Identify a common error in interpreting cohort results, such as confusing odds ratio with risk ratio in rare outcomes.

• A. Odds ratios are always equal to risk ratios, so misinterpretation never occurs
• B. With rare outcomes, OR approximates RR; misinterpretation occurs when using OR as RR for non-rare outcomes
• C. RR and OR are unrelated and cannot be compared
• D. Hazard ratio is the same as RR

Answer: (B)

The key idea is how risk ratio (relative risk) and odds ratio relate, and when they can be treated as interchangeable. In a cohort study, the risk ratio compares probabilities of the outcome between exposed and unexposed groups, while the odds ratio compares the odds of the outcome. When the outcome is rare, the probability of the event is small, so odds and probability are very close; therefore OR and RR are similar. But as the outcome becomes more common, odds diverge from probability and the odds ratio can overestimate (or, in some cases, distort) the true relative risk.

For example, if the event occurs in 20% of the exposed and 10% of the unexposed, the RR is 0.20/0.10 = 2. The odds are 0.20/0.80 = 0.25 in the exposed and 0.10/0.90 ≈ 0.111 in the unexposed, so the OR is 0.25/0.111 ≈ 2.25, slightly higher than the RR. If the event is rarer, say 1% vs 0.5%, RR is 2, and OR is about 2.02, much closer.

Thus the common error is using the odds ratio as if it were the risk ratio, especially when the outcome is not rare. The correct choice captures that OR approximates RR only for rare outcomes, and misinterpretation arises when treating OR as RR for non-rare outcomes. The other statements falsely claim OR always equals RR, or deny any relationship between RR and OR, or equate hazard ratio with RR; these oversimplifications are inaccurate.