Integrative analysis of genetical genomics data incorporating network structures

Abstract

In a living organism, tens of thousands of genes are expressed and interact with each other to achieve necessary cellular functions. Gene regulatory networks contain information on regulatory mechanisms and the functions of gene expressions. Thus, incorporating network structures, discerned either through biological experiments or statistical estimations, could potentially increase the selection and estimation accuracy of genes associated with a phenotype of interest. Here, we considered a gene selection problem using gene expression data and the graphical structures found in gene networks. Because gene expression measurements are intermediate phenotypes between a trait and its associated genes, we adopted an instrumental variable regression approach. We treated genetic variants as instrumental variables to address the endogeneity issue. We proposed a two-step estimation procedure. In the first step, we applied the LASSO algorithm to estimate the effects of genetic variants on gene expression measurements. In the second step, the projected expression measurements obtained from the first step were treated as input variables. A graph-constrained regularization method was adopted to improve the efficiency of gene selection and estimation. We theoretically showed the selection consistency of the estimation method and derived the $L_{\infty }$ bound of the estimates. Simulation and real data analyses were conducted to demonstrate the effectiveness of our method and to compare it with its counterparts.

Keywords: gene network; gene selection; graph-constrained penalization; instrumental variable regression; variable selection.