Suppose I have a scenario like this :
For every 1-point increase in X, odds ratio of event Y happening is 0.80
Does that mean the same as 'For every 1-point increase in X, odds of event Y happening is reduced by 20%'?
Whereas 'For every 1-point increase in X, event Y is 20% less likely to happen' is an incorrect interpretation of odds ratio (that's interpreting it as relative risk), am I correct?
Best Answer
As other answers have clearly articulated, you can't represent an odds ratio as a simple percent increase or decrease of an event happening, as this value depends on the baserate. However, if you have a meaningful baserate, you can calculate the percent success (or failure) relative to that rate.
For example, if we have an odds ratio of 0.75 for the effect of an intervention and we know that the baserate for failure (failure in the control group, for example) is 20%, then the failure rate for the treatment group based on an odds ratio of 0.75 is: $$ p_{treatment} = \frac{OR \times p_{control}}{1 + OR \times p_{control} - p_{control}} = \frac{.75 \times .2}{1 + (.75 \times .2) - .2} = .158 $$
Thus, an odds ratio of .75 translates into a failure rate of 15.8% in the treatment group relative to an assumed failure rate of 20% in the control group.
This translation of odds ratios into an easily understand metric is commonly used in meta-analyses of odds ratios.
This simplifies if we assume a baserate of .50 to: $$ p_{treatment} = \frac{OR}{1+OR} $$