Odds ratios less than 1, how to make interpretation ?

#1
Hello all,

How do I make interpretation of odds ratio equal to 0.02, given from a logistic model with a binary outcome and let's say 2 treatments ? The experimental treatment has many more 0's than the control one. How do I write the conclusion in plain English ?

Thanks !
 
#2
The odds ratio is the ratio of the odds of an event occurring in one group, to the odds of that event occurring in another group (the odds for group one divided by the odds for group two). For a correct interpretation, you need to know which group is in the denominator and which is in the numerator.

An odds ratio of 0.02 means that the odds of an event occurring for group one is 50 times less than the odds of the event occurring for group two, or rather, the event occurs twice in group one compared with one-hundred times in group two.

You could just as easily calculate the inverse to get the odds ratio for group two vs. group one, which is an odds ratio of 50. Either way, each one has the same information.