A case-control study examining the association between maternal smoking during pregnancy and congenital heart defects enrolled 150 mothers of children with CHD and 150 mothers of children without CHD. Among mothers of affected children, 90 had a history of smoking; among mothers of unaffected children, 45 had a history of smoking. Which of the following correctly interprets the odds ratio in this context?

Explanation

## Calculation of Odds Ratio **Odds of exposure among cases (CHD+):** 90/60 = 1.5 **Odds of exposure among controls (CHD−):** 45/105 = 0.43 **Odds Ratio = 1.5 / 0.43 ≈ 3.5 ≈ 4** (or using the formula: 90 × 105 / 60 × 45 = 3.5) ## Key Points **Key Point:** In a case-control study, the odds ratio is the appropriate measure of association because we cannot calculate incidence or prevalence directly (we selected subjects based on disease status, not exposure status). **High-Yield Fact:** The odds ratio approximates the relative risk when: - The disease is **rare** (prevalence < 10%) - The study is **case-control** (cannot calculate RR directly) - In cohort studies with common outcomes, OR and RR diverge significantly **Clinical Pearl:** CHD prevalence is approximately 0.8–1% in live births, making it a rare disease. Therefore, the OR ≈ 4 closely approximates the RR, meaning maternal smoking is associated with approximately a 4-fold increased odds/risk of CHD. ## Why OR ≠ RR in Case-Control Design In case-control studies, we cannot calculate relative risk because: - We do not know the incidence of disease in exposed vs. unexposed groups - We selected subjects *because* they had (or did not have) the disease - The odds ratio is the only valid measure of association When disease is rare, OR ≈ RR; when disease is common, OR overestimates RR.