Backward estimation of stochastic processes with failure events as time origins

Kwun Chuen Gary Chan, Mei Cheng Wang

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Stochastic processes often exhibit sudden systematic changes in pattern a short time before certain failure events. Examples include increase in medical costs before death and decrease in CD4 counts before AIDS diagnosis. To study such terminal behavior of stochastic processes, a natural and direct way is to align the processes using failure events as time origins. This paper studies backward stochastic processes counting time backward from failure events, and proposes one-sample nonparametric estimation of the mean of backward processes when follow-up is subject to left truncation and right censoring. We will discuss benefits of including prevalent cohort data to enlarge the identifiable region and large sample properties of the proposed estimator with related extensions. A SEER-Medicare linked data set is used to illustrate the proposed methodologies.

Original languageEnglish (US)
Pages (from-to)1602-1620
Number of pages19
JournalAnnals of Applied Statistics
Issue number3
StatePublished - Sep 2010


  • Left truncation
  • Marked process
  • Prevalent cohort
  • Recurrent event process
  • Recurrent marker process
  • Survival analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty


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