Efficient estimation for the proportional hazards model with interval censoring

The maximum likelihood estimator (MLE) for the proportional hazards model with case 1 interval censored data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with √n convergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at n 1/3 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 √n. The results are iliustrated by applying them to a data set from a tumorigenicity study.

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