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Misunderstandings involving different uses of the word "risk"

In everyday usage, "risk" is essentially synonymous with "danger." For example, we might say that someone walking alone on a poorly lit street after dark has a risk of being mugged.

However, "risk" is also used to quantify a danger. In the most basic form, a risk is a probability. For example, we might say that the risk that a U.S. resident dies from a heart attack is about 25%, meaning that about 25% of all deaths in the U.S. are from heart attacks.

Just this usage alone brings up the question of reference category, especially if we phrase the risk as "Your risk of dying of a heart attack is about 25%." The risk may be higher or lower depending on other factors (gender, occupation, age, etc.) in addition to being a U.S. resident.

Another common use of the word risk is in the term
relative risk (also called risk ratio).  This is a method of comparing the risk of one group with the risk of another. One group might be people with a certain condition (or receiving a certain treatment) and the other group people without that condition (or not receiving the treatment). Relative risk is the ratio of the risks for the two groups. This immediately brings  in two possible source of confusion:
  1. What are the two groups?
  2. Which group's risk is in the numerator and which group's risk is in the denominator?

Another source of misunderstanding when relative risks are given is that sometimes only the relative risk is given. We also need to know the "absolute risk" (the risk of at least one of the groups involved) in order to interpret what the relative risk is telling us.
Example: The report on a clinical trial of a new drug might say that the relative risk of a heart attack for people with high cholesterol in a certain age group who take the drug, compared with people in that same age group with high cholesterol who take a placebo instead of the drug, is 75%. (This might also be presented as  a 25% reduction in risk.) This might sound substantial. But whether or not it is depends on the absolute risks. 

For a consumer-oriented explanation of  health risks at a fiarly basic level of quantitative literacy, see
 Woloshin, Steven, Schwartz, Lisa, and Welch, H. Gilbert (2008). Know Your Chances, University of California Press.