One of the questions most often asked in the medical literature is “what is the risk of x?” It’s a pretty important question. I’d like to be able to tell my patient with high blood pressure what their risk of heart attack is, both with and without treatment. And risk is a sexy topic—the press loves it. Whether it’s cell phones and the “risk” of brain cancer, or vaccines and the “risk” of autism, risk makes for cool headlines. Take this one for example:
Migraines cut breast cancer risk 30 percent: study
What does this mean? Should I tell my wife to go out and find some migraines? I have a feeling one or more of my colleagues will give a more detailed critique of this study, but I’d like to talk to you a bit about what we mean by “risk”.
Risk, in the most basic sense, is a causal association. If, for example, I find that members of the “Thunderstorm-lovers Golf Association” have a higher incidence of being struck by lightning than golfers who don’t belong to this odd club, I may have stumbled upon a measurable risk. There is both a measurable association, and a plausible reason to causally link the associated variables. If I find that members of the National Association of Philatelists have a higher incidence of heart disease than other folks, I may or may not have stumbled on a risk. Is there a reason that philatelists should have more heart disease? Is it a coincidence? Is it worth investigating further? Is there a confounding variable, e.g. are philatelists in general older, and did I fail to control for this?
Then there is the question of the degree of risk. How strong is the risk observed?
Statisticians have ways of measuring risk, but many of these terms—such as relative risk, absolute risk reduction, odds ratio—are not intuitive concepts.
Let’s take the study in question. The premise is interesting. Migraines and breast cancer are both associated with estrogen. Many breast cancers are estrogen-dependent, and the risk of developing breast cancer correlates with exposure to estrogen.
Migraines appear to be associated with estrogen as well, but negatively. This is a much more tenuous connection. It has been observed that migraines tend to wax during estrogen-poor times, and wane during estrogen-rich times—high estrogen, fewer migraines; low estrogen, more migraines. Or so it’s been observed.
The authors of this study invoked migraine as a negative risk factor for breast cancer. The English meaning of “risk” is a bit lost here—what they are saying is that women who have migraines are less likely to develop breast cancer than women who don’t have migraines. This shouldn’t be all that surprising, as migraines and breast cancer are both associated with, well, womanhood.
But all this aside, it’s the “30%” headline annoys me. That a big number! Get me a migraine, stat! But thirty percent is an “odds ratio“, which is a mathematical way of describing an association in a case-control study such as this one. Odds ratios are not intuitive, and as a measure of risk, they tend to break down when looking at common occurrences, such as migraines.
If we look directly at the data from the study, the data used to calculate the odds ratio, we see something else. In this study, the control group was post-menopausal women without breast cancer. The case group was women with breast cancer. Among women without breast cancer, 19% had ever had a migraine. Among women with breast cancers, 14-15% had ever had a migraine. So, there was about a 4-5% difference in migraine rates between women with and without breast cancer. Does that still sound like a big number?
Statistics are non-intuitive. I have to work pretty hard to try to dig out the clinical meaning from stats, and I still get it wrong sometimes. The press gets it wrong much more often. Be very wary of banner headlines about risk. Besides the difficulty of understanding the difference between risk reduction and odds ratios, what does it mean in the real world?
R. W. Mathes, K. E. Malone, J. R. Daling, S. Davis, S. M. Lucas, P. L. Porter, C. I. Li (2008). Migraine in Postmenopausal Women and the Risk of Invasive Breast Cancer Cancer Epidemiology Biomarkers & Prevention, 17 (11), 3116-3122 DOI: 10.1158/1055-9965.EPI-08-0527