 Relative risk bounds from rounded group compositions

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.