Baseline survival function (source code)

= Baseline survival function
{title2=$S_0(t)$}

In a <proportional hazards model> $h(t\mid z)=h_0(t)e^{\beta^Tz}$, the <baseline survival function> is $S_0(t)=\exp\{-\int_0^t h_0(u)\,du\}$, corresponding to the reference covariate vector $z=0$. Integrating the <hazard function> gives $S(t\mid z)=S_0(t)^{e^{\beta^Tz}}$. Estimated <hazard ratios> alone therefore do not determine absolute survival probabilities: the <baseline hazard> or <baseline survival function> must also be estimated.