In a study done to establish smoking as a risk factor for a disease, 30 out of 50 smokers developed the disease while 10 out of 50 non-smokers developed the disease. Odds ratio is?

## **Core Concept**
The odds ratio (OR) is a measure of association between an exposure and an outcome. In this context, it quantifies the strength of the relationship between smoking and the development of a specific disease. The OR is calculated using the formula: 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 data:
- Smokers with disease (a): 30
- Smokers without disease (b): 20 (50 - 30)
- Non-smokers with disease (c): 10
- Non-smokers without disease (d): 40 (50 - 10)

The odds ratio formula in this context is: OR = (30/20) / (10/40) = (1.5) / (0.25) = 6.

This means that smokers are 6 times more likely to develop the disease compared to non-smokers.

## **Why Each Wrong Option is Incorrect**
- **Option A:**
This option is incorrect because the calculation does not match the provided numbers and the correct formula application.
- **Option B:**
This option is incorrect as it does not align with the correct calculation of the odds ratio based on the given data.
- **Option D:**
This option is incorrect because it also does not match the correct calculation of the odds ratio.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that an odds ratio of 1 indicates no association between the exposure and the outcome. An OR greater than 1 suggests an increased risk, while an OR less than 1 suggests a decreased risk. In this case, an OR of 6 indicates a strong positive association between smoking and the development of the disease.

## **Correct Answer:** C. 6