How to compute an Odds Ratio (OR)

Step 1: Identify the two probabilities you are going to compare:

For example: the 10-year mortality rate among older non-married people is 33% and the 10-year mortality among comparable married people is 20%.  So I am comparing 33% to 20%.

Step 2: Convert each probability to odds

Odds = p:(1-p), where p = the probability.  (Note: if you are using percentages rather then decimals, then the "1" means 100%)

33% means an odds of 33:67, meaning there are 33 chances of dying for every 67 chances of not dying. I can reduce this expression to 1:2 by dividing both sides by 33.

20% means an odds of 20:80, which can be reduced to 1:4

So I am comparing odds of 1:2 to odds of 1:4

Step 3: Take the ratio between the two odds

•      1:2
•      1:4

How do I do this division? The trick is that the ":" in the odds statement is really a "÷".

•       1÷2
•      1÷4  

Which equals 2

Step 4: How do I know which odds to put in the numerator and which in the denominator?
The reference case always goes in the denominator. So, if I said "How does being single influence mortality relative to being married?" that would indicate that the married odds should go in the denominator, as in the example above.

If the question doesn't make clear which group is the reference case, then either version of the odds ratio is acceptable. So the answer to this question could be 2, meaning that being single doubles your odds or mortality, or it could be 0.5, meaning that being married halves your odds of mortality. These two statements are equivalent.

Traditionally, odds ratios are constructed so that they are greater than 1. Thus, the current example would generally be presented as a 2 rather than as a 0.5. The exception would be if several risk factors with opposing effects were being discussed. For example, in the flu shot study discussed in class, belief that the vaccine was effective increased the odds of accepting the vaccine (OR > 1) but belief that the shot could cause a reaction decreased the odds of accepting the vaccine (OR <1).

The bottom line is that for the marriage example here, either 2 or 0.5 would be correct answers.