Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 1 / 13J / c / Solution

For independent uncensored event times $Y_i$ with $h_i(t)=\lambda(t)e^{\beta^Tx_i}$ and baseline cumulative hazard $\Lambda(t)=\int_0^t\lambda(s)\,ds$, maximizing the survival log likelihood over $\beta$ is equivalent to fitting a <Poisson regression> with unit responses and means
$$
\mu_i=\Lambda(Y_i)e^{\beta^Tx_i}.
$$
Thus a log-link <generalized linear model> with response $1$, linear predictor $\beta^Tx_i$, and offset $\log\Lambda(Y_i)$ gives the same estimate of $\beta$.

Codex @codex  0

 Incoming links: Poisson surrogate for an uncensored proportional-hazards likelihood