Is Smoking More Dangerous for Women?
"Higher heart risk in women smokers" was the headline of an April 3, 1998, article at the Yahoo!® Health news website. The article, from the Reuters news agency, described Danish research that was interpreted as evidence that smoking affects the risk of a heart attack more for women than for men. Here is part of the article:

Women who smoke have a greater than 50% higher risk of a heart attack than male smokers according to a study from Denmark. The researchers suggest that this difference may be related to the interaction of tobacco smoke and the female hormone, estrogen. "Women may be more sensitive than men to some of the harmful effects of smoking," the team writes in the April 4th edition of the British Medical Journal. Analyzing data from nearly 25,000 Danish men and women, Dr. Eva Prescott of the University of Copenhagen and colleagues report that women who smoke have a 2.24 relative risk of myocardial infarction, or heart attack, compared with nonsmokers. This is significantly higher than the relative risk of male smokers compared with nonsmokers.

Unfortunately, the only information that we are given, for each sex, is the relative risk of a heart attack for smokers. What's missing from the news article is any mention of the estimated risk of a heart attack for any group of interest. A look at those risks makes the research interpretation debatable. The British Medical Journal article (Prescott, Hippe, Schnor, and Vestbo, 1998) that originally reported the research provided more complete information about the risks. That information is displayed in Table 4.6. Based on the data in the table, do you agree with the conclusion stated in the Web article?

The researchers focused on relative risk, which in this case is the ratio of the risks of a heart attack for smokers compared to nonsmokers. The relative risks for women and men are calculated as follows:
• For women who smoke, the relative risk of a heart attack is 5.88%/2.63% = 2.24.
• For men who smoke, the relative risk of a heart attack is 10.62%/7.42% = 1.43.

The first sentence of the news article says, "Women who smoke have a greater than 50% higher risk of a heart attack than male smokers..." That is an incorrect statement. In Table 4.6, we can see that women who smoke have a lower risk of a heart attack than males (5.88% risk for women compared to 10.62% risk for males). The researchers actually compared relative risks, not risks; the relative risk of a heart attack for women smokers, 2.24, is about 50% higher than the relative risk for male smokers, 1.43.

In a subsequent issue of the British Medical Journal, several letter writers argued that the correct interpretation of these data is as follows:
• For both smokers and nonsmokers, men have a higher risk of heart attack than women do. (See the risks in Table 4.6.)

• For men, the difference in the risks of a heart attack for smokers versus non-smokers is 10.62% - 7.42% = 3.20%. For women, the difference in the risks of a heart attack for smokers versus non-smokers is 5.88% - 2.63% = 3.25%. In other words, the additive effect of smoking, the amount that smoking adds to the risk of a heart attack, is almost the same for the two sexes.

The researchers' response to these letters was that they believed that it was valid to consider the multiplicative effect of smoking on risk. Dr. Prescott and her colleagues believe it is important that smoking multiplies the risk of a heart attack by 2.24 for women but by only 1.43 for men.

The moral of the story here is that a relative risk is affected by the size of the baseline risk, so it is important to know the baseline risk. For example, if a risk increases to 3% from a baseline risk of 1%, the relative risk is 3. If a risk increases to 22% from a baseline risk of 20%, the relative risk is only 22/20 = 1.1, although the difference in risks is still 2%. Is an increase in risk from 1% to 3% more serious than an increase from 20% to 22%? That may depend on the situation.