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.