Efficient Estimation for the Cox Model with Interval Censoring

The maximum likelihood estimator (MLE) for the proportional hazards model with current status data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with vn-convergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at nI/3 rate. Estimation of the asymptotic variance matrix for the MLE of the regression parameter is also considered. To prove our main results, we also establish a general theorem showing that the MLE of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the MLE of the infinite dimensional parameter converges at a rate slower than vn. The results are illustrated by applying them to a data set from a tumoriginicity study.