Here’s some examples.
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. Well it depends on the prevalence of blood clots.
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. Is a 100% increase from 1 to 2 blood clots in a sample of 7,000 women something to get deeply concerned about? Not really when you consider that an overwhelming majority of women taking contraceptives do not get blood clots. 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 unfortunate few who get the disease.
This potential pitfall on interpreting relative risks works the other way – in preventing disease.
What if you were told that vaccine A cuts your risk of getting disease X in half? Sounds good, but we must consider the prevalence rate of disease X. If the prevalence rate of disease X is 2 in 10 thousand or 0.02% and you're vaccinated, the risk of getting the disease is cut in half to 1 in 10 thousand or 0.01%. We would need to vaccinate 10,000 people in order to prevent one person from getting disease X.
The upshot is that we need to consider prevalence when evaluating risk. If the prevalence rate of an unfortunate event is 1 in 10 and intervention cuts that risk in half to 5%, the treatment is worth considering. However, if the prevalence rate is 1 in 10000 and intervention cuts that risk in half from 0.01% to 0.005%, the intervention may not be worth considering, especially if it is expensive or comes with risky side effects.
When questions about risk and prevalence arise, a cost versus benefit analysis usually determines the best course of action. Interventions that cut the risk of a low prevalence disease in half may be worthwhile if the intervention is cheap and/or the disease fatal or contagious. Similarly, engaging in behavior that increases the risk of a low prevalence disease may be worthwhile if the behavior enriches one’s life, which is why I occasionally drink large, creamy, fat-laden, blueberry milkshakes.