Bayesian variable selection in high dimensional censored regression models

Yin, Wenjing

Permalink

https://hdl.handle.net/2142/109509 Copy

Description

Title

Bayesian variable selection in high dimensional censored regression models

Author(s)

Yin, Wenjing

Issue Date

2020-11-30

Director of Research (if dissertation) or Advisor (if thesis)

• Liang, Feng
• Narisetty, Naveen Naidu

Doctoral Committee Chair(s)

• Liang, Feng
• Narisetty, Naveen Naidu

Committee Member(s)

• Zhao, Sihai Dave
• Douglas, Jeffrey A

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2020-12

Type of Resource

Thesis

Permalink

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

Copyright and License Information

Copyright 2020 Wenjing Yin

Owning Collections