Epistasis analysis for quantitative traits by functional regression model

GRAMMAR-Lambda Delivers Efficient Understanding of the Genetic Basis for Head Size in Catfish

The shape of the skull plays a crucial role in the evolution and adaptation of species to their environments. In the case of aquaculture fish, the size of the head is also an important economic trait, as it is linked to fillet yield and ornamental value. This study applies our GRAMMAR-Lambda method to perform a genome-wide association study analysis on loci related to head size in catfish. Compared with traditional GWAS methods, the GRAMMAR-Lambda method offers higher computational efficiency, statistical power, and stability, especially in complex population structures. This research identifies many candidate genes closely related to cranial morphology in terms of head length, width, and depth in catfish, including bmpr1bb, fgfrl1b, nipbl, foxp2, and pax5, etc. Based on the results of gene-gene interaction analysis, we speculate that there may be frequent genetic interactions between chromosome 19 and chromosome 29 in bone development. Additionally, many candidate genes, gene families, and mechanisms (such as SOCE mechanisms) affecting skeletal development and morphology have been identified. These findings contribute to our understanding of the genetic architecture of head size and will support marker-assisted breeding in aquaculture, also reflecting the potential application of the GRAMMAR-Lambda method in genetic studies of complex traits.

Genome-wide association study and genotypic variation for the major tocopherol content in rice grain

Rice tocopherols, vitamin E compounds with antioxidant activity, play essential roles in human health. Even though the key genes involved in vitamin E biosynthetic pathways have been identified in plants, the genetic architecture of vitamin E content in rice grain remains unclear. A genome-wide association study (GWAS) on 179 genotypically diverse rice accessions with 34,323 SNP markers was conducted to detect QTLs that define total and α- tocopherol contents in rice grains. Total and α-tocopherol contents had a strong positive correlation and varied greatly across the accessions, ranging from 0.230-31.76 and 0.011-30.83 (μg/g), respectively. A total of 13 QTLs were identified, which were spread across five of the rice chromosomes. Among the 13 QTLs, 11 were considered major with phenotypic variation explained (PVE) greater than 10%. Twelve transcription factor (TF) genes, one microprotein (miP), and a transposon were found to be associated with the QTLs with putative roles in controlling tocopherol contents. Moreover, intracellular transport proteins, ABC transporters, nonaspanins, and SNARE, were identified as associated genes on chromosomes 1 and 8. In the vicinity of seven QTLs, protein kinases were identified as key signaling factors. Haplotype analysis revealed the QTLs qAlph1.1, qTot1.1, qAlph2.1, qAlph6.1, qTot6.1, and qTot8.3 to have significant haplogroups. Quantitative RT-PCR validated the expression direction and magnitude of WRKY39 (Os02g0265200), PIP5Ks (Os08g0450800), and MADS59 (Os06g0347700) in defining the major tocopherol contents. This study provides insights for ongoing biofortification efforts to breed and/or engineer vitamin E and antioxidant levels in rice and other cereals.

Compressed variance component mixed model reveals epistasis associated with flowering in Arabidopsis

Introduction

Epistasis is currently a topic of great interest in molecular and quantitative genetics. Arabidopsis thaliana, as a model organism, plays a crucial role in studying the fundamental biology of diverse plant species. However, there have been limited reports about identification of epistasis related to flowering in genome-wide association studies (GWAS). Therefore, it is of utmost importance to conduct epistasis in Arabidopsis.

Method

In this study, we employed Levene's test and compressed variance component mixed model in GWAS to detect quantitative trait nucleotides (QTNs) and QTN-by-QTN interactions (QQIs) for 11 flowering-related traits of 199 Arabidopsis accessions with 216,130 markers.

