Asymptotic Equivalence Between the Cox Estimator and the General ML Estimators of Regression and Survival Parameters in the Cox Model

The usual approach to estimating regression parameters in the Cox regression model uses the partial likelihood. If the covariates are not time-dependent, the model can be stated in terms of the survival function, which allows one to derive a generalized likelihood containing both regression and survival curve parameters. It is shown that, in the absence of ties, an estimator results which is asymptotically equivalent to the partial likelihood estimator. A joint information matrix leads simply to standard errors for both regression and survival curve parameters which are asymptotically correct.