Category Archives: Quantitative genetics

Our paper: Integrated analysis of variants and pathways in genome-wide association studies using polygenic models of disease

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[This author post is by Peter Carbonetto on Integrated analysis of variants and pathways in genome-wide association studies using polygenic models of disease, available from the arXiv here.]

I expect that most readers of this blog appreciate the impact that genome-wide association studies have had on our understanding of many common diseases. Still, I think it is important to reiterate a major appeal of genome-wide association studies: the analysis is conceptually straightforward to understand, even for people who have never had to suffer through a course on statistics or epidemiology. To find links between genetic loci and disease, the analysis consists of systematically searching across the genome for variants that show statistically significant correlation with susceptibility to disease. These correlations signal the presence of nearby genes—or perhaps DNA elements that regulate other genes—that are risk factors for disease.

Many readers of this blog will also appreciate, due to the multifactorial nature of most common diseases, the difficulty of establishing compelling evidence for disease-variant correlations. Hence the search for more effective data-driven strategies for discovering genetic factors underlying common diseases.

One strategy is to assess evidence for the accumulation, or “enrichment,” of disease-conferring mutations within known biological pathways. The intuition is that identifying the accumulation of small genetic effects acting in a common pathway is easier than mapping the individual genes within the pathway that contribute to disease susceptibility.

We asked whether identifying these enriched pathways can also give us useful feedback about the individual gene variants associated with disease. To answer this question, we developed a statistical method that adjusts the support for disease-variant associations to reflect enrichment of associations in a pathway. Our approach was to introduce an enrichment parameter that quantifies the increase in the probability that each variant in the pathway is associated with disease risk.

Is this a valid approach? To investigate, we applied our approach to data from the Wellcome Trust Crohn’s disease study from 2007. First, we identified a broad class of cytokine signaling genes that were enriched for genetic associations with Crohn’s disease. Next, by prioritizing variants in this pathway, we discovered candidates for association—including the STAT3 gene, the IBD5 locus, and the MHC class II genes—that were not identified in conventional analyses of the same data. These results help validate our approach, as these genetic associations have been independently confirmed in other studies and meta-analyses with much larger combined samples.

Several other important lessons emerged from our case study:

1. Interrogate as many pathways as possible. Because we collected over 3000 candidate pathways from several sources (Reactome, KEGG, BioCarta, BioCyc, etc.), many of the pathways highlighted in previous analyses of the same data were eclipsed by much stronger enrichment signals in our analysis.

2. Assess evidence for combinations of enriched pathways. Some pathways become interesting only after assessing enrichment of the pathway in combination with another pathway.

3. Account for the heterogeneity of effect sizes in Crohn’s disease. One of the assumptions we made in our analysis, mainly out of convenience, was that the additive effects on disease risk are normally distributed. While this assumption simplified this analysis, we suspect that a normal distribution does not adequately capture the smaller effect sizes in pathways, leading to a loss of power to detect enriched pathways.

At conferences, and around the lab, I’ve heard many complaints about pathway analysis (or gene set enrichment analysis) for genome-wide association studies. One complaint is that the results are difficult to interpret. Another common complaint is that the findings are sensitive to arbitrary significance thresholds. While we didn’t devote much space in the paper to a discussion of these issues, we believe that our approach offers a coherent solution to many of these problems.

Ultimately, we would like other researchers to use our methods to analyze data from their own genome-wide association studies. We tried to make our paper as accessible as possible, especially to biologists that are not well-acquainted with Bayesian approaches, by carefully explaining how to interpret the Bayes factors and posterior statistics used in the analysis. We are working on releasing the full source code (in R and MATLAB) for all our methods, and accompanying documentation.

Peter Carbonetto

Our paper: A genetic variant near olfactory receptor genes influences cilantro preference

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For our next guest post Nick Eriksson (@nkeriks) writes about his ArXived paper with other 23andMe folks: A genetic variant near olfactory receptor genes influences cilantro preference ArXived here

First a little background about research at 23andMe. We have over 150,000 genotyped customers, a large proportion of whom answer surveys online. We run GWAS on pretty much everything trait you can think of (at least everything that is easily reported and possibly related to genetics). Around 2010, we started to ask a couple of questions about cilantro: if people like it, and if they perceive a soapy taste to it.