Results

Our analysis detected 89 QTNs and 130 pairs of QQIs. Around these loci, 34 known genes previously reported in Arabidopsis were confirmed to be associated with flowering-related traits, such as SPA4, which is involved in regulating photoperiodic flowering, and interacts with PAP1 and PAP2, affecting growth of Arabidopsis under light conditions. Then, we observed significant and differential expression of 35 genes in response to variations in temperature, photoperiod, and vernalization treatments out of unreported genes. Functional enrichment analysis revealed that 26 of these genes were associated with various biological processes. Finally, the haplotype and phenotypic difference analysis revealed 20 candidate genes exhibiting significant phenotypic variations across gene haplotypes, of which the candidate genes AT1G12990 and AT1G09950 around QQIs might have interaction effect to flowering time regulation in Arabidopsis.

Discussion

These findings may offer valuable insights for the identification and exploration of genes and gene-by-gene interactions associated with flowering-related traits in Arabidopsis, that may even provide valuable reference and guidance for the research of epistasis in other species.

Cholecalciferol Supplementation Induced Up-Regulation of SARAF Gene and Down-Regulated miR-155-5p Expression in Slovenian Patients with Multiple Sclerosis

Multiple sclerosis is a common immune-mediated inflammatory and demyelinating disease. Lower cholecalciferol levels are an established environmental risk factor in multiple sclerosis. Although cholecalciferol supplementation in multiple sclerosis is widely accepted, optimal serum levels are still debated. Moreover, how cholecalciferol affects pathogenic disease mechanisms is still unclear. In the present study, we enrolled 65 relapsing-remitting multiple sclerosis patients who were double-blindly divided into two groups with low and high cholecalciferol supplementation, respectively. In addition to clinical and environmental parameters, we obtained peripheral blood mononuclear cells to analyze DNA, RNA, and miRNA molecules. Importantly, we investigated miRNA-155-5p, a previously published pro-inflammatory miRNA in multiple sclerosis known to be correlated to cholecalciferol levels. Our results show a decrease in miR-155-5p expression after cholecalciferol supplementation in both dosage groups, consistent with previous observations. Subsequent genotyping, gene expression, and eQTL analyses reveal correlations between miR-155-5p and the SARAF gene, which plays a role in the regulation of calcium release-activated channels. As such, the present study is the first to explore and suggest that the SARAF miR-155-5p axis hypothesis might be another mechanism by which cholecalciferol supplementation might decrease miR-155 expression. This association highlights the importance of cholecalciferol supplementation in multiple sclerosis and encourages further investigation and functional cell studies.

Gene Association Analysis of Quantitative Trait Based on Functional Linear Regression Model with Local Sparse Estimator

Functional linear regression models have been widely used in the gene association analysis of complex traits. These models retain all the genetic information in the data and take full advantage of spatial information in genetic variation data, which leads to brilliant detection power. However, the significant association signals identified by the high-power methods are not all the real causal SNPs, because it is easy to regard noise information as significant association signals, leading to a false association. In this paper, a method based on the sparse functional data association test (SFDAT) of gene region association analysis is developed based on a functional linear regression model with local sparse estimation. The evaluation indicators CSR and DL are defined to evaluate the feasibility and performance of the proposed method with other indicators. Simulation studies show that: (1) SFDAT performs well under both linkage equilibrium and linkage disequilibrium simulation; (2) SFDAT performs successfully for gene regions (including common variants, low-frequency variants, rare variants and mix variants); (3) With power and type I error rates comparable to OLS and Smooth, SFDAT has a better ability to handle the zero regions. The Oryza sativa data set is analyzed by SFDAT. It is shown that SFDAT can better perform gene association analysis and eliminate the false positive of gene localization. This study showed that SFDAT can lower the interference caused by noise while maintaining high power. SFDAT provides a new method for the association analysis between gene regions and phenotypic quantitative traits.

