Functional linear models for association analysis of quantitative traits

Bi-level structured functional analysis for genome-wide association studies

Genome-wide association studies (GWAS) have led to great successes in identifying genotype-phenotype associations for complex human diseases. In such studies, the high dimensionality of single nucleotide polymorphisms (SNPs) often makes analysis difficult. Functional analysis, which interprets SNPs densely distributed in a chromosomal region as a continuous process rather than discrete observations, has emerged as a promising avenue for overcoming the high dimensionality challenges. However, the majority of the existing functional studies continue to be individual SNP based and are unable to sufficiently account for the intricate underpinning structures of SNP data. SNPs are often found in groups (e.g., genes or pathways) and have a natural group structure. Additionally, these SNP groups can be highly correlated with coordinated biological functions and interact in a network. Motivated by these unique characteristics of SNP data, we develop a novel bi-level structured functional analysis method and investigate disease-associated genetic variants at the SNP level and SNP group level simultaneously. The penalization technique is adopted for bi-level selection and also to accommodate the group-level network structure. Both the estimation and selection consistency properties are rigorously established. The superiority of the proposed method over alternatives is shown through extensive simulation studies. A type 2 diabetes SNP data application yields some biologically intriguing results.

FunctanSNP: an R package for functional analysis of dense SNP data (with interactions)

SUMMARY

Densely measured SNP data are routinely analyzed but face challenges due to its high dimensionality, especially when gene-environment interactions are incorporated. In recent literature, a functional analysis strategy has been developed, which treats dense SNP measurements as a realization of a genetic function and can 'bypass' the dimensionality challenge. However, there is a lack of portable and friendly software, which hinders practical utilization of these functional methods. We fill this knowledge gap and develop the R package FunctanSNP. This comprehensive package encompasses estimation, identification, and visualization tools and has undergone extensive testing using both simulated and real data, confirming its reliability. FunctanSNP can serve as a convenient and reliable tool for analyzing SNP and other densely measured data.

AVAILABILITY AND IMPLEMENTATION

The package is available at https://CRAN.R-project.org/package=FunctanSNP.

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.

A comprehensive comparison of multilocus association methods with summary statistics in genome-wide association studies

BACKGROUND

Multilocus analysis on a set of single nucleotide polymorphisms (SNPs) pre-assigned within a gene constitutes a valuable complement to single-marker analysis by aggregating data on complex traits in a biologically meaningful way. However, despite the existence of a wide variety of SNP-set methods, few comprehensive comparison studies have been previously performed to evaluate the effectiveness of these methods.

RESULTS

We herein sought to fill this knowledge gap by conducting a comprehensive empirical comparison for 22 commonly-used summary-statistics based SNP-set methods. We showed that only seven methods could effectively control the type I error, and that these well-calibrated approaches had varying power performance under the simulation scenarios. Overall, we confirmed that the burden test was generally underpowered and score-based variance component tests (e.g., sequence kernel association test) were much powerful under the polygenic genetic architecture in both common and rare variant association analyses. We further revealed that two linkage-disequilibrium-free P value combination methods (e.g., harmonic mean P value method and aggregated Cauchy association test) behaved very well under the sparse genetic architecture in simulations and real-data applications to common and rare variant association analyses as well as in expression quantitative trait loci weighted integrative analysis. We also assessed the scalability of these approaches by recording computational time and found that all these methods can be scalable to biobank-scale data although some might be relatively slow.

CONCLUSION

In conclusion, we hope that our findings can offer an important guidance on how to choose appropriate multilocus association analysis methods in post-GWAS era. All the SNP-set methods are implemented in the R package called MCA, which is freely available at https://github.com/biostatpzeng/ .

sumSTAAR: A flexible framework for gene-based association studies using GWAS summary statistics

Gene-based association analysis is an effective gene-mapping tool. Many gene-based methods have been proposed recently. However, their power depends on the underlying genetic architecture, which is rarely known in complex traits, and so it is likely that a combination of such methods could serve as a universal approach. Several frameworks combining different gene-based methods have been developed. However, they all imply a fixed set of methods, weights and functional annotations. Moreover, most of them use individual phenotypes and genotypes as input data. Here, we introduce sumSTAAR, a framework for gene-based association analysis using summary statistics obtained from genome-wide association studies (GWAS). It is an extended and modified version of STAAR framework proposed by Li and colleagues in 2020. The sumSTAAR framework offers a wider range of gene-based methods to combine. It allows the user to arbitrarily define a set of these methods, weighting functions and probabilities of genetic variants being causal. The methods used in the framework were adapted to analyse genes with large number of SNPs to decrease the running time. The framework includes the polygene pruning procedure to guard against the influence of the strong GWAS signals outside the gene. We also present new improved matrices of correlations between the genotypes of variants within genes. These matrices estimated on a sample of 265,000 individuals are a state-of-the-art replacement of widely used matrices based on the 1000 Genomes Project data.

Gene-based association analysis is an effective gene mapping tool. Quite a few frameworks have been proposed recently for gene-based association analysis using a combination of different methods. However, all of these frameworks have at least one of the disadvantages: they use a fixed set of methods, they cannot use functional annotations, or they use individual phenotypes and genotypes as input data. To overcome these limitations, we propose sumSTAAR, a framework for gene-based association analysis using GWAS summary statistics. Our framework allows the user to arbitrarily define a set of the methods and functional annotations. Moreover, we adopted the methods for the analysis of genes with a large number of SNPs to decrease the running time. The framework includes the polygene pruning procedure to guard against the influence of the strong GWAS signals outside the gene. We also present new improved matrices of correlations between the genotypes of variants within genes, which now allows to include ultra-rare variants (MAF < 10⁻⁴) in analysis.

