Variational Bayes for high-dimensional proportional hazards models with applications within gene expression

Abstract

Motivation Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing maximum a posteriori estimates, or quantify the uncertainty at high (unscalable) computational expense. Results We bridge this gap and develop an interpretable and scalable Bayesian proportional hazards model for prediction and variable selection, referred to as SVB. Our method, based on a mean-field variational approximation, overcomes the high computational cost of MCMC whilst retaining useful features, providing a posterior distribution for the parameters and offering a natural mechanism for variable selection via posterior inclusion probabilities. The performance of our proposed method is assessed via extensive simulations and compared against other state-of-the-art Bayesian variable selection methods, demonstrating comparable or better performance. Finally, we demonstrate how the proposed method can be used for variable selection on two transcriptomic datasets with censored survival outcomes, and how the uncertainty quantification offered by our method can be used to provide an interpretable assessment of patient risk. Availability and implementation our method has been implemented as a freely available R package survival.svb (https://github.com/mkomod/survival.svb). Supplementary information Supplementary materials are available at Bioinformatics online.

Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models

“…Ray et al [ 39 ] describe a scalable mean-field variational family to approximate the posterior distribution of BVS in linear regression and extended this VB approximation to the logistic regression model in [ 40 ]. Komodromos et al [ 41 ] apply the Sparse Variational Bayes (SVB) method to approximate the posterior of proportional hazards models with partial likelihood. Other works develop a sampling strategy based on simulating piece-wise deterministic Markov processes (PDMPs) [ 42 , 43 ], which directly target the posterior distribution obtained from a spike-and-slab prior.…”