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.