Gene-level association analysis of ordinal traits with functional ordinal logistic regressions

In this paper, we develop functional ordinal logistic regression (FOLR) models to perform gene-based analysis of ordinal traits. In the proposed FOLR models, genetic variant data are viewed as stochastic functions of physical positions and the genetic effects are treated as a function of physical positions. The FOLR models are built upon functional data analysis which can be revised to analyze the ordinal traits and high dimension genetic data. The proposed methods are capable of dealing with dense genotype data which is usually encountered in analyzing the next-generation sequencing data. The methods are flexible and can analyze three types of genetic data: (1) rare variants only, (2) common variants only, and (3) a combination of rare and common variants. Simulation studies show that the likelihood ratio test statistics of the FOLR models control type I errors well and have good power performance. The proposed methods achieve the goals of analyzing ordinal traits directly, reducing high dimensionality of dense genetic variants, being computationally manageable, facilitating model convergence, properly controlling type I errors, and maintaining high power levels. The FOLR models are applied to analyze Age-Related Eye Disease Study data, in which two genes are found to strongly associate with four ordinal traits.

Gene Region Association Analysis of Longitudinal Quantitative Traits Based on a Function-On-Function Regression Model

In the process of growth and development in life, gene expressions that control quantitative traits will turn on or off with time. Studies of longitudinal traits are of great significance in revealing the genetic mechanism of biological development. With the development of ultra-high-density sequencing technology, the associated analysis has tremendous challenges to statistical methods. In this paper, a longitudinal functional data association test (LFDAT) method is proposed based on the function-on-function regression model. LFDAT can simultaneously treat phenotypic traits and marker information as continuum variables and analyze the association of longitudinal quantitative traits and gene regions. Simulation studies showed that: 1) LFDAT performs well for both linkage equilibrium simulation and linkage disequilibrium simulation, 2) LFDAT has better performance for gene regions (include common variants, low-frequency variants, rare variants and mixture), and 3) LFDAT can accurately identify gene switching in the growth and development stage. The longitudinal data of the Oryza sativa projected shoot area is analyzed by LFDAT. It showed that there is the advantage of quick calculations. Further, an association analysis was conducted between longitudinal traits and gene regions by integrating the micro effects of multiple related variants and using the information of the entire gene region. LFDAT provides a feasible method for studying the formation and expression of longitudinal traits.

Simulation Research on the Methods of Multi-Gene Region Association Analysis Based on a Functional Linear Model

Genome-wide association analysis is an important approach to identify genetic variants associated with complex traits. Complex traits are not only affected by single gene loci, but also by the interaction of multiple gene loci. Studies of association between gene regions and quantitative traits are of great significance in revealing the genetic mechanism of biological development. There have been a lot of studies on single-gene region association analysis, but the application of functional linear models in multi-gene region association analysis is still less. In this paper, a functional multi-gene region association analysis test method is proposed based on the functional linear model. From the three directions of common multi-gene region method, multi-gene region weighted method and multi-gene region loci weighted method, that test method is studied combined with computer simulation. The following conclusions are obtained through computer simulation: (a) The functional multi-gene region association analysis test method has higher power than the functional single gene region association analysis test method; (b) The functional multi-gene region weighted method performs better than the common functional multi-gene region method; (c) the functional multi-gene region loci weighted method is the best method for association analysis on three directions of the common multi-gene region method; (d) the performance of the Step method and Multi-gene region loci weighted Step for multi-gene regions is the best in general. Functional multi-gene region association analysis test method can theoretically provide a feasible method for the study of complex traits affected by multiple genes.

A Multi-Marker Test for Analyzing Paired Genetic Data in Transplantation

Emerging evidence suggests that donor/recipient matching in non-HLA (human leukocyte antigen) regions of the genome may impact transplant outcomes and recognizing these matching effects may increase the power of transplant genetics studies. Most available matching scores account for either single-nucleotide polymorphism (SNP) matching only or sum these SNP matching scores across multiple gene-coding regions, which makes it challenging to interpret the association findings. We propose a multi-marker Joint Score Test (JST) to jointly test for association between recipient genotype SNP effects and a gene-based matching score with transplant outcomes. This method utilizes Eigen decomposition as a dimension reduction technique to potentially increase statistical power by decreasing the degrees of freedom for the test. In addition, JST allows for the matching effect and the recipient genotype effect to follow different biological mechanisms, which is not the case for other multi-marker methods. Extensive simulation studies show that JST is competitive when compared with existing methods, such as the sequence kernel association test (SKAT), especially under scenarios where associated SNPs are in low linkage disequilibrium with non-associated SNPs or in gene regions containing a large number of SNPs. Applying the method to paired donor/recipient genetic data from kidney transplant studies yields various gene regions that are potentially associated with incidence of acute rejection after transplant.

A Constrained Generalized Functional Linear Model for Multi-Loci Genetic Mapping

In genome-wide association studies (GWAS), efficient incorporation of linkage disequilibria (LD) among densely typed genetic variants into association analysis is a critical yet challenging problem. Functional linear models (FLM), which impose a smoothing structure on the coefficients of correlated covariates, are advantageous in genetic mapping of multiple variants with high LD. Here we propose a novel constrained generalized FLM (cGFLM) framework to perform simultaneous association tests on a block of linked SNPs with various trait types, including continuous, binary and zero-inflated count phenotypes. The new cGFLM applies a set of inequality constraints on the FLM to ensure model identifiability under different genetic codings. The method is implemented via B-splines, and an augmented Lagrangian algorithm is employed for parameter estimation. For hypotheses testing, a test statistic that accounts for the model constraints was derived, following a mixture of chi-square distributions. Simulation results show that cGFLM is effective in identifying causal loci and gene clusters compared to several competing methods based on single markers and SKAT-C. We applied the proposed method to analyze a candidate gene-based COGEND study and a large-scale GWAS data on dental caries risk.

