A public health researcher in Delhi conducts a cross-sectional survey to investigate the association between occupational dust exposure and chronic obstructive pulmonary disease (COPD) among 500 construction workers. Among 250 workers with dust exposure, 80 developed COPD. Among 250 workers without dust exposure, 20 developed COPD. The researcher calculates both relative risk (RR) and odds ratio (OR) from this data. Which of the following statements correctly compares these two measures in this scenario?

Explanation

## Calculation of RR and OR ### Relative Risk (RR) Calculation RR compares the probability (risk) of disease in exposed versus unexposed groups: $$RR = \frac{Risk_{exposed}}{Risk_{unexposed}} = \frac{a/(a+b)}{c/(c+d)}$$ Where: - a = exposed with disease = 80 - b = exposed without disease = 170 - c = unexposed with disease = 20 - d = unexposed without disease = 230 $$RR = \frac{80/250}{20/250} = \frac{0.32}{0.08} = 4.0$$ ### Odds Ratio (OR) Calculation OR compares the odds of disease in exposed versus unexposed groups: $$OR = \frac{Odds_{exposed}}{Odds_{unexposed}} = \frac{a/b}{c/d} = \frac{a \times d}{b \times c}$$ $$OR = \frac{80 \times 230}{170 \times 20} = \frac{18400}{3400} = 5.41 \approx 5.4$$ **Key Point:** When disease prevalence is **not rare** (>10%), the OR will be notably larger than the RR. In this study, COPD prevalence is 100/500 = 20%, which is NOT rare. ## Relationship Between RR and OR | Scenario | RR vs OR | When It Occurs | |----------|----------|----------------| | Disease is **rare** (<1%) | RR ≈ OR | Case-control or cohort studies with low disease prevalence | | Disease is **common** (>10%) | OR > RR | Case-control or cohort studies with high disease prevalence | | Cross-sectional study | Both calculable | When baseline prevalence is known | **High-Yield:** The OR will **always be further from 1.0 than the RR** when disease is not rare. If RR = 4.0, OR will be >4.0 (in this case 5.4). ## Why OR Overestimates RR The mathematical reason: OR uses odds (probability of disease / probability of no disease), while RR uses only the probability of disease. When disease is common, the denominator in the odds calculation becomes smaller, inflating the ratio. **Clinical Pearl:** In case-control studies (where you cannot calculate RR directly), OR is the only measure available and serves as a proxy for RR when disease is rare. However, in cohort and cross-sectional studies where RR can be calculated, OR will overestimate the association when disease prevalence exceeds ~10%. ## Interpretation Both measures indicate a strong association between dust exposure and COPD: - **RR = 4.0:** Workers with dust exposure are 4 times more likely to develop COPD - **OR = 5.4:** The odds of COPD are 5.4 times higher in exposed workers The difference reflects the non-rarity of COPD in this population, not a methodological error.