Understanding statistics could save your life

The current addition of Scientific American Mind has an excellent article on the misuse and misunderstanding of statistics in medicine. They say that “individuals often shy away from statistics because they have an emotional need for certainty”. Unfortunately, almost everything in medicine is about probabilities. Here is one example:

Consider a woman who has just received a positive result from a mammogram and asks her doctor: Do I have breast cancer for sure, or what are the chances that I have the disease? In a 2007 continuing education course for gynecologists, Gigerenzer asked 160 of these practitioners to answer that question given the following information about women in the region:

· The probability that a woman has breast cancer (prevalence) is 1 percent.

· If a woman has breast cancer, the probability that she tests positive (sensitivity) is 90 percent.

· If a woman does not have breast cancer, the probability that she nonetheless tests positive (false-positive rate) is 9 percent.

What is the best answer to the patient’s query?

1. The probability that she has breast cancer is about 81 percent.

2. Out of 10 women with a positive mammogram, about nine have breast cancer.

3. Out of 10 women with a positive mammogram, about one has breast cancer.

4. The probability that she has breast cancer is about 1 percent.

Gynecologists could derive the answer from the statistics above, or they could simply recall what they should have known anyhow. In either case, the best answer is choice 3; only about one out of every 10 women who test positive in screening actually has breast cancer. The other nine are falsely alarmed. Prior to training, most (60 percent) of the gynecologists answered 90 percent or 81 percent, thus grossly overestimating the probability of cancer. Only 21 percent of physicians picked the best answer—one out of 10.

The risk involved in being falsely alarmed should not be overestimated. The article cites a number of examples when the lack of understanding of the statistics led doctors to recommend potentially dangerous invasive surgery; a few examples of individuals who were diagnosed as HIV positive and informed that they were HIV positive and committed suicide, only for it to be subsequently found that the test had showed a false positive.

The link between the mind and health has not yet been understood properly, but stress certainly has an impact on health, and creating unnecessary alarm for patients is likely to have a negative impact on their health.

The full article is here.