In a case-control study examining the association between oral contraceptive use and venous thromboembolism, the odds ratio is calculated as 3.5 (95% CI: 2.1–5.8). In contrast, a prospective cohort study on the same exposure-outcome pair reports a relative risk of 2.8 (95% CI: 1.9–4.2). Which feature best distinguishes the odds ratio from the relative risk in this scenario?

Explanation

## Distinguishing Odds Ratio from Relative Risk ### Study Design Dependency **Key Point:** The fundamental distinction between OR and RR lies in their applicability to different study designs and their mathematical definitions. | Feature | Odds Ratio (OR) | Relative Risk (RR) | |---------|-----------------|--------------------| | **Calculation** | Ratio of odds of exposure in cases vs controls | Ratio of incidence/risk in exposed vs unexposed | | **Study Design** | Case-control (primary use) | Cohort & RCT (primary use) | | **Outcome Frequency** | Can be used regardless of outcome prevalence | Valid for rare outcomes; overestimates when outcome is common | | **Temporal Sequence** | Retrospective (cases identified first) | Prospective (exposure identified first) | | **Interpretation** | Approximates RR when outcome is rare (<10%) | Direct measure of risk increase | ### Why OR is Suited to Case-Control Design **High-Yield:** In case-control studies, you START with the outcome (cases vs controls) and look BACKWARD to exposure. You cannot directly calculate incidence because: 1. Cases are deliberately oversampled (not population-representative) 2. You do not know the total population at risk 3. You cannot calculate true risk (incidence) from a case-control sample Therefore, **odds ratio is the only valid measure of association for case-control studies**. ### Why RR is Suited to Cohort Design In cohort studies, you START with exposure status and follow forward to outcome. You can directly measure: - Incidence in exposed group: $I_e = \frac{\text{cases in exposed}}{\text{total exposed}}$ - Incidence in unexposed group: $I_u = \frac{\text{cases in unexposed}}{\text{total unexposed}}$ - Relative Risk: $RR = \frac{I_e}{I_u}$ **Clinical Pearl:** In the given scenario, the case-control study MUST report OR (not RR), and the cohort study MUST report RR (not OR). The option stating "OR can be calculated from case-control studies; RR cannot" is the defining feature. ### Mathematical Relationship When the outcome is rare (prevalence <10%), OR ≈ RR. In this question, OR = 3.5 and RR = 2.8, suggesting a moderately common outcome (VTE is ~1–2 per 1000 in the general population, but higher in OCP users), which explains why OR > RR.