The odds ratio (OR) is a measure of association between an exposure and an outcome. It is the ratio of the odds of the outcome in the exposed group to the odds of the outcome in the unexposed group.
Calculating the Odds Ratio
To calculate the odds ratio, you need a 2x2 contingency table, which shows the number of individuals in each group (exposed/unexposed) with and without the outcome. Here's an example:
| Outcome Present | Outcome Absent | Total | |
|---|---|---|---|
| Exposed | a | b | a+b |
| Unexposed | c | d | c+d |
| Total | a+c | b+d | N |
The odds ratio is calculated as follows:
- OR = (a/b) / (c/d) = (a d) / (b c)
Example
Let's say we are interested in the association between smoking and lung cancer. We have a sample of 100 people, and the following data:
| Lung Cancer | No Lung Cancer | Total | |
|---|---|---|---|
| Smokers | 20 | 30 | 50 |
| Non-Smokers | 5 | 45 | 50 |
| Total | 25 | 75 | 100 |
OR = (20 45) / (30 5) = 6
This means that the odds of having lung cancer are 6 times higher in smokers compared to non-smokers.
Interpretation
An odds ratio of 1 indicates no association between the exposure and the outcome. An OR greater than 1 indicates a positive association, meaning that the exposure increases the odds of the outcome. An OR less than 1 indicates a negative association, meaning that the exposure decreases the odds of the outcome.
Practical Insights
- The odds ratio is often used in case-control studies, where the outcome is rare.
- It is important to note that the odds ratio is not the same as the relative risk. The relative risk is the ratio of the risk of the outcome in the exposed group to the risk of the outcome in the unexposed group.
- The odds ratio can be influenced by confounding factors, so it is important to control for these in the analysis.