A region-based method for causal mediation analysis of DNA methylation data

Exposure to environmental factors can affect DNA methylation at a 5'-cytosine-phosphate-guanine-3' (CpG) site or a genomic region, which can then affect an outcome. In other words, environmental effects on an outcome could be mediated by DNA methylation. To date, single CpG-site-based mediation analysis has been employed extensively. More recently, however, there has been considerable interest in studying differentially methylated regions (DMRs), both because DMRs are more likely to have functional effects than single CpG sites and because testing DMRs reduces multiple testing. In this report, we propose a novel causal mediation approach under the counterfactual framework to test the significance of total (TE), direct (DE), and indirect effects (IE) of predictors on response variable with a methylated region (MR) as the mediator (denoted as MR-Mediation). Functional linear transformation is used to reduce the possible high dimension of the CpG sites in a predefined MR and to account for their location information. In our simulation studies, MR-Mediation retained the desired Type I error rates for TE, DE, and IE tests. Furthermore, MR-Mediation had better power performance than testing mean methylation level as the mediator in most considered scenarios, especially for IE (i.e., mediated effect) test, which could be more interesting than the other two effect tests. We further illustrate our proposed method by analysing the methylation mediated effect of exposure to gun violence on total immunoglobulin E or atopic asthma among participants in the Epigenetic Variation and Childhood Asthma in Puerto Ricans study.

Gene-based analysis of bi-variate survival traits via functional regressions with applications to eye diseases

Genetic studies of two related survival outcomes of a pleiotropic gene are commonly encountered but statistical models to analyze them are rarely developed. To analyze sequencing data, we propose mixed effect Cox proportional hazard models by functional regressions to perform gene-based joint association analysis of two survival traits motivated by our ongoing real studies. These models extend fixed effect Cox models of univariate survival traits by incorporating variations and correlation of multivariate survival traits into the models. The associations between genetic variants and two survival traits are tested by likelihood ratio test statistics. Extensive simulation studies suggest that type I error rates are well controlled and power performances are stable. The proposed models are applied to analyze bivariate survival traits of left and right eyes in the age-related macular degeneration progression.

Integrative functional linear model for genome-wide association studies with multiple traits

In recent biomedical research, genome-wide association studies (GWAS) have demonstrated great success in investigating the genetic architecture of human diseases. For many complex diseases, multiple correlated traits have been collected. However, most of the existing GWAS are still limited because they analyze each trait separately without considering their correlations and suffer from a lack of sufficient information. Moreover, the high dimensionality of single nucleotide polymorphism (SNP) data still poses tremendous challenges to statistical methods, in both theoretical and practical aspects. In this article, we innovatively propose an integrative functional linear model for GWAS with multiple traits. This study is the first to approximate SNPs as functional objects in a joint model of multiple traits with penalization techniques. It effectively accommodates the high dimensionality of SNPs and correlations among multiple traits to facilitate information borrowing. Our extensive simulation studies demonstrate the satisfactory performance of the proposed method in the identification and estimation of disease-associated genetic variants, compared to four alternatives. The analysis of type 2 diabetes data leads to biologically meaningful findings with good prediction accuracy and selection stability.

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.

Gene-based association tests using GWAS summary statistics

MOTIVATION

A huge number of genome-wide association studies (GWAS) summary statistics freely available in databases provide a new material for gene-based association analysis aimed at identifying rare genetic variants. Only a few of the many popular gene-based methods developed for individual genotype and phenotype data are adapted for the practical use of the GWAS summary statistics as input.

RESULTS

We analytically prove and numerically illustrate that all popular powerful methods developed for gene-based association analysis of individual phenotype and genotype data can be modified to utilize GWAS summary statistics. We have modified and implemented all of the popular methods, including burden and kernel machine-based tests, multiple and functional linear regression, principal components analysis and others, in the R package sumFREGAT. Using real summary statistics for coronary artery disease, we show that the new package is able to detect genes not found by the existing packages.

AVAILABILITY AND IMPLEMENTATION

The R package sumFREGAT is freely and publicly available at: https://CRAN.R-project.org/package=sumFREGAT.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Adaptive Fisher method detects dense and sparse signals in association analysis of SNV sets

BACKGROUND

With the development of next generation sequencing (NGS) technology and genotype imputation methods, statistical methods have been proposed to test a set of genomic variants together to detect if any of them is associated with the phenotype or disease. In practice, within the set, there is an unknown proportion of variants truly causal or associated with the disease. There is a demand for statistical methods with high power in both dense and sparse scenarios, where the proportion of causal or associated variants is large or small respectively.

RESULTS

We propose a new association test - weighted Adaptive Fisher (wAF) that can adapt to both dense and sparse scenarios by adding weights to the Adaptive Fisher (AF) method we developed before. Using simulation, we show that wAF enjoys comparable or better power to popular methods such as sequence kernel association tests (SKAT and SKAT-O) and adaptive SPU (aSPU) test. We apply wAF to a publicly available schizophrenia dataset, and successfully detect thirteen genes. Among them, three genes are supported by existing literature; six are plausible as they either relate to other neurological diseases or have relevant biological functions.