Human L1 Transposition Dynamics Unraveled with Functional Data Analysis

Long INterspersed Elements-1 (L1s) constitute >17% of the human genome and still actively transpose in it. Characterizing L1 transposition across the genome is critical for understanding genome evolution and somatic mutations. However, to date, L1 insertion and fixation patterns have not been studied comprehensively. To fill this gap, we investigated three genome-wide data sets of L1s that integrated at different evolutionary times: 17,037 de novo L1s (from an L1 insertion cell-line experiment conducted in-house), and 1,212 polymorphic and 1,205 human-specific L1s (from public databases). We characterized 49 genomic features-proxying chromatin accessibility, transcriptional activity, replication, recombination, etc.-in the ±50 kb flanks of these elements. These features were contrasted between the three L1 data sets and L1-free regions using state-of-the-art Functional Data Analysis statistical methods, which treat high-resolution data as mathematical functions. Our results indicate that de novo, polymorphic, and human-specific L1s are surrounded by different genomic features acting at specific locations and scales. This led to an integrative model of L1 transposition, according to which L1s preferentially integrate into open-chromatin regions enriched in non-B DNA motifs, whereas they are fixed in regions largely free of purifying selection-depleted of genes and noncoding most conserved elements. Intriguingly, our results suggest that L1 insertions modify local genomic landscape by extending CpG methylation and increasing mononucleotide microsatellite density. Altogether, our findings substantially facilitate understanding of L1 integration and fixation preferences, pave the way for uncovering their role in aging and cancer, and inform their use as mutagenesis tools in genetic studies.

Gene-Based Association Testing of Dichotomous Traits With Generalized Functional Linear Mixed Models Using Extended Pedigrees: Applications to Age-Related Macular Degeneration

Genetics plays a role in age-related macular degeneration (AMD), a common cause of blindness in the elderly. There is a need for powerful methods for carrying out region-based association tests between a dichotomous trait like AMD and genetic variants on family data. Here, we apply our new generalized functional linear mixed models (GFLMM) developed to test for gene-based association in a set of AMD families. Using common and rare variants, we observe significant association with two known AMD genes: CFH and ARMS2. Using rare variants, we find suggestive signals in four genes: ASAH1, CLEC6A, TMEM63C, and SGSM1. Intriguingly, ASAH1 is down-regulated in AMD aqueous humor, and ASAH1 deficiency leads to retinal inflammation and increased vulnerability to oxidative stress. These findings were made possible by our GFLMM which model the effect of a major gene as a fixed mean, the polygenic contributions as a random variation, and the correlation of pedigree members by kinship coefficients. Simulations indicate that the GFLMM likelihood ratio tests (LRTs) accurately control the Type I error rates. The LRTs have similar or higher power than existing retrospective kernel and burden statistics. Our GFLMM-based statistics provide a new tool for conducting family-based genetic studies of complex diseases. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Genetic control of non-genetic inheritance in mammals: state-of-the-art and perspectives

Thought to be directly and uniquely dependent from genotypes, the ontogeny of individual phenotypes is much more complicated. Individual genetics, environmental exposures, and their interaction are the three main determinants of individual's phenotype. This picture has been further complicated a decade ago when the Lamarckian theory of acquired inheritance has been rekindled with the discovery of epigenetic inheritance, according to which acquired phenotypes can be transmitted through fertilization and affect phenotypes across generations. The results of Genome-Wide Association Studies have also highlighted a big degree of missing heritability in genetics and have provided hints that not only acquired phenotypes, but also individual's genotypes affect phenotypes intergenerationally through indirect genetic effects. Here, we review available examples of indirect genetic effects in mammals, what is known of the underlying molecular mechanisms and their potential impact for our understanding of missing heritability, phenotypic variation. and individual disease risk.

How to increase our belief in discovered statistical interactions via large-scale association studies?

The understanding that differences in biological epistasis may impact disease risk, diagnosis, or disease management stands in wide contrast to the unavailability of widely accepted large-scale epistasis analysis protocols. Several choices in the analysis workflow will impact false-positive and false-negative rates. One of these choices relates to the exploitation of particular modelling or testing strategies. The strengths and limitations of these need to be well understood, as well as the contexts in which these hold. This will contribute to determining the potentially complementary value of epistasis detection workflows and is expected to increase replication success with biological relevance. In this contribution, we take a recently introduced regression-based epistasis detection tool as a leading example to review the key elements that need to be considered to fully appreciate the value of analytical epistasis detection performance assessments. We point out unresolved hurdles and give our perspectives towards overcoming these.

