The Annals of Applied Statistics

Backward estimation of stochastic processes with failure events as time origins

Kwun Chuen Gary Chan and Mei-Cheng Wang

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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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Ann. Appl. Stat., Volume 4, Number 3 (2010), 1602-1620.

First available in Project Euclid: 18 October 2010

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Marked process left truncation prevalent cohort recurrent event process recurrent marker process survival analysis


Chan, Kwun Chuen Gary; Wang, Mei-Cheng. Backward estimation of stochastic processes with failure events as time origins. Ann. Appl. Stat. 4 (2010), no. 3, 1602--1620. doi:10.1214/09-AOAS319.

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