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. 2010 Sep 1;4(3):1602-1620.
doi: 10.1214/09-AOAS319.

BACKWARD ESTIMATION OF STOCHASTIC PROCESSES WITH FAILURE EVENTS AS TIME ORIGINS

Kwun Chuen Gary Chan  1 , Mei-Cheng Wang
Affiliations

BACKWARD ESTIMATION OF STOCHASTIC PROCESSES WITH FAILURE EVENTS AS TIME ORIGINS

Kwun Chuen Gary Chan et al. Ann Appl Stat. .

Abstract

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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Figures

FIG. 1
FIG. 1
Trajectories of forward and backward cost processes for 3 uncensored individuals in the SEER–Medicare linked data. (a) Forward cost processes. Circles represent failure events. (b) Backward cost processes. Circles represent diagnoses of cancer.
FIG. 2
FIG. 2
Estimates of survival probabilities for ovarian cancer patients in the SEER–Medicare data, using only incident cohort data (bold) and using data from both incident and prevalent cohorts (nonbold). Solid curves represent localized stage at diagnosis, dashed curves represent regional stage and dotted curves represent distant stage.
FIG. 3
FIG. 3
Estimates of the mean forward cost functions for ovarian cancer patients. Solid curve represents localized stage at diagnosis, dashed curve represents regional stage and dotted curve represents distant stage.
FIG. 4
FIG. 4
Estimates of the mean backward cost functions for ovarian cancer patients. Solid curves represent the estimates. Dotted curves represent 95% simultaneous confidence bands. Dashed curves represent pointwise 95% confidence intervals.
FIG. 5
FIG. 5
Estimates of the backward rate of cost accrual. Solid curve represents localized stage at diagnosis, dashed curve represents regional stage and dotted curve represents distant stage.
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References

    1. Bang H, Tsiatis AA. Estimating medical costs with censored data. Biometrika. 2000;87:329–343. MR1782482.
    1. Bilias Y, Gu M, Ying Z. Towards a general asymptotic theory for Cox model with staggered entry. Ann. Statist. 1997;25:662–682. MR1439318.
    1. Chan ISF, Neaton JD, Saravolatz LD, Crane LR, Osterberger J. Frequencies of opportunistic diseases prior to death among HIV-infected persons. Aids. 1995;9:1145–1151. - PubMed
    1. Cook RJ, Lawless JF. Marginal analysis of recurrent events and a terminating event. Stat. Med. 1997;16:911–924. - PubMed
    1. Ghosh D, Lin DY. Nonparametric analysis of recurrent events and death. Biometrics. 2000;56:554–562. MR1795021. - PubMed

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