Global Genetic Networks and the Genotype-to-Phenotype Relationship

Genetic interactions identify combinations of genetic variants that impinge on phenotype. With whole-genome sequence information available for thousands of individuals within a species, a major outstanding issue concerns the interpretation of allelic combinations of genes underlying inherited traits. In this Review, we discuss how large-scale analyses in model systems have illuminated the general principles and phenotypic impact of genetic interactions. We focus on studies in budding yeast, including the mapping of a global genetic network. We emphasize how information gained from work in yeast translates to other systems, and how a global genetic network not only annotates gene function but also provides new insights into the genotype-to-phenotype relationship.

Behçet's disease and genetic interactions between HLA-B*51 and variants in genes of autoinflammatory syndromes

Behçet’s disease (BD) is an immune-mediated systemic disorder with a well-established genetic base. In a previous study, using a next generation sequencing approach, we found many rare variants and some functional polymorphisms in genes related to autoinflammatory syndromes (AID): CECR1, MEFV, MVK, NLRP3, NOD2, PSTPIP1 and TNFRSF1A in our BD cohort. Our strategy did not allow us to establish either number of patients with variants, proportion of individuals accumulating them or relationship with other genetic factors. With the goal to answer these questions, the individual samples were sequenced. Additionally, three functional polymorphisms: NLRP3 p.Gln703Lys, NOD2 p.Arg702Trp and p.Val955Ile were genotyped using TaqMan assays. A total of 98 patients (27.6%) carried at least one rare variant and 13 of them (3.7%) accumulated two or three. Functional regression model analysis suggests epistatic interaction between B51 and MEFV (P = 0.003). A suggestive protective association of the minor allele of NOD2 p.Arg702Trp (P = 0.01) was found in both, B51 positive and negative individuals. Therefore, a high percentage of patients with BD have rare variants in AID genes. Our results suggest that the association of MEFV with BD could be modulated by the HLA molecules; whereas the protective effect of NOD2 p.Arg702Trp would be independent of HLA.

A rapid epistatic mixed-model association analysis by linear retransformations of genomic estimated values

Motivation

Epistasis provides a feasible way for probing potential genetic mechanism of complex traits. However, time-consuming computation challenges successful detection of interaction in practice, especially when linear mixed model (LMM) is used to control type I error in the presence of population structure and cryptic relatedness.

Results

A rapid epistatic mixed-model association analysis (REMMA) method was developed to overcome computational limitation. This method first estimates individuals' epistatic effects by an extended genomic best linear unbiased prediction (EG-BLUP) model with additive and epistatic kinship matrix, then pairwise interaction effects are obtained by linear retransformations of individuals' epistatic effects. Simulation studies showed that REMMA could control type I error and increase statistical power in detecting epistatic QTNs in comparison with existing LMM-based FaST-LMM. We applied REMMA to two real datasets, a mouse dataset and the Wellcome Trust Case Control Consortium (WTCCC) data. Application to the mouse data further confirmed the performance of REMMA in controlling type I error. For the WTCCC data, we found most epistatic QTNs for type 1 diabetes (T1D) located in a major histocompatibility complex (MHC) region, from which a large interacting network with 12 hub genes (interacting with ten or more genes) was established.

Availability and implementation

Our REMMA method can be freely accessed at https://github.com/chaoning/REMMA.

Contact

liujf@cau.edu.cn.

Supplementary information

Supplementary data are available at Bioinformatics online.

