 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 ${\varphi }_i{h}_0(t)$, the probability that cause $i$ wins is ${\varphi }_i/{\sum }_j{\varphi }_j$, independently of the baseline hazard and under independent censoring. This is the same cancellation derived above.