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Kunkel D, Sørensen P, Shankar V, Morgante F. Improving polygenic prediction from summary data by learning patterns of effect sharing across multiple phenotypes. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.05.06.592745. [PMID: 38766136 PMCID: PMC11100663 DOI: 10.1101/2024.05.06.592745] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2024]
Abstract
Polygenic prediction of complex trait phenotypes has become important in human genetics, especially in the context of precision medicine. Recently, Morgante et al. introduced mr.mash, a flexible and computationally efficient method that models multiple phenotypes jointly and leverages sharing of effects across such phenotypes to improve prediction accuracy. However, a drawback of mr.mash is that it requires individual-level data, which are often not publicly available. In this work, we introduce mr.mash-rss, an extension of the mr.mash model that requires only summary statistics from Genome-Wide Association Studies (GWAS) and linkage disequilibrium (LD) estimates from a reference panel. By using summary data, we achieve the twin goal of increasing the applicability of the mr.mash model to data sets that are not publicly available and making it scalable to biobank-size data. Through simulations, we show that mr.mash-rss is competitive with, and often outperforms, current state-of-the-art methods for single- and multi-phenotype polygenic prediction in a variety of scenarios that differ in the pattern of effect sharing across phenotypes, the number of phenotypes, the number of causal variants, and the genomic heritability. We also present a real data analysis of 16 blood cell phenotypes in UK Biobank, showing that mr.mash-rss achieves higher prediction accuracy than competing methods for the majority of traits, especially when the data has smaller sample size.
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Affiliation(s)
- Deborah Kunkel
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, United States of America
| | - Peter Sørensen
- Center for Quantitative Genetics and Genomics, Aarhus University, Aarhus, Denmark
| | - Vijay Shankar
- Center for Human Genetics, Clemson University, Greenwood, SC, United States of America
| | - Fabio Morgante
- Center for Human Genetics, Clemson University, Greenwood, SC, United States of America
- Department of Genetics and Biochemistry, Clemson University, Clemson, SC, United States of America
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Choquet H, Duot M, Herrera VA, Shrestha SK, Meyers TJ, Hoffmann TJ, Sangani PK, Lachke SA. Multi-tissue transcriptome-wide association study identifies novel candidate susceptibility genes for cataract. FRONTIERS IN OPHTHALMOLOGY 2024; 4:1362350. [PMID: 38984127 PMCID: PMC11182099 DOI: 10.3389/fopht.2024.1362350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Accepted: 04/01/2024] [Indexed: 07/11/2024]
Abstract
Introduction Cataract is the leading cause of blindness among the elderly worldwide. Twin and family studies support an important role for genetic factors in cataract susceptibility with heritability estimates up to 58%. To date, 55 loci for cataract have been identified by genome-wide association studies (GWAS), however, much work remains to identify the causal genes. Here, we conducted a transcriptome-wide association study (TWAS) of cataract to prioritize causal genes and identify novel ones, and examine the impact of their expression. Methods We performed tissue-specific and multi-tissue TWAS analyses to assess associations between imputed gene expression from 54 tissues (including 49 from the Genotype Tissue Expression (GTEx) Project v8) with cataract using FUSION software. Meta-analyzed GWAS summary statistics from 59,944 cataract cases and 478,571 controls, all of European ancestry and from two cohorts (GERA and UK Biobank) were used. We then examined the expression of the novel genes in the lens tissue using the iSyTE database. Results Across tissue-specific and multi-tissue analyses, we identified 99 genes for which genetically predicted gene expression was associated with cataract after correcting for multiple testing. Of these 99 genes, 20 (AC007773.1, ANKH, ASIP, ATP13A2, CAPZB, CEP95, COQ6, CREB1, CROCC, DDX5, EFEMP1, EIF2S2, ESRRB, GOSR2, HERC4, INSRR, NIPSNAP2, PICALM, SENP3, and SH3YL1) did not overlap with previously reported cataract-associated loci. Tissue-specific analysis identified 202 significant gene-tissue associations for cataract, of which 166 (82.2%), representing 9 unique genes, were attributed to the previously reported 11q13.3 locus. Tissue-enrichment analysis revealed that gastrointestinal tissues represented one of the highest proportions of the Bonferroni-significant gene-tissue associations (21.3%). Moreover, this gastrointestinal tissue type was the only anatomical category significantly enriched in our results, after correcting for the number of tissue donors and imputable genes for each reference panel. Finally, most of the novel cataract genes (e.g., Capzb) were robustly expressed in iSyTE lens data. Discussion Our results provide evidence of the utility of imputation-based TWAS approaches to characterize known GWAS risk loci and identify novel candidate genes that may increase our understanding of cataract etiology. Our findings also highlight the fact that expression of genes associated with cataract susceptibility is not necessarily restricted to lens tissue.
