Under what condition does the odds ratio approximate the relative risk in a case-control study?

Under what condition does the odds ratio approximate the relative risk in a case-control study?

• A. When the disease is rare in the population.
• B. When exposure is common.
• C. When the study uses cross-sectional data.
• D. When the outcome is immediately fatal.

Answer: (A)

In a case-control setup, you estimate how strongly exposure is associated with disease using the odds ratio. The odds ratio will closely match the relative risk when the disease is rare in the population. The reason is that with a rare outcome, the odds of disease among those exposed is nearly the same as the actual risk, and similarly for those not exposed. Mathematically, when P(D) is small, P(not D) ≈ 1, so the ratio of odds approximates the ratio of probabilities: OR ≈ RR. This is why the rare-disease assumption lets the case-control odds ratio serve as a good proxy for the relative risk.

In a case-control setup, you estimate how strongly exposure is associated with disease using the odds ratio. The odds ratio will closely match the relative risk when the disease is rare in the population. The reason is that with a rare outcome, the odds of disease among those exposed is nearly the same as the actual risk, and similarly for those not exposed. Mathematically, when P(D) is small, P(not D) ≈ 1, so the ratio of odds approximates the ratio of probabilities: OR ≈ RR. This is why the rare-disease assumption lets the case-control odds ratio serve as a good proxy for the relative risk.