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Here's a fun math/probability challenge for you

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mjrpes3

mjrpes3

Golden Member
Imagine a woman in the 40-50 age block gets a mammogram test and it comes back positive. What is the probability that she actually has breast cancer? Assume the following:

1. The probability that one of these women in this age block has breast cancer is 0.8 percent.
2. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram.
3. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram.

In a bit I'll linked to the article I was reading that posed this question with answer, along with some info about doctors who where also posed this question and how they answered.

If you've already read the article I'm talking about don't post it just yet 🙂
 
Pretty sure it's 9.4%.

Edit - Mr Pedantic edited his post AFTER I posted my answer, just FYI. Fucking New Zealanders. His previous answer was 51% and he's just trying to bask in my glorious maths skillz.
 
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It's just about there, 7/77, or 9.1%.

http://opinionator.blogs.nytimes.com/2010/04/25/chances-are/?ref=opinion

Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don’t have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer?

Since a total of 7 + 70 = 77 women have positive mammograms, and only 7 of them truly have breast cancer, the probability of having breast cancer given a positive mammogram is 7 out of 77, which is 1 in 11, or about 9 percent.
Click to expand...

Most startling is just how off American doctors were

As for the American doctors, 95 out of 100 estimated the woman’s probability of having breast cancer to be somewhere around 75 percent.
Click to expand...

Something doesn't seem right about this... I'm not surprised people are going to be off, but so many so way off is weird.
 
Edit - Mr Pedantic edited his post AFTER I posted my answer, just FYI. Fucking New Zealanders. His previous answer was 51% and he's just trying to bask in my glorious maths skillz.
Click to expand...
You're just jealous that I posted first. FYI, the 51% was obtained due to an error in typing the wrong number of 0s in...

Something doesn't seem right about this... I'm not surprised people are going to be off, but so many so way off is weird.
Click to expand...
Med students and doctors fucking suck at maths. I just happen to be an exception. Also, we're kind of indoctrinated by lecturers and other clinicians into only using specificity and sensitivity as a measure of the efficacy of a screening test, neither of which apply to the problem. It means that very few people slip through the net, as it were (according to the problem 0.87% of the eligible population will have breast cancer and not know it) which is the important metric, but it also means that we miss out on this sort of thing; since a lot of people believe that being positive for a screening test means that you're positive (kind of like how people think getting arrested pretty much equates to being guilty of the crime), this means that we put quite a lot of women through a month or so of anxious waiting and worrying waiting for the results of a more comprehensive and accurate test to come back.
 
Has someone checked the facts of the article? I remember a while ago reading a very well sourced article on HIV rates describing how some people had done the maths to achieve similar results with false positives in HIV tests. It turned out they had some very basic facts wrong, and false positives were actually very rare. It seems like perhaps the same fallacy is being committed here, but I honestly don't remember the details and it was a long time ago.

Also keep in mind that the article may have some serious biases, being that mammography is a hugely controversial subject right now, and some people have become quite polarised and irrational in their point of view.
 
mjrpes3 said:
Imagine a woman in the 40-50 age block gets a mammogram test and it comes back positive. What is the probability that she actually has breast cancer? Assume the following:

1. The probability that one of these women in this age block has breast cancer is 0.8 percent.
Click to expand...

Seems like the answer is stated, without doing the math.
 
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