Relative Risk

By the end of this post, you should be able to describe in words what "relative risk" is, understand its significance, and possibly even calculate it given the appropriate data.

Whenever you're evaluating a study of treatment effect, try to think in terms of outcomes and exposures.  (The term "exposure" should be understood broadly to include therapeutics and risk factors.)  The important questions usually revolve around the relationship between the incidence of an outcome (e.g. myocardial infarction) to an exposure (e.g. aspirin).  If the study you're reading doesn't give you the actual incidence of the outcome you're interested in, you can calculate it (and most measures of treatment effect) by creating a simple 4x4 table like this one:

(This table should remind you of something).  It's very similar to the one you use to calculate the characteristics of diagnostic tests.)

It's easy to see that the incidence of an outcome in either the exposed group or the unexposed group is simply the number of people with the outcome divided by the total number of people in either group.  So, for instance, the incidence of the outcome in those exposed is A/(A+B).  As described in a previous post, the absolute risk difference is arithmetic difference between the incidence in the group exposed and the incidence in the group not exposed - in mathematical terms, that's [A/(A+B) - C/(C+D)].  The relative risk, on the other hand, is the ratio between the two incidences - or, in mathematical terms, [A/(A+B) / C/(C+D)].

The crucial question with relative risk is always "relative to what?"  It gives you no information at all about the actual incidence of the problem in question.  Imagine two treatments, one of which reduces the incidence of a common condition from 30% per year to 20% per year, and another which reduces the incidence of a rare condition from 0.03% per year to 0.02% per year.  The first corresponds to a number needed to treat (NNT) of 10, the latter to a NNT of 10,000, but the relative risk difference is the same.

The reason this is important to understand is that a lot of therapeutic effects are small, and therefore the relative risk change is usually a bigger number than the absolute risk change.  Because of this, it's frequently reported by people who want their treatments to look successful; so when you see a study that only reports a relative risk change, you should smell a rat and try to figure out what the absolute risk change is.  Most of the time, you will find that it makes the relative risk change look significantly less impressive.