High-Dimensional Variable Selection for Multivariate and Survival Data with Applications to Brain Imaging and Genetic Association Studies.

Abstract

In this dissertation, we aim to solve important high-dimensional variable selection problems with either structured multivariate or discrete survival outcomes, with applications to brain imaging and genetic association studies.

First, we introduce the multivariate sparse group lasso for variable selection in multivariate multiple regressions with both grouped covariates and responses. We propose an efficient mixed coordinate descent algorithm for the penalized least square estimation. The method is able to effectively remove unimportant groups and unimportant individual coefficients within important groups, particularly for large p small n problems. It is flexible in handling various complex group structures. The finite sample oracle properties of the proposed method are established and the method is applied to an eQTL association study.

Secondly, we propose a multi-stage method for conducting structured brain-wide-genome-wide association studies via the multivariate sparse group lasso. It is more efficient in selecting the important signals and can avoid large number of multiple comparisons while effectively control the false discoveries by using the stability selection. We apply the proposed method to a brain-wide GWAS using ADNI PET imaging and genotype data. The proposed method considers the anatomic brain structure and the gene structure in the human genome. We confirm several previously reported and also find some novel genes that are either associated with brain glucose metabolism or with their associations significantly modified by Alzheimer's disease status.

Thirdly, we propose a full-likelihood based variable selection method for a discrete-time and cure-rate survival model with high-dimensional time-varying predictors. The method is motivated by the ADNI longitudinal brain imaging study to predict MCI-to-AD conversions. The conversion time was only observed on discrete time intervals and the studied sample consists of a mixture of a non-cure group and a cure group. The proposed method uses the full likelihood to jointly model the cure rate and the non-cure survival. Variable selection is carried out using the elastic net penalties. The method can efficiently and effectively select the important predictors in both models. We evaluate the method through extensive simulations and apply it to the ADNI PET brain imaging data to predict MCI-to-AD conversions.