Mammograms Revisited

Richard Thaler (coauthor of Nudge; I'll reference him often) wrote a piece for the NY Times about the current mammogram controversy. It's worth a read. He doesn't talk about "saving lives", he brings up the problems with prostate cancer treatment, and he provides some interesting numbers about the likelihood that breast cancer is not fatal and mammograms don't detect the types that are fatal, though not the expected life spans of women who are treated for breast cancer. I have a little commentary to add.

The stated false positive rate is 10% per test (which is huge for something with such serious consequences). For the math impaired, here's how that converts into the probability that women are likely to get a false positive over a decade. The simplest way to do this is to focus on the 90% chance that each test does not give a false positive. We use what is called the Multiplication Rule for Independent Events. For ten years, we multiply .9 (90%) by itself nine times: .9 * .9 * .9 * .9 * .9 * .9 * .9 * .9 * .9 * .9. This is more simply written as .9 ^ 10, and the product is about .35. So, there is a 35% over ten mammograms that a woman will not get a false positive, and a 65% chance that she will get a false positive. Of course, this assumes that there are no characteristics of a breast that would make it prone to false positives, which I imagine is unlikely. The 10% comes from aggregate data. I think it is more probable that women who produce false positives at age 40 are continuously more likely to do so each year than women who did not have false positives at age 40. Without the longitudinal data in front of me, I remain skeptical of the appropriateness of multiplying the false positive probabilities as though they are always independent events.

Thaler writes a little about the costs of all these mammograms in terms of unnecessary treatments that cause side effects, and the stress that women feel when diagnosed with breast cancer, but he avoids using dollar amounts to describe all the waste. What is missing is mention of opportunity costs. The cost of all the unnecessary procedures is not just the dollars exchanged for them, but also the other things we can not buy because our finite dollars were poorly allocated. I covered in my last post the idea that we could extend several times as many life years for Americans by taking the money spent on mammograms for women under 50 and spending on other endeavors, such as nutrition programs for children, or having nurses visit patients after operations to reduce treatment noncompliance complications. It is vital to consider opportunity costs. Mammograms for women under 50 don't just allocate $2 billion per year in exchange for a few thousand life years. They also cost us many thousands of other people's potential life years, and the unnecessary treatments and stress result in much lost work productivity. The practical net result, the way I see it, is that our system is effectively just killing other people early by insisting on giving mammograms to women under 50 who lack high risk indicators. Are women in their 40s more important than everyone else?

Many people have lost or almost lost loved ones to breast cancer. It is okay to feel empathy for them. If you are one of them, I feel empathy for you. That is not justification to ignore the data we have and allocate our limited resources on inferior practices. Emotions limit our perspectives and distract us from the ultimate goal of doing the most good we can with the resources we have. Please, let the cooler minds prevail and establish a system that gives America the greatest benefits it possibly can.