ABSTRACT
The proportional hazards model (Cox, 1972) specifies that the hazard function for the failure time T conditional on a set of covariates Z takes the form
λ(t|Z) = eβTZλ0(t),
where β is a set of unknown regression parameters, and λ0(·) is an arbitrary baseline hazard function. The partial likelihood (Cox, 1975) is used to estimate β. Breslow (1972) provided
an estimator for the cumulative baseline hazard function Λ0(t) ≡ ∫ t 0 λ0(s)ds. The asymptotic
properties of the maximum partial likelihood estimator and the Breslow estimator were established by Tsiatis (1981) and Andersen and Gill (1982) among others.