CONCLUSIONS

The proposed wAF method is a powerful disease-variants association test in both dense and sparse scenarios. Both simulation studies and real data analysis indicate the potential of wAF for new biological findings.

Gene-based association analysis for bivariate time-to-event data through functional regression with copula models

Several gene-based association tests for time-to-event traits have been proposed recently to detect whether a gene region (containing multiple variants), as a set, is associated with the survival outcome. However, for bivariate survival outcomes, to the best of our knowledge, there is no statistical method that can be directly applied for gene-based association analysis. Motivated by a genetic study to discover the gene regions associated with the progression of a bilateral eye disease, age-related macular degeneration (AMD), we implement a novel functional regression (FR) method under the copula framework. Specifically, the effects of variants within a gene region are modeled through a functional linear model, which then contributes to the marginal survival functions within the copula. Generalized score test statistics are derived to test for the association between bivariate survival traits and the genetic region. Extensive simulation studies are conducted to evaluate the type I error control and power performance of the proposed approach, with comparisons to several existing methods for a single survival trait, as well as the marginal Cox FR model using the robust sandwich estimator for bivariate survival traits. Finally, we apply our method to a large AMD study, the Age-related Eye Disease Study, and to identify the gene regions that are associated with AMD progression.

Gene-based association analysis of survival traits via functional regression-based mixed effect cox models for related samples

The importance to integrate survival analysis into genetics and genomics is widely recognized, but only a small number of statisticians have produced relevant work toward this study direction. For unrelated population data, functional regression (FR) models have been developed to test for association between a quantitative/dichotomous/survival trait and genetic variants in a gene region. In major gene association analysis, these models have higher power than sequence kernel association tests. In this paper, we extend this approach to analyze censored traits for family data or related samples using FR based mixed effect Cox models (FamCoxME). The FamCoxME model effect of major gene as fixed mean via functional data analysis techniques, the local gene or polygene variations or both as random, and the correlation of pedigree members by kinship coefficients or genetic relationship matrix or both. The association between the censored trait and the major gene is tested by likelihood ratio tests (FamCoxME FR LRT). Simulation results indicate that the LRT control the type I error rates accurately/conservatively and have good power levels when both local gene or polygene variations are modeled. The proposed methods were applied to analyze a breast cancer data set from the Consortium of Investigators of Modifiers of BRCA1 and BRCA2 (CIMBA). The FamCoxME provides a new tool for gene-based analysis of family-based studies or related samples.

A generalized model for combining dependent SNP-level summary statistics and its extensions to statistics of other levels

Here I propose a fundamentally new flexible model to reveal the association between a trait and a set of genetic variants in a genomic region/gene. This model was developed for the situation when original individual-level phenotype and genotype data are not available, but the researcher possesses the results of statistical analyses conducted on these data (namely, SNP-level summary Z score statistics and SNP-by-SNP correlations). The new model was analytically derived from the classical multiple linear regression model applied for the region-based association analysis of individual-level phenotype and genotype data by using the linear compression of data, where the SNP-by-SNP correlations are among the explanatory variables, and the summary Z score statistics are categorized as the response variables. I analytically show that the regional association analysis methods developed within the framework of the classical multiple linear regression model with additive effects of genetic variants can be reformulated in terms of the new model without the loss of information. The results obtained from the regional association analysis utilizing the classical model and those derived using the proposed model are identical when SNP-by-SNP correlations and SNP-level statistics are estimated from the same genetic data.

Linear mixed models for association analysis of quantitative traits with next-generation sequencing data

We develop linear mixed models (LMMs) and functional linear mixed models (FLMMs) for gene-based tests of association between a quantitative trait and genetic variants on pedigrees. The effects of a major gene are modeled as a fixed effect, the contributions of polygenes are modeled as a random effect, and the correlations of pedigree members are modeled via inbreeding/kinship coefficients. F -statistics and χ 2 likelihood ratio test (LRT) statistics based on the LMMs and FLMMs are constructed to test for association. We show empirically that the F -distributed statistics provide a good control of the type I error rate. The F -test statistics of the LMMs have similar or higher power than the FLMMs, kernel-based famSKAT (family-based sequence kernel association test), and burden test famBT (family-based burden test). The F -statistics of the FLMMs perform well when analyzing a combination of rare and common variants. For small samples, the LRT statistics of the FLMMs control the type I error rate well at the nominal levels α = 0.01 and 0.05 . For moderate/large samples, the LRT statistics of the FLMMs control the type I error rates well. The LRT statistics of the LMMs can lead to inflated type I error rates. The proposed models are useful in whole genome and whole exome association studies of complex traits.

Weighted functional linear regression models for gene-based association analysis

Functional linear regression models are effectively used in gene-based association analysis of complex traits. These models combine information about individual genetic variants, taking into account their positions and reducing the influence of noise and/or observation errors. To increase the power of methods, where several differently informative components are combined, weights are introduced to give the advantage to more informative components. Allele-specific weights have been introduced to collapsing and kernel-based approaches to gene-based association analysis. Here we have for the first time introduced weights to functional linear regression models adapted for both independent and family samples. Using data simulated on the basis of GAW17 genotypes and weights defined by allele frequencies via the beta distribution, we demonstrated that type I errors correspond to declared values and that increasing the weights of causal variants allows the power of functional linear models to be increased. We applied the new method to real data on blood pressure from the ORCADES sample. Five of the six known genes with P < 0.1 in at least one analysis had lower P values with weighted models. Moreover, we found an association between diastolic blood pressure and the VMP1 gene (P = 8.18×10-6), when we used a weighted functional model. For this gene, the unweighted functional and weighted kernel-based models had P = 0.004 and 0.006, respectively. The new method has been implemented in the program package FREGAT, which is freely available at https://cran.r-project.org/web/packages/FREGAT/index.html.

