My Nightmare: The Law of Diminishing Returns As Applied to Healthcare

Asymptote_croppedYears ago, as I began to look at medicine from the 30,000-foot perspective, a nightmarish image came into focus. It was a gradual realization. But when the image coalesced, it struck me like the hot kiss on the end of a wet fist. This image has informed all of my future expectations for medical advances as well as some expectations for change.

I had dreams of creating a PowerPoint presentation and presenting this image to my colleagues at Medical Executive Committee meetings, to my fellow board members during the educational component of Sibley Hospital trustee meetings and to administration executives of Sibley and Johns Hopkins (of which Sibley is now a part). Because I had no practical solution for those parties, I let the dreams slip away.

It is time to share my nightmare image: Asymptotic Excess

The image is a simple chart, above, where the X axis represents the elapsed time. The Y axis represents the item being measured. The blue curve plots the cost, effort or expense over time. The red curve plots the benefits, as observed over time. And the dotted line is an asymptote. (An asymptote is a straight line associated with a curve. As a point moves along the curve toward infinity the distance from the point to the line approaches zero and the slope of the curve approaches but never reaches the slope of the line. More definitions here and here, if you are interested.)

Chart of wound infections (the asymptote represents zero percent)


Let us look at wound infections as an example. Surgical wound infections are a potential problem with any surgery. They run from one to four percent depending on the site of the surgery. In the best of circumstances they are less than 1%. In a perfect world they are 0%, as represented by the asymptote. The blue curve represents the time, labor and expense spent to make the red curve approach the ideal of zero infections.

The question to be posed is: At what point does the exponentially increasing cost outweigh the incremental improvement?

My recurring nightmare is that this image can, and should, be applied to all levels of our health care delivery process from colonoscopy costs to robotic surgery costs, cancer pharmaceuticals to proton beam radiation therapy, administrative costs and, most globally, life expectancy cost/benefit.

My future blog posts will address these and other examples in order to highlight problems and a few proposed solutions.

So let us start at the high altitude view and apply this image to the concept of cost and life expectancy where the red curve (in my chart) represents the average life expectancy and the blue curve (in my chart) represents total U.S. Health Care dollars.

Chart of U.S. life expectancy

Are We Really Living That Much Longer 1At the turn of the 20th century, life expectancy for men was 46.3 years and for women was 48.3 years. By the turn of the 21st century they were 74 and 80, respectively. Now they are roughly 76 and 81.

Medicine has moved the life expectancy along the red curve very successfully for the last century and it is not clear where the asymptotic absolute actually lies but the rate of change of life expectancy is slowing.

Furthermore, as a physician, I think there are some scientific, moral and ethical limits to the expectation of our life expectancy. It would be irresponsible to think that future treatments offer the promise of infinite life. For purposes of this rant please set the life expectancy asymptote between 80 and 85 years of age.

Chart of U.S. spending on health care from 1960 to 2022


As you can see, the cost curve, at left, parallels the blue curve of my image. Yet U.S. life expectancy is 26th in the world of the top 36 developed countries, despite spending more absolute dollars and twice (18% v. 9%) the percentage of GDP than any other country. What is wrong with this picture and what implications can we draw?


Let’s divide the original asymptote chart into three zones


Zone 1: The first zone is below and to the left of the intersection of the blue and red lines. This is where significant advances are made with comparatively little cost. This is where maternal and infant mortality declined. It is where vaccinations limited the scourge of childhood diseases. It is where antibiotics cured the common, simple but fatal infections of pneumonia, urosepsis, etc. And it is where surgical advances have essentially cured the formerly fatal episodes of appendicitis, cholecystitis, abcesses, etc.

Zone 1 is the sweet spot for medical advances.

Zone 2: The next zone to consider is the area around the intersection of the two curves. This is where most medical progress is stalled in the current era. It is where the curves cross and incremental progress comes at exponential cost. It is where Proton Beam Radiation Treatment (PBRT) resides, for example. More on PBRT later.

