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Chandrashekar PB, Chen H, Lee M, Ahmadinejad N, Liu L. DeepCORE: An interpretable multi-view deep neural network model to detect co-operative regulatory elements. Comput Struct Biotechnol J 2024; 23:679-687. [PMID: 38292477 PMCID: PMC10825326 DOI: 10.1016/j.csbj.2023.12.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 12/14/2023] [Accepted: 12/27/2023] [Indexed: 02/01/2024] Open
Abstract
Gene transcription is an essential process involved in all aspects of cellular functions with significant impact on biological traits and diseases. This process is tightly regulated by multiple elements that co-operate to jointly modulate the transcription levels of target genes. To decipher the complicated regulatory network, we present a novel multi-view attention-based deep neural network that models the relationship between genetic, epigenetic, and transcriptional patterns and identifies co-operative regulatory elements (COREs). We applied this new method, named DeepCORE, to predict transcriptomes in various tissues and cell lines, which outperformed the state-of-the-art algorithms. Furthermore, DeepCORE contains an interpreter that extracts the attention values embedded in the deep neural network, maps the attended regions to putative regulatory elements, and infers COREs based on correlated attentions. The identified COREs are significantly enriched with known promoters and enhancers. Novel regulatory elements discovered by DeepCORE showed epigenetic signatures consistent with the status of histone modification marks.
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Affiliation(s)
- Pramod Bharadwaj Chandrashekar
- Waisman Center, University of Wisconsin-Madison, Madison, WI 53705, USA
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI 53076, USA
| | - Hai Chen
- College of Health Solutions, Arizona State University, Phoenix, AZ, United States
- Biodesign Institute, Arizona State University, Tempe, AZ, United States
| | - Matthew Lee
- College of Health Solutions, Arizona State University, Phoenix, AZ, United States
| | - Navid Ahmadinejad
- College of Health Solutions, Arizona State University, Phoenix, AZ, United States
- Biodesign Institute, Arizona State University, Tempe, AZ, United States
| | - Li Liu
- College of Health Solutions, Arizona State University, Phoenix, AZ, United States
- Biodesign Institute, Arizona State University, Tempe, AZ, United States
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Chandrashekar PB, Alatkar S, Wang J, Hoffman GE, He C, Jin T, Khullar S, Bendl J, Fullard JF, Roussos P, Wang D. DeepGAMI: deep biologically guided auxiliary learning for multimodal integration and imputation to improve genotype-phenotype prediction. Genome Med 2023; 15:88. [PMID: 37904203 PMCID: PMC10617196 DOI: 10.1186/s13073-023-01248-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Accepted: 10/16/2023] [Indexed: 11/01/2023] Open
Abstract
BACKGROUND Genotypes are strongly associated with disease phenotypes, particularly in brain disorders. However, the molecular and cellular mechanisms behind this association remain elusive. With emerging multimodal data for these mechanisms, machine learning methods can be applied for phenotype prediction at different scales, but due to the black-box nature of machine learning, integrating these modalities and interpreting biological mechanisms can be challenging. Additionally, the partial availability of these multimodal data presents a challenge in developing these predictive models. METHOD To address these challenges, we developed DeepGAMI, an interpretable neural network model to improve genotype-phenotype prediction from multimodal data. DeepGAMI leverages functional genomic information, such as eQTLs and gene regulation, to guide neural network connections. Additionally, it includes an auxiliary learning layer for cross-modal imputation allowing the imputation of latent features of missing modalities and thus predicting phenotypes from a single modality. Finally, DeepGAMI uses integrated gradient to prioritize multimodal features for various phenotypes. RESULTS We applied DeepGAMI to several multimodal datasets including genotype and bulk and cell-type gene expression data in brain diseases, and gene expression and electrophysiology data of mouse neuronal cells. Using cross-validation and independent validation, DeepGAMI outperformed existing methods for classifying disease types, and cellular and clinical phenotypes, even using single modalities (e.g., AUC score of 0.79 for Schizophrenia and 0.73 for cognitive impairment in Alzheimer's disease). CONCLUSION We demonstrated that DeepGAMI improves phenotype prediction and prioritizes phenotypic features and networks in multiple multimodal datasets in complex brains and brain diseases. Also, it prioritized disease-associated variants, genes, and regulatory networks linked to different phenotypes, providing novel insights into the interpretation of gene regulatory mechanisms. DeepGAMI is open-source and available for general use.
