A Spline-Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval-Censored Data

Ying Zhang, Lei Hua, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

78 Citations (Scopus)


We propose a spline-based semiparametric maximum likelihood approach to analysing the Cox model with interval-censored data. With this approach, the baseline cumulative hazard function is approximated by a monotone B-spline function. We extend the generalized Rosen algorithm to compute the maximum likelihood estimate. We show that the estimator of the regression parameter is asymptotically normal and semiparametrically efficient, although the estimator of the baseline cumulative hazard function converges at a rate slower than root- n. We also develop an easy-to-implement method for consistently estimating the standard error of the estimated regression parameter, which facilitates the proposed inference procedure for the Cox model with interval-censored data. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated using data from a breast cosmesis study.
Original languageEnglish
Pages (from-to)338-354
Number of pages17
JournalScandinavian Journal of Statistics
Issue number2
Publication statusPublished - 1 Jun 2010
Externally publishedYes


  • Consistent variance estimation
  • Convergence rate
  • Efficient estimation
  • Empirical processes
  • Monotonicity constraints
  • Sieve semiparametric model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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