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Odds Ratios

Definition

The Odds Ratio is the ratio of the odds of disease for the experimental group relative to the odds of disease in the control group (in prospective case-control studies, overviews) or the odds in favour of being exposed in diseased subjects divided by the odds in favour of being exposed in non-diseased, control subjects.

Calculation

To calculate the odds ratio, you need to know the odds for disease in each group. Since odds are derived by dividing the event rate by the non-event rate for each group, we get: 

OR = (EER/(1-EER)) / (CER/(1-CER))

You can also calculate this in terms of numbers of patients, as shown below.

Example

Odds Ratio Example 
CER = c / (c+d) = 0.30 ;  EER = a / (a+b) = 0.033;

Control Event Odds = CER / (1-CER) = c/d = 0.43;

Experimental Event Odds = EER / (1-EER) = a/b = 0.034;

Relative Risk = EER/CER = 0.11;

Relative Odds = Odds Ratio = (a/b) / (c/d) = (a*d) / (b*c) = 0.08