How to interpret an odds ratio of less than 1

In a recent paper, I read that an OR of 0.7 means a 30% risk reduction.  Let’s have a look on the following table to see why this is wrong


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) = a*c / b*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%. Read more.