Boobies. There I had to say it. This is a post about boobies, and math, and consulting with experts before making too many claims.

In this click bait article that I found somehow searching on Google News for unrelated topics, I see that some "Medical Anthropologists" are claiming that Bras seem to cause breast cancer (not a new claim, their book came out in 1995, but their push against the scientific establishment is reignited I guess). At least part of this conclusion seems to be based on the observation from their PDF

Dressed To Kill described our 1991-93 Bra and Breast Cancer Study, examining the bra wearing habits and attitudes of about 4,700 American women, nearly half of whom had had breast cancer. The study results showed that wearing a bra over 12 hours daily dramatically increases breast cancer incidence. Bra-free women were shown to have about the same incidence of breast cancer as men, while those who wear a bra 18-24 hours daily have over 100 times greater incidence of breast cancer than do bra-free women. This link was 3-4 times greater than that between cigarettes and lung cancer!

They further claim "bras are the leading cause of breast cancer."

That's pretty shocking data! I mean really? Now, according to http://seer.cancer.gov/statfacts/html/breast.html there are about 2 Million women in the US living with breast cancer, and 12% overall will be diagnosed throughout their lives. There are around 150M women in the US overall. So $P(BC) = 2/150 = O(0.01)$

However, in our sample $P(BC) = 0.5$ That's 50 times the background rate (ok 37.5 if you do the math precisely).

Doesn't it maybe seem plausible that in winnowing through the 1% of women living with breast cancer and are still alive, or even the 5 or 6 percent who have been diagnosed in the past but are still alive (figure half of women who are alive today who will at some point be diagnosed have already been diagnosed at this point) that maybe, just maybe they could have introduced a bias in whether or not their sample wears bras?

So "looking for cancer patients causes us to find bra wearing women" is actually maybe the more likely story here? Perhaps "cancer patients who were non bra wearers were overwhelmingly more likely to have died from their breast cancer, and so we couldn't find any of them?" That's somehow not as reassuring to the non-bra-wearers in the audience I think.

Symbolically: $P(Alive \& BC \& NBra) = P(Alive | BC \& NBra) P(BC|NBra) P(NBra) = 1/100 P(Alive \& BC \& Bra)\\ = 1/100 P(Alive | BC\&Bra) P(BC|Bra) P(Bra)$ pretend BC and Bra are independent. We conclude $P(Alive | BC \& NBra) = 1/100 P(Alive | BC \& Bra) P(Bra)/(1-P(Bra))$ or not wearing a bra reduces your chance of surviving by a factor of 10 or so if P(Bra) ~ 0.9? Put on those bras ladies! The exact opposite of their conclusion!

I personally suspect something else spurious in their research. But nothing in their PDF convinces me that they know what they are doing.

Note that wikipedia has some discussion of their book.

3 Responses leave one →
1. Martha S permalink
July 31, 2014

An alternate hypothesis to be investigated: large breast size may plausibly be a causative factor in incidence of breast cancer (more breast tissue to develop cancer), as well as a causative factor in wearing a bra (women with very large breasts often wear a bra for comfort, even for sleeping) . So there might be a correlation from a common causal factor, but not a causal relationship. Much like the classic example of kids with larger feet have higher reading scores (both tend to increase with age in kids).

• July 31, 2014

Absolutely, though the factor of 100 these people claim seems to me so outrageous that it seems like they must have induced some kind of bias themselves, on top of any causal processes in the actual cancer incidence.

2. August 1, 2014

So, how could they design a data collection process that might better represent the situation?

First, you want to avoid survivorship bias. So in sampling from cancer patients, it makes the most sense to sample patients who were diagnosed very recently, perhaps within the first 2 months or so. Second, you want to sample from a variety of hospitals to get a reasonable cross section of the socioeconomic spectrum. Third, you would want to sample control patients from the same hospitals, and hence the same socioeconomic spectrum etc. You would probably want to at least partially match the controls on a variety of important categories, such as females, with similar age range, race, weight range, etc (and then use Poststratification for dealing with mismatches). The controls should probably be completely cancer free (except maybe minor skin cancers or something) and better yet if they are not being treated for any serious disease, so you might choose patients getting screening mammograms that turn up negative, and patients with minor injuries.

Breast size is clearly important, so it would be useful to record both breast size, and the cup size that the patient chooses (one portion of the theory is related to "squeezing" so it's useful to know if there is a mismatch between measured size and cup size choice).

Is this the kind of thing they did? I have no idea, and their PDF gives me no confidence to think that spending money on their book to find out would be worthwhile. Even the snippet from the "look inside" on Amazon seems fairly, shall we say, non-scientific. There are a lot of opinions given about the medical and biological research establishment and its social dynamic though. In such a popular audience oriented book with such a controversial subject, I don't have much hope for a well thought out and technical description of their data collection protocol. Perhaps someone with an interest, and access to the book from a library could give a summary of what's in the book about the sampling methodology.