Efficient estimation of regression coefficients and baseline hazard under proportionality of conditional hazards

Efficient estimation of the regression parameter and the cumulative baseline hazard function under proportionality assumptions of the conditional hazards is considered in this paper. The cases of complete and incomplete information on the censoring indicators are studied. In both cases, a convenient reparametrization of the likelihood for a single observation places this problem in the setting investigated by Ritov and Wellner (1988). Their results on information bounds for the regression parameter and the cumulative baseline hazard function of the Cox model for the uncensored case apply here. The asymptotic properties of proposed estimators are derived and the estimators are shown to be asymptotically efficient.