Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bayesian variable and hazard structure selection in the General Hazard model

Yulong Chen, Jim Griffin, Francisco Javier Rubio

TL;DR

This work develops a Bayesian framework for simultaneous variable selection and hazard-structure selection within the General Hazard (GH) model, unifying PH, AFT, and AH as special cases. It introduces two g-prior formulations (likelihood-curvature matching and product) and a hierarchical, multiplicity-adjusted model-space prior to enable principled model uncertainty quantification and consistency. Computation relies on marginal-likelihood approximations and an extended Add-Delete-Swap MCMC sampler that moves within and between hazard structures, with theoretical guarantees for model selection consistency. Simulations show accurate recovery of active variables and hazard structure across sample sizes and censoring levels; real-data analyses (FLC and NKI70) illustrate practical performance and hazard-structure interpretation in high-dimensional, censored settings. The approach provides a flexible, principled tool for hazard-structure learning in survival analysis, with potential extensions to broader distributional-regression contexts.

Abstract

The proportional hazards (PH) and accelerated failure time (AFT) models are the most widely used hazard structures for analysing time-to-event data. When the goal is to identify variables associated with event times, variable selection is typically performed within a single hazard structure, imposing strong assumptions on how covariates affect the hazard function. To allow simultaneous selection of relevant variables and the hazard structure itself, we develop a Bayesian variable selection approach within the general hazard (GH) model, which includes the PH, AFT, and other structures as special cases. We propose two types of g-priors for the regression coefficients that enable tractable computation and show that both lead to consistent model selection. We also introduce a hierarchical prior on the model space that accounts for multiplicity and penalises model complexity. To efficiently explore the GH model space, we extend the Add-Delete-Swap algorithm to jointly sample variable inclusion indicators and hazard structures. Simulation studies show accurate recovery of both the true hazard structure and active variables across different sample sizes and censoring levels. Two real-data applications are presented to illustrate the use of the proposed methodology and to compare it with existing variable selection methods.

Bayesian variable and hazard structure selection in the General Hazard model

TL;DR

This work develops a Bayesian framework for simultaneous variable selection and hazard-structure selection within the General Hazard (GH) model, unifying PH, AFT, and AH as special cases. It introduces two g-prior formulations (likelihood-curvature matching and product) and a hierarchical, multiplicity-adjusted model-space prior to enable principled model uncertainty quantification and consistency. Computation relies on marginal-likelihood approximations and an extended Add-Delete-Swap MCMC sampler that moves within and between hazard structures, with theoretical guarantees for model selection consistency. Simulations show accurate recovery of active variables and hazard structure across sample sizes and censoring levels; real-data analyses (FLC and NKI70) illustrate practical performance and hazard-structure interpretation in high-dimensional, censored settings. The approach provides a flexible, principled tool for hazard-structure learning in survival analysis, with potential extensions to broader distributional-regression contexts.

Abstract

The proportional hazards (PH) and accelerated failure time (AFT) models are the most widely used hazard structures for analysing time-to-event data. When the goal is to identify variables associated with event times, variable selection is typically performed within a single hazard structure, imposing strong assumptions on how covariates affect the hazard function. To allow simultaneous selection of relevant variables and the hazard structure itself, we develop a Bayesian variable selection approach within the general hazard (GH) model, which includes the PH, AFT, and other structures as special cases. We propose two types of g-priors for the regression coefficients that enable tractable computation and show that both lead to consistent model selection. We also introduce a hierarchical prior on the model space that accounts for multiplicity and penalises model complexity. To efficiently explore the GH model space, we extend the Add-Delete-Swap algorithm to jointly sample variable inclusion indicators and hazard structures. Simulation studies show accurate recovery of both the true hazard structure and active variables across different sample sizes and censoring levels. Two real-data applications are presented to illustrate the use of the proposed methodology and to compare it with existing variable selection methods.
Paper Structure (19 sections, 5 theorems, 21 equations, 2 figures, 3 tables)

This paper contains 19 sections, 5 theorems, 21 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Model and Variable Selection for the GH Structure
  3. Hazard structure and variable selection
  4. Priors
  5. Likelihood curvature matching prior for model-specific coefficients
  6. Product prior for model-specific coefficients
  7. Prior on the model space
  8. Computations
  9. Marginal Likelihood Approximations
  10. Model Space Exploration
  11. Asymptotic Theory
  12. Simulation Study
  13. Interpretation of results
  14. Real Data Applications
  15. Serum free light chain data set (FLC)
  16. ...and 4 more sections

Key Result

Proposition 1

The $[\bm{\theta}_{\bm{\gamma}},\bm{\eta}_{\bm{\gamma}}]$ block of the expected Fisher information could be decomposed into where $\nabla^2_{\bm{\theta}_{\bm{\gamma}},\bm{\eta}_{\bm{\gamma}}} \ell({\bm{\Psi}_{\bm{\gamma}}})$ is the Hessian matrix of $\ell({\bm{\Psi}_{\bm{\gamma}}})$ with respect to $[\bm{\theta}_{\bm{\gamma}},\bm{\eta}_{\bm{\gamma}}]$, and $v_k = \exp\left({ e^{-\nu}\tilde{{\bf x

Figures (2)

  • Figure 1: Illustration of the extended ADS sampler. The bold letters represent different moves.
  • Figure 2: Mean sensitivity and specificity of variable selection (VS) and hazard selection (HS) across the $250$ Monte Carlo simulations. (a)(b)(c) Mean VS sensitivity and specificity and HS accuracy under LCM prior; (d)(e)(f) Mean VS sensitivity and specificity and HS accuracy under Product prior.

Theorems & Definitions (5)

  • Proposition 1
  • Proposition 2
  • Corollary 1
  • Proposition 3
  • Corollary 2