Conditional latent event-time density under competing risks
= Conditional latent event-time density under competing risks
For independent continuous event times, conditioning on $T_A<T_B$ weights the density of $T_A$ by the <survivor function> of $T_B$. Conditioning on $T_B<T_A$ instead weights it by one minus that <survivor function>. These are distributions of the latent $T_A$, not the distribution of the observed first event in every case.