Verticillium dahliae Disease Resistance and the Regulatory Pathway for Maturity and Tuberization in Potato

Kleb. is a pathogenic fungus causing wilting, chlorosis, and early dying in potato ( L.). Genetic mapping of resistance to was done using a diploid population of potato. The major quantitative trait locus (QTL) for resistance was found on chromosome 5. The gene, controlling earliness of maturity and tuberization, was mapped within the interval. Another QTL on chromosome 9 co-localized with the wilt resistance gene marker. Epistasis analysis indicated that the loci on chromosomes 5 and 9 had a highly significant interaction, and that functioned downstream of The alleles were sequenced and found to encode StCDF1.1 and StCDF1.3. Interaction between the resistance allele and the was demonstrated, but not for Genome-wide expression QTL (eQTL) analysis was performed and genes with eQTL at the and loci were both found to have similar functions involving the chloroplast, including photosynthesis, which declines in both maturity and wilt. Among the gene ontology (GO) terms that were specific to genes with eQTL at the , but not the locus, were those associated with fungal defense. These results suggest that controls fungal defense and reduces early dying in wilt through affecting genetic pathway controlling tuberization timing.

Functional regression method for whole genome eQTL epistasis analysis with sequencing data

Background

Epistasis plays an essential rule in understanding the regulation mechanisms and is an essential component of the genetic architecture of the gene expressions. However, interaction analysis of gene expressions remains fundamentally unexplored due to great computational challenges and data availability. Due to variation in splicing, transcription start sites, polyadenylation sites, post-transcriptional RNA editing across the entire gene, and transcription rates of the cells, RNA-seq measurements generate large expression variability and collectively create the observed position level read count curves. A single number for measuring gene expression which is widely used for microarray measured gene expression analysis is highly unlikely to sufficiently account for large expression variation across the gene. Simultaneously analyzing epistatic architecture using the RNA-seq and whole genome sequencing (WGS) data poses enormous challenges.

Methods

We develop a nonlinear functional regression model (FRGM) with functional responses where the position-level read counts within a gene are taken as a function of genomic position, and functional predictors where genotype profiles are viewed as a function of genomic position, for epistasis analysis with RNA-seq data. Instead of testing the interaction of all possible pair-wises SNPs, the FRGM takes a gene as a basic unit for epistasis analysis, which tests for the interaction of all possible pairs of genes and use all the information that can be accessed to collectively test interaction between all possible pairs of SNPs within two genome regions.

Results

By large-scale simulations, we demonstrate that the proposed FRGM for epistasis analysis can achieve the correct type 1 error and has higher power to detect the interactions between genes than the existing methods. The proposed methods are applied to the RNA-seq and WGS data from the 1000 Genome Project. The numbers of pairs of significantly interacting genes after Bonferroni correction identified using FRGM, RPKM and DESeq were 16,2361, 260 and 51, respectively, from the 350 European samples.

Conclusions

The proposed FRGM for epistasis analysis of RNA-seq can capture isoform and position-level information and will have a broad application. Both simulations and real data analysis highlight the potential for the FRGM to be a good choice of the epistatic analysis with sequencing data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-017-3777-4) contains supplementary material, which is available to authorized users.

Meta-analysis of quantitative pleiotropic traits for next-generation sequencing with multivariate functional linear models

To analyze next-generation sequencing data, multivariate functional linear models are developed for a meta-analysis of multiple studies to connect genetic variant data to multiple quantitative traits adjusting for covariates. The goal is to take the advantage of both meta-analysis and pleiotropic analysis in order to improve power and to carry out a unified association analysis of multiple studies and multiple traits of complex disorders. Three types of approximate F -distributions based on Pillai-Bartlett trace, Hotelling-Lawley trace, and Wilks's Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants. Simulation analysis is performed to evaluate false-positive rates and power of the proposed tests. The proposed methods are applied to analyze lipid traits in eight European cohorts. It is shown that it is more advantageous to perform multivariate analysis than univariate analysis in general, and it is more advantageous to perform meta-analysis of multiple studies instead of analyzing the individual studies separately. The proposed models require individual observations. The value of the current paper can be seen at least for two reasons: (a) the proposed methods can be applied to studies that have individual genotype data; (b) the proposed methods can be used as a criterion for future work that uses summary statistics to build test statistics to meta-analyze the data.

