A kernel machine method for detecting effects of interaction between multidimensional variable sets: An imaging genetics application

Abstract

Measurements derived from neuroimaging data can serve as markers of disease and/or healthy development, are largely heritable, and have been increasingly utilized as (intermediate) phenotypes in genetic association studies. To date, imaging genetic studies have mostly focused on discovering isolated genetic effects, typically ignoring potential interactions with non-genetic variables such as disease risk factors, environmental exposures, and epigenetic markers. However, identifying significant interaction effects is critical for revealing the true relationship between genetic and phenotypic variables, and shedding light on disease mechanisms. In this paper, we present a general kernel machine based method for detecting effects of interaction between multidimensional variable sets. This method can model the joint and epistatic effect of a collection of single nucleotide polymorphisms (SNPs), accommodate multiple factors that potentially moderate genetic influences, and test for nonlinear interactions between sets of variables in a flexible framework. As a demonstration of application, we applied the method to data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to detect the effects of the interactions between candidate Alzheimer's disease (AD) risk genes and a collection of cardiovascular disease (CVD) risk factors, on hippocampal volume measurements derived from structural brain magnetic resonance imaging (MRI) scans. Our method identified that two genes, CR1 and EPHA1, demonstrate significant interactions with CVD risk factors on hippocampal volume, suggesting that CR1 and EPHA1 may play a role in influencing AD-related neurodegeneration in the presence of CVD risks.

Predictive Modeling of Anatomy with Genetic and Clinical Data

“…We seek the maximum likelihood estimates of parameters β̄ and $\mathrm{bold-italic\theta }=false({\tau }_G^2,{\tau }_C^2,{\tau }_I^2,{\sigma }^{2}false)$ by adapting standard procedures for LMMs [5,8]. As standard LMM solutions become computationally expensive for thousands of observations, we take advantage of the fact that while the entire genetic and the image phenotype data is large, the use of kernels on baseline data reduces the model size substantially.…”

“…Under the LSKM interpretation, the terms h (·) are estimated by minimizing a penalized squared-error loss function, which leads to the following solution [5,7,8,16]: $$hfalse(z_{i}false)=\sum _{j=1}^N{\alpha }_{j}Kfalse({\mathit{z}}_i,{\mathit{z}}_{j}false)\text{ or }\mathrm{bold-italich}={\mathit{\alpha }}^T\mathrm{bold-italicK}$$ for some vector α . Combining with the definitions of the LMM, we estimate coefficients vectors α G , α C and α I from a linear system of equations that involves our estimates of β̂ and θ.…”

FGWAS: Functional genome wide association analysis

“…Moreover, these neurological disorders often are regarded as the end result of abnormal trajectories of brain development, which may be caused by the additive and interactive effects of perhaps hundreds of risk genes and multiple environmental risk factors, each with small individual effects. A promising approach to overcome such difficulties is to discover genetic factors associated with brain changes that may lead to key insights in neurological disorders and our understanding of the origins of these conditions (Hibar et al, 2011; Chen et al, 2012; Ge et al, 2012; Thompson et al, 2013; Medland et al, 2014; Ge et al, 2015a,b; Hibar et al, 2015; Lin et al, 2014a; Huang et al, 2015; Tao et al, 2017). Such efforts may inspire new approaches to urgently needed preventions, diagnoses, and treatments.…”

A Set-Based Mixed Effect Model for Gene-Environment Interaction and Its Application to Neuroimaging Phenotypes

“…For example, genetics may modulate the effects of various risk factors on the manifestation of a disease, causing varying severities of the disease across individuals even though they may be exposed to the same risk factors. Recently, G×E has been incorporated into burden tests (Jiao et al, 2013) and variance component tests (Lin et al, 2013, 2016; Ge et al, 2015). However, as mentioned earlier, burden tests and variance component tests make assumptions on the underlying nature of the effects of individual genetic variants on disease, and these tests become less powerful when the assumptions do not hold.…”