Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 40 / 1 / b / iii / Solution

Replace the expected total person-time and failure count in the preceding identity by their observed values, $E={\sum }_i{x}_i$ and $d$. The resulting estimating equation is $\theta E=d$, soThis events divided by exposure estimator is failures per unit observed person-time. We assume positive total exposure; if $d=0$, it gives the boundary estimate zero.