A Comparison Study of Fixed and Mixed Effect Models for Gene Level Association Studies of Complex Traits

In association studies of complex traits, fixed-effect regression models are usually used to test for association between traits and major gene loci. In recent years, variance-component tests based on mixed models were developed for region-based genetic variant association tests. In the mixed models, the association is tested by a null hypothesis of zero variance via a sequence kernel association test (SKAT), its optimal unified test (SKAT-O), and a combined sum test of rare and common variant effect (SKAT-C). Although there are some comparison studies to evaluate the performance of mixed and fixed models, there is no systematic analysis to determine when the mixed models perform better and when the fixed models perform better. Here we evaluated, based on extensive simulations, the performance of the fixed and mixed model statistics, using genetic variants located in 3, 6, 9, 12, and 15 kb simulated regions. We compared the performance of three models: (i) mixed models that lead to SKAT, SKAT-O, and SKAT-C, (ii) traditional fixed-effect additive models, and (iii) fixed-effect functional regression models. To evaluate the type I error rates of the tests of fixed models, we generated genotype data by two methods: (i) using all variants, (ii) using only rare variants. We found that the fixed-effect tests accurately control or have low false positive rates. We performed simulation analyses to compare power for two scenarios: (i) all causal variants are rare, (ii) some causal variants are rare and some are common. Either one or both of the fixed-effect models performed better than or similar to the mixed models except when (1) the region sizes are 12 and 15 kb and (2) effect sizes are small. Therefore, the assumption of mixed models could be satisfied and SKAT/SKAT-O/SKAT-C could perform better if the number of causal variants is large and each causal variant contributes a small amount to the traits (i.e., polygenes). In major gene association studies, we argue that the fixed-effect models perform better or similarly to mixed models in most cases because some variants should affect the traits relatively large. In practice, it makes sense to perform analysis by both the fixed and mixed effect models and to make a comparison, and this can be readily done using our R codes and the SKAT packages.

Integration and Fixation Preferences of Human and Mouse Endogenous Retroviruses Uncovered with Functional Data Analysis

Endogenous retroviruses (ERVs), the remnants of retroviral infections in the germ line, occupy ~8% and ~10% of the human and mouse genomes, respectively, and affect their structure, evolution, and function. Yet we still have a limited understanding of how the genomic landscape influences integration and fixation of ERVs. Here we conducted a genome-wide study of the most recently active ERVs in the human and mouse genome. We investigated 826 fixed and 1,065 in vitro HERV-Ks in human, and 1,624 fixed and 242 polymorphic ETns, as well as 3,964 fixed and 1,986 polymorphic IAPs, in mouse. We quantitated >40 human and mouse genomic features (e.g., non-B DNA structure, recombination rates, and histone modifications) in ±32 kb of these ERVs' integration sites and in control regions, and analyzed them using Functional Data Analysis (FDA) methodology. In one of the first applications of FDA in genomics, we identified genomic scales and locations at which these features display their influence, and how they work in concert, to provide signals essential for integration and fixation of ERVs. The investigation of ERVs of different evolutionary ages (young in vitro and polymorphic ERVs, older fixed ERVs) allowed us to disentangle integration vs. fixation preferences. As a result of these analyses, we built a comprehensive model explaining the uneven distribution of ERVs along the genome. We found that ERVs integrate in late-replicating AT-rich regions with abundant microsatellites, mirror repeats, and repressive histone marks. Regions favoring fixation are depleted of genes and evolutionarily conserved elements, and have low recombination rates, reflecting the effects of purifying selection and ectopic recombination removing ERVs from the genome. In addition to providing these biological insights, our study demonstrates the power of exploiting multiple scales and localization with FDA. These powerful techniques are expected to be applicable to many other genomic investigations.

