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.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 207 / 5 / a / Solution

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{wiki=Proportional_hazards_model#The_partial_likelihood}

The Cox partial likelihood conditions each event on its risk set, eliminating the baseline hazard.


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