Solution
= Solution
In a <competing risks model>, the latent times to different event types form such a race: only the smallest time and its cause are observed. With proportional cause-specific hazards $\phi_i h_0(t)$, the probability that cause $i$ wins is $\phi_i/\sum_j\phi_j$, independently of the baseline hazard and under independent censoring. This is the same cancellation derived above.