Kernel-Based Measure of Variable Importance for Genetic Association Studies

Abstract

The identification of genetic variants that are associated with disease risk is an important goal of genetic association studies. Standard approaches perform univariate analysis where each genetic variant, usually Single Nucleotide Polymorphisms (SNPs), is tested for association with disease status. Though many genetic variants have been identified and validated so far using this univariate approach, for most complex diseases a large part of their genetic component is still unknown, the so called missing heritability. We propose a Kernel-based measure of variable importance (KVI) that provides the contribution of a SNP, or a group of SNPs, to the joint genetic effect of a set of genetic variants. KVI can be used for ranking genetic markers individually, sets of markers that form blocks of linkage disequilibrium or sets of genetic variants that lie in a gene or a genetic pathway. We prove that, unlike the univariate analysis, KVI captures the relationship with other genetic variants in the analysis, even when measured at the individual level for each genetic variable separately. This is specially relevant and powerful for detecting genetic interactions. We illustrate the results with data from an Alzheimer's disease study and show through simulations that the rankings based on KVI improve those rankings based on two measures of importance provided by the Random Forest. We also prove with a simulation study that KVI is very powerful for detecting genetic interactions.

Keywords: Kernel methods; genetic association studies; variable importance.