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Affiliation(s)
- Pramod Bharadwaj Chandrashekar
- Waisman Center, University of Wisconsin-Madison, Madison, WI, 53705, USA
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, 53076, USA
| | - Sayali Alatkar
- Waisman Center, University of Wisconsin-Madison, Madison, WI, 53705, USA
- Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI, 53076, USA
| | - Jiebiao Wang
- Department of Biostatistics, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Gabriel E Hoffman
- Center for Disease Neurogenomics, Department of Psychiatry and Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, 10029, USA
| | - Chenfeng He
- Waisman Center, University of Wisconsin-Madison, Madison, WI, 53705, USA
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, 53076, USA
| | - Ting Jin
- Waisman Center, University of Wisconsin-Madison, Madison, WI, 53705, USA
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, 53076, USA
| | - Saniya Khullar
- Waisman Center, University of Wisconsin-Madison, Madison, WI, 53705, USA
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, 53076, USA
| | - Jaroslav Bendl
- Center for Disease Neurogenomics, Department of Psychiatry and Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, 10029, USA
| | - John F Fullard
- Center for Disease Neurogenomics, Department of Psychiatry and Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, 10029, USA
| | - Panos Roussos
- Center for Disease Neurogenomics, Department of Psychiatry and Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, 10029, USA
- Mental Illness Research, Education and Clinical Centers, James J. Peters VA Medical Center, Bronx, NY, 10468, USA
- Center for Dementia Research, Nathan Kline Institute for Psychiatric Research, Orangeburg, NY, 10962, USA
| | - Daifeng Wang
- Waisman Center, University of Wisconsin-Madison, Madison, WI, 53705, USA.
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, 53076, USA.
- Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI, 53076, USA.
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Lasher B, Hendrix DA. bpRNA-align: improved RNA secondary structure global alignment for comparing and clustering RNA structures. RNA (NEW YORK, N.Y.) 2023; 29:584-595. [PMID: 36759128 PMCID: PMC10159002 DOI: 10.1261/rna.079211.122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 01/14/2023] [Indexed: 05/06/2023]
Abstract
Ribonucleic acid (RNA) is a polymeric molecule that is fundamental to biological processes, with structure being more highly conserved than primary sequence and often key to its function. Advances in RNA structure characterization have resulted in an increase in the number of accurate secondary structures. The task of uncovering common RNA structural motifs with a collective function through structural comparison, providing a level of similarity, remains challenging and could be used to improve RNA secondary structure databases and discover new RNA families. In this work, we present a novel secondary structure alignment method, bpRNA-align. bpRNA-align is a customized global structural alignment method, utilizing an inverted (gap extend costs more than gap open) and context-specific affine gap penalty along with a structural, feature-specific substitution matrix to provide similarity scores. We evaluate our similarity scores in comparison to other methods, using affinity propagation clustering, applied to a benchmarking data set of known structure types. bpRNA-align shows improvement in clustering performance over a broad range of structure types.
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Affiliation(s)
- Brittany Lasher
- Department of Biochemistry and Biophysics, Oregon State University, Corvallis, Oregon 97331, USA
| | - David A Hendrix
- Department of Biochemistry and Biophysics, Oregon State University, Corvallis, Oregon 97331, USA
- School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, Oregon 97331, USA
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Chandrashekar PB, Chen H, Lee M, Ahmadinejad N, Liu L. DeepCORE: An interpretable multi-view deep neural network model to detect co-operative regulatory elements. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.04.19.536807. [PMID: 37131697 PMCID: PMC10153112 DOI: 10.1101/2023.04.19.536807] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Gene transcription is an essential process involved in all aspects of cellular functions with significant impact on biological traits and diseases. This process is tightly regulated by multiple elements that co-operate to jointly modulate the transcription levels of target genes. To decipher the complicated regulatory network, we present a novel multi-view attention-based deep neural network that models the relationship between genetic, epigenetic, and transcriptional patterns and identifies co-operative regulatory elements (COREs). We applied this new method, named DeepCORE, to predict transcriptomes in 25 different cell lines, which outperformed the state-of-the-art algorithms. Furthermore, DeepCORE translates the attention values embedded in the neural network into interpretable information, including locations of putative regulatory elements and their correlations, which collectively implies COREs. These COREs are significantly enriched with known promoters and enhancers. Novel regulatory elements discovered by DeepCORE showed epigenetic signatures consistent with the status of histone modification marks.
