  We propose an extension of the regular Cox's proportional hazards model which
allows the estimation of the probabilities of rare events. It is known that
when the data are heavily censored at the upper end of the survival
distribution, the estimation of the tail of the survival distribution is not
reliable. To estimate the distribution beyond the last observed data, we
suppose that the survival data are in the domain of attraction of the Fr\'echet
distribution conditionally to covariates. Under this condition, by the
Fisher-Tippett-Gnedenko theorem, the tail of the baseline distribution can be
adjusted by a Pareto distribution with parameter $\theta$ beyond a threshold
$\tau$. The survival distributions conditioned to the covariates are easily
computed from the baseline. We also propose an aggregated estimate of the
survival probabilities. A procedure allowing an automatic choice of the
threshold and an application on two data sets are given.
