Statistical Science

Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary

Mei-Ling Ting Lee and G. A. Whitmore

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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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Statist. Sci., Volume 21, Number 4 (2006), 501-513.

First available in Project Euclid: 23 April 2007

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


Lee, Mei-Ling Ting; Whitmore, G. A. Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary. Statist. Sci. 21 (2006), no. 4, 501--513. doi:10.1214/088342306000000330.

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