Variable Selection in Log-linear Birnbaum-Saunders Regression Models for High-dimensional Survival Data via the Elastic-Net and Stochastic EM

Abstract

Birnbaum-Saunders (BS) distribution is broadly used to model failure times with reliability and survival data. In this thesis, we propose a simultaneous parameter estimation and variable selection procedure in a log-linear BS regression model for high-dimensional survival data. We introduce a path-wise algorithm via cyclical coordinate descent method based on the elastic-net penalty. To deal with censored survival data, we iteratively run a combination of Stochastic Expectation Maximization algorithm (SEM) and variable selection procedure to generate pseudo-complete data and select variables until convergence. Treating pseudo-complete data as uncensored data via SEM simplifies computation and makes it possible to incorporate iterative least squares for parameter estimation and variable selection simultaneously. We demonstrate the efficacy of our method using simulated and real data sets.