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

TL;DR

This paper reviews threshold regression models based on first hitting times of stochastic processes for survival analysis, emphasizing their ability to incorporate covariates and latent processes.

Contribution

It provides a comprehensive review of threshold regression models in survival analysis and discusses future research directions in this area.

Findings

Highlights the use of stochastic processes in modeling survival times.

Discusses covariate integration in first hitting time models.

Explores applications with latent processes in survival data.

Abstract

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.