Luke R. Lloyd-Jones

The Genetic Architecture of Gene Expression in Peripheral Blood

We analyzed the mRNA levels for 36,778 transcript expression traits (probes) from 2,765 individuals to comprehensively investigate the genetic architecture and degree of missing heritability for gene expression in peripheral blood. We identified 11,204 cis and 3,791 trans independent expression quantitative trait loci (eQTL) by using linear mixed models to perform genome-wide association analyses. Furthermore, using information on both closely and distantly related individuals, heritability was estimated for all expression traits. Of the set of expressed probes (15,966), 10,580 (66%) had an estimated narrow-sense heritability (h2) greater than zero with a mean (median) value of 0.192 (0.142). Across these probes, on average the proportion of genetic variance explained by all eQTL (hCOJO2) was 31% (0.060/0.192), meaning that 69% is missing, with the sentinel SNP of the largest eQTL explaining 87% (0.052/0.060) of the variance attributed to all identified cis- and trans-eQTL. For the same set of probes, the genetic variance attributed to genome-wide common (MAF > 0.01) HapMap 3 SNPs (hg2) accounted for on average 48% (0.093/0.192) of h2. Taken together, the evidence suggests that approximately half the genetic variance for gene expression is not tagged by common SNPs, and of the variance that is tagged by common SNPs, a large proportion can be attributed to identifiable eQTL of large effect, typically in cis. Finally, we present evidence that, compared with a meta-analysis, using individual-level data results in an increase of approximately 50% in power to detect eQTL.

Genotype–covariate interaction effects and the heritability of adult body mass index

Obesity is a worldwide epidemic, with major health and economic costs. Here we estimate heritability for body mass index (BMI) in 172,000 sibling pairs and 150,832 unrelated individuals and explore the contribution of genotype–covariate interaction effects at common SNP loci. We find evidence for genotype–age interaction (likelihood ratio test (LRT) = 73.58, degrees of freedom (df) = 1, P = 4.83 × 10−18), which contributed 8.1% (1.4% s.e.) to BMI variation. Across eight self-reported lifestyle factors, including diet and exercise, we find genotype–environment interaction only for smoking behavior (LRT = 19.70, P = 5.03 × 10−5 and LRT = 30.80, P = 1.42 × 10−8), which contributed 4.0% (0.8% s.e.) to BMI variation. Bayesian association analysis suggests that BMI is highly polygenic, with 75% of the SNP heritability attributable to loci that each explain <0.01% of the phenotypic variance. Our findings imply that substantially larger sample sizes across ages and lifestyles are required to understand the full genetic architecture of BMI.

The Genetic Architecture of Gene Expression in Peripheral Blood (vol 100, pg 228, 2017)

(The American Journal of Human Genetics 100, 228–237; February 2, 2017) In the version of this paper published on January 5, the author Jing Zhao was accidently omitted. The corrected author list appears here and in the published paper. The authors apologize for this error.

Signatures of negative selection in the genetic architecture of human complex traits

We develop a Bayesian mixed linear model that simultaneously estimates single-nucleotide polymorphism (SNP)-based heritability, polygenicity (proportion of SNPs with nonzero effects), and the relationship between SNP effect size and minor allele frequency for complex traits in conventionally unrelated individuals using genome-wide SNP data. We apply the method to 28 complex traits in the UK Biobank data (N = 126,752) and show that on average, 6% of SNPs have nonzero effects, which in total explain 22% of phenotypic variance. We detect significant (P < 0.05/28) signatures of natural selection in the genetic architecture of 23 traits, including reproductive, cardiovascular, and anthropometric traits, as well as educational attainment. The significant estimates of the relationship between effect size and minor allele frequency in complex traits are consistent with a model of negative (or purifying) selection, as confirmed by forward simulation. We conclude that negative selection acts pervasively on the genetic variants associated with human complex traits.BayesS estimates SNP-based heritability, polygenicity, and the relationship between effect size and minor allele frequency using genome-wide SNP data. Applying BayesS to UK Biobank data identifies signatures of natural selection for 23 complex traits.

A universal approximation theorem for mixture-of-experts models

The mixture-of-experts (MoE) model is a popular neural network architecture for nonlinear regression and classification. The class of MoE mean functions is known to be uniformly convergent to any unknown target function, assuming that the target function is from a Sobolev space that is sufficiently differentiable and that the domain of estimation is a compact unit hypercube. We provide an alternative result, which shows that the class of MoE mean functions is dense in the class of all continuous functions over arbitrary compact domains of estimation. Our result can be viewed as a universal approximation theorem for MoE models. The theorem we present allows MoE users to be confident in applying such models for estimation when data arise from nonlinear and nondifferentiable generative processes.

Integrative analysis of omics summary data reveals putative mechanisms underlying complex traits

The identification of genes and regulatory elements underlying the associations discovered by GWAS is essential to understanding the aetiology of complex traits (including diseases). Here, we demonstrate an analytical paradigm of prioritizing genes and regulatory elements at GWAS loci for follow-up functional studies. We perform an integrative analysis that uses summary-level SNP data from multi-omics studies to detect DNA methylation (DNAm) sites associated with gene expression and phenotype through shared genetic effects (i.e., pleiotropy). We identify pleiotropic associations between 7858 DNAm sites and 2733 genes. These DNAm sites are enriched in enhancers and promoters, and >40% of them are mapped to distal genes. Further pleiotropic association analyses, which link both the methylome and transcriptome to 12 complex traits, identify 149 DNAm sites and 66 genes, indicating a plausible mechanism whereby the effect of a genetic variant on phenotype is mediated by genetic regulation of transcription through DNAm.The identification of the causal gene at a GWAS locus remains to be a challenging task. Here, using the SMR & HEIDI method to integrate GWAS, eQTL and mQTL data, Wu et al. map DNA methylation sites to the transcriptome and thereby prioritize functionally relevant genes for 12 human complex traits.

