What is the difference between a relative risk and an odds ratio, and when are each appropriate?

• A. Relative risk is risk in exposed vs unexposed; odds ratio is odds of exposure among cases vs controls; RR is appropriate in cohort studies; OR approximates RR when disease is rare.
• B. Relative risk is only for case-control; odds ratio for cohort.
• C. Relative risk approximates OR when disease is common.
• D. Both identical in all studies.

Answer: (A)

The main idea is how these two measures relate to probability versus odds and when each design allows you to estimate them. A relative risk compares probabilities directly: it looks at how likely the disease is among those exposed compared with those unexposed. This is most straightforward in a cohort study, where you can follow people over time and observe how many in each group develop the disease. So, the relative risk is the risk in the exposed group divided by the risk in the unexposed group.

An odds ratio, on the other hand, uses odds rather than probabilities. In a case-control study, you start with people who have the disease (cases) and those who don’t (controls) and look back to see who was exposed. You can’t reliably estimate the true incidence or risk from this design because the study sample fixes the number of cases and controls. Therefore, you compute the odds of exposure among cases and the odds of exposure among controls and form their ratio—the odds ratio.

The two measures align under a specific condition: when the disease is rare in the population. Under that rare-disease assumption, the odds of exposure among cases relative to controls mirrors the relative risk of disease in exposed versus unexposed, so the odds ratio serves as a good approximation of the relative risk. When the disease is common, the odds ratio tends to overstate the relative risk and becomes harder to interpret as a direct risk comparison.

So, in summary: relative risk is a probability-based measure best derived from cohort data; odds ratio is an exposure-odds measure derived from case-control data and approximates relative risk only when the disease is rare.