In a case-control study of oral contraceptive use and venous thromboembolism, the odds of exposure among cases is 0.8 and among controls is 0.2. What is the odds ratio?

Explanation

## Odds Ratio Calculation in Case-Control Studies ### Definition **Odds Ratio (OR)** = (Odds of exposure in cases) / (Odds of exposure in controls) ### Calculation Given: - Odds of exposure in cases = 0.8 - Odds of exposure in controls = 0.2 $$OR = \frac{0.8}{0.2} = 4.0$$ ### Interpretation **Key Point:** An OR of 4.0 means that individuals with the disease (cases) are 4 times more likely to have been exposed to oral contraceptives compared to those without the disease (controls). ### When to Use Odds Ratio **High-Yield:** Odds ratio is the appropriate measure of association in **case-control studies** because: - Cases are selected based on disease status, not exposure - We cannot calculate incidence or prevalence directly - OR approximates Relative Risk (RR) when the disease is rare (prevalence < 10%) ### Odds vs Probability | Concept | Definition | Range | |---------|-----------|-------| | **Odds** | Ratio of probability of event to probability of non-event: $\frac{p}{1-p}$ | 0 to ∞ | | **Probability** | Likelihood of an event occurring | 0 to 1 | | **Odds Ratio** | Ratio of odds in two groups | 0 to ∞ | **Clinical Pearl:** An OR = 1 indicates no association; OR > 1 indicates increased odds of exposure in cases; OR < 1 indicates decreased odds of exposure in cases. ### Formula Reminder $$OR = \frac{\text{Odds of exposure in cases}}{\text{Odds of exposure in controls}} = \frac{a/b}{c/d} = \frac{ad}{bc}$$ Where in a 2×2 table: - a = cases with exposure - b = cases without exposure - c = controls with exposure - d = controls without exposure