When is the odds ratio an unbiased estimate of relative risk, and how is it calculated in a case-control study?

• A. In rare diseases; OR = (a/c) / (b/d) = ad/bc
• B. In rare diseases; OR = (a+b)/(c+d)
• C. In rare diseases; OR = (a/c) * (b/d)
• D. In common diseases; OR = (a/c) / (b/d)

Answer: (A)

When a disease is rare, the odds ratio from a case-control study closely estimates the relative risk. In a case-control design you can only directly measure odds—the odds of exposure among cases versus controls. The 2x2 setup uses a = cases with exposure, b = controls with exposure, c = cases without exposure, and d = controls without exposure. The odds ratio is calculated as (a/c) divided by (b/d), which simplifies to ad/bc. Under the rare-disease assumption, this odds ratio approximates the relative risk because the probability of the disease in each exposure group is small, making odds and risk nearly the same. In more common diseases the two measures can diverge, so the odds ratio is no longer an unbiased estimate of relative risk.