M.S. (Master of Science)
Department of Statistics and Actuarial Science
This thesis examines the use of Bayesian LASSO regression for survival data to estimate the survival function and to select significant covariates simultaneously. We consider survival times of patients with adenocarcinoma lung cancer. The survival and genetic data are available in the Cancer Genome Atlas (TCGA) Research Network. As a pilot study, within chromosome 5, we apply Bayesian LASSO regression to explore genetic markers that may help to identify crucial genes to determine survival times of patients. Using Gibbs sampling we can obtain Markov Chain Monte Carlo samples for regression coefficients and model variance as well as LASSO penalty from their full conditional distribution. However,under the Cox Proportional Hazard model sampling from the full conditional distribution for the Bayesian LASSO regression coefficients is computationally difficult. Therefore, we use latent variables for survival likelihood and perform Bayesian inference. We compare the Bayesian LASSO with a common variable selection method and a Frequentist LASSO for the estimation of the survival function and identified critical covariates.
Neely, Justin P., "Bayesian LASSO Survival Analysis" (2019). Graduate Research Theses & Dissertations. 7487.
Northern Illinois University
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