Linear models in genomic studies

Abstract

With the help of molecular markers, genome-wide association studies (GWAS) are conducted to identify genes associated with diseases. Association mapping uses unrelated individuals from the same population that has undergone recombination in many generations since the inception of the mutant gene and is the basis for detection of causal genes. The data that forms the basis for computational detection of causal genes are of three kinds, phenotypic values (single trait or several traits), genotypes of hundreds of thousands of SNP markers, and data on gene expression, a sort of intermediate phenotypes that are used to associate genes with disease phenotypes. Most of the studies except a few, however, consider single trait at a time and take either phenotypes and marker genotypes only or considers phenotypes, genotypes and gene expression all together. In actual situations, on the other hand, the problem is multivariate since many complex disease syndromes consist of a large number of highly related clinical or molecular phenotypes. For instance, asthma is influenced by as many as 53 clinical traits that can be represented as a quantitative trait network (QTN). The methodological issue is then to conduct association analysis that takes into account jointly all the relevant traits instead of a single trait only. Linear models in which a dependent variable (expression of a disease trait) is related to a set of independent variables (for instance, SNPs) provide with a very versatile tool that can be used for the association analysis both for a single as well as multiple traits. To this end, we systematically discuss the sparse regression methodology of Ridge Regression, Lasso, and GFLasso with illustrations from published literature.