Fast forward a couple of years, and we have tens of thousands of people answering these questions. We start to see an interesting finding: one SNP significantly associated with both cilantro dislike and perceiving a soapy taste. Best of all, it was in a cluster of olfactory receptor genes.

The sense of smell is pretty cool. Humans have hundreds of olfactory receptor genes that encode G protein-coupled receptors. We perceive smells due to the binding of specific chemicals (“odorants”) to these receptors. There are maybe 1000 total olfactory receptors in various mammalian genomes, but it’s not totally clear which are pseudogenes. There has probably been some loss of these genes in humans as our sense of smell has become less critical. These genes appear in clusters in the genome, which makes it pretty hard for GWAS to pick out a specific gene. For example, in the first 23andMe paper, we identified a variant in a different cluster of olfactory receptors that affected whether you perceive a certain smell in your urine after eating asparagus. However, we still don’t know what the true functional variant in that region is.

Luckily, one of the olfactory receptors near our cilantro SNP turns out to be very well studied. It is known to bind to about 30 different aldehydes, including some of the chemicals that give cilantro its famous odor. So at the core this is a pretty simple paper. We found one significant association; it has as good of a functional story as you’ll see in nearly any GWAS. There are a couple of complications, however. First, we studied two related traits: soapy taste detection and cilantro dislike. They’re relatively correlated (r^2 about 0.33), and they are both associated with the same SNP. It looks like the association is stronger with soapy taste detection (and this trait seemed like it would be less influenced by environment than cilantro dislike), so we used soapy taste as the main phenotype.

The second complicated story is our heritability calculation. We saw about 9% heritability (tagged by the SNPs on our array). However, the confidence interval was pretty huge (-3% to 21%). Roughly, you could think of things falling into three heritability classes: high (height, celiac, type 1 diabetes), medium (type 2 diabetes, Crohn’s) and low (lung, colorectal, and maybe breast cancer). I think that’s about as accurate as the current heritability numbers can get. Our calculation puts cilantro soapy-taste detection into the low heritability group. There is the complication that this is only additive heritability tagged by common SNPs, so this phenotype could actually be very heritable, with most of the action coming from rare variants. But in my opinion, that’s doubtful.

Coming out of mathematics, I’ve always posted my papers to preprint servers. Luckily, this fits in well with 23andMe’s mission of making research faster, more participatory, and more fun. We’ve published all our papers so far in open access journals and have posted a couple of them to Nature Preceedings (before it shut down). I also write everything in LaTeX, so posting to the arXiv is a refreshing change (as compared to most biology journals where you have to undergo a conversion from LaTeX to word that makes everything look terrible (a particular pet peeve of mine with PLOS journals, which I otherwise love)).

I’m very curious to see how posting to the arXiv will affect publicity. Our papers tend to get a fair bit of press. However, I don’t know how the press will deal with one opportunity to report on the paper now (when the results are fresh and novel, but published on a site reporters will mostly not know about) and then another opportunity when the paper gets “blessed” via peer review. Because most of our papers are relatively straightforward GWAS (and we have a lot of coauthors here who have read and written a huge number of such papers), I think getting the data out on a preprint server is particularly important. However, we really need a Genetics category in q-bio!

Feedback on the paper would be most welcome. I’d love to see a replication or a nice functional study to followup, of course. I also think this is a good example for teaching people about genetics. A number of the issues that come up in this paper are a little tricky, but are good examples for understanding the how difficult it is to predict something based on genetics. On the technical side, I’m most curious if there are methods that might give a nice way of analyzing these two correlated traits together. We’ve tried a few regression based approaches for this sort of problem, but haven’t thought of anything entirely satisfactory.

Nick Eriksson

Genome-wide analysis points to roles for extracellular matrix remodeling, the visual cycle, and neuronal development in myopia

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Genome-wide analysis points to roles for extracellular matrix remodeling, the visual cycle, and neuronal development in myopia

Amy K. Kiefer, Joyce Y. Tung, Chuong B. Do, David A. Hinds, Joanna L. Mountain, Uta Francke, Nicholas Eriksson
(Submitted on 10 Sep 2012)

