In a cohort study, under what condition does the odds ratio approximate the relative risk?

• A. When the outcome is common in both groups.
• B. When the exposure is rare.
• C. When follow-up is complete.
• D. When the outcome is rare in both groups.

Answer: (D)

The main idea here is that the odds ratio behaves like the relative risk when the outcome is rare. In a cohort study, relative risk compares risks (probabilities) of developing the outcome between exposed and unexposed groups, while the odds ratio compares odds (p/(1−p)) between those groups. When the outcome is rare in both groups, the odds are very close to the actual probabilities because p is small and 1−p is near 1. Therefore the ratio of odds (the OR) closely mirrors the ratio of risks (the RR).

For example, if 2% of the exposed and 1% of the unexposed develop the outcome, RR ≈ 2, and OR ≈ 2.02—nearly the same. If the outcome is more common (e.g., 30% vs 10%), RR = 3 but OR becomes about 3.86, which overstates the association. Hence the condition that makes OR approximate RR is when the outcome is rare in both groups.