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Affiliation(s)
- Hélène Choquet
- Kaiser Permanente Northern California (KPNC), Division of Research, Oakland, CA, United States
| | - Matthieu Duot
- Department of Biological Sciences, University of Delaware, Newark, DE, United States
- The National Centre for Scientific Research (CNRS), IGDR (Institut de Génétique et Développement de Rennes) - Joint Research Units (UMR), Univ Rennes, Rennes, France
| | - Victor A Herrera
- Kaiser Permanente Northern California (KPNC), Division of Research, Oakland, CA, United States
| | - Sanjaya K Shrestha
- Department of Biological Sciences, University of Delaware, Newark, DE, United States
| | - Travis J Meyers
- Kaiser Permanente Northern California (KPNC), Division of Research, Oakland, CA, United States
| | - Thomas J Hoffmann
- Institute for Human Genetics, University of California San Francisco (UCSF), San Francisco, CA, United States
- Department of Epidemiology and Biostatistics, UCSF, San Francisco, CA, United States
| | - Poorab K Sangani
- Department of Ophthalmology, KPNC, South San Francisco, CA, United States
| | - Salil A Lachke
- Department of Biological Sciences, University of Delaware, Newark, DE, United States
- Center for Bioinformatics and Computational Biology, University of Delaware, Newark, DE, United States
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Mai J, Lu M, Gao Q, Zeng J, Xiao J. Transcriptome-wide association studies: recent advances in methods, applications and available databases. Commun Biol 2023; 6:899. [PMID: 37658226 PMCID: PMC10474133 DOI: 10.1038/s42003-023-05279-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 08/24/2023] [Indexed: 09/03/2023] Open
Abstract
Genome-wide association study has identified fruitful variants impacting heritable traits. Nevertheless, identifying critical genes underlying those significant variants has been a great task. Transcriptome-wide association study (TWAS) is an instrumental post-analysis to detect significant gene-trait associations focusing on modeling transcription-level regulations, which has made numerous progresses in recent years. Leveraging from expression quantitative loci (eQTL) regulation information, TWAS has advantages in detecting functioning genes regulated by disease-associated variants, thus providing insight into mechanisms of diseases and other phenotypes. Considering its vast potential, this review article comprehensively summarizes TWAS, including the methodology, applications and available resources.
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Affiliation(s)
- Jialin Mai
- National Genomics Data Center, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China
- CAS Key Laboratory of Genome Sciences and Information, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Mingming Lu
- National Genomics Data Center, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China
- CAS Key Laboratory of Genome Sciences and Information, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Qianwen Gao
- National Genomics Data Center, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China
- CAS Key Laboratory of Genome Sciences and Information, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Jingyao Zeng
- National Genomics Data Center, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China.
- CAS Key Laboratory of Genome Sciences and Information, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China.
| | - Jingfa Xiao
- National Genomics Data Center, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China.
- CAS Key Laboratory of Genome Sciences and Information, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, Beijing, 100101, China.
- University of Chinese Academy of Sciences, Beijing, 100049, China.
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Ren J, Lin Z, He R, Shen X, Pan W. Using GWAS summary data to impute traits for genotyped individuals. HGG ADVANCES 2023; 4:100197. [PMID: 37181332 PMCID: PMC10173780 DOI: 10.1016/j.xhgg.2023.100197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Accepted: 04/07/2023] [Indexed: 05/16/2023] Open
Abstract
Genome-wide association study (GWAS) summary data have become extremely useful in daily routine data analysis, largely facilitating new methods development and new applications. However, a severe limitation with the current use of GWAS summary data is its exclusive restriction to only linear single nucleotide polymorphism (SNP)-trait association analyses. To further expand the use of GWAS summary data, along with a large sample of individual-level genotypes, we propose a nonparametric method for large-scale imputation of the genetic component of the trait for the given genotypes. The imputed individual-level trait values, along with the individual-level genotypes, make it possible to conduct any analysis as with individual-level GWAS data, including nonlinear SNP-trait associations and predictions. We use the UK Biobank data to highlight the usefulness and effectiveness of the proposed method in three applications that currently cannot be done with only GWAS summary data (for SNP-trait associations): marginal SNP-trait association analysis under non-additive genetic models, detection of SNP-SNP interactions, and genetic prediction of a trait using a nonlinear model of SNPs.
