Random censoring in set-indexed survival analysis

B. Gail Ivanoff, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Using the theory of set-indexed martingales, we develop a general model for survival analysis with censored data which is parameterized by sets instead of time points. We define a set-indexed Nelson-Aalen estimator for the integrated hazard function with the presence of a censoring by a random set which is a stopping set. We prove that this estimator is asymptotically unbiased and consistent. A central limit theorem is given. This model can be applied to cases when censoring occurs in geometrical objects or patterns, and is a generalization of models with multidimensional failure times.

Original languageEnglish
Pages (from-to)944-971
Number of pages28
JournalAnnals of Applied Probability
Issue number3
StatePublished - Aug 2002


  • Censoring
  • Central limit theorem
  • Estimator
  • Hazard function
  • Set-indexed martingale
  • Stopping set
  • Survival analysis
  • Volterra equation


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