Efficient estimation for the proportional hazards model with interval censoring

Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

332 Citations (Scopus)


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 n1/3rate. 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 illustrated by applying them to a data set from a tumorigenicity study.
Original languageEnglish
Pages (from-to)540-568
Number of pages29
JournalAnnals of Statistics
Issue number2
Publication statusPublished - 1 Jan 1996
Externally publishedYes


  • Current status data
  • Information
  • Interval censoring
  • Maximum (profile) likelihood estimator
  • Proportional hazards model
  • Semiparametric model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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