## Understanding RR vs OR Relationship ### Key Differences | Feature | Relative Risk (RR) | Odds Ratio (OR) | |---------|-------------------|----------------| | **Calculation** | Incidence in exposed / Incidence in unexposed | (a×d) / (b×c) in 2×2 table | | **Study design** | Cohort, RCT (prospective) | Case-control (retrospective) | | **Interpretation** | Direct probability comparison | Approximates RR when disease rare | | **Magnitude** | Closer to 1 when disease rare | Approximates RR (disease rare) | | **Always larger?** | No — depends on baseline risk | No — depends on baseline risk | ### Critical Concept: When Does OR ≈ RR? **Key Point:** Odds Ratio approximates Relative Risk **only when disease prevalence is <10%** (rare disease assumption). When disease is common, OR is substantially larger than RR — this is a fundamental mathematical property, NOT a universal rule. **High-Yield:** The relationship is: $$OR = \frac{RR}{(1 - RR_0 + RR_0 \times RR)}$$ where RR₀ is baseline risk. As RR₀ → 0 (rare disease), OR → RR. ### Why Option 2 is Correct (The Wrong Statement) Option 2 claims "Odds Ratio is always numerically larger than Relative Risk regardless of disease frequency." This is **FALSE**. - When disease is rare (e.g., 1% prevalence): OR ≈ RR (both ≈ 2.0 if true RR = 2.0) - When disease is common (e.g., 50% prevalence): OR >> RR (OR may be 4.0 while RR = 2.0) - OR is NOT always larger; it depends on baseline disease frequency **Warning:** A common exam trap is assuming OR is always bigger. This is only true when disease is common; when rare, they are nearly equal. ### Why the Other Three Statements Are Correct 1. **Option 0 (TRUE):** The rare disease assumption is the foundation of case-control study interpretation. When disease prevalence <10%, OR ≈ RR, allowing case-control studies to approximate cohort findings. 2. **Option 1 (TRUE):** RR requires knowledge of incidence in both exposed and unexposed groups — only available in prospective designs (cohort, RCT). Case-control studies cannot calculate RR directly because they start with disease status, not exposure status. 3. **Option 3 (TRUE):** Case-control studies are retrospective; they cannot calculate RR. OR is the appropriate and only directly calculable measure of association in case-control designs. **Clinical Pearl:** In interpreting case-control studies from Indian epidemiology literature, always remember: if disease is common (e.g., TB, malaria in high-burden regions), the OR reported may overestimate the true RR. [cite:Park 26e Ch 3]
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