Solution (source code)

= Solution

A <proportional hazards family> has <hazard functions> related by
$$
h(t\mid z)=c(z)h_0(t),
$$
where the <hazard ratio> $c(z)$ is positive and independent of time. Equivalently, its <cumulative hazard functions> satisfy $H(t\mid z)=c(z)H_0(t)$ and its <survivor functions> satisfy $S(t\mid z)=S_0(t)^{c(z)}$.