How many times have you heard a claim like: Doing X increases your risk of getting disease A by 75%? Or how about a claim like: Taking supplement Y cuts your risk of getting a disease B in half? Such statements of relative risk can be very misleading. Here’s why.

In 1995, Britain’s National Committee on Safety of Medicines issued the following warning to women taking contraceptives: Rigorous studies have found that women taking 3rd generation contraceptives (contraceptives made after 1990) experienced a twofold (100%) increase in blood clots compared to a similar cohort of women who took 2nd generation (pre 1990s) contraceptives. In other words, newer contraceptives are doubling a woman’s risk of blood clots compared to older contraceptives.

It sounds like young women should avoid 3rd generation contraceptives because of the increased risk of blood clots, right?
Wrong.

Here are the hidden, yet important details on prevalence:

In reality, the contraceptive studies found that one out of every 7,000 women who took the 2nd generation pills had blood clots. This number doubled with 3rd generation pills where two out of every 7,000 women who took 3rd generation pills had blood clots. Hmm? So is a 100% increase from 1 to 2 blood clots in a sample of 7,000 women something to get deeply concerned about? Not likely.

If the prevalence rate of a disease is low, then a 2, 3, or 4 fold increase may not be important, unless you are among the few who get the disease. 

This fallacy also works its deceptive magic the other way – in preventing disease.

What if I told you that vaccine A cuts your child’s risk of getting disease X in half? Hmm? Sounds good, eh? Wait a minute. What is disease X’s prevalence rate? The prevalence rate/risk of getting disease X is 2 in 10 million, or 0.00002%. Now if your child is vaccinated, the risk of getting the disease is cut in half to 1 in 10 million, or 0.00001%. Does this sound reasonable? Probably not. Think about it this way: we would need to vaccinate 10,000,000 children in order to prevent one child from getting disease X.

Should we spend millions to vaccinate children against a disease most will never get? To do so might be a waste of healthcare resources and dollars that could be utilized elsewhere. 

So the next time you read or hear a result like “It increases the risk of disease X by 200%” or "It cuts the likelihood of developing disease X in half," look for the prevalence rate. As the prevalence in the population goes up, so does the significance of the risk. For instance, if the prevalence rate is 10% (10% of people are at risk for developing disease X), then a vaccination that cuts that risk in half to 5% is something to crow about.

(Source: Gigerenzer et al. (2008). Helping doctors and patients make sense of health statistics. Psychological Science in the Public Interest, 8(2), 53-96.)