The Multivariate Normal Distribution Framework for Analyzing Association Studies: Overview

The use of the multivariate normal (MVN) model has been a powerful tool in our groups research and it has been utilized in many of our papers. Jose Lozano (University of the Basque Country, San Sebastian, Spain), along with Eleazar Eskin and three ZarLab alumni—Farhad Hormozdiari (postdoc at Harvard), Jong Wha (Joanne) Joo (faculty at Dongguk University in Seoul), and Buhm Han (faculty at University of Ulsan College of Medicine in Seoul)—recently published a review of the multivariate normal (MVN) distribution framework in genome-wide association studies (GWAS) studies.

Genome-wide association studies (GWAS) have discovered thousands of variants involved in common human diseases. In these studies, frequencies of genetic variants are compared between a population of individuals with a disease (cases) and a population of healthy individual controls). Any variant that has a significantly different frequency between the two populations is considered an associated variant.

A major challenge in the analysis of GWAS studies is the fact that human population history causes nearby genetic variants in the genome to be correlated with each other. In this review, we demonstrate how to utilize the MVN distribution to explicitly take into account the correlation between genetic variants and provide a comprehensive framework for analysis of GWAS.

In this paper, we show how the MVN framework can be applied to perform association testing, correct for multiple hypothesis, testing, estimate statistical power, and perform fine mapping and imputation. In future blog posts, we will highlight different ways the MVN framework can be used in association studies.

An illustration of the multivariate normal model (a) Type I Error (b) Power.

Many of the authors are the alumni of the group who pioneered the use of the MVN in various problems in association studies. Here is a list of papers that our group published using the MVN framework:

Joo, Jong Wha J; Hormozdiari, Farhad; Han, Buhm; Eskin, Eleazar

Multiple testing correction in linear mixed models. Journal Article

In: Genome Biol, 17 (1), pp. 62, 2016, ISSN: 1474-760X.

Abstract | Links | BibTeX

Hormozdiari, Farhad ; Kang, Eun Yong ; Bilow, Michael ; Ben-David, Eyal ; Vulpe, Chris ; McLachlan, Stela ; Lusis, Aldons J; Han, Buhm ; Eskin, Eleazar

Imputing Phenotypes for Genome-wide Association Studies. Journal Article

In: Am J Hum Genet, 99 (1), pp. 89-103, 2016, ISSN: 1537-6605.

Abstract | Links | BibTeX

Duong, Dat ; Zou, Jennifer ; Hormozdiari, Farhad ; Sul, Jae Hoon ; Ernst, Jason ; Han, Buhm ; Eskin, Eleazar

Using genomic annotations increases statistical power to detect eGenes. Journal Article

In: Bioinformatics, 32 (12), pp. i156-i163, 2016, ISSN: 1367-4811.

Abstract | Links | BibTeX

Hormozdiari, Farhad; van de Bunt, Martijn; Segrè, Ayellet V; Li, Xiao; Joo, Jong Wha J; Bilow, Michael; Sul, Jae Hoon; Sankararaman, Sriram; Pasaniuc, Bogdan; Eskin, Eleazar

Colocalization of GWAS and eQTL Signals Detects Target Genes. Journal Article

In: Am J Hum Genet, 2016, ISSN: 1537-6605.

Abstract | Links | BibTeX

Joo, Jong Wha J; Kang, Eun Yong; Org, Elin; Furlotte, Nick; Parks, Brian; Hormozdiari, Farhad; Lusis, Aldons J; Eskin, Eleazar

Efficient and Accurate Multiple-Phenotype Regression Method for High Dimensional Data Considering Population Structure. Journal Article

In: Genetics, 204 (4), pp. 1379-1390, 2016, ISSN: 1943-2631.

Abstract | Links | BibTeX

Hormozdiari, Farhad; Kichaev, Gleb; Yang, Wen-Yun Y; Pasaniuc, Bogdan; Eskin, Eleazar

Identification of causal genes for complex traits. Journal Article

In: Bioinformatics, 31 (12), pp. i206-i213, 2015, ISSN: 1367-4811.

