Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 37 / 2 / i / Solution

Interpret $h_A,h_B$ as cause-specific hazards: their conditioning population consists of individuals still free of both events. WriteIn a short interval, either event removes an individual from that population. Hence the survivor function satisfies $S^{\prime }(t)=-S(t)[h_A(t)+h_B(t)]$, with $S(0)=1$. Integrating givesNo independence assumption on hypothetical latent event times is needed: this follows directly from the specified cause-specific hazards.