Solution
= Solution
The probability of a first event of type $A$ in $(u,u+du)$ is the probability $S(u)$ of still being at risk times $h_A(u)du$. Thus its <cumulative incidence function> is
$$
\boxed{F_A(t)=\int_0^t h_A(u)\exp\{-H_A(u)-H_B(u)\}\,du.}
$$
Similarly $F_B(t)=\int_0^t h_B(u)S(u)\,du$. In general $F_A(t)\ne1-e^{-H_A(t)}$: that latter expression ignores the competing removal caused by $B$ and instead describes a <net survival> complement.