A case-control study of a newly described cancer finds an odds ratio of 4.0 for a suspected dietary exposure. The disease affects fewer than 1 in 1000 people annually. The odds ratio can be interpreted as a good approximation of the relative risk primarily because:

• A Controls were selected from the community rather than hospitals
• B Matching eliminated all confounding in the study
• C Odds ratios are always numerically equal to relative risks
• D When the outcome is rare, the odds of disease approximate its risk ✓

Explanation

Risk equals odds divided by one plus odds. When disease is rare, the denominator approaches one, so risk approximates odds and the exposure odds ratio approximates the relative risk. This rare-disease assumption is conventionally taken to hold when cumulative incidence falls below roughly 5 percent. Community control selection improves validity generally but does not create the mathematical equivalence, and the identity never holds exactly except trivially.

Reference: Gordis Epidemiology, 6th ed.

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