Abstract | Links | BibTeX

Hormozdiari, Farhad; Kichaev, Gleb; Yang, Wen-Yun Y; Pasaniuc, Bogdan; Eskin, Eleazar

Identification of causal genes for complex traits. Journal Article

In: Bioinformatics, 31 (12), pp. i206-i213, 2015, ISSN: 1367-4811.

Abstract | Links | BibTeX

Hormozdiari, Farhad; Kostem, Emrah ; Kang, Eun Yong ; Pasaniuc, Bogdan ; Eskin, Eleazar

Identifying causal variants at Loci with multiple signals of association. Journal Article

In: Genetics, 198 (2), pp. 497-508, 2014, ISSN: 1943-2631.

Abstract | Links | BibTeX

Kichaev, Gleb; Yang, Wen-Yun Y; Lindstrom, Sara ; Hormozdiari, Farhad ; Eskin, Eleazar ; Price, Alkes L; Kraft, Peter ; Pasaniuc, Bogdan

Integrating functional data to prioritize causal variants in statistical fine-mapping studies. Journal Article

In: PLoS Genet, 10 (10), pp. e1004722, 2014, ISSN: 1553-7404.

Abstract | Links | BibTeX

Darnell, Gregory; Duong, Dat ; Han, Buhm ; Eskin, Eleazar

Incorporating prior information into association studies. Journal Article

In: Bioinformatics, 28 (12), pp. i147-i153, 2012, ISSN: 1367-4811.

Abstract | Links | BibTeX

Flint, Jonathan; Eskin, Eleazar

Genome-wide association studies in mice Journal Article

In: Nature Reviews Genetics, 13 (11), pp. 807-17, 2012, ISSN: 1471-0064.

Abstract | Links | BibTeX

Han, Buhm; Kang, Hyun Min ; Eskin, Eleazar

Rapid and accurate multiple testing correction and power estimation for millions of correlated markers. Journal Article

In: PLoS Genet, 5 (4), pp. e1000456, 2009, ISSN: 1553-7404.

Abstract | Links | BibTeX

Eskin, Eleazar

Increasing power in association studies by using linkage disequilibrium structure and molecular function as prior information. Journal Article

In: Genome Res, 18 (4), pp. 653-60, 2008, ISSN: 1088-9051.

Abstract | Links | BibTeX

Eskin, Eleazar

Increasing Power in Association Studies by Using Linkage Disequilibrium Structure and Molecular Function as Prior Information Conference

Lecture Notes in Computer Science, 4955/2008 , Lecture Notes in Computer Science Springer Berlin / Heidelberg, 2008, ISSN: 0302-9743 (Print) 1611-3349 (Online).

Abstract | Links | BibTeX

  • Farhad Hormozdiari, Anthony Zhu, Gleb Kichaev, Chelsea J.-T. Ju, Ayellet V. Segre, Jong Wha J. Joo, Hyejung Won, Sriram Sankararaman, Bogdan Pasaniuc, Sagiv Shifman, and Eleazar Eskin. Widespread allelic heterogeneity in complex traits. The American Journal of Human Genetics, 100(5):789{802, may 2017.
  • Yue Wu, Farhad Hormozdiari, Jong Wha J. Joo, and Eleazar Eskin. Improving imputation accuracy by inferring causal variants in genetic studies. In Lecture Notes in Computer Science, pages 303{317. Springer International Publishing, 2017.

The paper was written by Jose A. Lozano, Farhad Hormozdiari, Jong Wha (Joanne) Joo, Buhm Han, and Eleazar Eskin, and it is available at: https://www.biorxiv.org/content/early/2017/10/28/208199.

The full citation to our paper is:

Jose A. Lozano, Farhad Hormozdiari, Jong Wha (Joanne) Joo, Buhm Han, Eleazar Eskin. 2017. The Multivariate Normal Distribution Framework for Analyzing Association Studies. bioRxiv doi: https://doi.org/10.1101/208199.

