Variable selection for generalized linear mixed models and non-Gaussian Genome-wide associated study data

Abstract

Genome-wide associated study (GWAS) aims to identify associated single nucleotide polymorphisms (SNP) for phenotypes. SNP has the characteristic that the number of SNPs is from hundred of thousands to millions. If p is the number of SNPs and n is the sample size, it is a p>>n variable selection problem. To solve this p>>n problem, the common method for GWAS is single marker analysis (SMA). However, since SNPs are highly correlated, SMA identifies true causal SNPs with high false discovery rate. In addition, SMA does not consider interaction between SNPs. In this dissertation, we propose novel Bayesian variable selection methods BG2 and IBG3 for non-Gaussian GWAS data. To solve ultra-high dimension problem and highly correlated SNPs problem, BG2 and IBG3 have two steps: screening step and fine-mapping step. In the screening step, BG2 and IBG3, like SMA method, only have one SNP in one model and screen to obtain a subset of most associated SNPs. In the fine-mapping step, BG2 and IBG3 consider all possible combinations of screened candidate SNPs to find the best model. Fine-mapping step helps to reduce false positives. In addition, IBG3 iterates these two steps to detect more SNPs with small effect size. In simulation studies, we compare our methods with SMA methods and fine-mapping methods. We also compare our methods with different priors for variables, including nonlocal prior, unit information prior, Zellner-g prior, and Zellner-Siow prior. Our methods are applied to substance use disorder (alcohol comsumption and cocaine dependence), human health (breast cancer), and plant science (the number of root-like structure).