A <semiparametric proportional hazards model> specifies
$$
h(t\mid z)=h_0(t)e^{\beta z}
$$
with finite-dimensional parameter $\beta$ but an unspecified baseline hazard $h_0$. A <partial likelihood> uses a component of the data likelihood that depends on $\beta$ while eliminating the nuisance function. In the <Cox proportional-hazards model>, conditioning on which member of each <risk set> experiences the event produces the <Cox partial likelihood>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 5 / c / Solution

A semiparametric proportional hazards model specifies a finite-dimensional hazard ratio while leaving the baseline hazard function unspecified.


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