A Game Theoretic Analysis of Hospital Strategy Selection in Response to the Hospital Readmissions Reduction Program

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1 Rizzotti 1 Matthew Rizzotti ECON 400M A Game Theoretic Analysis of Hospital Strategy Selection in Response to the Hospital Readmissions Reduction Program Healthcare in the United States is known across the world as innovative, modern, and high quality. While American hospitals do provide this level of care, it is not without flaw. It is estimated that more than twenty percent of all Medicare patients are readmitted to the hospital within thirty days of discharge. These readmissions cost Medicare nearly eighteen billion dollars annually, and represent a significant failure in our healthcare system. On October 1 st, 2012, the Hospital Readmission and Reduction Program officially went into effect. This legislation, as part of President Obama s Patient Protection and Affordable Care Act, is designed to decrease Medicare costs, and to improve the quality of patient care by increasing hospital accountability. In this program, Medicare will penalize certain hospitals whose 30-day readmission rate is higher than average for patients recovering from myocardial infarction (heart attack), heart failure, and pneumonia. Currently the penalty is a one percent reduction in Medicare reimbursements, but this figure will be increasing by one percentage point annually until 2015 (Berenson, Paulus, & Kalman, 2012). Legislators hope that this act will decrease Medicare costs significantly, while at the same time improve the quality of health care for patients suffering from the three conditions listed above. To avoid the Medicare penalty, it is expected that hospitals will provide more comprehensive post discharge care. They will provide better pre-discharge education, more coordination with rehabilitative services, and will partner with higher quality nursing and assisted living facilities. In order for hospitals to provide these services, they will have to incur the higher costs associated with the higher level of care. While those who passed this legislation believe that the benefits of avoiding the Medicare penalty will provide incentive to incur these costs, I will argue the opposite. Hospitals and healthcare providers will be forced to enter a coordination game with the patients they serve. Depending on

2 Rizzotti 2 the perceived actions of the patient or the costs of providing comprehensive rehabilitative care, hospitals might be incentivized to avoid providing these services. In my previous paper, it was argued that doctors and patients interact through the assurance game, reaching Nash equilibria when both parties cooperate and when both parties defect, but Pareto optimality only when there is mutual cooperation. Using the same framework, we will analyze the way hospitals decide on post discharge patient care. The hospital has two choices: incur the expense of providing high quality post-discharge care and rehabilitation in order to maximize the probability of patient recovery, or avoid these interventions and allow the patient to recover on their own. The patient, just as in the previous paper, can choose either to follow the prescribed rehabilitation plan or defect and not adhere to their doctor s guidelines. This matrix represents the choices that are made at the moment of discharge, after the patient has received all the necessary interventions in the hospital. In the top left cell, the patient is going to comply with the recovery plan, and the hospital is going to offer the full complement of rehabilitative resources. Both players receive positive utility: the patient has the highest probability of recovery, and the hospital has the lowest probability of incurring a readmission penalty. In the top right, the patient is compliant with the recovery process, but the hospital defects. The patient receives negative utility, because they were not provided with recovery resources they would have utilized. The hospital, however, neither receives nor loses utility. While they saved on the cost of providing these resources, this is counterbalanced because the patient has a higher probability of being readmitted within the next thirty days and incurring a readmission penalty. In the bottom left cell, both the patient and the hospital receive negative utility. The patient chose to defect in the presence of the resources the hospital provided, decreasing their chances for successful recovery. The hospital also loses utility, since there is an increased probability that the patient will be

3 Rizzotti 3 readmitted in the next 30 days. They invested a significant amount of money in providing services for the patient who was non-compliant with them. In the bottom right cell, neither the patient nor the hospital gain or lose utility. The patient would have been non-compliant with the rehabilitation, so they are not missing out on opportunities when the hospital does not provide them. This patient will have a higher risk of readmission, but the hospital did not invest any money in resources for a patient that would have wasted them anyway. Looking at this matrix and assuming that the moves are made simultaneously, there are two Nash equilibria. Given that the patient intends to cooperate, it is in the best interest of the hospital to do so as well. Conversely, given that the patient plans on defecting, the hospital is incentivized to do the same. When we consider the policy, these two equilibria make sense. If the patient is going to utilize the resources provided, it is in the best interest of the hospital to incur the expenses in order to decrease the probability of readmission as much as possible. On the other hand, given a patient who is not going to take advantage of the resources, it makes sense for the hospital to avoid providing them. This patient has a much higher probability of being readmitted, as they are not going to be facilitating their own recovery. It does not make sense for the hospital to spend money to rehabilitate a patient who will likely be readmitted regardless of the resources they are provided with. The challenge of this game is the lack of communication. The players do not discuss their strategies with each other, so the hospital must determine their best strategy based solely upon the perceived choices of the patient. This uncertainty can be reduced slightly through cheap talk, but it still places the hospital in an ethical and potential legal dilemma should they withhold full rehabilitative services to a patient who would have utilized them. Because of the stakes of this uncertainty, certain policies and programs need to be implemented to protect both the hospitals and the patients they serve. While the Readmission Reduction Program is still in its infancy, one of the inherent problems with the model is that hospitals are accountable for readmissions due to patient non-compliance. For instance, a patient who is readmitted because they did not take their medications will still be factored into the hospital s

