The recent controversy over hormone replacement theory (HRT) for menopausal women provides a good case study in the uncritical use of the notion of "relative risk."
Relative risk is not, as one chat room correspondent apparently thought, the risk of communicating a disease to one's relatives, but rather a way to numerically compare the rate of some disease among people receiving a certain treatment (or engaging in a certain activity) to the rate among people not so treated.
Here's how it's calculated: If 5,000 people, say, regularly ingest some natural food supplement and 16 develop cases of a dangerous blood condition and only 12 in 10,000 people who don't ingest the supplement develop the condition, then the relative risk of ingesting the supplement is (16/5,000) / (12/10,000), or 2.67. This means that, all other relevant factors being equal, people ingesting the natural supplement incur roughly 2.67 times the risk of people not ingesting it.
More generally, the relative risk is the rate of the disease or condition among those receiving the treatment divided by the rate among those not receiving it.
As long as the sample sizes are reasonably large, relative risks far from one (more than 2 or less than .5) are more indicative of a real effect. If the relative risk is close to one (that is, the rates between the control groups and the treatment groups are similar), then the difference is more likely to be due to random variation. In addition to the natural variations in the treatment group and the control group chosen for comparison, there are often hidden, but systematic biasing factors sufficient to bring about the effect.
Systematic Bias in Studies?
For years, for example, HRT was seen as conferring cardiovascular benefits on the women who took the combination of estrogen and progestin because they suffered somewhat fewer heart attacks, strokes, and the like. That is, treatment with HRT seemed to have a relative risk a bit less than 1; women taking it seemed to incur these conditions at a lower rate than did a control group of women who did not take HRT.
There was, it's now clear, a biasing variable in these earlier studies: the women involved were, for the most part, relatively affluent and health-conscious, and their lower rate of cardiovascular problems was probably due to this and not to their taking HRT.
If they rubbed mustard on their elbows every morning, their rate of cardiovascular disease would no doubt still be smaller.
The large new study on HRT published in July in the Journal of the American Medical Association by the Women's Health Initiative (WHI) overturned the conventional wisdom about the treatment. Eliminating the self-selection bias, it found that the relative risks of heart attack, stroke, and breast cancer were 1.29, 1.41, and 1.24, respectively, suggesting that women taking HRT incur, respectively, 1.29, 1.41, and 1.24 times the risk of women not taking it.
Alternatively stated, this means that women on HRT face a 29 percent, 41 percent, and 24 percent greater risk from these respective conditions. The annual rates for these conditions are generally very low, however. Instead of the 19 strokes, 24 heart attacks, and 33 breast cancers that one might expect annually among 10,000 women not taking HRT, 10,000 women on the hormones will, on average, suffer 27 strokes, 31 heart attacks, and 41 breast cancers.
There was positive news in the study as well. The relative risks for colon cancer and hip fracture were both .67, suggesting that women on HRT will suffer only 67 percent the number of colon cancers (12 instead of 18 out of 10,000) and hip fractures (10 instead of 15) as women not on it. In addition, the women on HRT suffered far fewer other fractures, debilitating breaks of the shoulders, arms, and legs often associated with osteoporosis. The study did not attempt to measure the considerable value of HRT in treating hot flashes, sleep disturbances, depressions, skin and hair problems, and perceived lapses in mental acuity.
Still Not Clear-Cut
The decision whether to begin or continue HRT treatment is a complicated and personal one, but, the tenor of the coverage notwithstanding, there are reasons to do so.
The primary one, of course, is that the benefits in the previous paragraph (as well as others) sometimes manifestly outweigh the risks. Related to this is the fact that the relative risks are not that great. Another consideration is that the study's conclusions may merely be the result of a hidden statistical bias (as there was with the opposite conclusions reached by earlier studies). Terminating the study prematurely as the WHI researchers did, for example, might have introduced some bias by stopping a naturally fluctuating sequence of numbers on an upswing.
Although some of the study's conclusion were statistically significant, they were just barely so. As mentioned, relative risks of less than two are often not taken very seriously. (They can even arise from publication bias — the throwing out of studies that find no or slightly beneficial effects and the hyping of spurious slightly harmful effects.)
By contrast, the relative risk of lung cancer among smokers is flat-out undeniable — somewhere around 15 (with different studies producing values ranging between 10 and 25); that is, smokers are roughly 15 times as likely to develop lung cancer as are non-smokers.
Compare this with the HRT relative risks of approximately 1.3.
Hormone replacement therapy is not the panacea it was once touted to be. Neither is it the significant carcinogen that some accounts have described it to be. Like a lot of treatments, like a lot of life, it appears to be a trade-off.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.