Estimation of Total Effect of Selected Variables on an Outcome in Presence of Numerous Weak Effects

Estimation of the total effect of a set of selected variables in high-dimensional linear model under sparsity assumption is complex due to the selection bias. This task is even more chal- lenging when the sparsity assumption is violated and individual variable effects are weak, which is common in genomic studies. Without variable selection, Yang et al have proposed an effec- tive approach to estimating the total effects of single-nucleotide polymorphisms (SNPs) on a quantitative trait when effects of SNPs are numerous and weak. In the thesis, we extended Yang et al’s approach to estimating the total effect of a set of selected variables in a linear model. The extension allows us to effectively reduce the scope of search for the causal SNPs for a quantitative trait in presence of numerous weak effects. We also modify our proposed approach to make it suitable for correlated SNPs. We perform extensive simulation studies to demonstrate the effectiveness of the proposed approach in comparison to alternative approaches to this problem. The method is applied to detecting the expression quantitative trait locus (eQTL) in gene-expression study of human brain tissues.