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Affiliation(s)
- Jingchen Ren
- School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA
- Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA
| | - Zhaotong Lin
- Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA
| | - Ruoyu He
- School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA
- Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA
| | - Xiaotong Shen
- School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA
| | - Wei Pan
- Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA
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Meyers TJ, Yin J, Herrera VA, Pressman AR, Hoffmann TJ, Schaefer C, Avins AL, Choquet H. Transcriptome-wide association study identifies novel candidate susceptibility genes for migraine. HGG ADVANCES 2023; 4:100211. [PMID: 37415806 PMCID: PMC10319829 DOI: 10.1016/j.xhgg.2023.100211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 06/05/2023] [Indexed: 07/08/2023] Open
Abstract
Genome-wide association studies (GWASs) have identified more than 130 genetic susceptibility loci for migraine; however, how most of these loci impact migraine development is unknown. To identify novel genes associated with migraine and interpret the transcriptional products of those genes, we conducted a transcriptome-wide association study (TWAS). We performed tissue-specific and multi-tissue TWAS analyses to assess associations between imputed gene expression from 53 tissues and migraine susceptibility using FUSION software. Meta-analyzed GWAS summary statistics from 26,052 migraine cases and 487,214 controls, all of European ancestry and from two cohorts (the Kaiser Permanente GERA and the UK Biobank), were used. We evaluated the associations for genes after conditioning on variant-level effects from GWAS, and we tested for colocalization of GWAS migraine-associated loci and expression quantitative trait loci (eQTLs). Across tissue-specific and multi-tissue analyses, we identified 53 genes for which genetically predicted gene expression was associated with migraine after correcting for multiple testing. Of these 53 genes, 10 (ATF5, CNTNAP1, KTN1-AS1, NEIL1, NEK4, NNT, PNKP, RUFY2, TUBG2, and VAT1) did not overlap known migraine-associated loci identified from GWAS. Tissue-specific analysis identified 45 gene-tissue pairs and cardiovascular tissues represented the highest proportion of the Bonferroni-significant gene-tissue pairs (n = 22 [49%]), followed by brain tissues (n = 6 [13%]), and gastrointestinal tissues (n = 4 [9%]). Colocalization analyses provided evidence of shared genetic variants underlying eQTL and GWAS signals in 18 of the gene-tissue pairs (40%). Our TWAS reports novel genes for migraine and highlights the important contribution of brain, cardiovascular, and gastrointestinal tissues in migraine susceptibility.
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Affiliation(s)
- Travis J. Meyers
- Division of Research, Kaiser Permanente Northern California, Oakland, CA 94612, USA
| | - Jie Yin
- Division of Research, Kaiser Permanente Northern California, Oakland, CA 94612, USA
| | - Victor A. Herrera
- Division of Research, Kaiser Permanente Northern California, Oakland, CA 94612, USA
| | - Alice R. Pressman
- Department of Epidemiology and Biostatistics, University of California, San Francisco, San Francisco, CA 94158, USA
- Sutter Health, San Francisco, CA 94107, USA
| | - Thomas J. Hoffmann
- Department of Epidemiology and Biostatistics, University of California, San Francisco, San Francisco, CA 94158, USA
- Institute for Human Genetics, University of California, San Francisco, San Francisco, CA 94143, USA
| | - Catherine Schaefer
- Division of Research, Kaiser Permanente Northern California, Oakland, CA 94612, USA
| | - Andrew L. Avins
- Division of Research, Kaiser Permanente Northern California, Oakland, CA 94612, USA
- Department of Epidemiology and Biostatistics, University of California, San Francisco, San Francisco, CA 94158, USA
| | - Hélène Choquet
- Division of Research, Kaiser Permanente Northern California, Oakland, CA 94612, USA
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Morgante F, Carbonetto P, Wang G, Zou Y, Sarkar A, Stephens M. A flexible empirical Bayes approach to multivariate multiple regression, and its improved accuracy in predicting multi-tissue gene expression from genotypes. PLoS Genet 2023; 19:e1010539. [PMID: 37418505 PMCID: PMC10355440 DOI: 10.1371/journal.pgen.1010539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 06/02/2023] [Indexed: 07/09/2023] Open
Abstract
