In what scenario is the odds ratio a good approximation of relative risk?

In what scenario is the odds ratio a good approximation of relative risk?

• A. When the disease is common.
• B. When the sample size is large.
• C. When the disease is rare.
• D. When the exposure is rare.

Answer: (C)

When the disease is rare, the odds ratio closely estimates the relative risk. This works because odds are defined as p/(1−p) and relative risk is the probability p. If p is small, (1−p) is near 1, so odds ≈ probability. Consequently, the ratio of odds between exposed and unexposed (the OR) approximates the ratio of probabilities (the RR). For example, with 1% disease in the unexposed and 2% in the exposed, RR is about 2.0 and OR is about 2.02—nearly the same. If the disease is common, say 20% vs 40%, RR is 2.0 but OR becomes about 2.67, overestimating the association. So the best scenario for using OR as a close stand-in for RR is when the disease is rare.

When the disease is rare, the odds ratio closely estimates the relative risk. This works because odds are defined as p/(1−p) and relative risk is the probability p. If p is small, (1−p) is near 1, so odds ≈ probability. Consequently, the ratio of odds between exposed and unexposed (the OR) approximates the ratio of probabilities (the RR).

For example, with 1% disease in the unexposed and 2% in the exposed, RR is about 2.0 and OR is about 2.02—nearly the same. If the disease is common, say 20% vs 40%, RR is 2.0 but OR becomes about 2.67, overestimating the association. So the best scenario for using OR as a close stand-in for RR is when the disease is rare.