Bayesian linear survival analysis with shrinkage priors in Stan

Introduction

This repository includes some Stan codes for survival analysis with shrinkage priors (Gaussian, Laplace, and horseshoe) and Weibull observation model. See the reference for the model description (note that the priors on a_c, b_c, a_s, and b_s have been changed to half-normal in the codes). The codes have been rewritten for Stan 2.4.0 (reference used Stan 2.2).

Contents

• example.R: R-script which generates some simulated data and fits the models.
• wei_hs_joint.stan: Joint model with horseshoe prior on candidate biomarkers.
• wei_lap_joint.stan: Joint model with Laplace prior on candidate biomarkers.
• wei_gau_joint.stan: Joint model with Gaussian prior on candidate biomarkers.
• wei_bg_joint.stan: Joint model with only established risk factors.
• wei_hs.stan: Single-group model with horseshoe prior on candidate biomarkers.
• wei_lap.stan: Single-group model with Laplace prior on candidate biomarkers.
• wei_gau.stan: Single-group model with Gaussian prior on candidate biomarkers.
• wei_bg.stan: Single-group model with only established risk factors.

Updates

2015-12-18: Change the Cauchy distributions defining local shrinkage parameters in the horseshoe prior to t-distributions that allow setting the degress of freedom nu (Cauchy is nu = 1). nu > 1 can be computationally more stable (see Piironen and Vehtari, 2015).

Reference

Peltola, Havulinna, Salomaa, Vehtari. Hierarchical Bayesian Survival Analysis and Projective Covariate Selection in Cardiovascular Event Risk Prediction. In Proceedings of the Eleventh UAI Bayesian Modeling Applications Workshop, CEUR Workshop Proceedings, Vol-1218, 79-88 (pdf)

Contact

E-mail: tomi.peltola@aalto.fi