Making sense of medical results

A 50-year old woman, no symptoms, participates in routine mammography screening. She tests positive, is alarmed, and wants to know from you whether she has breast cancer for certain or what the chances are. Apart from the screening results, you know nothing else about this woman. How many women who test positive actually have breast cancer? What is the best answer? You might like to make a guess, or wait until I give you some background information.

9 in 10 / 8 in ten / 1 in ten / 1 in 100

I will now give you the relevant information to answer the question about the chance of cancer after a positive test. First, I’ll present it in the way that is customary in medicine, in probabilities.

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

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

·  If a women does not have breast cancer, the probability that she nevertheless tests positive is 9 percent (false alarm rate)

So. . . . what are the chances she has cancer?

Adapted from Gigerenzer, G. (2014). Risk Savvy - How to make good decisions. London: Allen Lane, page 162, 163

The picture shows 1000 women.

Use coloured pens to show

·  How many women will get breast cancer (prevalence)

·  How many of the women who get breast cancer would get a positive mammogram (sensitivity)

·  How many of the women who don't get breast cancer would get a positive mammogram (false positive rate)

Now use your picture to think about a woman who has had a positive mammogram.

What’s the likelihood that she has breast cancer?

Adapted from Gigerenzer, G. (2014). Risk Savvy - How to make good decisions. London: Allen Lane, page 162, 163