Which statement describes the effect of a tenfold reduction in incidence in both exposed and unexposed on RR and AR?

• A. RR remains unchanged; AR decreases.
• B. Both RR and AR decrease by the same factor.
• C. RR decreases; AR remains unchanged.
• D. A tenfold reduction in incidence in both groups would reduce AR but not RR.

Answer: (D)

When both groups experience the same proportional reduction in incidence, the effect on these two measures differs because they are defined differently.

Relative risk is a ratio: RR = Ie / Io. If Ie and Io are both reduced by the same factor (tenfold in this case), the factor cancels in the ratio, so RR stays the same.

Attributable risk is a difference: AR = Ie − Io. If Ie and Io are both reduced by the same factor, the difference also reduces by that factor: AR' = (Ie/10) − (Io/10) = (Ie − Io)/10 = AR/10. So AR decreases tenfold.

Example: start with Ie = 20 per 1000 and Io = 5 per 1000. RR = 4; AR = 15 per 1000. After a tenfold reduction, Ie' = 2 per 1000 and Io' = 0.5 per 1000. RR' = 4 (unchanged) and AR' = 1.5 per 1000 (tenfold smaller).

Therefore, the statement that a tenfold reduction in incidence in both groups would reduce AR but not RR is correct.