Zone 3: The final zone is the area above the asymptote. This is where money is spent without benefit. This is where commercial profit overwhelms medical judgment. It is where PR, advertising, rapacious profits and outright criminal behavior exists. It is where unfettered commerce is about making consumers believe in, and pay for, a product, service or technology that looks good but adds nothing.

We are in zone 3 and getting nothing for our money

Clearly, with respect to U.S. dollars and average life expectancy, we are in Zone 3 and getting nothing for our money.

Competition, as defined by the free market proponents, may benefit consumers and patients in Zone 1 but it complicates Zone 2 – where difficult choices must be made over cost benefit – and it is criminal in Zone 3. And because most health care dollars are now spent in the second and third zones, free market competition should be discarded, or at least minimized, as a principle behind health care delivery.

Stay tuned for more detailed discussions of these issues and their unintended consequences.


6 Responses to My Nightmare: The Law of Diminishing Returns As Applied to Healthcare

  1. Minor January 16, 2014 at 10:33 pm #

    This is interesting. Are you imagining that the marginal benefit and marginal cost curves are fixed over time? That doesn’t seem right to me. In fact, I suspect the only reason health outcomes improve over time is because the cost curve shifts down and to the right. When there’s some new medical technology — whether it’s a machine like a imaging device, a chemical compound, or a new procedure — the costs of treating something go down. After the development of antibiotics, the cost of treating cholera dropped dramatically. You needed a pill, more or less. The actual cash outlay may have gone up because you had to buy a pill, where you didn’t before. But comparing only the cash outlay now to the cash outlay before is deeply misleading. The costs of treating cholera before antibiotics were enormously high (there wasn’t much you could do not matter how much you spent), but the costs dropped dramatically after antibiotics. Similarly, to get a look at someone’s spine before X-RAYs or MRIs or other devices was hugely costly. You’d have to cut someone open and look with your eyes. Even though devices like that are very expensive to use, the crucial thing is that they are a *cheaper* way to look inside someone than what came before. So I wonder whether the important question ought to be: How do we make sure we provide incentives that are strong enough to induce people to develop new technologies with medical applications?

  2. Sam January 18, 2014 at 10:36 am #

    Minor, Thank you for your close analysis. As a non-economist I clearly need help formulating a title for, and explaination of, this image of an asymptotic ceiling to benefit and exponential cost, over time.

    Yes, there are many examples of marginal cost improvement with scientific and technological advances over time and the triumph of antibiotics and vaccinations over common infectious diseases is one of them. One could argue that radiologic imaging is another when it does obviate the need for exploratory surgery. But these are both advances of the last century.

    Currently the overuse of antibiotics and radiology is rampant. The benefit of this overuse is hard to demonstrate.

    In future blogs I will supply examples of technological “advances” that cost astronomical amounts and have little or no demonstrable benefit.

    I recognize that my curves are exagerrated for effect. Please understand that as a physician I come to this from a caregiver’s perspective. The marginal cost of a unit dose of antibiotics might go down over time but the cost of saving or prolonging a life continues to rise rapidly.

    Getting back to average life expectancy, it is my opinion that if the US is spending twice as much as other developed countries and getting second rate results then those excess expenditures are wasted. Future postings will explore this issue. Stay tuned for Proton Beam Radiation Therapy.

  3. Ron W January 18, 2014 at 8:00 pm #

    How in the world do we discard free market competition? Too many stakeholders in the health care business. And we live in a society that worships at the alter of free markets. How do we reward young doctors like your daughters apart from some form of free markets? I may be wrong but I suspect that the monetary rewards for providers – doctors, pharmaceuticals, equipment, etc – are diminished in single payer systems. I’ll continue to read your blog, looking for answers.

  4. Ron W January 21, 2014 at 12:22 pm #

    Ron, Thank you for bringing this up. I should not have confused this post with a reference to the concept of “free markets” in health care. As I wrote last summer, I do not think “free markets” exist in the health care sphere and therefore cannot be counted on to reduce costs in most areas. I will dedicate a blog to this in the near future. Sam


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