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Zhou YH, Gallins PJ, Etheridge AS, Jima D, Scholl E, Wright FA, Innocenti F. A resource for integrated genomic analysis of the human liver. Sci Rep 2022; 12:15151. [PMID: 36071064 PMCID: PMC9452507 DOI: 10.1038/s41598-022-18506-z] [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: 07/27/2021] [Accepted: 08/08/2022] [Indexed: 11/18/2022] Open
Abstract
In this study, we generated whole-transcriptome RNA-Seq from n = 192 genotyped liver samples and used these data with existing data from the GTEx Project (RNA-Seq) and previous liver eQTL (microarray) studies to create an enhanced transcriptomic sequence resource in the human liver. Analyses of genotype-expression associations show pronounced enrichment of associations with genes of drug response. The associations are primarily consistent across the two RNA-Seq datasets, with some modest variation, indicating the importance of obtaining multiple datasets to produce a robust resource. We further used an empirical Bayesian model to compare eQTL patterns in liver and an additional 20 GTEx tissues, finding that MHC genes, and especially class II genes, are enriched for liver-specific eQTL patterns. To illustrate the utility of the resource to augment GWAS analysis with small sample sizes, we developed a novel meta-analysis technique to combine several liver eQTL data sources. We also illustrate its application using a transcriptome-enhanced re-analysis of a study of neutropenia in pancreatic cancer patients. The associations of genotype with liver expression, including splice variation and its genetic associations, are made available in a searchable genome browser.
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Affiliation(s)
- Yi-Hui Zhou
- Department of Biological Sciences, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA.
- Bioinformatics Research Center, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA.
| | - Paul J Gallins
- Bioinformatics Research Center, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA
| | - Amy S Etheridge
- Division of Pharmacotherapy and Experimental Therapeutics, UNC Eshelman School of Pharmacy, University of North Carolina, Chapel Hill, NC, 27599, USA
| | - Dereje Jima
- Bioinformatics Research Center, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA
| | - Elizabeth Scholl
- Bioinformatics Research Center, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA
| | - Fred A Wright
- Department of Biological Sciences, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA
- Bioinformatics Research Center, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA
- Department of Statistics, North Carolina State University, Raleigh NC State University, Raleigh, NC, 27695, USA
| | - Federico Innocenti
- Division of Pharmacotherapy and Experimental Therapeutics, UNC Eshelman School of Pharmacy, University of North Carolina, Chapel Hill, NC, 27599, USA.
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Xie Y, Li M, Dong W, Jiang W, Zhao H. M-DATA: A statistical approach to jointly analyzing de novo mutations for multiple traits. PLoS Genet 2021; 17:e1009849. [PMID: 34735430 PMCID: PMC8568192 DOI: 10.1371/journal.pgen.1009849] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 09/29/2021] [Indexed: 11/22/2022] Open
Abstract
Recent studies have demonstrated that multiple early-onset diseases have shared risk genes, based on findings from de novo mutations (DNMs). Therefore, we may leverage information from one trait to improve statistical power to identify genes for another trait. However, there are few methods that can jointly analyze DNMs from multiple traits. In this study, we develop a framework called M-DATA (Multi-trait framework for De novo mutation Association Test with Annotations) to increase the statistical power of association analysis by integrating data from multiple correlated traits and their functional annotations. Using the number of DNMs from multiple diseases, we develop a method based on an Expectation-Maximization algorithm to both infer the degree of association between two diseases as well as to estimate the gene association probability for each disease. We apply our method to a case study of jointly analyzing data from congenital heart disease (CHD) and autism. Our method was able to identify 23 genes for CHD from joint analysis, including 12 novel genes, which is substantially more than single-trait analysis, leading to novel insights into CHD disease etiology.
