Relative risk bounds from rounded group compositions ($\frac{a_L(1-p_U)}{p_U(1-a_L)}\le \mathrm{RR}\le \frac{a_U(1-p_L)}{p_L(1-a_U)}$)

Suppose $0<p_L\le p\le p_U<1$ and $0<a_L\le a\le a_U<1$. The formula for relative risk from group compositions increases with $a$ and decreases with $p$, since $a/(1-a)$ increases and $(1-p)/p$ decreases. This monotonicity proves the displayed bounds. If percentages are rounded to the nearest whole percentage point, each corresponding proportion lies within $0.005$ of its displayed value. These bounds describe rounding uncertainty; they are not a confidence interval for sampling uncertainty.