Efficient estimation of SNP heritability using Gaussian predictive process in large scale cohort studies

Abstract

With the advent of high throughput genetic data, there have been attempts to estimate heritability from genome-wide SNP data on a cohort of distantly related individuals using linear mixed model (LMM). Fitting such an LMM in a large scale cohort study, however, is tremendously challenging due to its high dimensional linear algebraic operations. In this paper, we propose a new method named PredLMM approximating the aforementioned LMM motivated by the concepts of genetic coalescence and Gaussian predictive process. PredLMM has substantially better computational complexity than most of the existing LMM based methods and thus, provides a fast alternative for estimating heritability in large scale cohort studies. Theoretically, we show that under a model of genetic coalescence, the limiting form of our approximation is the celebrated predictive process approximation of large Gaussian process likelihoods that has well-established accuracy standards. We illustrate our approach with extensive simulation studies and use it to estimate the heritability of multiple quantitative traits from the UK Biobank cohort.

SMASH: Scalable Method for Analyzing Spatial Heterogeneity of genes in spatial transcriptomics data

“…SpatialDE uses a Gaussian process (GP)-based spatial regression model [43, 65]. It assumes that at every location s ∈ S ⊆ ℝ 3 , the expression of the k -th gene is a process y k ( s ) of the following form, where w k ( s ) is a zero-centered GP with variance and covariance function C ( s, s ′) for s ′ ∈ 𝒮.…”

“…SpatialDE uses a Gaussian process (GP)-based spatial regression model [43,65]. It assumes that at every location s ∈ S ⊆ R 3 , the expression of the k-th gene is a process y k (s) of the following form,…”

DenVar: density-based variation analysis of multiplex imaging data

“…Test based on linear mixed model : The distance matrix can be transformed into a similarity matrix ( Vert et al , 2004 ) as, . When Y is a continuous outcome, G k can be incorporated in a linear mixed model framework, particularly popular in the context of heritability estimation ( Hoffman, 2013 ; Seal et al , 2022 ), as, where is the vector of fixed effects, is the vector of random effects following MVN( ) and ϵ is an error vector following MVN( 0 , The null hypothesis: can be tested using a LRT ( Crainiceanu and Ruppert, 2004 ). Note that, such a linear mixed model setup has been shown to be equivalent to a kernel machine regression framework by Liu et al (2008) .…”

“…The matrix of distances between the subjects can then be used to classify them into meaningful groups using hierarchical clustering ( Murtagh and Legendre, 2014 ), and the group-labels can be tested for association with clinical outcomes in a linear regression framework. Alternatively, the distance matrix can also be used directly in a linear mixed model ( Hoffman, 2013 ; Seal et al , 2022 ) or equivalently, a kernel machine regression framework ( Jensen et al , 2019 ; Liu et al , 2008 ) to test for association with clinical outcomes.…”

Comparing heritability estimators under alternative structures of linkage disequilibrium

“…The random-SNP-effect models assume an infinitesimal model for the SNP effects and use of genome-wide SNP data on distantly related individuals ( Haseman and Elston 1972 ; Yang et al 2010 , 2011 , 2012 ; Lee et al 2011 , 2012 ; Speed et al 2012 ; Bulik-Sullivan et al 2015 ; Seal et al 2022 ) to estimate the pairwise genetic relatedness between sampled individuals. These approaches assume that each causal SNP makes a random contribution to the phenotype, and these contributions are correlated between individuals who have similar genotypes.…”