## Why Odds Ratio Is Correct for Case-Control Studies **Key Point:** In case-control studies, the outcome (disease) is already determined at enrollment. Participants are selected based on whether they have the disease (cases) or not (controls). Therefore, we cannot calculate true incidence or prevalence, and Relative Risk cannot be directly computed. ### Study Design Constraint Case-control studies are **retrospective** — we look backward from disease status to exposure history. The sampling fraction is determined by disease status, not exposure status. This violates the assumption needed for RR calculation. ### Odds Ratio Calculation **High-Yield:** The OR is the ratio of odds of exposure among cases to odds of exposure among controls: $$OR = \frac{\text{Odds of exposure in cases}}{\text{Odds of exposure in controls}} = \frac{a/c}{b/d} = \frac{ad}{bc}$$ Where: - a = cases exposed (120) - b = cases unexposed (80) - c = controls exposed (80) - d = controls unexposed (320) $$OR = \frac{120 \times 320}{80 \times 80} = \frac{38,400}{6,400} = 6.0$$ This means women with VTE are 6 times more likely to have used OCPs compared to controls. ### Why OR Approximates RR **Clinical Pearl:** When the disease is rare (< 10% in the population), the OR approximates the RR. VTE is relatively rare, making OR a valid proxy for RR in this context. | Measure | Study Design | Can Calculate Directly? | Formula | |---------|--------------|------------------------|----------| | **Relative Risk (RR)** | Cohort, RCT | Yes | Risk in exposed ÷ Risk in unexposed | | **Odds Ratio (OR)** | Case-control, Cohort | Yes (case-control) | (a×d) ÷ (b×c) | | **Attributable Risk** | Cohort | Yes | Risk exposed − Risk unexposed | | **NNH** | RCT, Cohort | Yes | 1 ÷ Absolute Risk Difference |
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