The Odds Ratio is a measure of association which compares the odds of disease of those exposed to the odds of disease those unexposed.
- OR = (odds of disease in exposed) / (odds of disease in the non-exposed)
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:
(didn’t eat fish)
- 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
- 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
- Association does not infer causation! *epidemiology golden rule*