Functional Regression Models for Epistasis Analysis of Multiple Quantitative Traits

To date, most genetic analyses of phenotypes have focused on analyzing single traits or analyzing each phenotype independently. However, joint epistasis analysis of multiple complementary traits will increase statistical power and improve our understanding of the complicated genetic structure of the complex diseases. Despite their importance in uncovering the genetic structure of complex traits, the statistical methods for identifying epistasis in multiple phenotypes remains fundamentally unexplored. To fill this gap, we formulate a test for interaction between two genes in multiple quantitative trait analysis as a multiple functional regression (MFRG) in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants. We use large-scale simulations to calculate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare the power with multivariate pairwise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for epistasis analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 267 pairs of genes that formed a genetic interaction network showed significant evidence of epistasis influencing five traits. The results demonstrate that the joint interaction analysis of multiple phenotypes has a much higher power to detect interaction than the interaction analysis of a single trait and may open a new direction to fully uncovering the genetic structure of multiple phenotypes.

The widely used statistical methods test interaction for single phenotype. However, we often observe pleotropic genetic interaction effects. The simultaneous gene-gene (GxG) interaction analysis of multiple complementary traits will increase statistical power to detect GxG interactions. Although GxG interactions play an important role in uncovering the genetic structure of complex traits, the statistical methods for detecting GxG interactions in multiple phenotypes remains less developed owing to its potential complexity. Therefore, we extend functional regression model from single variate to multivariate for simultaneous GxG interaction analysis of multiple correlated phenotypes. Large-scale simulations are conducted to evaluate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare power with traditional multivariate pair-wise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for interaction analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic GxG interactions. 267 pairs of genes that formed a genetic interaction network showed significant evidence of interactions influencing five traits.

Gene-Based Association Analysis for Censored Traits Via Fixed Effect Functional Regressions

Genetic studies of survival outcomes have been proposed and conducted recently, but statistical methods for identifying genetic variants that affect disease progression are rarely developed. Motivated by our ongoing real studies, here we develop Cox proportional hazard models using functional regression (FR) to perform gene-based association analysis of survival traits while adjusting for covariates. The proposed Cox models are fixed effect models where the genetic effects of multiple genetic variants are assumed to be fixed. We introduce likelihood ratio test (LRT) statistics to test for associations between the survival traits and multiple genetic variants in a genetic region. Extensive simulation studies demonstrate that the proposed Cox RF LRT statistics have well-controlled type I error rates. To evaluate power, we compare the Cox FR LRT with the previously developed burden test (BT) in a Cox model and sequence kernel association test (SKAT), which is based on mixed effect Cox models. The Cox FR LRT statistics have higher power than or similar power as Cox SKAT LRT except when 50%/50% causal variants had negative/positive effects and all causal variants are rare. In addition, the Cox FR LRT statistics have higher power than Cox BT LRT. The models and related test statistics can be useful in the whole genome and whole exome association studies. An age-related macular degeneration dataset was analyzed as an example.

Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models

We developed generalized functional linear models (GFLMs) to perform a meta-analysis of multiple case-control studies to evaluate the relationship of genetic data to dichotomous traits adjusting for covariates. Unlike the previously developed meta-analysis for sequence kernel association tests (MetaSKATs), which are based on mixed-effect models to make the contributions of major gene loci random, GFLMs are fixed models; i.e., genetic effects of multiple genetic variants are fixed. Based on GFLMs, we developed chi-squared-distributed Rao's efficient score test and likelihood-ratio test (LRT) statistics to test for an association between a complex dichotomous trait and multiple genetic variants. We then performed extensive simulations to evaluate the empirical type I error rates and power performance of the proposed tests. The Rao's efficient score test statistics of GFLMs are very conservative and have higher power than MetaSKATs when some causal variants are rare and some are common. When the causal variants are all rare [i.e., minor allele frequencies (MAF) < 0.03], the Rao's efficient score test statistics have similar or slightly lower power than MetaSKATs. The LRT statistics generate accurate type I error rates for homogeneous genetic-effect models and may inflate type I error rates for heterogeneous genetic-effect models owing to the large numbers of degrees of freedom and have similar or slightly higher power than the Rao's efficient score test statistics. GFLMs were applied to analyze genetic data of 22 gene regions of type 2 diabetes data from a meta-analysis of eight European studies and detected significant association for 18 genes (P < 3.10 × 10(-6)), tentative association for 2 genes (HHEX and HMGA2; P ≈ 10(-5)), and no association for 2 genes, while MetaSKATs detected none. In addition, the traditional additive-effect model detects association at gene HHEX. GFLMs and related tests can analyze rare or common variants or a combination of the two and can be useful in whole-genome and whole-exome association studies.

