Calculating the Odds Ratio
The odds ratio for this case-control study is 9.0, indicating that smokers have 9 times the odds of developing lung cancer compared to non-smokers.
Step-by-Step Calculation
To calculate the odds ratio from a case-control study, you need to construct a 2x2 table and apply the standard formula:
Constructing the 2x2 Table
| Lung Cancer (Cases) | No Lung Cancer (Controls) | |
|---|---|---|
| Smokers | 150 | 50 |
| Non-smokers | 50 | 150 |
Applying the Formula
The odds ratio (OR) is calculated as:
OR = (a × d) / (b × c)
Where:
- a = exposed cases (smokers with lung cancer) = 150
- b = exposed controls (smokers without lung cancer) = 50
- c = unexposed cases (non-smokers with lung cancer) = 50
- d = unexposed controls (non-smokers without lung cancer) = 150
OR = (150 × 150) / (50 × 50) = 22,500 / 2,500 = 9.0
Clinical Context and Interpretation
Understanding the Magnitude of Risk
- This odds ratio of 9.0 is consistent with established epidemiological data showing that smoking substantially increases lung cancer risk 1, 2
- The National Comprehensive Cancer Network reports that the relative risk for lung cancer is approximately 20-fold higher for heavy, long-term smokers compared to non-smokers, though this OR of 9.0 likely represents a mixed population of varying smoking intensities 2
- In Chinese populations, combined case-control studies have shown summary odds ratios of 2.17 overall, with higher ratios (3.09) in males, demonstrating population-specific variations 3
Dose-Response Relationship
- Smoking demonstrates a clear dose-response relationship with lung cancer risk, with no safe level of tobacco exposure 2
- Studies show increasing odds ratios with greater cigarette consumption: 1.03 for minimal smoking, 2.04 for moderate smoking, and 3.33 for heavy smoking 3
- Duration of smoking and age at initiation also significantly modify risk, with longer duration and earlier initiation conferring higher odds ratios 3
Important Caveats
- Case-control studies can overestimate relative risk when the outcome is common, though lung cancer prevalence makes this less of a concern 4
- Comprehensive adjustment for multiple smoking dimensions (status, pack-years, time since cessation) is critical to avoid confounding, as inadequate smoking adjustment can artificially inflate associations with other risk factors 4
- This odds ratio represents the association in the specific study population and may not generalize to all populations due to differences in smoking patterns, genetic susceptibility, and environmental exposures 1, 3