Tag Info

The relative risk (also called 'risk ratio') is the quotient of the probabilities of an event under two conditions (ie, p1/p2). The RR has a possible range of [0, +infinity). It is a common measure of effect size in biomedical research.

The relative risk (also called 'risk ratio') is the quotient of the probabilities of an event under two conditions (i.e., $p_1/p_2$). The RR has a possible range of $[0, +\infty)$. It is a common measure of effect size in biomedical research.

In a typical study with two categories (say, treatments), and two outcomes (say, relapse or not), the data can be represented by a 2x2 table:

            outcome1   outcome2
treatment1      a         b
treatment2      c         d


The relative-risk is estimated by:
$$\text{RR}=\frac{\frac{a}{a+b}}{\frac{c}{c+d}}$$ Note that the RR is not symmetrical: when the outcome is unrelated to the treatment, RR = 1, when outcome1 is more likely given treatment1 than treatment2, RR > 1, but when it is less likely, RR < 1. Moreover, as outcome1 is increasingly more likely with treatment1, RR goes on infinitely, but as outcome1 becomes less likely, RR 'only' goes to 0. In addition, note that the relative risk between two treatments with a fixed difference diminishes as the the base rate increases. That is, when the probabilities are 2% and 1%, RR = 2, but when they are 99% and 98%, RR = 1.01. For this reason, the less frequent of the two outcomes is often used as 'outcome1' when calculating the RR.