Myopia, or nearsightedness, is the most common eye disorder, resulting primarily from excess elongation of the eye. The etiology of myopia, although known to be complex, is poorly understood. Here we report the largest ever genome-wide association study (43,360 participants) on myopia in Europeans. We performed a survival analysis on age of myopia onset and identified 19 significant associations (p < 5e-8), two of which are replications of earlier associations with refractive error. These 19 associations in total explain 2.7% of the variance in myopia age of onset, and point towards a number of different mechanisms behind the development of myopia. One association is in the gene PRSS56, which has previously been linked to abnormally small eyes; one is in a gene that forms part of the extracellular matrix (LAMA2); two are in or near genes involved in the regeneration of 11-cis-retinal (RGR and RDH5); two are near genes known to be involved in the growth and guidance of retinal ganglion cells (ZIC2, SFRP1); and five are in or near genes involved in neuronal signaling or development. These novel findings point towards multiple genetic factors involved in the development of myopia and suggest that complex interactions between extracellular matrix remodeling, neuronal development, and visual signals from the retina may underlie the development of myopia in humans.

A genetic variant near olfactory receptor genes influences cilantro preference

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A genetic variant near olfactory receptor genes influences cilantro preference

Nicholas Eriksson, Shirley Wu, Chuong B. Do, Amy K. Kiefer, Joyce Y. Tung, Joanna L. Mountain, David A. Hinds, Uta Francke
(Submitted on 10 Sep 2012)

The leaves of the Coriandrum sativum plant, known as cilantro or coriander, are widely used in many cuisines around the world. However, far from being a benign culinary herb, cilantro can be polarizing—many people love it while others claim that it tastes or smells foul, often like soap or dirt. This soapy or pungent aroma is largely attributed to several aldehydes present in cilantro. Cilantro preference is suspected to have a genetic component, yet to date nothing is known about specific mechanisms. Here we present the results of a genome-wide association study among 14,604 participants of European ancestry who reported whether cilantro tasted soapy, with replication in a distinct set of 11,851 participants who declared whether they liked cilantro. We find a single nucleotide polymorphism (SNP) significantly associated with soapy-taste detection that is confirmed in the cilantro preference group. This SNP, rs72921001, (p=6.4e-9, odds ratio 0.81 per A allele) lies within a cluster of olfactory receptor genes on chromosome 11. Among these olfactory receptor genes is OR6A2, which has a high binding specificity for several of the aldehydes that give cilantro its characteristic odor. We also estimate the heritability of cilantro soapy-taste detection in our cohort, showing that the heritability tagged by common SNPs is low, about 0.087. These results confirm that there is a genetic component to cilantro taste perception and suggest that cilantro dislike may stem from genetic variants in olfactory receptors. We propose that OR6A2 may be the olfactory receptor that contributes to the detection of a soapy smell from cilantro in European populations.

An experimental test for genetic constraints in Drosophila melanogaster

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An experimental test for genetic constraints in Drosophila melanogaster
Ian Dworkin, David Tack, Jarrod Hadfield
(Submitted on 7 Sep 2012)

In addition to natural selection, adaptive evolution requires genetic variation to proceed. Yet the G-matrix may have limited ‘genetic degrees of freedom’, with certain combinations of trait values unavailable to evolution. Such limitations are often referred to as genetic constraints. Unfortunately, clear predictions about when to expect constraints are rarely available. Therefore, we developed an experimental system that provides specific predictions regarding constraints. Such tests are important as disagreements persist regarding the evidence for genetic constraints, possibly due to differences in methodology, study system or both. Numerous measures of genetic constraints have been suggested, and generally focus on whether some axes of G have eigenvalues=~0, indicating a lack of genetic variance.The mutation Ultrabithorax1 causes a mild homeotic transformation of segmental identity. We predicted that this mutation would induce a genetic constraint due to this homeosis. We measured genetic co-variation for a set of traits in a panel of strains with and without Ubx1. As expected, Ubx1 induced homeotic transformations, and altered patterns of allometry. Yet, no changes in correlational structure nor in the distribution of eigenvalues of G were observed. We discuss the role of using genetic manipulations to refine hypotheses of constraints in natural systems.

