Which statement best describes the relationship between odds ratio and relative risk in epidemiological studies?

Explanation

## Relationship Between Odds Ratio and Relative Risk ### Key Distinction **Key Point:** The odds ratio (OR) approximates the relative risk (RR) when the disease is **rare** (prevalence < 10%). As disease prevalence increases, OR increasingly overestimates RR. ### Mathematical Relationship When disease is rare: $$OR \approx RR$$ When disease is common, OR diverges from RR: $$OR = RR \times \frac{1 - P_0}{1 - P_1}$$ Where P₀ and P₁ are baseline and exposed group disease prevalences. ### Study Design Implications | Feature | Relative Risk | Odds Ratio | |---------|---------------|------------| | **Calculated in** | Cohort studies, RCTs, cross-sectional | Case-control studies | | **Interpretation** | Risk in exposed vs unexposed | Odds of exposure in diseased vs non-diseased | | **Range** | 0 to ∞ | 0 to ∞ | | **Approximates each other** | When disease is rare | When disease is rare | | **Directly comparable** | Across study designs when rare disease | Limited comparability | ### Why This Matters **High-Yield:** In case-control studies, we **cannot calculate RR directly** because: - We select subjects based on disease status (not exposure) - We cannot determine incidence or true prevalence - We use OR as a proxy for RR when disease is uncommon **Clinical Pearl:** When interpreting case-control studies reporting OR for a common disease (e.g., hypertension, obesity), remember that the OR **overestimates** the true relative risk. ### Mnemonic **RARE = RR ≈ OR** — When disease is RARE, Relative Risk approximates Odds Ratio. ### Example If a case-control study reports OR = 2.5 for smoking and lung cancer: - Lung cancer is rare in the general population (~0.5%) - The OR of 2.5 closely approximates the true RR - We can interpret it as: smokers are ~2.5 times more likely to develop lung cancer If the same OR were reported for smoking and hypertension (common disease, ~30% prevalence): - The OR would substantially overestimate the true RR - The actual RR might be closer to 1.8 or 1.9, not 2.5