Saving Costs While Saving Lives

Pritha Dutta

by Pritha Dutta
Ph.D. Candidate in Management Science, Isenberg School of Management, University of Massachusetts at Amherst

Keywords: healthcare, game theory, supply chains

“A new army is marching into the war against rising health care costs: engineer-mathematicians. These individuals occupy a field called operations research” wrote journalist Joel Shurkin (2013). With national discussions on healthcare topics such as the Affordable Care Act (ACA), opioid crisis, and drug pricing and shortages, it is clear that high costs and inefficient management of health care systems in the United States continue to be major concerns for government officials, policy makers and the general public.

In 2016, healthcare spending in the United States reached 3.3 trillion dollars and accounted for 17.9 percent of the country’s Gross Domestic Product (GDP) according to Centers for Medicare and Medicaid Services. The figure below illustrates the widening gap between health care spending in the United States and other developed countries around the world; highlighting the need for a more efficient system in the United States.

Source: Squires, D. (2015, October 8). U.S. healthcare from a global perspective. The Commonwealth Fund.
Retrieved from https://www.commonwealthfund.org/chart/2015/health-care-spending-percentage-gdp-1980-2013

It is not surprising that, being problem solvers, Operations Research scholars and practitioners are using their “weapons” to fight rising health care costs and its immense consequences for the society at large. One such “weapon” is game theory; primarily used to analyze competition, and in many cases cooperative behavior, between stakeholders in a market or industry. 

Supply chains in the health care industry are complex systems with several stakeholders such as hospitals, physicians, Group Purchasing Organizations (GPOs), pharmaceutical companies, medical equipment manufacturers, blood banks, insurance companies and patients who often have conflicting objectives. Game theory has been used extensively to study the economics of product supply chains. As individual stakeholders try to maximize their own gains, we end up with a system that does not function optimally. For example, if a payer (insurance company) rejects a claim made by a provider (hospital, clinic, nursing facility), the provider might benefit from providing low quality service at a lower cost. On the other hand, irrespective of the quality of service provided and cost incurred, a payer is always better off rejecting the claim (Fazulyanov (2017)). This is a classic example of the game theory concept called Prisoner’s dilemma where both rational decision makers act selfishly and do not cooperate, even though it would be beneficial for both decision makers (refer to this issue’s article Game Theory and Reinforcement Learning for more details on the Prisoner’s dilemma). In the long run, this is detrimental for both the patient and the health care system. Patients may avoid seeking care if the payer rejects their claims and providers could discharge patients early to avoid costs, both leading to increased readmission rates and more severe health outcomes for the patient and, consequently, increasing costs to the system. Hence, decisions encouraging cooperation among the stakeholders in health care are critical to both reducing costs and providing the best quality of care for patients. Game theory can be used to develop strategies for negotiations between stakeholders with the ultimate goal of reducing the societal cost of health care in the United States. These strategies can be used to balance objectives between the payer and provider as described above and for interactions between other entities (provider-GPOs, GPOs-pharmaceutical companies, etc.); a few examples described in the following paragraphs.

Health care professionals often point to high prices of pharmaceutical drugs as major contributors to the high costs of health care in the United States. In addition to pricing, there are concerns and uncertainties regarding patients’ response when a new drug is introduced in the market. Mahjoub, Ødegaard and Zaric (2018) used game theory to develop a pay-for-performance risk-sharing contract between a payer and a pharmaceutical company. In such a contract a new drug is prescribed to patients whose probability of response exceeds a certain threshold, then, for patients who do not respond to the drug, the manufacturer provides a rebate to the payer. Mahjoub, Ødegaard and Zaric modeled the problem as a Stackelberg game where a leader makes the first move and the follower moves sequentially. In this case the drug manufacturer is the leader who first sets the price of the drug to maximize its expected profit and the payer then decides the rebate rate and the patients who are eligible for treatment. This successful and fascinating application of game theory, among other results, found a threshold value for the rebate rate at which the net benefits for responding and nonresponding patients become equal.

