Variational Bayes for high-dimensional proportional hazards models with applications to gene expression variable selection

The development of high-throughput sequencing technologies has led to the production of largescale molecular profiling data, allowing us to gain insights into underlying biological processes (Wid lak, 2013). One such technology is microarray sequencing, in which mRNA counts are used to describe gene expression. Such data, known as transcriptomics, are widely used in the biomedical domain and when analyzed alongside survival times have provided extraordinary opportunities for biomarker characterization and prognostic modelling (Bøvelstad et al., 2007; Lloyd et al., 2015; Lightbody et al., 2019; Lu et al., 2021). However, profiling data is often high-dimensional, which introduces several statistical challenges including: (i) variable selection, (ii) effect estimation of the features, and (iii) scalable computation. The task of variable selection is particularly important, as few genes typically have an effect on the outcome. Motivated by clinical applicability, we propose a state-of-the-art scalable (variational) Bayesian variable selection method for the proportional hazards models. In recent years, several methods have been proposed to analyze sparse high-dimensional data, with one of the most popular being the LASSO (Tibshirani, 1996). As biomedical studies are often concerned with clinical phenotypes, such as time to disease recurrence or overall survival time, these methods have been adapted to support survival analysis (Antoniadis et al., 2010; Witten and Tibshirani, 2010). For instance, the LASSO, ridge and elastic-net penalties have all been extended to the proportional hazards model (Tibshirani, 1997; Gui and Li, 2005; Zou and Hastie, 2005; Simon et al., 2011).