4 Rizzotti 4 readmission rate, even if they were provided with all of the education and services necessary to facilitate a full recovery. The government needs to supplement the Readmission Reduction Program with a policy that gives hospitals immunity in the case of non-compliance readmission. One way to track these readmissions is through community paramedicine (Jones, 2012). Community paramedicine is a very new approach to pre-hospital care. Paramedics who are working in the field are assigned to certain post-discharge patients on a daily basis, and make house visits to help ensure that patients are recovering. If a patient is not actively facilitating their own recovery, daily visits by the paramedic may encourage the patient to take their condition more seriously. While the most stubborn patients will be non-compliant regardless of the house visits, community paramedicine will enable adequate documentation of the non-compliance. This will protect hospital from liability should the patient be readmitted. In addition to being used as a means of identifying non-compliant patients, community paramedicine can also yield mutual benefits when the hospital and patients are operating at the pareto optimal complyprovide equilibrium. Daily visits will allow providers to track progress, and identify problems with the patient s recovery that could lead to readmission. Recently, after a visit by a community paramedic, a patient was found to be taking three different Coumadin pills each day, as each pill was prescribed by a different doctor. Coumadin is a blood thinner, so even minor cuts lead to extensive bleeding. This patient, taking three times the normal dosage, had an incredibly high mortality risk from severe blood loss. The community paramedic who noticed this likely prevented this patient from being readmitted, but more importantly, almost certainly saved this patients life (Jones, 2012). The benefit of community paramedicine is that it yields benefits to the hospital regardless of the achieved equilibrium. In the event of a non-compliant patient, community paramedicine would enable the hospital to justify termination of expensive resources, and afford them protection in the event of a readmission. Equally, community paramedicine would benefit both parties when there is mutual cooperation.

5 Rizzotti 5 The program would serve to improve the level of care the patient receives, while at the same time lowering the probability of incurring a readmission penalty. The final aspect of our discussion of the Readmission Reduction Program is based on critics who suggest the cost of the penalty is too low (Jones, 2012). This argument suggests that the steps required to lower the readmission rate will actually exceed the cost of the penalty, effectively making the only strategy to defect. When we consider the numbers, it seems plausible for this to be the case. Medicare plans to save $280 million in through penalties levied to 2,217 hospitals with excessive readmission rates, for an average penalty of $126,296 per hospital. If the cost of reducing readmission rates below the penalty level is in excess of this figure, the hospital would be behaving rationally if their strategy was to defect all the time and accept the penalty. As the penalty rate increases, hospitals could continue this cost benefit analysis, and eventually resume the coordination game above once it was no longer cost effective to defect unconditionally. While the legislators who implemented the Readmissions Reduction Program suggest that hospitals will be incentivized to prevent readmissions, our analysis of game theory has highlighted several flaws in this logic. To summarize, hospitals enter a coordination game in which their strategy is directly correlated with their perceptions of patient strategy, only choosing to provide extensive post-discharge care for a patient who will be compliant with it. One means of providing hospitals with strategic information is community paramedicine, which can serve both as a means of identifying non-compliant patients, and as a way to provide compliant patients with additional individualized care. An additional component to hospital strategy choice is cost benefit analysis. The legislation may actually discourage hospitals from even entering the game, as the cost of avoiding the penalty is greater than simply paying the penalty. While this legislation is designed to help Medicare patients, the inherent game it creates leaves room for hospitals to put their financial interests ahead of their duty to provide optimal patient care. As this policy becomes more mature, it will be important to continually reevaluate its impact and the incentives it creates. This will be the only way to ensure that the patient remains the number one priority in our healthcare system.

6 Rizzotti 6 Works Cited Berenson, R. MD., Paulus, R. MD., & Kalman, N. (2012). Medicare Readmissions Reduction Program - A Positive Alternative. The New England Journal of Medicine, Jones, D. NREMT-P. (2012, October 29). A prehospital providers interpretation of the Readmissions Reduction Act. (M. Rizzotti, Interviewer)

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