Definition
The Odds Ratio is a measure of association which compares the odds of disease of those exposed to the odds of disease those unexposed.
Formulae
- OR = (odds of disease in exposed) / (odds of disease in the non-exposed)
Example
I often think food poisoning is a good scenario to consider when interpretting ORs: Imagine a group of 20 friends went out to the pub – the next day a 7 were ill. They suspect that it may have been something they ate, maybe the fish casserole… here are the numbers:
| Cases (ill) |
Controls (not ill) |
Total | |
| Exposed (ate fish) |
5 | 3 | 8 |
| Unexposed (didn’t eat fish) |
2 | 10 | 12 |
| 7 | 13 | 20 |
- Odds of exposure in cases = a/c = 5/2 = 2.5
- Odds of exposure in controls = b/d = 3/10 = 0.3
- Odds Ratio = (a/c) / (b/d) = 2.5/0.3 = 8.33
Interpretation: What does this mean?
- OR of 1 would suggests that there is no difference between the groups; i.e. there would be no association between the suggested exposure (fish) and the outcome (being ill)
- OR of > 1 suggests that the odds of exposure are positively associated with the adverse outcome compared to the odds of not being exposed
- OR of < 1 suggests that the odds of exposure are negatively associated with the adverse outcomes compared to the odds of not being exposed. Potentially, there could be a protective effect
In the example above, we can conclude that those who ate the fish casserole (exposure) were 8.3 times more likely (OR = 8.3) to be ill (outcome), compared to those who did not eat the fish casserole. Of course this is an entirely ficticious example, and I have nothing against fish
Advantages
- Appropriate to analyse associations between groups from case-control and prevalent (or cross-sectional) data.
- For rare diseases (or diseases with long latency periods) the OR can be an approximate measure to the RR (relative risk)
- Doesn’t require denominator (i.e. total number in population) unlike measuring risk
- Good method to estimate the strength of an association between exposures and outcomes
Disadvantages
- Association does not infer causation! *epidemiology golden rule*
Bean Around The World 
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Good post. I learn something new and challenging on blogs I stumbleupon
on a daily basis. It will always be helpful to read
articles from other writers and practice something from their websites.
Great analogy, really helped me to understand odds ration in a simple straightforward manner. Thank you! Christie
Thanks for this definition, my text book (Jekel’s Epidemiology, Biostatistics,Preventive Medicine, and Public Health) was not getting meaning across. You did.
Thanks for all your help! Using this for my research!
Very nice example, thanks. But think that your conclusion was not accurate: “.. we can conclude that those who ate the fish casserole (exposure) were 8.3 times more likely..”. If the effect estimate had been risk ratio, this would be true but in this example, because the outcome was so common(about 30%), the odds ratio value is much greater than the actual risk. But anyhow, very nice definition. I will use this in my teachings.
Under your table of odds ratio you have (a/c) / (b/d) = (a*d / b*c)
It is more commonly written as (a/b) / (c/d) = (a*d / b*c) but they produce the same results. Nice article.
Thank you very helpful. S. Lindani