Polygenic Modeling with Bayesian Sparse Linear Mixed Models

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Polygenic Modeling with Bayesian Sparse Linear Mixed Models
Xiang Zhou, Peter Carbonetto, Matthew Stephens
(Submitted on 6 Sep 2012)

Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling. These two approaches make very different assumptions, so are expected to perform well in different situations. However, in practice, for a given data set one typically does not know which assumptions will be more accurate. Motivated by this, we consider a hybrid of the two, which we refer to as a “Bayesian sparse linear mixed model” (BSLMM) that includes both these models as special cases. We address several key computational and statistical issues that arise when applying BSLMM, including appropriate prior specification for the hyper-parameters, and a novel Markov chain Monte Carlo algorithm for posterior inference. We apply BSLMM and compare it with other methods for two polygenic modeling applications: estimating the proportion of variance in phenotypes explained (PVE) by available genotypes, and phenotype (or breeding value) prediction. For estimating PVE, we demonstrate that BSLMM combines the advantages of both standard LMMs and sparse regression modeling. For phenotype prediction it considerably outperforms either of the other two methods, as well as several other large-scale regression methods previously suggested for this problem. Software implementing our method is freely available from this http URL

Bayesian Methods for Genetic Association Analysis with Heterogeneous Subgroups: from Meta-Analyses to Gene-Environment Interactions

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Bayesian Methods for Genetic Association Analysis with Heterogeneous Subgroups: from Meta-Analyses to Gene-Environment Interactions

Xiaoquan Wen, Matthew Stephens
(Submitted on 4 Nov 2011 (v1), last revised 8 Nov 2011 (this version, v2))

In genetic association analyses, it is often desired to analyze data from multiple potentially-heterogeneous subgroups. The amount of expected heterogeneity can vary from modest (as might typically be expected in a meta-analysis of multiple studies of the same phenotype, for example), to large (e.g. a strong gene-environment interaction, where the environmental exposure defines discrete subgroups). Here, we consider a flexible set of Bayesian models and priors that can capture these different levels of heterogeneity. We provide accurate numerical approaches to compute approximate Bayes Factors for these different models, and also some simple analytic forms which have natural interpretations and, in some cases, close connections with standard frequentist test statistics. These approximations also have the convenient feature that they require only summary-level data from each subgroup (in the simplest case, a point estimate for the genetic effect, and its standard error, from each subgroup). We illustrate the flexibility of these approaches on three examples: an analysis of a potential gene-environment interaction for a recombination phenotype, a large scale meta-analysis of genome-wide association data from the Global Lipids consortium, and a cross-population analysis for expression quantitative trait loci (eQTLs).

Integrated analysis of variants and pathways in genome-wide association studies using polygenic models of disease

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Integrated analysis of variants and pathways in genome-wide association studies using polygenic models of disease

Peter Carbonetto, Matthew Stephens
(Submitted on 21 Aug 2012)

Many common diseases are highly polygenic, modulated by a large number genetic factors with small effects on susceptibility to disease. These small effects are difficult to map reliably in genetic association studies. To address this problem, researchers have developed methods that aggregate information over sets of related genes, such as biological pathways, to identify gene sets that are enriched for genetic variants associated with disease. However, these methods fail to answer a key question: which genes and genetic variants are associated with disease risk? We develop a method based on sparse multiple regression that simultaneously identifies enriched pathways, and prioritizes the variants within these pathways, to locate additional variants associated with disease susceptibility. A central feature of our approach is an estimate of the strength of enrichment, which yields a coherent way to prioritize variants in enriched pathways. We illustrate the benefits of our approach in a genome-wide association study of Crohn’s disease with ~440,000 genetic variants genotyped for ~4700 study subjects. We obtain strong support for enrichment of IL-12, IL-23 and other cytokine signaling pathways. Furthermore, prioritizing variants in these enriched pathways yields support for additional disease-association variants, all of which have been independently reported in other case-control studies for Crohn’s disease.

Finding the sources of missing heritability in a yeast cross

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Finding the sources of missing heritability in a yeast cross

Joshua S. Bloom, Ian M. Ehrenreich, Wesley Loo, Thúy-Lan Võ Lite, Leonid Kruglyak
(Submitted on 14 Aug 2012)

For many traits, including susceptibility to common diseases in humans, causal loci uncovered by genetic mapping studies explain only a minority of the heritable contribution to trait variation. Multiple explanations for this “missing heritability” have been proposed. Here we use a large cross between two yeast strains to accurately estimate different sources of heritable variation for 46 quantitative traits and to detect underlying loci with high statistical power. We find that the detected loci explain nearly the entire additive contribution to heritable variation for the traits studied. We also show that the contribution to heritability of gene-gene interactions varies among traits, from near zero to 50%. Detected two-locus interactions explain only a minority of this contribution. These results substantially advance our understanding of the missing heritability problem and have important implications for future studies of complex and quantitative traits.