Bayesian variable selection in high dimensional censored regression models

The development in technologies drives research in variable selection in various fields, especially in bio-medical areas where high-dimensional gene expression data are present. Various approaches have been developed for associating patients' data with patients' survival times, however, not many can deal with high-dimensional data while being able to handle censoring. We focus on developing scalable algorithms for variable selection problem in a high-dimensional censored regression model that can handle gene expression data with hundreds of thousands of features. We propose an EM-like iterative algorithm for accelerated failure models (AFT models) with censored survival data under no distributional assumption. Unlike existing methods, the proposed method is able to handle high-dimensional variable selection with less stringent assumption which adopts the scalable feature from Bayesian framework with a continuous spike-and-slab prior specification. We show that the method can be further extended to bivariate survival data by assuming independence between the two events such that the connections between events are carried in the join prior distribution of the unknown coefficient matrix. Lastly, we work with a relatively new regression model, named Restricted Mean Survival Times (RMST) regression models, targeting at variable selection problem when the proportional hazards assumption is invalid and prediction problems for RMST. With a spike-and-slab Lasso prior, we transform the Bayesian variable selection framework of the RMST regression model to a penalized logistic regression problem with a proper choice of the link function. The proposed work can be treated as a more generalized variable selection method comparing to either Cox model or AFT model when the true model is misspecified.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Yin, Wenjing

Contributors dc:contributor

• Liang, Feng
• Narisetty, Naveen Naidu
• Zhao, Sihai Dave
• Douglas, Jeffrey A

• Bayesian Variable Selection
• Survival Analysis
• Censored Regression Models
• Spike-and-slab Priors

Statement dc:rights

• Copyright 2020 Wenjing Yin

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/109509

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/109509