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September 2010 Backward estimation of stochastic processes with failure events as time origins
Kwun Chuen Gary Chan, Mei-Cheng Wang
Ann. Appl. Stat. 4(3): 1602-1620 (September 2010). DOI: 10.1214/09-AOAS319


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.


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Kwun Chuen Gary Chan. Mei-Cheng Wang. "Backward estimation of stochastic processes with failure events as time origins." Ann. Appl. Stat. 4 (3) 1602 - 1620, September 2010.


Published: September 2010
First available in Project Euclid: 18 October 2010

zbMATH: 1202.62108
MathSciNet: MR2758343
Digital Object Identifier: 10.1214/09-AOAS319

Keywords: left truncation , Marked process , prevalent cohort , recurrent event process , recurrent marker process , Survival analysis

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.4 • No. 3 • September 2010
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