In case-control study there weve 35 cases of lung cancer and 82 controls (without lung cancer). Among cases 33 had positive history of smoking and among controls 55 had positive history of smoking. Odds ratio in this study is –

**Core Concept**
The odds ratio (OR) is a measure of association between an exposure (in this case, smoking) and an outcome (lung cancer) in a case-control study. It represents the odds that an individual with the exposure will have the outcome compared to those without the exposure.

**Why the Correct Answer is Right**
To calculate the odds ratio, we need to first calculate the odds of exposure (smoking) among cases and controls. The odds of exposure among cases is the number of cases with a positive history of smoking (33) divided by the number of cases without a positive history of smoking (35 - 33 = 2). The odds of exposure among controls is the number of controls with a positive history of smoking (55) divided by the number of controls without a positive history of smoking (82 - 55 = 27). The odds ratio is then calculated as (odds of exposure among cases) / (odds of exposure among controls) = (33/2) / (55/27).

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not provide a valid formula for calculating the odds ratio in a case-control study.
**Option B:** This option is incorrect because it does not take into account the number of cases without a positive history of smoking.
**Option C:** This option is incorrect because it does not provide a valid formula for calculating the odds ratio in a case-control study.

**Clinical Pearl / High-Yield Fact**
When calculating the odds ratio in a case-control study, it's essential to remember that the odds of exposure among cases is the ratio of the number of cases with exposure to the number of cases without exposure, while the odds of exposure among controls is the ratio of the number of controls with exposure to the number of controls without exposure.

**Correct Answer: D. (33/2) / (55/27)**