Organ donation is another interesting application of the concept of the Stackelberg game. Arora and Subramanian (2016) point out the significant gap between demand and supply of organs in the United States; leading to immense socioeconomic costs. In studying an organ donation value chain (ODVC), consisting of a social planner, an organ procurement organization (OPO) and a hospital, the authors explored how the operational decisions of the OPO and the hospital affect their individual payoffs as well as social outcomes. The interactions between the (OPO) and the hospital were modeled as a Stackelberg game with the hospital acting as the leader who decides the level of effort and the operating room priority assigned to organ recovery, both of which have associated costs, while the OPO decides the level of effort to commit towards interacting with potential donors’ families and seeking their authorization. In the end, administratively feasible, Pareto improving contracts were recommended to achieve optimal performance for the ODVC. Thus, showing game theory can be applied to complex problems in healthcare where efficiency in the process can save lives and ensure cost effectiveness.

Group Purchasing Organizations (GPOs) play a crucial role in saving costs for hospitals and health care providers. GPOs act as mediators between health care providers and manufacturers of medical supplies, blood banks, and pharmaceutical companies. Since they serve multiple health care facilities, GPOs can aggregate purchasing volumes and leverage that to get discounts from manufacturers and distributors, thereby saving costs for the health care systems. Game theory tools can be used to examine the role of GPOs in providing economies of scale in health care supply chains. Hu, Schwarz and Uhan (2012) studied how the presence of a GPO impacts the providers’ total purchasing costs by developing a game-theoretic model to study a health care product supply chain consisting of a profit-maximizing manufacturer, a profit-maximizing GPO, a competitive supplier and n providers who seek to minimize their total purchasing costs. Results for this case study revealed that contract manufacturing fees charged by the GPO to the manufacturer affect the distribution of profits between manufacturers and the GPO but that contracting with the GPO did not lower the providers' total purchasing costs. This is an interesting result since the incentive for a provider to join a GPO versus directly contracting with the manufacturer is to reduce its purchasing costs.

This article displays the wide spectrum of interesting problems pertaining to health care supply chains and the various ways game theory can be applied to find a solution. Scholars in the fields of Operations Research and Management Science are studying the associated operational challenges and their socioeconomic implications by addressing issues such as nurse scheduling, organ donations, blood banking, competition among pharmaceutical firms and ambulance routing.  There exists a rich body of work that uses game theory to handle some, if not all the above-mentioned problems, thus highlighting the strength of this well-established methodology in modeling complex problems, deriving optimal solutions, and potentially reducing the cost of health care delivery and services. So, the question remains, are you ready to join the "army" of OR scholars and which problem are you addressing in your next project?

References

 Arora, P., & Subramanian, R. (2016). Improving societal outcomes in the organ donation value chain. Retrieved from https://ssrn.com/abstract=2602329 or http://dx.doi.org/10.2139/ssrn.2602329.

 Fazulyanov, I. (2017, September 18). Blockchain and Nash equilibrium in healthcare, oh my! Medium. Retrieved from https://medium.com/@ildarfazulyanov/blockchain-and-nash-equilibrium-in-healthcare-oh-my-1-6ba0e80ea03b.

 Hu, Q., Schwarz, L. B., & Uhan, N. A. (2012). The impact of group purchasing organizations on healthcare-product supply chains. Manufacturing & Service Operations Management14(1), 7-23.

 Mahjoub, R., Ødegaard, F., & Zaric, G. S. (2018). Evaluation of a pharmaceutical risk‐sharing agreement when patients are screened for the probability of success. Health economics27(1), 15-25.

 Shurkin, J. (2013, April 12). Game theory tackles rising healthcare costs. Inside Science. Retrieved from https://www.insidescience.org/news/game-theory-tackles-rising-health-care-costs.