Assessing Rare Variation in Complex Traits

While genome-wide association studies have been very successful in identifying associations of common genetic variants with many different traits, the rarer frequency spectrum of the genome has not yet been comprehensively explored. Technological developments increasingly lift restrictions to access rare genetic variation. Dense reference panels enable improved genotype imputation for rarer variants in studies using DNA microarrays. Moreover, the decreasing cost of next generation sequencing makes whole exome and genome sequencing increasingly affordable for large samples. Large-scale efforts based on sequencing, such as ExAC, 100,000 Genomes, and TopMed, are likely to significantly advance this field.The main challenge in evaluating complex trait associations of rare variants is statistical power. The choice of population should be considered carefully because allele frequencies and linkage disequilibrium structure differ between populations. Genetically isolated populations can have favorable genomic characteristics for the study of rare variants.One strategy to increase power is to assess the combined effect of multiple rare variants within a region, known as aggregate testing. A  range of methods have been developed for this. Model performance depends on the genetic architecture of the region of interest.

Iterative hard thresholding for model selection in genome-wide association studies

A genome-wide association study (GWAS) correlates marker and trait variation in a study sample. Each subject is genotyped at a multitude of SNPs (single nucleotide polymorphisms) spanning the genome. Here, we assume that subjects are randomly collected unrelateds and that trait values are normally distributed or can be transformed to normality. Over the past decade, geneticists have been remarkably successful in applying GWAS analysis to hundreds of traits. The massive amount of data produced in these studies present unique computational challenges. Penalized regression with the ℓ₁ penalty (LASSO) or minimax concave penalty (MCP) penalties is capable of selecting a handful of associated SNPs from millions of potential SNPs. Unfortunately, model selection can be corrupted by false positives and false negatives, obscuring the genetic underpinning of a trait. Here, we compare LASSO and MCP penalized regression to iterative hard thresholding (IHT). On GWAS regression data, IHT is better at model selection and comparable in speed to both methods of penalized regression. This conclusion holds for both simulated and real GWAS data. IHT fosters parallelization and scales well in problems with large numbers of causal markers. Our parallel implementation of IHT accommodates SNP genotype compression and exploits multiple CPU cores and graphics processing units (GPUs). This allows statistical geneticists to leverage commodity desktop computers in GWAS analysis and to avoid supercomputing.

AVAILABILITY

Source code is freely available at https://github.com/klkeys/IHT.jl.

A functional U-statistic method for association analysis of sequencing data

Although sequencing studies hold great promise for uncovering novel variants predisposing to human diseases, the high dimensionality of the sequencing data brings tremendous challenges to data analysis. Moreover, for many complex diseases (e.g., psychiatric disorders) multiple related phenotypes are collected. These phenotypes can be different measurements of an underlying disease, or measurements characterizing multiple related diseases for studying common genetic mechanism. Although jointly analyzing these phenotypes could potentially increase the power of identifying disease-associated genes, the different types of phenotypes pose challenges for association analysis. To address these challenges, we propose a nonparametric method, functional U-statistic method (FU), for multivariate analysis of sequencing data. It first constructs smooth functions from individuals' sequencing data, and then tests the association of these functions with multiple phenotypes by using a U-statistic. The method provides a general framework for analyzing various types of phenotypes (e.g., binary and continuous phenotypes) with unknown distributions. Fitting the genetic variants within a gene using a smoothing function also allows us to capture complexities of gene structure (e.g., linkage disequilibrium, LD), which could potentially increase the power of association analysis. Through simulations, we compared our method to the multivariate outcome score test (MOST), and found that our test attained better performance than MOST. In a real data application, we apply our method to the sequencing data from Minnesota Twin Study (MTS) and found potential associations of several nicotine receptor subunit (CHRN) genes, including CHRNB3, associated with nicotine dependence and/or alcohol dependence.

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 multivariate fixed models and Gene Association with Multiple Traits (GAMuT) for next-generation sequencing

In this paper, extensive simulations are performed to compare two statistical methods to analyze multiple correlated quantitative phenotypes: (1) approximate F-distributed tests of multivariate functional linear models (MFLM) and additive models of multivariate analysis of variance (MANOVA), and (2) Gene Association with Multiple Traits (GAMuT) for association testing of high-dimensional genotype data. It is shown that approximate F-distributed tests of MFLM and MANOVA have higher power and are more appropriate for major gene association analysis (i.e., scenarios in which some genetic variants have relatively large effects on the phenotypes); GAMuT has higher power and is more appropriate for analyzing polygenic effects (i.e., effects from a large number of genetic variants each of which contributes a small amount to the phenotypes). MFLM and MANOVA are very flexible and can be used to perform association analysis for (i) rare variants, (ii) common variants, and (iii) a combination of rare and common variants. Although GAMuT was designed to analyze rare variants, it can be applied to analyze a combination of rare and common variants and it performs well when (1) the number of genetic variants is large and (2) each variant contributes a small amount to the phenotypes (i.e., polygenes). MFLM and MANOVA are fixed effect models that perform well for major gene association analysis. GAMuT can be viewed as an extension of sequence kernel association tests (SKAT). Both GAMuT and SKAT are more appropriate for analyzing polygenic effects and they perform well not only in the rare variant case, but also in the case of a combination of rare and common variants. Data analyses of European cohorts and the Trinity Students Study are presented to compare the performance of the two methods.

