Doctors don’t know Bayes’ Theorem
The article I read was about probability in medicine. It turns out, most doctors don’t know actually know probability. The article mainly concerns Gerd Gigerenzer, the director of the Harding Center for Risk Literacy in Berlin, who wrote a book called Risk Savvy which “takes aim at health professionals for not giving patients the information they need to make choices about healthcare.” The first statistical problem presented to doctors was the following:
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?
- nine in 10
- eight in 10
- one in 10
- one in 100
Given:
- The probability that a woman has breast cancer is 1% (“prevalence”)
- If a woman has breast cancer, the probability that she tests positive is 90% (“sensitivity”)
- If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9% (“false alarm rate”)
This, to any Networks student, should immediately present itself as a Bayes’ Theorem question. While the article simply presents the answer of 1 in 10 without explanation (which 21% of doctors answered correctly), the math goes as follows. The probability of having breast cancer given a positive result is the probability of a positive result giving the patient has breast cancer multiplied by the probability of having breast cancer, divided by the probability of a positive result. The positive result probability requires the total probability theorem, which is the probability of a positive result given the patient has breast cancer multiplied by the probability of having breast cancer plus the probability of a positive result given the patient does not have breast cancer multiplied by the probability of not having breast cancer. In numbers, this is .9 * .01 / (.9 * .01 + .09 * .99), which equals .917, or about 9 in 10.
The crazy thing is, when Gigernerenzer asked 1,000 gynecologists this question, nearly half answered that the women would have a 9/10 probability of having breast cancer, while (as mentioned above), only 21% got the right answer. More examples are laid out where it is clear that doctors don’t fully grasp concepts such as survival rate and mortality rate. Of course, this isn’t the fault of the doctors themselves, but the curricula in which they receive training.
Another curious phenomenon mentioned was that of “defensive medicine,” where doctors practice medicine in a way to mitigate risk of litigation, not fully focusing on actually helping the patient. This, however, isn’t what I really wanted to discuss. (but interesting nonetheless). The author explains that proper wording of questions to coax the correct answer out of a physician might be the best way to get good care, suggesting “it’s often good to ask doctors not ‘What would you recommend?’ but, ‘If it were your mother or your brother, what would you do?'” The takeaway quote at the end is:
“A physician is someone who can help you but also someone you need to challenge in order to get the best treatment.”
which I think speaks volumes about the medical landscape and how a patient should navigate it.
http://www.bbc.com/news/magazine-28166019
Please fix: 0.917 does not equal even closely to 1 in 10.
“which equals .917, or about 1 in 10.”
Thank you, I have corrected my mistake.
I know this is an old post, but you corrected your post incorrectly, Arthur.
The expression you provide yields .0917 (about 1 in 10), NOT .917 (about 9 in 10).
Ironically, by changing the text to “about 9 in 10” rather than correcting your wrong decimal result, you’ve ended up endorsing the same wrong answer you call “crazy” in the next paragraph. This is pretty confusing for the reader.
Re: Sue’s correct comment supra. I have added [brackets] and {missing words} to the text of the original post.
The positive result probability requires the total probability theorem, which is [the probability of a positive result given the patient has breast cancer] multiplied by [the probability of having breast cancer] {xxxplusxxx divided by the sum of} [{the probability of a True Positive} {plus} [the probability of a positive result given the patient does not have breast cancer] multiplied by [the probability of not having breast cancer]].
Corrected, this is
[.9] * [.01] / ([.9 * .01] + [.09 * .99]), which equals .0917, or about 1 in 10.
More directly:
Positive result probability = (True Positive probability) / [(True Positive Probability) + (False Positive probability)]
Positive result probability = (0.9*0.01)/[(0.9*0.01)+(0.09*0.99)] = 9.17%
Or about one in ten.
I got here six years late from TheZvi, via an old “Compass Rose” post.