In a recent paper (see page 122 ) I have read that an odds ratio OR of 0.7 means a 30% risk reduction which is wrong.
The OR is a measure of association not a risk ratio (which requires random sampling of the population and a slightly different formula).
Let’s have a look on the following table to see why this is all wrong
| Disease+ | Disease- | |
|---|---|---|
| Exposure+ | a=7 | b=10 |
| Exposure- | c=10 | d=10 |
The odds of an event is the number of those who experience the event divided by the number of those who do not.
Comparing the odds in an exposed and a not exposed group results in the simple odds ratio OR formula.
OR = (a/b) / (c/d)
But the odds is not the risk. The risk (incidence proportion) of an event is the number who experience it divided by everyone in that group – those who do and those who do not.
Risk for the exposed is 42.7%, for the unexposed 50%.
RR = ( a/(a+b) / c/c+b) )
Note the denominators: for the odds it was b and d (only the disease-free), for the risk it is the whole row (a+b and c+d). That single change is the whole difference between the two measures.
The risk ratio is then RR= 0.82 and the risk reduction 18%.