Long Odds

[rinue]

Via the Boston Globe, reporting on a Harvard Medical Center survey to establish the effectiveness of mammograms by age group screened:

They calculated that 10 in 10,000 women in their 50s who are screened every year for a decade will avoid a breast cancer death; 6130 women, on the other hand, will have a false positive result that requires extra X-rays and 940 will have biopsies for non-malignant findings.

So if you're in your 50s and have a mammogram with a positive finding for breast cancer, the odds that you have breast cancer are more than 6000 to 1. (No, not 600 to one. You didn't have one mammogram; you had 10, a mammogram per year.) Odds that you are a woman in your 50s who develops breast cancer: somewhere around 1 in 60.

Seems like we might be better off randomly biopsying the population. We could use social security numbers like for the draft.

Or use a magic 8 ball. (Outlook good.)

Early detection is maybe not a thing we can actually do.

Then again, I just sent in my CV to be considered for a Studio Canal paid internship. (I have so much love for Studio Canal.) Any time you apply for something and say in the cover letter "I don't speak French, but I still think I would do really well at this job in France," you gotta think: here is somebody who doesn't care about the odds.

Comments

[rinue]

Technically, I think it works out to 6000+ false positives per 100,000 screenings (10 screenings each of 10,000 women). Which also means 10 lives saved per 100,000 screenings.

[movingfinger]

Yes, you're right.

It is awful to contemplate that a goodly number could be getting multiple false positives. Man, that would be a stress merry-go-round, wouldn't it.

(I guess it depends on whether you count numbers-of-women-screened or numbers-of-screenings. I was figuring one woman per false positive...)

The 10 actual positives begin to look like statistical noise. We don't know the false negative rate, from that piece.

[rinue]

Indeed. I got my estimated 1 in 60 women in their 50s has breast cancer figure from a British study not mentioned in the Globe, but there is no good way for me to guess whether those women are getting annual mammograms. Since they're voluntary and tied to both ability and willingness to pay, it may be that annual mammogram women are less likely to have cancer than the general population (wealth effect or concern about cancer which leads them to other protective lifestyle behaviors) or more likely to have cancer than the general population (cautious because of genetic predisposition).

The Harvard finding in the Globe concluded mammograms decrease a woman's risk of dying by 19%, but it seems like most of that comes from the over-60 category.

Also worth noting: it's 10 women whose lives are saved, not 10 women who have cancer. Although I don't think this is true, I have to acknowledge the possibility that there are loads of true positives where the woman dies. Which would also cast doubt on the effectiveness of early detection, but a different kind of doubt. It may be that women under 60 who get breast cancer tend to have very aggressive and hard to treat breast cancer (which we already know is true; much more likely to be tied to BRCA mutations).

Overall, it seems to me we'd save a lot more women by putting that screening time and money into stuff like early childhood nutrition, but that's not the kind of tradeoff that tends to be available in politics.

[valancy_jane]

Oddly, this is the kind of stuff I comfort myself with when I wake up in the night wondering how my mother's going to die, since she doesn't remotely take care of herself and absolutely refuses all medical care excepting, oddly, dental.

We're pretty sure her heart is going.