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Affiliation(s)
- Yuhan Xie
- Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, United States of America
| | - Mo Li
- Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, United States of America
| | - Weilai Dong
- Department of Genetics, Yale School of Medicine, New Haven, Connecticut, United States of America
| | - Wei Jiang
- Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, United States of America
| | - Hongyu Zhao
- Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, United States of America
- Department of Genetics, Yale School of Medicine, New Haven, Connecticut, United States of America
- Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut, United States of America
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A Multi-Omics Perspective of Quantitative Trait Loci in Precision Medicine. Trends Genet 2020; 36:318-336. [PMID: 32294413 DOI: 10.1016/j.tig.2020.01.009] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2019] [Revised: 01/05/2020] [Accepted: 01/21/2020] [Indexed: 02/07/2023]
Abstract
Quantitative trait loci (QTL) analysis is an important approach to investigate the effects of genetic variants identified through an increasing number of large-scale, multidimensional 'omics data sets. In this 'big data' era, the research community has identified a significant number of molecular QTLs (molQTLs) and increased our understanding of their effects. Herein, we review multiple categories of molQTLs, including those associated with transcriptome, post-transcriptional regulation, epigenetics, proteomics, metabolomics, and the microbiome. We summarize approaches to identify molQTLs and to infer their causal effects. We further discuss the integrative analysis of molQTLs through a multi-omics perspective. Our review highlights future opportunities to better understand the functional significance of genetic variants and to utilize the discovery of molQTLs in precision medicine.
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Abstract
Expression quantitative trait loci (eQTL) analysis identifies genetic variants that regulate the expression level of a gene. The genetic regulation may persist or vary in different tissues. When data are available on multiple tissues, it is often desired to borrow information across tissues and conduct an integrative analysis. Here we describe a multi-tissue eQTL analysis procedure, which improves the identification of different types of eQTL and facilitates the assessment of tissue specificity.
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Affiliation(s)
- Gen Li
- Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, NY, USA.
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Ray EL, Qian J, Brecha R, Reilly MP, Foulkes AS. Stochastic imputation for integrated transcriptome association analysis of a longitudinally measured trait. Stat Methods Med Res 2019; 29:1167-1180. [PMID: 31172883 DOI: 10.1177/0962280219852720] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The mechanistic pathways linking genetic polymorphisms and complex disease traits remain largely uncharacterized. At the same time, expansive new transcriptome data resources offer unprecedented opportunity to unravel the mechanistic underpinnings of complex disease associations. Two-stage strategies involving conditioning on a single, penalized regression imputation for transcriptome association analysis have been described for cross-sectional traits. In this manuscript, we propose an alternative two-stage approach based on stochastic regression imputation that additionally incorporates error in the predictive model. Application of a bootstrap procedure offers flexibility when a closed form predictive distribution is not available. The two-stage strategy is also generalized to longitudinally measured traits, using a linear mixed effects modeling framework and a composite test statistic to evaluate whether the genetic component of gene-level expression modifies the biomarker trajectory over time. Simulations studies are performed to evaluate relative performance with respect to type-1 error rates, coverage, estimation error, and power under a range of conditions. A case study is presented to investigate the association between whole blood expression for each of five inflammasome genes with inflammatory response over time after endotoxin challenge.
