary care physician groups and then for hospitals to adopt hospitalists on their own, thereby lessening the need for HMOs to mandate their use.

Vertically Integrated Health Care Systems

Up to this point in the analysis, the primary care physician group and the hospital were regarded as separate components of the vertical care continuum that behave like players in a noncooperative game. The players' choice was limited to the decision whether to employ hospitalists directly. Significantly, the analysis ruled out any side payments that one player might offer the other in return for changing that player's decision. This restriction could result in inefficient equilibria. For example, suppose that primary care physicians have all bargaining power, that the costs of employing hospitalists exceed the benefits of doing so, and that the benefits of using hospitalists employed by the hospital are nonnegative for primary care physicians. (8) In this case, (0,0) is the unique equilibrium, and the aggregate payoff is 0. If [[beta].sub.P][B.sub.P] > [F.sub.H] - [B.sub.H] however, and if the primary care physicians could credibly promise to pay the hospital at least [F.sub.H] - [B.sub.H] in return for setting up a hospitalist program, both players' payoffs would increase.

Pauly (1979) examines the welfare effects of fee splitting among physicians, a practice that is illegal and regarded as unethical. He argues that it is possible for kickbacks to offer incentives that are in line with patient preferences and raise patient welfare. This argument can be extended to fee splitting between hospitals and physicians. Applied to the current context, fraud and abuse laws, as well as ethical considerations and increasing scrutiny, make it difficult to share any potential gains from using hospitalists unless the party employs them directly. Hospitals interested in preserving their referral bases can recruit physicians or acquire group practices. By developing vertically integrated working structures in which physicians are salaried by the hospital, incentives of physicians and hospitals are more closely aligned. As bona fide employment relationships are one salient exception to the antikickback statute, vertical integration allows hospitals to control costs by supervising physicians through utilization management techniques, practice guidelines, and other care protocols. (9)

While the trend toward vertical integration is a relatively recent phenomenon, for the most part it precedes the adoption of hospitalists. A priori, it is not clear whether vertically integrated systems would be more or less likely to adopt hospitalists. On the one hand, the carecoordination and cost-containment gains from the introduction of hospitalists are probably smaller for vertically integrated systems than for health care chains, as cost reduction was an explicit aim of hospital--physician alliances. This would predict a higher adoption rate for the latter. On the other hand, to the extent that competitive pressure led to vertical integration in the first place, these systems might also be under pressure to adopt hospitalists in their effort to remain at the frontier of quality improvement and utilization management. Therefore, this is largely an empirical question. Burns et al. (2001) argue that while health care systems have developed many types of contractual arrangements with physicians, to date most of these arrangements have failed to improve physician commitment. To the extent that the noncooperative elements are left intact in the presence of integration, our model extends to health care systems.

5. Conclusion

Hospitalists have the potential to generate substantial benefits for all the parties involved in the health care continuum. Yet the proscription of kickbacks between the parties, designed to prevent financially driven medical decision making, also potentially jeopardizes the selection of the efficient solution, namely, the employment model that maximizes the aggregate gains from introducing hospital medicine.

At the same time, a regulator with the power to affect relative reimbursement rates can correct the distortion created by antikickback laws by setting prices that will prompt referring physicians and hospitals to adopt the efficient solution. Therefore, rather than take the organization of the health care continuum as given when setting a menu of reimbursement rates, the regulator must take into account that these rates will affect the degree of specialization along the health care continuum and, thus, influence the effectiveness of the ratesetting policy in achieving the regulator's overall objectives.

To reflect the regulatory constraints of the health care market, we develop a conceptual framework in which primary care physicians and hospitals decide independently whether to use and employ hospitalists themselves. We show that under this assumption, multiple equilibria are possible. In particular, we show that a declining hospitalization rate will prompt providers to adopt the use of hospitalists and lead to a widespread switch of employment arrangements.

We thank David Bradford, Marisa Domino, and Laurence Wellikson for excellent comments and Robert Henderson and Sara Borelli for superb research assistance. Financial support from the Wharton Center for Health Management and Economics is gratefully acknowledged. We benefited from comments by participants at the 2005 Southeastern Health Economics Study Group conference.

Received July 2006; accepted July 2006.

References

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(1) Utilization management is the hospital's evaluation of the necessity, appropriateness, and efficiency of health care services, making sure that hospital stays, surgeries, tests, or other treatments are necessary.

(2) From the primary care physician's problem 1, it is obvious that the physician's maximum income increases with [mu], providing a potential foundation for physician-induced demand. In this analysis, we assume that [mu] is given.

(3) Because of the constraint in the primary care physician's problem 1, the only way for the primary care physician to raise s further is to abandon office-based care entirely and spend all his time in the hospital, [s.sup.*] = 1, effectively becoming a hospitalist. From Figure 2, it might seem that for sufficiently high [R.sub.H] relative to [R.sub.O], all primary care physicians would like to switch and become hospitalists. In equilibrium, incomes of primary care physicians and hospitalists must be equal, however. David and Helmchen (2006) show how the average number of patients referred to hospitalists adjusts to equalize earnings.