Review: High-performance computing to detect epistasis in genome scale data sets

It is becoming clear that most human diseases have a complex etiology that cannot be explained by single nucleotide polymorphisms (SNPs) or simple additive combinations; the general consensus is that they are caused by combinations of multiple genetic variations. The limited success of some genome-wide association studies is partly a result of this focus on single genetic markers. A more promising approach is to take into account epistasis, by considering the association of multiple SNP interactions with disease. However, as genomic data continues to grow in resolution, and genome and exome sequencing become more established, the number of combinations of variants to consider increases rapidly. Two potential solutions should be considered: the use of high-performance computing, which allows us to consider a larger number of variables, and heuristics to make the solution more tractable, essential in the case of genome sequencing. In this review, we look at different computational methods to analyse epistatic interactions within disease-related genetic data sets created by microarray technology. We also review efforts to use epistatic analysis results to produce biomarkers for diagnostic tests and give our views on future directions in this field in light of advances in sequencing technology and variants in non-coding regions.

Mixed Linear Model Approaches of Association Mapping for Complex Traits Based on Omics Variants

Precise prediction for genetic architecture of complex traits is impeded by the limited understanding on genetic effects of complex traits, especially on gene-by-gene (GxG) and gene-by-environment (GxE) interaction. In the past decades, an explosion of high throughput technologies enables omics studies at multiple levels (such as genomics, transcriptomics, proteomics, and metabolomics). The analyses of large omics data, especially two-loci interaction analysis, are very time intensive. Integrating the diverse omics data and environmental effects in the analyses also remain challenges. We proposed mixed linear model approaches using GPU (Graphic Processing Unit) computation to simultaneously dissect various genetic effects. Analyses can be performed for estimating genetic main effects, GxG epistasis effects, and GxE environment interaction effects on large-scale omics data for complex traits, and for estimating heritability of specific genetic effects. Both mouse data analyses and Monte Carlo simulations demonstrated that genetic effects and environment interaction effects could be unbiasedly estimated with high statistical power by using the proposed approaches.

Powerful Tukey's One Degree-of-Freedom Test for Detecting Gene-Gene and Gene-Environment Interactions

Genome-wide association studies (GWASs) have identified thousands of single nucleotide polymorphisms (SNPs) robustly associated with hundreds of complex human diseases including cancers. However, the large number of GWAS-identified genetic loci only explains a small proportion of the disease heritability. This “missing heritability” problem has been partly attributed to the yet-to-be-identified gene–gene (G × G) and gene–environment (G × E) interactions. In spite of the important roles of G × G and G × E interactions in understanding disease mechanisms and filling in the missing heritability, straightforward GWAS scanning for such interactions has very limited statistical power, leading to few successes. Here we propose a two-step statistical approach to test G × G/G × E interactions: the first step is to perform principal component analysis (PCA) on the multiple SNPs within a gene region, and the second step is to perform Tukey’s one degree-of-freedom (1-df) test on the leading PCs. We derive a score test that is computationally fast and numerically stable for the proposed Tukey’s 1-df interaction test. Using extensive simulations we show that the proposed approach, which combines the two parsimonious models, namely, the PCA and Tukey’s 1-df form of interaction, outperforms other state-of-the-art methods. We also demonstrate the utility and efficiency gains of the proposed method with applications to testing G × G interactions for Crohn’s disease using the Wellcome Trust Case Control Consortium (WTCCC) GWAS data and testing G × E interaction using data from a case–control study of pancreatic cancer.