 Poisson surrogate for an uncensored proportional-hazards likelihood

For independent uncensored event times $Y_i$ with $h_i(t)=\lambda (t)e^{{\beta }^T{x}_i}$ 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 meansThus a log-link generalized linear model with response $1$, linear predictor ${\beta }^T{x}_i$, and offset $\log \Lambda (Y_i)$ gives the same estimate of $\beta$.