In a cohort study of 2,000 Indian factory workers exposed to silica dust, 120 developed silicosis over 10 years, while among 1,500 unexposed workers, 15 developed silicosis. Which of the following statements about the association is NOT correct?

Explanation

## Comparing RR and OR in a Cohort Study ### Study Data Summary | Group | Silicosis | No Silicosis | Total | Risk (%) | |-------|-----------|--------------|-------|----------| | **Exposed** | 120 | 1,880 | 2,000 | 6.0% | | **Unexposed** | 15 | 1,485 | 1,500 | 1.0% | **Key Point:** In a cohort study, we can directly calculate both RR and OR. Their relationship depends on outcome prevalence. ### Calculating RR and OR **Relative Risk:** $$RR = \frac{\text{Risk in exposed}}{\text{Risk in unexposed}} = \frac{120/2000}{15/1500} = \frac{0.06}{0.01} = 6.0$$ **Odds Ratio:** $$OR = \frac{\text{Odds of disease | exposed}}{\text{Odds of disease | unexposed}} = \frac{120/1880}{15/1485} = \frac{0.0638}{0.0101} \approx 6.3$$ ### When Do OR and RR Diverge? | Outcome Prevalence | OR vs RR | Why | |-------------------|----------|-----| | **< 10% (rare)** | OR ≈ RR | Odds ≈ probability; values nearly identical | | **10–50% (moderate)** | OR > RR | Odds diverge from probability; OR overestimates RR | | **> 50% (common)** | OR >> RR | Odds diverge substantially; OR much larger than RR | **High-Yield:** In this cohort, silicosis prevalence is 6% (exposed) and 1% (unexposed) — both **rare outcomes**. Therefore, OR ≈ RR (6.3 ≈ 6.0). **Warning:** Option D claims "OR is greater than RR because silicosis is common." This is backwards. Silicosis is *rare* in this cohort (6% at most), so OR and RR are nearly equal. If silicosis were common (> 50%), then OR would substantially exceed RR. ### Analysis of Each Option - **Option A (TRUE):** RR = 6.0 is correctly calculated. Exposed workers have 6 times the risk. - **Option B (TRUE):** OR ≈ 6.3 and RR = 6.0 are nearly identical because the outcome is rare. This is the expected behavior. - **Option C (TRUE):** Odds calculations are correct: exposed odds = 120/1880 ≈ 0.0638; unexposed odds = 15/1485 ≈ 0.0101. - **Option D (FALSE):** This reverses the epidemiological principle. OR > RR occurs when disease is *common*, not rare. Since silicosis is rare here, OR ≈ RR, not OR >> RR. **Clinical Pearl:** Silicosis prevalence in occupational cohorts is typically low (< 10%) unless workers are highly exposed for decades. In this study, even among exposed workers, only 6% developed silicosis — confirming rarity and validating the OR ≈ RR approximation.