A new statistical framework for genetic pleiotropic analysis of high dimensional phenotype data

BACKGROUND

The widely used genetic pleiotropic analyses of multiple phenotypes are often designed for examining the relationship between common variants and a few phenotypes. They are not suited for both high dimensional phenotypes and high dimensional genotype (next-generation sequencing) data. To overcome limitations of the traditional genetic pleiotropic analysis of multiple phenotypes, we develop sparse structural equation models (SEMs) as a general framework for a new paradigm of genetic analysis of multiple phenotypes. To incorporate both common and rare variants into the analysis, we extend the traditional multivariate SEMs to sparse functional SEMs. To deal with high dimensional phenotype and genotype data, we employ functional data analysis and the alternative direction methods of multiplier (ADMM) techniques to reduce data dimension and improve computational efficiency.

RESULTS

Using large scale simulations we showed that the proposed methods have higher power to detect true causal genetic pleiotropic structure than other existing methods. Simulations also demonstrate that the gene-based pleiotropic analysis has higher power than the single variant-based pleiotropic analysis. The proposed method is applied to exome sequence data from the NHLBI's Exome Sequencing Project (ESP) with 11 phenotypes, which identifies a network with 137 genes connected to 11 phenotypes and 341 edges. Among them, 114 genes showed pleiotropic genetic effects and 45 genes were reported to be associated with phenotypes in the analysis or other cardiovascular disease (CVD) related phenotypes in the literature.

CONCLUSIONS

Our proposed sparse functional SEMs can incorporate both common and rare variants into the analysis and the ADMM algorithm can efficiently solve the penalized SEMs. Using this model we can jointly infer genetic architecture and casual phenotype network structure, and decompose the genetic effect into direct, indirect and total effect. Using large scale simulations we showed that the proposed methods have higher power to detect true causal genetic pleiotropic structure than other existing methods.

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.

Utilizing mutual information for detecting rare and common variants associated with a categorical trait

Background. Genome-wide association studies have succeeded in detecting novel common variants which associate with complex diseases. As a result of the fast changes in next generation sequencing technology, a large number of sequencing data are generated, which offers great opportunities to identify rare variants that could explain a larger proportion of missing heritability. Many effective and powerful methods are proposed, although they are usually limited to continuous, dichotomous or ordinal traits. Notice that traits having nominal categorical features are commonly observed in complex diseases, especially in mental disorders, which motivates the incorporation of the characteristics of the categorical trait into association studies with rare and common variants.

Methods. We construct two simple and intuitive nonparametric tests, MIT and aMIT, based on mutual information for detecting association between genetic variants in a gene or region and a categorical trait. MIT and aMIT can gauge the difference among the distributions of rare and common variants across a region given every categorical trait value. If there is little association between variants and a categorical trait, MIT or aMIT approximately equals zero. The larger the difference in distributions, the greater values MIT and aMIT have. Therefore, MIT and aMIT have the potential for detecting functional variants.

Results.We checked the validity of proposed statistics and compared them to the existing ones through extensive simulation studies with varied combinations of the numbers of variants of rare causal, rare non-causal, common causal, and common non-causal, deleterious and protective, various minor allele frequencies and different levels of linkage disequilibrium. The results show our methods have higher statistical power than conventional ones, including the likelihood based score test, in most cases: (1) there are multiple genetic variants in a gene or region; (2) both protective and deleterious variants are present; (3) there exist rare and common variants; and (4) more than half of the variants are neutral. The proposed tests are applied to the data from Collaborative Studies on Genetics of Alcoholism, and a competent performance is exhibited therein.

Discussion. As a complementary to the existing methods mainly focusing on quantitative traits, this study provides the nonparametric tests MIT and aMIT for detecting variants associated with categorical trait. Furthermore, we plan to investigate the association between rare variants and multiple categorical traits.

Some pitfalls in application of functional data analysis approach to association studies

One of the most effective methods for gene-based mapping employs functional data analysis, which smoothes data using standard basis functions. The full functional linear model includes a functional representation of genotypes and their effects, while the beta-smooth only model smoothes the genotype effects only. Benefits and limitations of the beta-smooth only model should be studied before using it in practice. Here we analytically compare the full and beta-smooth only models under various scenarios. We show that when the full model employs two sets of basis functions equal in type and number, genotypes smoothing is eliminated from the model and it becomes analytically equivalent to the beta-smooth only model. If the basis functions differ only in type, genotypes smoothing is also eliminated from the full model, but the type of basis functions used for smoothing genotype effects becomes redefined. This leads to misinterpretation of the results and may reduce statistical power. When basis functions differ in number, no analytical comparison of the full and beta-smooth only models is possible. However, we show that the numbers of basis functions set unequal can become equal during the analysis, and the full model becomes disadvantageous.

Uncovering Local Trends in Genetic Effects of Multiple Phenotypes via Functional Linear Models

Recent technological advances equipped researchers with capabilities that go beyond traditional genotyping of loci known to be polymorphic in a general population. Genetic sequences of study participants can now be assessed directly. This capability removed technology-driven bias toward scoring predominantly common polymorphisms and let researchers reveal a wealth of rare and sample-specific variants. Although the relative contributions of rare and common polymorphisms to trait variation are being debated, researchers are faced with the need for new statistical tools for simultaneous evaluation of all variants within a region. Several research groups demonstrated flexibility and good statistical power of the functional linear model approach. In this work we extend previous developments to allow inclusion of multiple traits and adjustment for additional covariates. Our functional approach is unique in that it provides a nuanced depiction of effects and interactions for the variables in the model by representing them as curves varying over a genetic region. We demonstrate flexibility and competitive power of our approach by contrasting its performance with commonly used statistical tools and illustrate its potential for discovery and characterization of genetic architecture of complex traits using sequencing data from the Dallas Heart Study.

