A case-control study examining the association between oral contraceptive use and venous thromboembolism (VTE) in Indian women reports an odds ratio (OR) of 3.2 (95% CI: 2.1–4.8). Which of the following statements about this OR is NOT true?

Explanation

## Understanding Odds Ratio in Case-Control Studies **Key Point:** The odds ratio (OR) is the primary measure of association in case-control studies. Its mathematical relationship to relative risk (RR) depends critically on disease prevalence. ### When OR Approximates RR The OR approximates RR under specific conditions: | Condition | OR ≈ RR? | Explanation | |-----------|----------|-------------| | **Disease rare** (< 10% prevalence) | **YES** | When disease is uncommon, the odds of disease ≈ probability of disease; OR → RR | | **Disease common** (> 50% prevalence) | **NO** | When disease is common, odds diverge substantially from probability; OR ≠ RR | | **Exposure rare** | **YES** | Rarity of exposure favors OR ≈ RR regardless of disease prevalence | **High-Yield:** The mathematical basis: When prevalence is low, `$OR = \frac{a \cdot d}{b \cdot c} \approx RR = \frac{a/(a+b)}{c/(c+d)}$` because the denominators become negligible. ### Interpretation of OR = 3.2 The correct interpretation is: - **Odds of exposure among cases** are 3.2 times the **odds of exposure among controls** - This does NOT directly mean women are "3.2 times more likely to develop VTE" — that phrasing conflates OR with RR - The RR interpretation is only valid if VTE is rare in this population **Warning:** Option B uses RR language ("3.2 times more likely to develop") when describing an OR. This is a common trap in exam questions. The OR and RR are distinct measures; their numerical values coincide only when disease is rare. ### Why Each Statement Matters - **Option A (TRUE):** VTE is a relatively rare outcome (~0.1–0.5% annual incidence in general population). In rare diseases, OR ≈ RR, so the OR of 3.2 can reasonably estimate the RR. - **Option B (MISLEADING/WRONG):** This statement uses RR language ("3.2 times more likely to develop") to describe an OR. Technically, the OR tells us about odds of *exposure* given disease status, not the probability of developing disease. - **Option C (TRUE):** This is the definition of OR in a case-control study: $OR = \frac{\text{odds of exposure | case}}{\text{odds of exposure | control}}$ - **Option D (FALSE):** This inverts the rule. OR approximates RR when disease is **rare**, not common. When disease is common, OR overestimates RR. **Clinical Pearl:** In VTE epidemiology, the disease is rare enough that OR ≈ RR; therefore, stating "women using OCs have ~3.2× the risk" is acceptable. However, the mathematical basis of this approximation requires low prevalence, not high.