## Calculating Both Measures from Cohort Data **Key Point:** In a cohort study, both **Relative Risk (RR)** and **Odds Ratio (OR)** can be directly calculated. The relationship between them depends on the frequency of the outcome. ## Step-by-Step Calculation ### Relative Risk RR is the ratio of the **risk (probability) of disease in exposed versus unexposed groups**: $$RR = \frac{\text{Risk in exposed}}{\text{Risk in unexposed}} = \frac{150/500}{50/500} = \frac{0.30}{0.10} = 3.0$$ This means pregnant women with anemia have **3 times the risk** of delivering a low birth weight infant compared to non-anemic women. ### Odds Ratio OR is the ratio of the **odds of disease in exposed versus unexposed groups**: $$OR = \frac{\text{Odds in exposed}}{\text{Odds in unexposed}} = \frac{150/350}{50/450} = \frac{0.4286}{0.1111} \approx 3.27$$ Where: - Odds in exposed = cases with disease / cases without disease = 150 / 350 - Odds in unexposed = cases with disease / cases without disease = 50 / 450 ## Why OR > RR When Outcome is Common **High-Yield:** When the outcome is **not rare** (prevalence > 10%), the Odds Ratio will be **larger than the Relative Risk**. This occurs because: 1. When disease is common, the denominator in the odds calculation (number without disease) becomes smaller. 2. This amplifies the odds ratio relative to the risk ratio. 3. In this study, LBW occurs in 30% of anemic women and 10% of non-anemic women — both are substantial frequencies, not rare. ## Comparison: Rare vs. Common Outcomes | Outcome Frequency | RR vs. OR | Approximation | Example | | --- | --- | --- | --- | | **Rare** (< 10%) | OR ≈ RR | OR closely approximates RR | Rare adverse drug reaction | | **Common** (≥ 10%) | OR > RR | OR substantially exceeds RR | LBW (30% in exposed, 10% in unexposed) | **Clinical Pearl:** In this maternal anemia–LBW study, LBW is common enough that OR (3.27) is noticeably larger than RR (3.0). The difference becomes more pronounced as the outcome becomes more frequent. ## Why This Matters Clinically **Mnemonic:** **RARE-RR, COMMON-OR** — When disease is rare, use RR (or OR as approximation). When disease is common, OR will be notably larger than RR, and interpretation must account for this difference. **Warning:** Do not assume RR ≈ OR in all studies. Always check the outcome frequency. In maternal and child health studies, many outcomes (LBW, preterm delivery, maternal complications) are common, so OR will exceed RR.
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