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November 2006 Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary
Mei-Ling Ting Lee, G. A. Whitmore
Statist. Sci. 21(4): 501-513 (November 2006). DOI: 10.1214/088342306000000330


Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state of the underlying process represents the strength of an item or the health of an individual. The item fails or the individual experiences a clinical endpoint when the process reaches an adverse threshold state for the first time. The time scale can be calendar time or some other operational measure of degradation or disease progression. In many applications, the process is latent (i.e., unobservable). Threshold regression refers to first-hitting-time models with regression structures that accommodate covariate data. The parameters of the process, threshold state and time scale may depend on the covariates. This paper reviews aspects of this topic and discusses fruitful avenues for future research.


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Mei-Ling Ting Lee. G. A. Whitmore. "Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary." Statist. Sci. 21 (4) 501 - 513, November 2006.


Published: November 2006
First available in Project Euclid: 23 April 2007

zbMATH: 1129.62095
MathSciNet: MR2380714
Digital Object Identifier: 10.1214/088342306000000330

Keywords: Accelerated testing , calendar time , Competing risk , cure rate , duration , environmental studies , First hitting time , gamma process , latent variable models , lifetime , maximum likelihood , occupational exposure , operational time , Ornstein–Uhlenbeck process , Poisson process , running time , stochastic process , stopping time , Survival analysis , threshold regression , time-to-event , Wiener diffusion process

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.21 • No. 4 • November 2006
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