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Affiliation(s)
- Evan L Ray
- Department of Mathematics and Statistics, Mount Holyoke College, South Hadley, MA, USA
| | - Jing Qian
- Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences, University of Massachusetts, Amherst, MA, USA
| | - Regina Brecha
- Department of Mathematics and Statistics, Mount Holyoke College, South Hadley, MA, USA
| | | | - Andrea S Foulkes
- Department of Mathematics and Statistics, Mount Holyoke College, South Hadley, MA, USA
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Xiang D, Zhao SD, Tony Cai T. Signal classification for the integrative analysis of multiple sequences of large-scale multiple tests. J R Stat Soc Series B Stat Methodol 2019. [DOI: 10.1111/rssb.12323] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Dongdong Xiang
- East China Normal University; Shanghai People's Republic of China
| | | | - T. Tony Cai
- University of Pennsylvania; Philadelphia USA
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11
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Hu Y, Li M, Lu Q, Weng H, Wang J, Zekavat SM, Yu Z, Li B, Gu J, Muchnik S, Shi Y, Kunkle BW, Mukherjee S, Natarajan P, Naj A, Kuzma A, Zhao Y, Crane PK, Lu H, Zhao H. A statistical framework for cross-tissue transcriptome-wide association analysis. Nat Genet 2019; 51:568-576. [PMID: 30804563 PMCID: PMC6788740 DOI: 10.1038/s41588-019-0345-7] [Citation(s) in RCA: 245] [Impact Index Per Article: 40.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Accepted: 01/09/2019] [Indexed: 12/12/2022]
Abstract
Transcriptome-wide association analysis is a powerful approach to studying the genetic architecture of complex traits. A key component of this approach is to build a model to impute gene expression levels from genotypes by using samples with matched genotypes and gene expression data in a given tissue. However, it is challenging to develop robust and accurate imputation models with a limited sample size for any single tissue. Here, we first introduce a multi-task learning method to jointly impute gene expression in 44 human tissues. Compared with single-tissue methods, our approach achieved an average of 39% improvement in imputation accuracy and generated effective imputation models for an average of 120% more genes. We describe a summary-statistic-based testing framework that combines multiple single-tissue associations into a powerful metric to quantify the overall gene-trait association. We applied our method, called UTMOST (unified test for molecular signatures), to multiple genome-wide-association results and demonstrate its advantages over single-tissue strategies.
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Affiliation(s)
- Yiming Hu
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Mo Li
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Qiongshi Lu
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA
| | - Haoyi Weng
- Division of Biostatistics, The Jockey Club School of Public Health and Primary Care, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
| | - Jiawei Wang
- Program of Computational Biology and Bioinformatics, Yale University, New Haven, CT, USA
| | - Seyedeh M Zekavat
- Yale School of Medicine, New Haven, CT, USA
- Cardiovascular Research Center, Massachusetts General Hospital, Boston, MA, USA
- Program in Medical and Population Genetics, Broad Institute of MIT and Harvard, Cambridge, MA, USA
| | - Zhaolong Yu
- Program of Computational Biology and Bioinformatics, Yale University, New Haven, CT, USA
| | - Boyang Li
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Jianlei Gu
- SJTU-Yale Joint Center for Biostatistics, Department of Bioinformatics and Biostatistics, School of Life Sciences and Biotechnology, Shanghai Jiaotong University, Shanghai, China
| | - Sydney Muchnik
- Department of Genetics, Yale School of Medicine, New Haven, CT, USA
| | - Yu Shi
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Brian W Kunkle
- John P. Hussman Institute for Human Genomics, University of Miami Miller School of Medicine, Miami, FL, USA
| | | | - Pradeep Natarajan
- Cardiovascular Research Center, Massachusetts General Hospital, Boston, MA, USA
- Program in Medical and Population Genetics, Broad Institute of MIT and Harvard, Cambridge, MA, USA
- Department of Medicine, Harvard Medical School, Boston, MA, USA
- Center for Genomic Medicine, Massachusetts General Hospital, Boston, MA, USA
| | - Adam Naj
- Center for Clinical Epidemiology and Biostatistic, and the Department of Biostatistics, Epidemiology, and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
- Department of Pathology and Laboratory Medicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
| | - Amanda Kuzma
- Department of Pathology and Laboratory Medicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
| | - Yi Zhao
- Department of Pathology and Laboratory Medicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
| | - Paul K Crane
- Department of Medicine, University of Washington, Seattle, WA, USA
| | - Hui Lu
- SJTU-Yale Joint Center for Biostatistics, Department of Bioinformatics and Biostatistics, School of Life Sciences and Biotechnology, Shanghai Jiaotong University, Shanghai, China
| | - Hongyu Zhao
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA.
- Program of Computational Biology and Bioinformatics, Yale University, New Haven, CT, USA.
- SJTU-Yale Joint Center for Biostatistics, Department of Bioinformatics and Biostatistics, School of Life Sciences and Biotechnology, Shanghai Jiaotong University, Shanghai, China.
- Department of Genetics, Yale School of Medicine, New Haven, CT, USA.
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