Variable Selection in Threshold Regression Models for Survival Data

Music City Center 

Threshold regression, or first-hitting-time regression, is an alternative to the Cox proportional hazards model when the proportional hazards assumption is violated for survival data. It defines the event time as the first time a latent stochastic process hits a boundary. When the underlying process is a Wiener diffusion process, the event time follows an inverse Gaussian distribution. This process is characterized by the initial level at time zero and the degradation rate, it can be used to model health trajectories through separate functions for baseline health and degradation rate but complicates variable selection. This study evaluated variable selection methods for threshold regression using simulations, comparing frequentist approaches (forward selection, backward selection, ThregBAR) and Bayesian methods (horseshoe, LASSO). Bayesian LASSO demonstrated accurate, stable performance, while Bayesian horseshoe was sensitive to scaling. Among frequentist methods, forward selection performed best, ThregBAR had the lowest false-negative rates, and backward selection was least effective.

First hitting time regression model

Survival Data

Bayesian Methods

Variable selection 

Section on Bayesian Statistical Science