In a case control study on smoking and lung cancer, out of 35 lung cancer patients, 33 are smokers. Out of 82 controls, 27 are non smokers. Find the odds ratio:
## **Core Concept**
The odds ratio (OR) is a measure of association between an exposure and an outcome in a case-control study. It represents the odds that an exposure is present in cases versus controls. The formula to calculate the odds ratio in a case-control study is: OR = (a/b) / (c/d), where a, b, c, and d are derived from a 2x2 contingency table.
## **Why the Correct Answer is Right**
To calculate the odds ratio, we first construct a 2x2 contingency table based on the given information:
- Lung cancer patients (cases): 33 smokers, 2 non-smokers (total = 35)
- Controls: 27 non-smokers, 55 smokers (total = 82)
The 2x2 table is:
| | Smokers | Non-smokers | Total |
|----------|---------|-------------|-------|
| **Cases**| 33 | 2 | 35 |
| **Controls**| 55 | 27 | 82 |
Using the formula for the odds ratio: OR = (a/b) / (c/d), where a = 33, b = 2, c = 55, and d = 27.
OR = (33/2) / (55/27) = (33*27) / (2*55) = 891 / 110 = 8.10
## **Why Each Wrong Option is Incorrect**
**Option A:** This option would be incorrect because the calculation does not match the provided numbers and the correct formula application.
**Option B:** Similarly, this option does not align with the correct calculation of the odds ratio based on the given data.
**Option D:** This option is incorrect for the same reason; it does not reflect the accurate computation of the odds ratio.
## **Clinical Pearl / High-Yield Fact**
In case-control studies, the odds ratio is a crucial measure to assess the strength and direction of the association between an exposure (e.g., smoking) and an outcome (e.g., lung cancer). An odds ratio greater than 1 indicates an increased risk of the outcome in the exposed group compared to the unexposed group.
## **Correct Answer:** C. 8.1