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Saturday, February 27, 2010

Mathematical analysis and healthcare

One of the first skills mathematics students develop when learning to solve difficult problems is analysis - the resolution of complex objects into simple elements. Problems often seem insurmountable when viewed as an indivisible whole. Mathematicians learn to tease out less formidable subproblems; unravelling string by string often suffices to overcome amazingly complex questions. (Of course, questions are often left for the mathematicians of later generations or centuries to solve.)

Let's analyse the current healthcare problem. First we must define the problem. The usual assertion is that health care costs are rising so quickly that neither businesses nor individuals can sustain the cost. Economic disaster will ensue unless costs are reined in. As costs rise, fewer people purchase insurance, pushing their healthcare costs onto the remaining insurance customers, driving prices yet higher in an unfortunate feedback mechanism. Republicans address these issues by identifying and attempting to rein in cost drivers such as rapacious malpractice lawyers, restriction of interstate competition in insurance markets, tax policy distortion of market incentives, and of course the shifting of Medicare and Medicaid patients' costs onto the backs and wallets of the insurance buying public. I'll give the Republicans a B for their analysis. The Democrats are unwilling to break the problem into its constituent parts because their answer to all healthcare problems is the same: surrender all healthcare decisions to the government. Mathematicians don't inflate grades as much as Humanities faculty do, so I'll award the Democrats an F, but will allow them to attempt to redo the assignment.

Why do the Republicans only earn a B? Their analysis misses part of the solution (admittedly a politically tricky part). To see this, we begin by enumerating several basic healthcare costs:
  • Insurance costs.
  • Drugs.
  • Physician fees.
  • Hospital costs.

In this post, I restrict attention to the first two costs - currently the object of the greatest demagoguery - insurance and drugs. How can we separate insurance costs from all other healthcare costs? First let's imagine that we are an insurance company pricing a policy for a 40 year old male. As a first pass, we should compute the average cost of healthcare for 40 year old males. Next we add a risk premium. This is the payment the company receives for shouldering the risk that the policy holder incurs medical costs which significantly exceed the average. Then the company adds charges for administrative costs. The sum of the average cost, the risk premium, and the administrative costs gives the total cost of the policy.

When computing the cost of insurance, we can compute in two ways. For the overall system, the cost is total policy cost minus total company payouts to healthcare providers. For the individual, the insurance cost is his policy cost minus total company payouts to healthcare providers for his healthcare. When politicians complain about the rising cost of insurance, are they complaining about administrative costs, risk premiums, or the average payout? The first two costs are a small percentage of the total healthcare cost; hence complaint about insurance cost is really a mislabelled concern about the average payout to healthcare providers. Is it proper to attribute the rapid rise in this cost to our insurance system? More precisely, does the insurance system contribute to inflation of the average healthcare cost?

There are obvious defects in our system which lead to increased consumption of healthcare. When rational people purchase their own insurance, their goal is to guard against the possibility that they incur financially devastating costs. It is irrational (ignoring tax incentives) to insure for any predictable or expected cost. If all 55 year olds are advised to have a colonoscopy, then 55 years olds should not purchase insurance that pays for colonoscopies. Insuring a predictable expense can only increase its cost. Moreover, if you happen to decide to avoid the procedure, you pay for it anyway. Therefore, self purchased insurance should only cover extreme events and should have high deductibles. When employers provide health insurance as a benefit, they are effectively purchasing both a coupon for predictable healthcare expenses plus insurance for extreme events. The coupon encourages the buffet effect - consume until you get your coupon's worth. This effect is targeted in Republican plans to alter the preferential tax treatment of employer sponsored insurance plans.

The fact that people are priced out of the insurance market implies this analysis is still missing something: rationing. Opponents of government controlled healthcare object that all government healthcare schemes require government rationing of healthcare. Left unsaid is the fact that all healthcare insurance necessarily implies some rationing. The fundamental difference is between concentration of rationing power in a single, too powerful, remote government body and rationing decisions spread out over a multitude of actors from private insurers to employers to individual policy holders, each making their individual judgments of priorities and tradeoffs. If people significantly above the poverty line are priced out of the insurance market, perhaps we should ask whether the average cost of healthcare is too narrowly defined. Consider, for example, the cost of drugs. Suppose you had the following options: (i) go without drug insurance because you could not afford to pay the high average cost for your age group or (ii) buying affordable drug insurance with the restriction that the policy paid only for drugs approved before 2001 (unless more recent therapies are cheaper). Which would you choose?

If regulations were simplified so that insurance companies could offer more differentiation of coverage than now allowed, it would have dramatic impact on our healthcare system. Currently, the latest advances in drugs, imaging technology, etc., propel healthcare costs ever higher. If we had a multitiered system, the rich would bear a greater part of the burden of funding the development of new technologies (and the occasional horrific errors such as thalidomide), while the rest of us could pay for well vetted albeit older techniques and technologies. The left abhors any such differential outcome, but it is clear that under government run healthcare, technical advance would stagnate anyway, consigning the entire population to older treatment regimens. Under a multitiered system, we provide a mechanism for the wealthy to fund advances while the rest of us merely wait a bit longer to reap the benefits. We then may choose what we value most: whether to use our funds to buy a bigger house or better car, private schooling for our children, or advance from, say, a 2001 level healthcare plan to a 2005 level healthcare plan. The actual details of how such a differentiated healthcare system would function would presumably be much more complicated than my toy model offered here, but with regulations relaxed to allow such differentiation, individuals and insurers would determine the optimal way for such a system to evolve.

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