= Competing risks model with transient surgical mortality
{title2=$S(t)=e^{-a\min(t,\tau)-bt}$}
If one <cause-specific hazard> acts at constant rate $a$ only until time $\tau$, and another acts at constant rate $b>0$ indefinitely, overall survival is $S(t)=e^{-a\min(t,\tau)-bt}$. The first cause has ultimate <cumulative incidence function> $a(1-e^{-(a+b)\tau})/(a+b)$; the second accounts for all remaining eventual failures. This illustrates how a transient competing hazard modifies a persistent cause's cumulative risk.
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