The odds ratio (OR) is calculated by dividing the odds of an event occurring in one group by the odds of it occurring in another group. Specifically, it's often used to compare an exposure group to a control or non-exposure group.
Here's a breakdown of the calculation:
2x2 Contingency Table
The odds ratio is commonly derived from a 2x2 contingency table. This table summarizes the relationship between an exposure and an outcome.
| Event Present | Event Absent | |
|---|---|---|
| Exposure Present | a | b |
| Exposure Absent | c | d |
- a: Number of individuals with both exposure and event.
- b: Number of individuals with exposure but no event.
- c: Number of individuals without exposure but with the event.
- d: Number of individuals without exposure and without the event.
Formula
The odds ratio is calculated as follows:
OR = (odds of event in exposed group) / (odds of event in unexposed group)
Odds of event in exposed group = a / b
Odds of event in unexposed group = c / d
Therefore,
OR = (a/b) / (c/d) = ad / bc
Example
Let's say we're investigating the relationship between smoking and lung cancer. We collect data and create the following table:
| Lung Cancer Present | Lung Cancer Absent | |
|---|---|---|
| Smoker | 100 | 100 |
| Non-Smoker | 50 | 200 |
Here, a = 100, b = 100, c = 50, and d = 200.
OR = (100 200) / (100 50) = 20000 / 5000 = 4
This means the odds of having lung cancer are 4 times higher for smokers compared to non-smokers.
Interpretation
- OR > 1: Exposure is associated with higher odds of the event.
- OR < 1: Exposure is associated with lower odds of the event.
- OR = 1: Exposure is not associated with the event.
Important Considerations
- The odds ratio is an estimate of relative risk, especially when the event is rare.
- Confidence intervals should always be reported alongside the odds ratio to indicate the precision of the estimate.
