  A class of estimating functions is introduced for the regression parameter of
the Cox proportional hazards model to allow unknown failure statuses on some
study subjects. The consistency and asymptotic normality of the resulting
estimators are established under mild conditions. An adaptive estimator which
achieves the minimum variance-covariance bound of the class is constructed.
Numerical studies demonstrate that the asymptotic approximations are adequate
for practical use and that the efficiency gain of the adaptive estimator over
the complete-case analysis can be quite substantial. Similar methods are also
developed for the nonparametric estimation of the survival function of a
homogeneous population and for the estimation of the cumulative baseline hazard
function under the Cox model.
