A math problem for accountable care organizations

On Oct. 25, 2013, the Baker Institute Health Policy Forum hosted its fourth biennial conference on health care reform. This series of blogs discusses the implications of the 2010 Affordable Care Act for the U.S. health care system and the well-being of the population.

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A paper by Brigham Frandsen and James Rebitzer offers a concise explanation of Medicare accountable care organizations (ACOs) and then a math problem. Let’s start with the explanation:

ACOs are comprised of a network of hospitals and providers that contract with the Center for Medicare and Medicaid Services (CMS) to provide care to a large bloc of Medicare patients (5,000 or more). The contracts, which last for three years, create a single risk-bearing entity with incentives to control costs. ACOs that come in under their specified cost benchmarks earn a fraction of the savings. In order to receive these payments the ACO must also clear stringent threshold quality levels on a number of indicators.

So, by federal rules, an organization must serve at least 5,000 beneficiaries to be a Medicare ACO. Why?

One reason is that the bonuses for which cost-saving ACOs would be eligible are contingent on meeting quality benchmarks. For example, there are quality targets relating to appropriate care for patients with diabetes, hypertension, coronary artery disease, etc. (Details available in this PDF.) However, as is true for any measurement, an ACO’s quality metrics will be, statistically speaking, relatively imprecise if they are only computed for a small number of patients. The more patients, the lower the standard error of a mean value. Consequently, as argued by Elliot Fisher and colleagues, an ACO needs at least 5,000 beneficiaries for reasonable statistical accuracy of quality measures.

To serve 5,000 patients an ACO has to encompass a large number of physicians, both primary care and specialists. To get a sense of how large, David Nyweide and colleagues found that the median number of Medicare beneficiaries in a practice is 260. However, a typical practice includes more than one physician. Consequently, it is not unreasonable that an ACO would likely have to encompass several dozen or more physicians.

Now, imagine you’re a physician in an N-physician ACO, designed so that precision of quality measures is 1/√N lower than it would be for a single physician. If you practice just so, you can help improve the ACO’s measured quality. But how much can you do? On average you only see 1/N of the ACO’s patients. So, you can only affect quality by a factor of 1/N. The more physicians who join you in the ACO, the more precise the quality measures, but the less influence you will have over them. At some point, the time and effort it costs you to improve quality by a factor of 1/N isn’t worth the return you’ll receive. This gives rise to free-riding.

And what might that return be? It could be a share of the ACO’s bonus if it meets quality and cost benchmarks. This leads to a math problem, as articulated by Frandsen and Rebitzer. Their model predicts that for an ACO to yield substantial savings, and hence substantial bonuses to motivate physician behavior, it can’t be very large. Free-riding dilutes the incentive to contribute effort toward quality improvement too quickly with team size.

This is shown in the figure below. If one constrains the ACO to be self-funding in the sense of using bonuses as payments to team physicians, then as the ACO’s target savings increases as a fraction of the theoretical maximum (the horizontal axis), the maximum team size (N, vertical axis) falls. This is, of course, problematic because a large N is needed (indeed, required, given the 5,000 patient constraint) for quality measurement precision.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The obvious implication of Figure 2 is that with all but the most trivial cost reduction targets, ACOs with self-funding pay-for-performance systems must operate with under-powered financial incentives.

All is not lost, however. This only means that ACOs may need to find other ways to motivate physician behavior. It could, for example, supplement the financial incentives implied by ACO bonuses by using a fraction of what would otherwise be base salary as bonus payments. Or it could promote an organizational culture more conducive to cooperation in quality improvement. That, of course, is easier said than done, and it may be particularly challenging for hybrid organizations as opposed to fully integrated ones. This is yet another incentive for integration, as well as a source of concern for the ACO model.

Austin Frakt is a health economist with an educational background in physics and engineering. He has appointments with Health Care Financing and Economics at the VA Boston Healthcare System, U.S. Department of Veterans Affairs and with the Department of Psychiatry and the Department of Health Policy and Management at Boston University. Since 1999, he has studied economic issues pertaining to U.S. health care policy with a recent but not exclusive focus on Medicare and the uninsured. Frakt has authored numerous peer-reviewed, scholarly publications relevant to health care financing, economics and policy, and he is the creator, co-manager and a primary author of The Incidental Economist.