Solution
= Solution
The <Cox proportional-hazards model> is
$$
h_i(t)=h_0(t)e^{\beta z_i},
$$
where $h_0$ is an unspecified baseline hazard and $z_i$ indicates treatment. With no tied events, the <Cox partial likelihood> is
$$
L(\beta)=\prod_{i:\,v_i=1}
\frac{e^{\beta z_i}}{\sum_{j\in R(x_i)}e^{\beta z_j}}.
$$
Equality of the two hazard functions is $H_0:\beta=0$, testable with a likelihood-ratio, score, or Wald test from this likelihood.