This is a classic case-control study odds ratio calculation. Let me work through it directly.
Setting up the 2x2 table:
| Lung Cancer (Cases) | No Lung Cancer (Controls) | Total | |
|---|---|---|---|
| Smokers | 150 | 150 | 300 |
| Non-smokers | 50 | 50 | 100 |
| Total | 200 | 200 | 400 |
OR formula for a case-control study:
$$OR = \frac{a \times d}{b \times c}$$
Where:
- a = smokers with lung cancer = 150
- b = non-smokers with lung cancer = 50
- c = smokers without lung cancer = 150
- d = non-smokers without lung cancer = 50
Calculation:
$$OR = \frac{150 \times 50}{50 \times 150} = \frac{7500}{7500} = \mathbf{1}$$
Interpretation:
An OR of 1.0 means there is no association between smoking and lung cancer in this dataset. Smokers and non-smokers have equal odds of lung cancer.
This is a counterintuitive result, and it highlights a major methodological flaw in the study design: the controls were selected from patients admitted for non-respiratory illnesses - but these patients have an unusually high smoking rate (75%), similar to the cases. This is a classic example of Berkson's bias (admission rate bias), where using hospitalized patients as controls over-represents smokers, artificially pulling the OR toward 1 and masking the true association.
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