relative risk

The Cochrane Handbook, the methods manual for evidence synthesis, defines the risk ratio, also called relative risk, as the ratio of the risk of an event in the two groups being compared. It is one probability divided by another. A value of 1 means no difference between the groups. A value of 3 means the event was three times as probable in the first group; a value of 0.25 means it was a quarter as probable, which is the same as saying the relative risk was reduced by 75 percent.

The handbook is emphatic that a relative risk is not an odds ratio, though the two are often reported in the same sentence and read as though interchangeable. When an event is common, the odds ratio is substantially further from 1 than the risk ratio is, so treating one as the other will tend to overestimate the size of the effect. There is also a mathematical ceiling that keeps risk ratios honest: a risk ratio cannot exceed 1 divided by the risk in the comparison group, so where that group's risk is already 0.66, no risk ratio above 1.5 is arithmetically possible.

The important limit is what a relative risk leaves out. It is a multiplication, not an amount, so it says nothing on its own about how many people are affected. The handbook's own illustration is a risk ratio of 0.75, which might describe a fall from 80 percent to 60 percent or a fall from 4 percent to 3 percent. Those are the same relative figure and vastly different in consequence. This is why the baseline risk has to be stated alongside it, and why a relative figure quoted alone is the most common way health findings are made to sound larger than they are.