Predicting phenotypes from genotypes is a fundamental task in quantitative genetics. With technological advances, it is now possible to measure multiple phenotypes in large samples. Multiple phenotypes can share their genetic component; therefore, modeling these phenotypes jointly may improve prediction accuracy by leveraging effects that are shared across phenotypes. However, effects can be shared across phenotypes in a variety of ways, so computationally efficient statistical methods are needed that can accurately and flexibly capture patterns of effect sharing. Here, we describe new Bayesian multivariate, multiple regression methods that, by using flexible priors, are able to model and adapt to different patterns of effect sharing and specificity across phenotypes. Simulation results show that these new methods are fast and improve prediction accuracy compared with existing methods in a wide range of settings where effects are shared. Further, in settings where effects are not shared, our methods still perform competitively with state-of-the-art methods. In real data analyses of expression data in the Genotype Tissue Expression (GTEx) project, our methods improve prediction performance on average for all tissues, with the greatest gains in tissues where effects are strongly shared, and in the tissues with smaller sample sizes. While we use gene expression prediction to illustrate our methods, the methods are generally applicable to any multi-phenotype applications, including prediction of polygenic scores and breeding values. Thus, our methods have the potential to provide improvements across fields and organisms.
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Affiliation(s)
- Fabio Morgante
- Center for Human Genetics, Clemson University, Greenwood, South Carolina, United States of America
- Department of Genetics and Biochemistry, Clemson University, Clemson, South Carolina, United States of America
- Section of Genetic Medicine, Department of Medicine, University of Chicago, Chicago, Illinois, United States of America
| | - Peter Carbonetto
- Department of Human Genetics, University of Chicago, Chicago, Illinois, United States of America
- Research Computing Center, University of Chicago, Chicago, Illinois, United States of America
| | - Gao Wang
- Department of Human Genetics, University of Chicago, Chicago, Illinois, United States of America
- Department of Neurology, Columbia University, New York, New York, United States of America
- Gertrude H. Sergievsky Center, Columbia University, New York, New York, United States of America
| | - Yuxin Zou
- Department of Statistics, University of Chicago, Chicago, Illinois, United States of America
- Regeneron Genetics Center, Regeneron Pharmaceuticals Inc., Tarrytown, New York, United States of America
| | - Abhishek Sarkar
- Department of Human Genetics, University of Chicago, Chicago, Illinois, United States of America
| | - Matthew Stephens
- Department of Human Genetics, University of Chicago, Chicago, Illinois, United States of America
- Department of Statistics, University of Chicago, Chicago, Illinois, United States of America
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Lin Z, Xue H, Malakhov MM, Knutson KA, Pan W. Accounting for nonlinear effects of gene expression identifies additional associated genes in transcriptome-wide association studies. Hum Mol Genet 2022; 31:2462-2470. [PMID: 35043938 PMCID: PMC9307319 DOI: 10.1093/hmg/ddac015] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2021] [Revised: 01/08/2022] [Accepted: 01/10/2022] [Indexed: 01/21/2023] Open
Abstract
Transcriptome-wide association studies (TWAS) integrate genome-wide association study (GWAS) data with gene expression (GE) data to identify (putative) causal genes for complex traits. There are two stages in TWAS: in Stage 1, a model is built to impute gene expression from genotypes, and in Stage 2, gene-trait association is tested using imputed gene expression. Despite many successes with TWAS, in the current practice, one only assumes a linear relationship between GE and the trait, which however may not hold, leading to loss of power. In this study, we extend the standard TWAS by considering a quadratic effect of GE, in addition to the usual linear effect. We train imputation models for both linear and quadratic gene expression levels in Stage 1, then include both the imputed linear and quadratic expression levels in Stage 2. We applied both the standard TWAS and our approach first to the ADNI gene expression data and the IGAP Alzheimer's disease GWAS summary data, then to the GTEx (V8) gene expression data and the UK Biobank individual-level GWAS data for lipids, followed by validation with different GWAS data, suitable model checking and more robust TWAS methods. In all these applications, the new TWAS approach was able to identify additional genes associated with Alzheimer's disease, LDL and HDL cholesterol levels, suggesting its likely power gains and thus the need to account for potentially nonlinear effects of gene expression on complex traits.
