Arnold Kling  

Costs, Benefits, and Health Care

Macro Econoblog... The Missing Martyrs...

I do the arithmetic.

Suppose that a medical test costs $1000, and 98 percent of the time it fails to turn up anything that would affect treatment. The other 2 percent of the time, it results in a treatment choice that extends life by 5 years. How much does a year of life have to be worth in order for the test to have an expected value that exceeds its cost?

The answer is that the "expected number of life-years saved" is .02 times 5, or one-tenth of one year. If one year is worth more than $10,000, then one-tenth of one year is worth more than $1000, so that the test is worthwhile.

David Cutler argues that the value of a healthy life-year is $100,000. I see two problems with using that figure to assess individual health decisions.

First, if per capita GDP is about $33,000, then it takes three year's of an individual's GDP to pay for one health-year of life. That is not sustainable. If I am the average person and produce $33,000 a year, and every year I have an opportunity to pay $100,000 to extend my healthy lifespan by one year, then I will run out of money.

Second, imagine that one medical procedure has an expected saving of two life-years, another procedure has an expected saving of three life-years, etc. If you add together all of the life extensions, it might suggest that I could live to 150. The fallacy is that although the costs are additive, the benefits are not. There is a diminishing-returns aspect of health care that is not captured by simple expected-value calculations.

UPDATE: See additional comments from John Ford.

For Discussion. In practice, do my objections matter, or is Cutler's approach reasonable for realistic circumstances?

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The author at Business Word Blog in a related article titled Calculating the costs and benefits of health care and tests writes:

    What are the costs and benefits of health care, specifically a $1,000 test with a 2% chance of finding a problem? Arnold Kling does the math and generates some comments.

    [Tracked on April 27, 2005 4:52 PM]
COMMENTS (9 to date)
Brent Buckner writes:

Unsustainability is not a critical issue, in that people do not have unlimited opportunities to extend their healthy lifespans.

A procedure has different expected consequences for different individuals. An expected value calculation done for an individual could take that into account (e.g. based upon the age of the patient); nonetheless, the average expected value figure is useful.

A "value" of a healthy life year may be approximated from (amongst other things) the market price of safety features and the actuarial effects of those safety features.

Cutler's approach is reasonable for realistic circumstances for broad-brush issues.

Randy writes:

"Value" is inherently subjective. What's missing here is the question, value to who?

Is a year in my life worth $100,000 to me? Yes, and probably more.

Is it worth $100,000 to society as a whole? Probably not, especially if they are going to be asked to foot the bill.

Ask your neighbor for a couple of bucks to buy some aspirin and you'll probably get it. Ask him for $100 and he'll say sorry, but no.

Jim Erlandson writes:

Coincidentally, the Freakonomics weblog today talks about the time value of life.

When you eat high calorie, high fat foods, you pay not only a price in dollars, but also indirectly in terms of slightly increasing the chance of premature death. My colleague Kevin Murphy (who, like me, loves McDonalds) has done back-of-the-envelope estimates that suggest that each hamburger you eat shortens your life enough that the typical person would be willing to pay $2 to $3 to get rid of the adverse health impact. So, in other words, the health costs of a hamburger are about the same as the price you pay at McDonalds.

"Would you like a Lipitor with that Quarter Pounder?"

William Polley writes:

$100,000 seems a bit arbitrary and imprecise. Does that get adjusted for inflation? $103,000 next year? Is that the value to society? If so, I think it is way overstated.

The problem with a one-size-fits-all value (regardless of what that number actually is--even assuming we could measure the social value properly) is that individuals willingness to pay varies. In other words, we all have a different demand curve for... uh, extra years of life. (Boy that sounds weird, doesn't it?)

It may sound odd, but I challenge anyone to show otherwise. Thus, the real question becomes one of allocating a scarce resource (extra years of life, or more properly, the tests and treatments that get you there) to people with differing willingness (read, ability) to pay.

But any way you slice it, that's always been the real question, hasn't it? I don't see that Cutler's approach adds anything useful.

Lancelot Finn writes:

If I was so thirsty that I would die if I didn't get water, I would pay $1,000 a gallon if I had to.

Of course, if I had to pay that for every glass of water I drink, I'd go broke very fast.

I extract consumer surplus from goods that I buy. How much? One can draw that on a graph: the region above the line P=price, and below the demand curve. But how high does the demand curve go? That's anybody's guess. There are a lot of goods that are necessary to survival, so we'd probably give everything we had for them if that were really necessary. Our consumer surplus on the purchase of these goods is equal to our total resources.

I think the solution to your apparent paradox is to be discovered somewhere along the path. (I can't be bothered to work through the problem fully at the moment.)

Lawrance George Lux writes:

Here you have the irrationality of Medical care argument. Such Dollar costs can be assessed, but they must be affected by external elements; the greatest consisting of the general health level of the Patient. Returns get better or worse due to health, access to Care, previous Ailments and Injuries, and weakness of specific Organs, It always becomes a Judgement call.

The trouble is American medical practice overproscribes at almost every level. lgl

richard writes:

Cost-benefit analyses can be used for two purposes (1) to rank alternatives given a limited budget and (2) to decide if an activity is worthwhile.

An example of (1): would we save more lives per dollar if we spent money on treatment A or treatment B?

An example of (2): Is treatment A worthwhile?

To me, (1) is an excellent exercise, albeit rarely used in policy. (2) is much too fuzzy to be of much use.

Cutler's approach is clearly within the (2) camp.

Paul N writes:

I think Lancelot Finn is on the right track. Isn't Arnold confusing utility with cost?

$100k/yr to me seems consistent with the ~$6M average that comes from death-risk-for-$ studies.

John Fembup writes:

Value of your life? $5.98

Value of my life ? Priceless

Therefore YOU should pay to subidize the activities of MY life, whether it be commercially, medically, or actuarially.

And what if we ALL think this way? Well if we all think this way, wouldn't I be stoopid not to?

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