Bayesian Semiparametric Threshold Regression

• Activity Number: 466 - First-Hitting-Time Based Threshold Regression and Applications
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Jonathan Race* and Michael Pennell
• Companies: and Ohio State University
• Keywords: Threshold regression; Bayesian; Semi-parametric; Survival analysis; Dirichlet process mixture

Abstract

Threshold regression (TR) is a relatively new method for survival analysis which assumes a latent health process underlies time-to-event. A common approach is to model the latent health process using a Wiener process with drift resulting in an inverse Gaussian distribution for time-to-event. TR has several advantages over more traditional parametric and semiparametric regression models including biologically meaningful covariate effects and the ability to model nonproportional hazards. However, the restrictive assumption of an inverse Gaussian distribution could lead to poor fit in certain scenarios. For instance, the model may fit poorly due to unexplained heterogeneity in the initial state and drift of the Wiener process. To address this limitation we propose modeling time-to-event using a Dirichlet Process Mixture of inverse Gaussians. Two different types of models are considered: one which models heterogeneity in the drift and another that simultaneously models heterogeneity in the drift and initial state. Posterior inference proceeds using a blocked Gibbs sampler. The methods are applied to data from a two year carcinogenicity study by the National Toxicology Program.