Chronic diseases are a costly burden on health care systems. In the US, for example, 60% of the population suffer from at least one chronic disease. Further, chronically ill patients account for 90% of health care expenditures (Buttorff, 2017). According to Bodenheimer et al. (2009), one barrier to the efficient provision of chronic care is that health care systems are built around the treatment of acute problems rather than the long-term health of the patient. One of the measures they propose to improve chronic care is to provide it in teams rather than solo practices. In a meta analysis, Pascucci et al. (2020) find that inter-professional collaboration improves a number of health related outcomes for chronically ill patients indeed. Lemieux-Charles and McGuire (2006) analyze studies relating to the effectiveness of health care teams compared to usual care. They also find improvements in patient treatment for some interventions. However, they also find that team care may increase costs. This begs the question under which circumstances team care can enhance the efficiency of treatment compared to solo practice care. This paper’s aim is to provide theoretical guidance regarding this question.

In this paper, I consider two important aspects of chronic care. Firstly, chronically ill patients should receive treatment from an appropriate physician. Which physician should treat a patient crucially depends on the patient’s disease severity. Whereas a primary care physician (PCP) is able to efficiently (as measured by expected net benefit of treatment) treat a patient in mild condition, a specialist’s services are required for a more severe case. This aspect is especially important for chronic diseases as the disease severity of chronically ill patients may change over time. Secondly, treatment efforts exerted today impact health outcomes and costs in the future. The preventive effort of a PCP can decrease the need for future treatment and, thus, decrease costs for the health care system (Dusheiko et al., 2011, de Bruin et al., 2001, Li et al., 2010). Similarly, high-quality specialist treatment can lead to quicker recovery of the patient.

In the main part of the paper I consider two profit-oriented physicians, a PCP and a specialist, who do not internalize patient benefit.1 A profit-oriented physician may provide too little effort because she suffers the costs of effort provision but does not internalize the future health losses of patients. Furthermore, she ignores patient health losses when considering whether to refer a patient.2 As an extension I consider partially altruistic physicians, who care about both their own profits and the patient’s wellbeing.

If physicians work in solo practices, they do not consider the other physician’s profit in their treatment and effort decisions. This can lead to unnecessary costs if patients are not referred who could be treated efficiently by the other physician. Another potential problem is that too little treatment effort may be exerted because cost savings generated by effort exertion may accrue to both physicians. If there is no asymmetric information between the physicians, this coordination problem can be solved by delivering chronic care in health care teams that are reimbursed by (risk-adjusted) per patient payments as Bodenheimer et al. (2009) propose.3 In this case, cost savings that accrue because of a physician’s decisions can be transferred to that physician with the help of internal profit sharing rules. However, solving the coordination problem is not necessarily efficient if physicians do not fully internalize the patient’s health losses. In this case, they may allocate patients in a way that minimizes costs at the expense of the patient’s health. Furthermore, organizing physicians in a team provides them an opportunity to collude in order to earn larger profits. For example, if specialists are paid larger treatment fees than PCPs, there is an incentive for the PCP to over-refer patients to the specialist. Conversely, assuming that kickback payments between physicians are not allowed, the PCP faces no such incentive in the solo practices. Due to the reasons outlined above, it is not clear which organizational form leads to more efficient treatment.4

The aim of this paper is to answer the following question. Under which conditions should a chronically ill patient receive care from a physician team (PCP and specialist) or from independent physicians who work in solo practices? In order to answer this question I derive optimal treatment fees for both physicians in each setting and compare the second-best optimal outcomes between both organizational forms. As an extension, I consider the restriction that the team is paid by a flat treatment fee which does not differ between physicians. The main difference between organizational forms is that in a team, physicians coordinate their referral and effort decisions, whereas in solo practices they do not.

To answer the research question, I develop a model with a PCP and a specialist who treat a fixed number of chronic patients for an indefinite time frame. Patients can either be in a mild condition, which is inexpensive to treat, or in a severe condition, which is costly to treat. The severe condition could, for example, correspond to a diabetes patient who is hyperglycemic or suffers from neuropathic or retinopathic complications. Physicians can exert tertiary preventive effort (time spent on patient, self-help support, appropriate medication, support personnel...) in order to lower the probability that a patient’s condition deteriorates or they can exert curative effort in order to increase the probability that a patient’s condition improves. Further, physicians refer patients between each other and can accept or reject each other’s referrals.

The main innovation of the paper is to analyze physicians’ agency problems relating to effort and referral efficiency in a model that captures the dynamic nature of the chronic care market. Patients’ severity in each period is determined by a competitive Markov decision process (see Filar and Vrieze, 1996, for the theoretical background for this type of game). A patient’s probability distribution over the disease severity in the next period is determined by the patient’s current severity, the type of physician treating him, and the exerted effort of the treating physician. Consequently, treatment decisions made by physicians in one period affect the expected costs of care and expected patient health losses in all periods to follow.

Both the severity of the patient’s disease (hidden information) and the effort exerted by the physicians (hidden action) are unknown to the payer contracting with the physicians. In order to achieve efficient outcomes, both physicians should be incentivized to exert effort. Further, patients in the mild condition should receive care from the PCP and patients in the severe condition should receive specialist care. I derive conditions under which physicians in each organizational form exert more effort and/or more adequately refer patients.

There are several advantages of using a dynamic model rather than a static model. First, it captures the provision of non-contractible effort without reference to altruism or pay-for-performance mechanisms that require the payer to have information on outcomes ex-post. Instead, physicians provide effort in order to reduce their own (or their team’s) future costs of care. This allows for contracts with less stringent information requirements and it offers an alternative explanation to altruism for effort in a credence good market. Second, a dynamic model allows for the study of the complete set of treatments and referrals undergone by the patient. This includes a back-referral to the PCP after successful specialist treatment.

I find that if profit-maximizing physicians work in solo practices, it is not possible for the payer to implement optimal referral patterns, though it may be possible in the team. Whether or not this is possible depends on the cost structure and the effectiveness of the physicians’ treatments. In particular, the expected treatment cost differences between the patient types need to be relatively large for the PCP and small for the specialist, i.e. the PCP must have the relative cost advantage when treating patients in mild condition. Markups should be used for PCP treatment, whereas the specialist should be paid below-cost. In the converse case, in which the specialist has the relative cost advantage for mildly ill patients, it can be optimal to organize the physicians in solo practices. This allows the PCP to act as a gatekeeper for the specialist. Mildly ill patients are initially received by the PCP and only referred to specialist care when their state deteriorates. This cannot be implemented in the team because the PCP would always refer mildly ill patients if doing so increases the team’s profits.

The remainder of the paper is structured as follows. Section 2 reviews the theoretical literature on the topic. Section 3 describes the model used in this paper. Section 4 defines the first-best benchmark. In Section 5, treatment fees for both the team and the solo practice are derived to implement potentially second-best optimal outcomes under the assumption that the payer cannot verify effort provision or the type of the patient. Subsequently, the second-best optimal outcomes for team and solo practice cases are compared. Conditions are derived under which either organizational form is superior. In Section B of the appendix, the case that teams are paid with flat fees and the case that physicians are partially altruistic are considered as extensions. Section 6 concludes.