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)
The interpretation is straightforward for more patients in the exposed group: With a=13 we get an OR=1.3.
An odds of 0.7 however is less intuitive to interprete. 0.7 people will experience the event for every event that does not occur. This translates to one event for every 1,42 non-events, the reciprocal value of 0,7. The percent change PC is therefore
PC = 1/0,7 - 1 = 1,42 -1 = 0,42 = 42%
42% and not 30%.
Sorry not only the math, also the biology is wrong there.