Efficient and accurate multiple-phenotype regression method for high dimensional data considering population structure

Jong Wha (Joanne) Joo developed an approach to simultaneously analyze multiple phenotypes in a genome-wide association studies (GWAS) dataset. She introduces this new methodology, referred to as GAMMA (Generalized Analysis of Molecular variance for Mixed model Analysis), in a paper recently published in Genetics.

GWASs have identified many genetic variants involved in traits and development of human diseases by examining for correlation of a single phenotype and individual genotype one phenotype at a time. Since initial development of the standard GWAS approach, GWAS data collection has become larger in scale and higher in resolution. Today’s large-scale datasets include expression data and often contain thousands of phenotypes per individual. Performing the standard single-phenotype analysis on these datasets is slow and potentially fails to detect unmeasured aspects of complex biological networks.

Analyzing many phenotypes simultaneously increases the power to detect more variants and capture previously unmeasured aspects of the genome. However, standard GWAS approaches capable of simultaneously testing multiple phenotypes fail to account for the distorting effects of population structure, a phenomenon present in large cohorts that inevitably contain individuals sharing common ancestry from multiple populations. As a result, standard GWAS approaches either fail to detect true effects or produce many false positive identifications.

GAMMA is an efficient, robust approach capable of simultaneously analyzing many phenotypes while correcting for population structure. GAMMA uses the principles behind existing linear mixed models to analyze for many phenotypes simultaneously and a multiple regression technique to correct for population structure.

Joanne’s paper presents the results of testing GAMMA for accuracy in three scenarios: a simulated dataset containing population structure, a yeast dataset containing many trans-regulatory hotspots, and a complex gut microbiome dataset. In the simulated study using data implanted with true population structure effects, GAMMA accurately identifies these true effects without producing false positives. In the simulation with yeast data, GAMMA successfully corrected for the bias of technical artifacts such as batch effects and identified significant signals on most of the putative hotspots. In the third test, Joanne and her team assesses GAMMA’s ability to perform a multiple-phenotypes analysis with microbiome data. Here, results identified nine loci likely to have true biological mechanisms in the taxa.

In each scenario, results of GAMMA were compared to those of the standard t-test, EMMA, and MDMR. The standard t-test and EMMA failed to identify true variants, because the phenotypic effects in each example is smaller than the amount these methods are powered to detect. MDMR produced no significant signals in the yeast dataset and identified many false associations in the simulated and gut microbiome datasets. Both GAMMA and MDMR have sufficient power to detect small association signals in these complex datasets, but only GAMMA successfully corrects for population structure.

This project was led by Joanne Joo and involved Eun Yong Kang and Farhad Hormozdiari. The article is available at: http://www.genetics.org/content/204/4/1379.

GAMMA was developed by Joanne Joo, Eun Yong Kang, Elin Org, Nick Furlotte, Brian Parks, Aldons J. Lusis, and Eleazar Eskin. Visit the following page to download GAMMA: http://genetics.cs.ucla.edu/GAMMA/

The full citation to our paper is:

Joo, Jong Wha J; Kang, Eun Yong; Org, Elin; Furlotte, Nick; Parks, Brian; Hormozdiari, Farhad; Lusis, Aldons J; Eskin, Eleazar

Efficient and Accurate Multiple-Phenotype Regression Method for High Dimensional Data Considering Population Structure. Journal Article

In: Genetics, 204 (4), pp. 1379-1390, 2016, ISSN: 1943-2631.

Abstract | Links | BibTeX

The results of GAMMA and three standard GWAS methods applied to a simulated dataset. The x-axis shows SNP locations and the y-axis shows log10p-value of associations between each SNP and all the genes. Blue arrows show the location of the true trans-regulatory hotspots.

Colocalization of GWAS and eQTL Signals Detects Target Genes

Farhad Hormozdiari recently developed a method for combining genome-wide association studies (GWASs) and quantitative trait loci (eQTL) studies in a statistical framework that quantifies the probability of each variant to be causal while allowing an arbitrary number of causal variants. Together with collaborators at the University of Oxford and Broad Institute of MIT and Harvard, we present a paper in The American Journal of Human Genetics. Here, we describe eQTL and GWAS CAusal Variants Identification in Associated Regions (eCAVIAR). We apply our approach to datasets from several GWASs and eQTL studies in order to assess its accuracy and potential contributions to colocalization and fine-mapping.

