## **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 association between smoking and renal cell cancer. The formula to calculate the odds ratio in a case-control study is: OR = (a/b) / (c/d), where a, b, c, and d represent the number of exposed cases, unexposed cases, exposed controls, and unexposed controls, respectively.

## **Why the Correct Answer is Right**
To calculate the odds ratio, we first identify the values: a = 30 (smokers with renal cell cancer), b = 20 (non-smokers with renal cell cancer), c = 10 (smokers without renal cell cancer), and d = 40 (non-smokers without renal cell cancer). Plugging these into the formula gives OR = (30/20) / (10/40) = (1.5) / (0.25) = 6. This means that smokers are 6 times more likely to develop renal cell cancer compared to non-smokers.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option suggests an odds ratio of 1, implying no association between smoking and renal cell cancer, which contradicts the observed data.
- **Option B:** This option suggests an odds ratio of 3, which underestimates the association based on the provided numbers.
- **Option D:** This option suggests an odds ratio of 12, which overestimates the association based on the calculations.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the odds ratio is a measure of effect size that can be useful in case-control studies where the incidence of disease cannot be directly measured. An odds ratio of 1 indicates no effect, while an OR greater than 1 indicates an increased risk, and an OR less than 1 indicates a decreased risk.

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