Partially linear hazard regression with varying coefficients for multivariate survival data

Jianwen Cai, Jianqing Fan, Jiancheng Jiang, Haibo Zhou

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


The paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudo-partial-likelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo-partial-likelihood, whereas the varying-coefficient functions are considered as nuisance parameters that are profiled out of the likelihood. It is shown that the estimators of the parameters are root n consistent and the estimators of the non-parametric coefficient functions achieve optimal convergence rates. Asymptotic normality is obtained for the estimators of the finite parameters and varying-coefficient functions. Consistent estimators of the asymptotic variances are derived and empirically tested, which facilitate inference for the model. We prove that the varying-coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent. Simulations are conducted to demonstrate the performance of the estimators proposed. A real data set is analysed to illustrate the methodology proposed.

Original languageEnglish (US)
Pages (from-to)141-158
Number of pages18
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
StatePublished - Feb 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Local pseudo-partial-likelihood
  • Marginal hazard model
  • Multivariate failure time
  • Partially linear model
  • Profile pseudo-partial-likelihood
  • Varying coefficients


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