(4) The primary care physician's problem 1 without the constraint is a version of Rosen (1983). The figure shows Rosen's key result that even when wage rates are equal, that is, [R.sub.O] = [R.sub.H], workers may prefer to specialize in only one task.

(5) If the total number of hospitalized patients does not support even a single hospitalist, physicians might still prefer to specialize in office-based care. To generate enough revenue for hospitalists, however, they would either have to supplement hospitalists' reimbursement for hospital care with illegal fee-splitting arrangements or refer more patients for hospital care than is medically indicated. A precise characterization of how equilibrium in the markets for hospitalist and office-based care is brought about in this case is given in David and Helmchen (2006).

(6) The outside opportunities include working as a hospitalist for a primary care physician group, working as a member of a hospitalist-only group, and working as a primary care physician.

(7) If C is strictly increasing in effort e, basing the hospitalist's bonus w on the observed C is equivalent to basing it on the hospitalist's effort e.

(8) The conditions are [[theta].sub.H] = 0, [F.sub.P] > [B.sub.P], [[beta].sub.P][B.sub.P] [greater than or equal to] 0, and [F.sub.H] > [B.sub.H].

(9) That exception simply states that the statute will not apply to "any amount paid by an employer to an employee (who has a bona fide employment relationship with such employer) for employment in the provision of covered items or services."

Guy David * and Lorens A. Helmchent [dagger]

* The Wharton School, University of Pennsylvania, 3641 Locust Walk, Philadelphia, PA 19104, USA; E-mail [e-mail]; corresponding author.

[dagger] Division of Health Policy and Administration, School of Public Health, University of Illinois at Chicago, 1603 West Taylor Street, Chicago, IL 60612-4394, USA; E-mail [e-mail].

Table 1. Hospitals Using Hospitalists, by Employment Arrangement,
2003 and 2004

                                         AHA 2003        AHA 2004

                                         n       %       n      %

Hospitals using hospitalists who are    1115  100        1366   100
  Employed by a hospital or university   443   39.7       501    36.7
  Employed by a physician group          281   25.2       376    27.5
  Employed by a hospitalist-only group   311   27.9       386    28.3
  Employed by another arrangements        80    7.2       103     7.5
Hospitals surveyed                      4963   22.5 (b)   4873   28 (b)

Source: American Hospital Association (AHA) Annual Survey for fiscal
years 2003 and 2004 and authors' calculations.

(a) This category includes hospitalists employed by managed care
organizations and groups operating mixed models.

(b) This figure is the fraction of hospitals among all entities
surveyed that reported using hospitalists in the respective year.

Table 2. Hospitalist Groups, by Employment Arrangement, 2003

                                             SHM 2003

                                              n     %

Hospitalist groups                          298    100
Employed by a hospital or university        161     54.0
Employed by a physician group                53     17.8
Employed by a hospitalist-only group         71     23.8
Employed by another arrangement (a)          13      4.4

Source: 2003-2004 Survey by the Society of Hospital Medicine (SHM).

(a) This category includes hospitalists employed by managed care
organizations and groups operating mixed models.

Table 3. Equilibrium Employment Arrangements When the Physician Group
Has All the Bargaining Power (a)

                                                      Hospital

Physician Group                                  FH < BH     FH > BH

[F.sub.P] < [B.sub.P]
  [F.sub.P] < (1 - [[beta].sub.P])[B.sub.P]       (1,0)       (1,0)
  [F.sub.P] > (1 - [[beta].sub.P])[B.sub.P]     (0,1)(1,0)    (1,0)
[F.sub.P] > [B.sub.P]
  [[beta].sub.P][B.sub.P] [greater                (0,1)       (0,0)
    than or equal to] 0
  [[beta].sub.P][B.sub.P] < 0                     (0,0)       (0,0)

(a) The number pairs in parentheses represent the equilibrium employment
choices by the physician group and the hospital, respectively. For
instance, (1,0) refers to an equilibrium in which only the physician
group decides to employ hospitalists.

Table 4. Equilibrium Employment Arrangements When the Hospital Has All
the Bargaining Power (a)

                                            Hospital

                                      [F.sub.H] < [B.sub.H]

                               [F.sub.H] <             [F.sub.H] >
                           (1 - [[beta].sub.H])    (1 - [[beta].sub.H])
Physician Group                 [B.sub.H]               [B.sub.H]

[F.sub.P] < [B.sub.P]             (0,1)                (1,0)(0,1)
[F.sub.P] > [B.sub.P]             (0,1)                   (0,1)

                                Hospital

                          [F.sub.H] > [B.sub.H]

                               [F.sub.H] >
                           (1 - [[beta].sub.H])
Physician Group                 [B.sub.H]

[F.sub.P] < [B.sub.P]             (1,0)
[F.sub.P] > [B.sub.P]             (0,1)

(a) The number pairs in parentheses represent the equilibrium
employment choices by the physician group and the hospital,
respectively. For instance, (1,0) refers to an equilibrium in which
only the physician group decides to employ hospitalists. Note that
[[beta].sub.H][B.sub.H]BH < [B.sub.H] - [F.sub.H] is ruled out by
definition: [[beta].sub.H][B.sub.H] is assumed to be nonnegative.