FREGAT: an R package for region-based association analysis

Several approaches to the region-based association analysis of quantitative traits have recently been developed and successively applied. However, no software package has been developed that implements all of these approaches for either independent or structured samples. Here we introduce FREGAT (Family REGional Association Tests), an R package that can handle family and population samples and implements a wide range of region-based association methods including burden tests, functional linear models, and kernel machine-based regression. FREGAT can be used in genome/exome-wide region-based association studies of quantitative traits and candidate gene analysis. FREGAT offers many useful options to empower its users and increase the effectiveness and applicability of region-based association analysis.

AVAILABILITY AND IMPLEMENTATION

https://cran.r-project.org/web/packages/FREGAT/index.html

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics Online.

CONTACT

belon@bionet.nsc.ru.

A marginal rank-based inverse normal transformation approach to comparing multiple clinical trial endpoints

The increase in incidence of obesity and chronic diseases and their health care costs have raised the importance of quality diet on the health policy agendas. The healthy eating index is an important measure for diet quality which consists of 12 components derived from ratios of dependent variables with distributions hard to specify, measurement errors and excessive zero observations difficult to model parametrically. Hypothesis testing involving data of such nature poses challenges because the widely used multiple comparison procedures such as Hotelling's T(2) test and Bonferroni correction may suffer from substantial loss of efficiency. We propose a marginal rank-based inverse normal transformation approach to normalizing the marginal distribution of the data before employing a multivariate test procedure. Extensive simulation was conducted to demonstrate the ability of the proposed approach to adequately control the type I error rate as well as increase the power of the test, with data particularly from non-symmetric or heavy-tailed distributions. The methods are exemplified with data from a dietary intervention study for type I diabetic children. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

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.

A Novel Statistic for Global Association Testing Based on Penalized Regression

Natural genetic structures like genes may contain multiple variants that work as a group to determine a biologic outcome. The effect of rare variants, mutations occurring in less than 5% of samples, is hypothesized to be explained best as groups collectively associated with a biologic function. Therefore, it is important to develop powerful association tests to identify a true association between an outcome of interest and a group of variants, in particular a group with many rare variants. In this article we first delineate a novel penalized regression-based global test for the association between sets of variants and a disease phenotype. Next, we use Genetic Analysis Workshop 18 (GAW18) data to assess the power of the new global association test to capture a relationship between an aggregated group of variants and a simulated hypertension status. Rare variant only, common variant only, and combined variant groups are studied. The power values are compared to those obtained from eight well-regarded global tests (Score, Sum, SSU, SSUw, UminP, aSPU, aSPUw, and sequence kernel association test (SKAT)) that do not use penalized regression and a set of tests using either the SSU or score statistics and least absolute shrinkage and selection operator penalty (LASSO) logistic regression. Association testing of rare variants with our method was the top performer when there was low linkage disequilibrium (LD) between and within causal variants. This was similarly true when simultaneously testing rare and common variants in low LD scenarios. Finally, our method was able to provide meaningful variant-specific association information.

Common Variants at Putative Regulatory Sites of the Tissue Nonspecific Alkaline Phosphatase Gene Influence Circulating Pyridoxal 5'-Phosphate Concentration in Healthy Adults

BACKGROUND

Vitamin B-6 interconversion enzymes are important for supplying pyridoxal 5'-phosphate (PLP), the co-enzyme form, to tissues. Variants in the genes for these enzymes [tissue nonspecific alkaline phosphatase (ALPL), pyridoxamine 5'-phosphate oxidase, pyridoxal kinase, and pyridoxal phosphatase] could affect enzyme function and vitamin B-6 status.

OBJECTIVES

We tested whether single-nucleotide polymorphisms (SNPs) in these genes influence vitamin B-6 status markers [plasma PLP, pyridoxal (PL), and 4-pyridoxic acid (PA)], and explored potential functional effects of the SNPs.

METHODS

Study subjects were young, healthy adults from Ireland (n = 2345). We measured plasma PLP, PL, and PA with liquid chromatography-tandem mass spectrometry and genotyped 66 tag SNPs in the 4 genes. We tested for associations with single SNPs in candidate genes and also performed genome-wide association study (GWAS) and gene-based analyses.

RESULTS

Seventeen SNPs in ALPL were associated with altered plasma PLP in candidate gene analyses (P < 1.89 × 10(-4)). In the GWAS, 5 additional ALPL SNPs were associated with altered plasma PLP (P < 5.0 × 10(-8)). Gene-based analyses that used the functional linear model β-spline (P = 4.04 × 10(-15)) and Fourier spline (P = 5.87 × 10(-15)) methods also showed associations between ALPL and altered plasma PLP. No SNPs in other genes were associated with plasma PLP. The association of the minor CC genotype of 1 ALPL SNP, rs1256341, with reduced ALPL expression in the HapMap Northern European ancestry population is consistent with the positive association between the CC genotype and plasma PLP in our study (P = 0.008). No SNP was associated with altered plasma PL or PA.

CONCLUSIONS

In healthy adults, common variants in ALPL influence plasma PLP concentration, the most frequently used biomarker for vitamin B-6 status. Whether these associations are indicative of functional changes in vitamin B-6 status requires more investigation.

