Which statement best describes the relationship between relative risk and attributable risk?

• A. A tenfold reduction in incidence among both exposed and unexposed would reduce AR but would have no effect on RR.
• B. RR changes with changes in baseline incidence, while AR remains constant.
• C. RR and AR are always proportional in all settings.
• D. AR increases as RR decreases.

Answer: (B)

The relationship hinges on how these two measures are defined. Relative risk is a ratio of risks: RR = Ie / Iu. Attributable risk is a difference: AR = Ie – Iu. If you apply a proportional change to both groups (for example, a universal intervention that reduces all risks by the same factor), the ratio stays the same (RR remains unchanged) while the difference scales with that factor (AR changes). In algebra terms, if Ie = RR × Iu, then AR = Ie – Iu = (RR – 1) × Iu, which shows AR depends on the baseline risk in the unexposed group (Iu), while RR depends on the strength of the association (the ratio) and is not determined by the baseline level.

For a concrete feel: with a baseline Iu of 5% and RR = 3, Ie = 15% and AR = 10%. If both groups’ risks drop tenfold, Ie becomes 1.5% and Iu becomes 0.5%, RR stays at 3, but AR drops to 1%. If the baseline risk in the unexposed rises to 20% with the same RR, Ie becomes 60% and AR becomes 40%. This illustrates that AR changes with baseline incidence, while RR tends to be more stable across different baseline risks (in the absence of effect modification).