Which statement correctly describes the relation of odds ratio to relative risk when the outcome is rare?

Which statement correctly describes the relation of odds ratio to relative risk when the outcome is rare?

• A. Odds ratio approximates relative risk when the outcome is rare.
• B. Relative risk approximates odds ratio when the outcome is rare.
• C. Hazard ratio approximates relative risk when the outcome is rare.
• D. Absolute risk reduction approximates relative risk when the outcome is rare.

Answer: (B)

When the outcome is rare, the probability of the event is small in both groups, so the odds and the actual risk are almost the same. Because risk ratios compare probabilities and odds ratios compare odds, their values become very close in this rare-event scenario. In practice, you can see that the relative risk and the odds ratio approximate each other as the event becomes rarer, so saying that relative risk approximates odds ratio is a natural way to express this relationship. For example, if the risk in the exposed group is 2% and in the unexposed group is 1%, the relative risk is 2.0. The corresponding odds are about 0.0204 in the exposed group and 0.0102 in the unexposed group, giving an odds ratio also around 2.0. As the outcome becomes even rarer, the two measures converge even more.

When the outcome is rare, the probability of the event is small in both groups, so the odds and the actual risk are almost the same. Because risk ratios compare probabilities and odds ratios compare odds, their values become very close in this rare-event scenario. In practice, you can see that the relative risk and the odds ratio approximate each other as the event becomes rarer, so saying that relative risk approximates odds ratio is a natural way to express this relationship. For example, if the risk in the exposed group is 2% and in the unexposed group is 1%, the relative risk is 2.0. The corresponding odds are about 0.0204 in the exposed group and 0.0102 in the unexposed group, giving an odds ratio also around 2.0. As the outcome becomes even rarer, the two measures converge even more.