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In a study of treatment effects, the odds of an outcome in a treatment comparison group is the number of people experiencing an outcome divided by the number not experiencing it.
The odds ratio is the odds of the outcome in one comparison group divided by the odds in another comparison group. It is sometimes used as a measure of the relative effectiveness of treatments.
For example, if 20 people died in one treatment comparison group and 80 did not (odds = 20/80 = 0.25) and in the other group 50 people died and 50 did not (odds = 50/50 = 1), the odds ratio would be 0.25/1 = 0.25. This is different from the risk ratio, which is the probability of dying in one group divided by the probability of dying in the other group. In this example, the risk ratio would be 20/100 = 0.2 (20%) divided by 50/100 = 0.50 (50%), which is 0.40.
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