Integrating GWASs and eQTL studies is a promising way to explore the mechanism of non-coding variants on diseases. Integration of GWAS and eQTL data is challenging due to the uncertainty induced by linkage disequilibrium (LD), the non-random association of alleles at different loci, and presence of loci that harbor multiple causal variants (allelic heterogeneity). Current methods assume that each locus contains a single causal variant and expect loci to be independent and associated randomly.

eCAVIAR is a novel probabilistic model for integrating GWAS and eQTL data that extends the CAVIAR (Hormozdiari et al. 2014) framework to explicitly estimate the posterior probability of the same variant being causal in both GWAS and eQTL studies, while accounting for allelic heterogeneity and LD. Our approach can quantify the strength between a causal variant and its associated signals in both studies, and it can be used to colocalize variants that pass the genome-wide significance threshold in GWAS. For any given peak variant identified in GWAS, eCAVIAR considers a collection of variants around that peak variant as one single locus.

We apply eCAVIAR to the Meta-Analyses of Glucose and Insulin-related traits Consortium (MAGIC) dataset and GTEx dataset to detect the target gene and most relevant tissue for each GWAS risk locus. When applied to the MAGIC dataset’s 2 phenotypes, eCAVIAR identifies genetic variants that are causal in both eQTL and GWAS. Further, eCAVIAR detects a large number of loci where the GWAS causal variants are clearly distinct from the causal variants in the eQTL data. Interestingly, eCAVIAR also identifies genes that colocalize in one tissue yet can be excluded in others. For the majority of loci in which we identify a single variant causal for both GWAS and eQTL, eCAVIAR implicates more than one causal variant across the 45 tissues.

We observe that eCAVIAR outperforms existing methods even when there are different values of non-colocalization. Using simulated datasets, we compared accuracy, precision, and recall rate of eCAVIAR to RTC (Nica et al. 2010) and COLOC (Giambartolomei et al. 2014), two current methods for eQTL and GWAS colocalization. Our results show that eCAVIAR has high confidence for selecting loci to be colocalized between the GWAS and eQTL data and is conservative in selecting a locus to be colocalized.

We hope that future applications of eCAVIAR will advance identification of specific GWAS loci that share a causal variant with eQTL studies in a tissue, thus providing insight into presently unclear disease mechanisms.

Figure2

Overview of eCAVIAR.

 

eCAVIAR was created by Farhad Hormozdiari, Ayellet V. Segre, Martijn van de Bunt, Xiao Li, Jong Wha J Joo, Michael Bilow, Jae Hoon Sul, Bogdan Pasaniuc and Eleazar Eskin. The article is available at: http://www.cell.com/ajhg/abstract/S0002-9297(16)30439-6.

Visit the following page to download CAVIAR and eCAVIAR: http://genetics.cs.ucla.edu/caviar/

The full citation to our paper is:

Hormozdiari, Farhad; van de Bunt, Martijn; Segrè, Ayellet V; Li, Xiao; Joo, Jong Wha J; Bilow, Michael; Sul, Jae Hoon; Sankararaman, Sriram; Pasaniuc, Bogdan; Eskin, Eleazar

Colocalization of GWAS and eQTL Signals Detects Target Genes. Journal Article

In: Am J Hum Genet, 2016, ISSN: 1537-6605.

Abstract | Links | BibTeX

Our paper builds upon a method introduced in a previous publication:

Hormozdiari, Farhad; Kostem, Emrah ; Kang, Eun Yong ; Pasaniuc, Bogdan ; Eskin, Eleazar

Identifying causal variants at Loci with multiple signals of association. Journal Article

In: Genetics, 198 (2), pp. 497-508, 2014, ISSN: 1943-2631.

Abstract | Links | BibTeX