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Affiliation(s)
- Zhaotong Lin
- Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA
| | - Haoran Xue
- Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA
| | - Mykhaylo M Malakhov
- Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA
| | - Katherine A Knutson
- Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA
| | - Wei Pan
- To whom correspondence should be addressed at: A460 Mayo Building, 420 Delaware St SE, Minneapolis, MN 55455, USA. Tel: (612)626-2705; Fax: (612)626-0660;
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Bae YE, Wu L, Wu C. InTACT: An adaptive and powerful framework for joint-tissue transcriptome-wide association studies. Genet Epidemiol 2021; 45:848-859. [PMID: 34255882 PMCID: PMC8604767 DOI: 10.1002/gepi.22425] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Revised: 06/22/2021] [Accepted: 06/24/2021] [Indexed: 11/05/2022]
Abstract
Transcriptome-wide association studies (TWAS) that integrate transcriptomic reference data and genome-wide association studies (GWAS) have successfully enhanced the discovery of candidate genes for many complex traits. However, existing methods may suffer from substantial power loss because they fail to effectively consider that expression of many genes tends to be consistent across tissues. Here we propose a computationally efficient testing method, referred to as Integrative Test for Associations via Cauchy Transformation (InTACT), that effectively combines information across multiple tissues and thus improves the power of identifying associated genes. Through simulation studies, we show that InTACT maintains high power while properly controls for Type 1 error rates. We applied InTACT to the largest GWAS of Alzheimer's disease (AD) to date and identified 227 genome-wide significant genes, of which 130 were not identified by benchmark methods, TWAS and MultiXcan. Importantly, InTACT identified five novel loci for AD. We implemented InTACT in publicly available software, "InTACT."
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Affiliation(s)
- Ye Eun Bae
- Department of Statistics, Florida State University
| | - Lang Wu
- Cancer Epidemiology Division, Population Sciences in the Pacific Program, University of Hawaii Cancer Center, University of Hawaii at Manoa
| | - Chong Wu
- Department of Statistics, Florida State University
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Grinberg NF, Wallace C. Multi-tissue transcriptome-wide association studies. Genet Epidemiol 2021; 45:324-337. [PMID: 33369784 PMCID: PMC8048510 DOI: 10.1002/gepi.22374] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Revised: 11/04/2020] [Accepted: 11/18/2020] [Indexed: 12/20/2022]
Abstract
A transcriptome-wide association study (TWAS) attempts to identify disease associated genes by imputing gene expression into a genome-wide association study (GWAS) using an expression quantitative trait loci (eQTL) data set and then testing for associations with a trait of interest. Regulatory processes may be shared across related tissues and one natural extension of TWAS is harnessing cross-tissue correlation in gene expression to improve prediction accuracy. Here, we studied multi-tissue extensions of lasso regression and random forests (RF), joint lasso and RF-MTL (multi-task learning RF), respectively. We found that, on our chosen eQTL data set, multi-tissue methods were generally more accurate than their single-tissue counterparts, with RF-MTL performing the best. Simulations showed that these benefits generally translated into more associated genes identified, although highlighted that joint lasso had a tendency to erroneously identify genes in one tissue if there existed an eQTL signal for that gene in another. Applying the four methods to a type 1 diabetes GWAS, we found that multi-tissue methods found more unique associated genes for most of the tissues considered. We conclude that multi-tissue methods are competitive and, for some cell types, superior to single-tissue approaches and hold much promise for TWAS studies.
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Affiliation(s)
- Nastasiya F. Grinberg
- Department of Medicine, Jeffrey Cheah Biomedical Centre, Cambridge Biomedical Campus, Cambridge Institute of Therapeutic Immunology and Infectious DiseaseUniversity of CambridgeCambridgeUK
| | - Chris Wallace
- Department of Medicine, Jeffrey Cheah Biomedical Centre, Cambridge Biomedical Campus, Cambridge Institute of Therapeutic Immunology and Infectious DiseaseUniversity of CambridgeCambridgeUK
- MRC Biostatistics UnitUniversity of CambridgeCambridgeUK
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