Tag Info

The risk-difference is the difference between the probabilities of an event under two conditions (ie, p1-p2). The RD has a possible range of [-1, 1]. It is a common measure of effect size in biomedical research.

The risk-difference is the difference between the probabilities of an event under two conditions (i.e., $p_1-p_2$). The RD has a possible range of $[-1, 1]$. 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 risk-difference is estimated by:
$$\text{RD}=\frac{a}{a+b}-\frac{c}{c+d}$$ Many practitioners prefer the RD because of its immediately accessible interpretation. When the treatment is unrelated to the outcome, RD = 0. When outcome1 is more likely given treatment1 than treatment2, RD is positive, and when it is less likely, RD is negative.

Note however, that the magnitude of a change of a fixed increment is typically not constant irrespective of the base rate. That is, increasing from 1% to 2%, or 98% to 99%, is typically not the same as moving from 50% to 51%. For this reason, the RD is often used when the probabilities are in the 'mid-range', but the relative risk is often used instead when the probabilities are quite small.