Estimating Survivor Functions
As we have seen, the form of the dependence of the hazard on time is left unspecified in the proportional hazards model. Furthermore, the partial likelihood method discards that portion of the likelihood function that contains information about the dependence of the hazard on time. Nevertheless, it is still possible to get nonparametric estimates of the survivor function based on a fitted proportional hazards model.
When there are no time-dependent covariates, the Cox model can be written as
S(t) = [S0(t)]exp(βx)
where S(t) is the survival probability at time t for an individual with covariate values x, and S0(t) is the baseline survivor function, that is, the survivor function for an individual whose covariate ...