Transformation of Summary Statistics from Linear Mixed Model Association on All-or-None Traits to Odds Ratio

Genome-wide association studies (GWAS) have identified thousands of loci that are robustly associated with complex diseases. The use of linear mixed model (LMM) methodology for GWAS is becoming more prevalent due to its ability to control for population structure and cryptic relatedness and to increase power. The odds ratio (OR) is a common measure of the association of a disease with an exposure (e.g., a genetic variant) and is readably available from logistic regression. However, when the LMM is applied to all-or-none traits it provides estimates of genetic effects on the observed 0–1 scale, a different scale to that in logistic regression. This limits the comparability of results across studies, for example in a meta-analysis, and makes the interpretation of the magnitude of an effect from an LMM GWAS difficult. In this study, we derived transformations from the genetic effects estimated under the LMM to the OR that only rely on summary statistics. To test the proposed transformations, we used real genotypes from two large, publicly available data sets to simulate all-or-none phenotypes for a set of scenarios that differ in underlying model, disease prevalence, and heritability. Furthermore, we applied these transformations to GWAS summary statistics for type 2 diabetes generated from 108,042 individuals in the UK Biobank. In both simulation and real-data application, we observed very high concordance between the transformed OR from the LMM and either the simulated truth or estimates from logistic regression. The transformations derived and validated in this study improve the comparability of results from prospective and already performed LMM GWAS on complex diseases by providing a reliable transformation to a common comparative scale for the genetic effects.

Inference on the Genetic Basis of Eye and Skin Colour in an Admixed Population via Bayesian Linear Mixed Models.

Genetic association studies in admixed populations are underrepresented in the genomics literature, with a key concern for researchers being the adequate control of spurious associations due to population structure. Linear mixed models (LMMs) are well suited for genome-wide association studies (GWAS) because they account for both population stratification and cryptic relatedness and achieve increased statistical power by jointly modeling all genotyped markers. Additionally, Bayesian LMMs allow for more flexible assumptions about the underlying distribution of genetic effects, and can concurrently estimate the proportion of phenotypic variance explained by genetic markers. Using three recently published Bayesian LMMs, Bayes R, BSLMM, and BOLT-LMM, we investigate an existing data set on eye (n = 625) and skin (n = 684) color from Cape Verde, an island nation off West Africa that is home to individuals with a broad range of phenotypic values for eye and skin color due to the mix of West African and European ancestry. We use simulations to demonstrate the utility of Bayesian LMMs for mapping loci and studying the genetic architecture of quantitative traits in admixed populations. The Bayesian LMMs provide evidence for two new pigmentation loci: one for eye color (AHRR) and one for skin color (DDB1).

Autosomal genetic control of human gene expression does not differ across the sexes

BackgroundDespite their nearly identical genomes, males and females differ in risk, incidence, prevalence, severity and age-at-onset of many diseases. Sexual dimorphism is also seen in human autosomal gene expression, and has largely been explored by examining the contribution of genotype-by-sex interactions to variation in gene expression.ResultsIn this study, we use data from a mixture of pedigree and unrelated individuals with verified European ancestry to investigate the sex-specific genetic architecture of gene expression measured in whole blood across n=1048 males and n=1005 females by treating gene expression intensities in the sexes as two distinct traits and estimating the genetic correlation (rG) between them. These correlations measure the similarity of the combined additive genetic effects of all single-nucleotide polymorphisms across the autosomal chromosomes, and thus the level of common genetic control of gene expression across the sexes. Genetic correlations are estimated across the sexes for the expression levels of 12,528 autosomal gene expression probes using bivariate GREML, and tested for differences in autosomal genetic control of gene expression across the sexes. Overall, no deviation of the distribution of test statistics is observed from that expected under the null hypothesis of a common autosomal genetic architecture for gene expression across the sexes.ConclusionsThese results suggest that males and females share the same common genetic control of gene expression.

Constraints on eQTL Fine Mapping in the Presence of Multisite Local Regulation of Gene Expression

Expression quantitative trait locus (eQTL) detection has emerged as an important tool for unraveling of the relationship between genetic risk factors and disease or clinical phenotypes. Most studies use single marker linear regression to discover primary signals, followed by sequential conditional modeling to detect secondary genetic variants affecting gene expression. However, this approach assumes that functional variants are sparsely distributed and that close linkage between them has little impact on estimation of their precise location and the magnitude of effects. We describe a series of simulation studies designed to evaluate the impact of linkage disequilibrium (LD) on the fine mapping of causal variants with typical eQTL effect sizes. In the presence of multisite regulation, even though between 80 and 90% of modeled eSNPs associate with normally distributed traits, up to 10% of all secondary signals could be statistical artifacts, and at least 5% but up to one-quarter of credible intervals of SNPs within r2 > 0.8 of the peak may not even include a causal site. The Bayesian methods eCAVIAR and DAP (Deterministic Approximation of Posteriors) provide only modest improvement in resolution. Given the strong empirical evidence that gene expression is commonly regulated by more than one variant, we conclude that the fine mapping of causal variants needs to be adjusted for multisite influences, as conditional estimates can be highly biased by interference among linked sites, but ultimately experimental verification of individual effects is needed. Presumably similar conclusions apply not just to eQTL mapping, but to multisite influences on fine mapping of most types of quantitative trait.