Region-Based Association Test for Familial Data under Functional Linear Models

Region-based association analysis is a more powerful tool for gene mapping than testing of individual genetic variants, particularly for rare genetic variants. The most powerful methods for regional mapping are based on the functional data analysis approach, which assumes that the regional genome of an individual may be considered as a continuous stochastic function that contains information about both linkage and linkage disequilibrium. Here, we extend this powerful approach, earlier applied only to independent samples, to the samples of related individuals. To this end, we additionally include a random polygene effects in functional linear model used for testing association between quantitative traits and multiple genetic variants in the region. We compare the statistical power of different methods using Genetic Analysis Workshop 17 mini-exome family data and a wide range of simulation scenarios. Our method increases the power of regional association analysis of quantitative traits compared with burden-based and kernel-based methods for the majority of the scenarios. In addition, we estimate the statistical power of our method using regions with small number of genetic variants, and show that our method retains its advantage over burden-based and kernel-based methods in this case as well. The new method is implemented as the R-function 'famFLM' using two types of basis functions: the B-spline and Fourier bases. We compare the properties of the new method using models that differ from each other in the type of their function basis. The models based on the Fourier basis functions have an advantage in terms of speed and power over the models that use the B-spline basis functions and those that combine B-spline and Fourier basis functions. The 'famFLM' function is distributed under GPLv3 license and is freely available at http://mga.bionet.nsc.ru/soft/famFLM/.

Gene Level Meta-Analysis of Quantitative Traits by Functional Linear Models

Meta-analysis of genetic data must account for differences among studies including study designs, markers genotyped, and covariates. The effects of genetic variants may differ from population to population, i.e., heterogeneity. Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed. In this article, functional linear models are developed for meta-analyses that connect genetic data to quantitative traits, adjusting for covariates. The models can be used to analyze rare variants, common variants, or a combination of the two. Both likelihood-ratio test (LRT) and F-distributed statistics are introduced to test association between quantitative traits and multiple variants in one genetic region. Extensive simulations are performed to evaluate empirical type I error rates and power performance of the proposed tests. The proposed LRT and F-distributed statistics control the type I error very well and have higher power than the existing methods of the meta-analysis sequence kernel association test (MetaSKAT). We analyze four blood lipid levels in data from a meta-analysis of eight European studies. The proposed methods detect more significant associations than MetaSKAT and the P-values of the proposed LRT and F-distributed statistics are usually much smaller than those of MetaSKAT. The functional linear models and related test statistics can be useful in whole-genome and whole-exome association studies.

Pleiotropy analysis of quantitative traits at gene level by multivariate functional linear models

In genetics, pleiotropy describes the genetic effect of a single gene on multiple phenotypic traits. A common approach is to analyze the phenotypic traits separately using univariate analyses and combine the test results through multiple comparisons. This approach may lead to low power. Multivariate functional linear models are developed to connect genetic variant data to multiple quantitative traits adjusting for covariates for a unified analysis. Three types of approximate F-distribution tests 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 in one genetic region. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and optimal sequence kernel association test (SKAT-O). Extensive simulations were performed to evaluate the false positive rates and power performance of the proposed models and tests. We show that the approximate F-distribution tests control the type I error rates very well. Overall, simultaneous analysis of multiple traits can increase power performance compared to an individual test of each trait. The proposed methods were applied to analyze (1) four lipid traits in eight European cohorts, and (2) three biochemical traits in the Trinity Students Study. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and SKAT-O for the three biochemical traits. The approximate F-distribution tests of the proposed functional linear models are more sensitive than those of the traditional multivariate linear models that in turn are more sensitive than SKAT-O in the univariate case. The analysis of the four lipid traits and the three biochemical traits detects more association than SKAT-O in the univariate case.

Functional-mixed effects models for candidate genetic mapping in imaging genetic studies

The aim of this paper is to develop a functional-mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for efficiently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of the genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function.

Generalized functional linear models for gene-based case-control association studies

By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT-O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT-O. In practice, it is not known whether rare variants or common variants in a gene region are disease related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT-O on real neural tube defects and Hirschsprung's disease datasets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT-O in the real data analysis. Our methods can be used in either gene-disease genome-wide/exome-wide association studies or candidate gene analyses.

Functional analysis of variance for association studies

While progress has been made in identifying common genetic variants associated with human diseases, for most of common complex diseases, the identified genetic variants only account for a small proportion of heritability. Challenges remain in finding additional unknown genetic variants predisposing to complex diseases. With the advance in next-generation sequencing technologies, sequencing studies have become commonplace in genetic research. The ongoing exome-sequencing and whole-genome-sequencing studies generate a massive amount of sequencing variants and allow researchers to comprehensively investigate their role in human diseases. The discovery of new disease-associated variants can be enhanced by utilizing powerful and computationally efficient statistical methods. In this paper, we propose a functional analysis of variance (FANOVA) method for testing an association of sequence variants in a genomic region with a qualitative trait. The FANOVA has a number of advantages: (1) it tests for a joint effect of gene variants, including both common and rare; (2) it fully utilizes linkage disequilibrium and genetic position information; and (3) allows for either protective or risk-increasing causal variants. Through simulations, we show that FANOVA outperform two popularly used methods - SKAT and a previously proposed method based on functional linear models (FLM), - especially if a sample size of a study is small and/or sequence variants have low to moderate effects. We conduct an empirical study by applying three methods (FANOVA, SKAT and FLM) to sequencing data from Dallas Heart Study. While SKAT and FLM respectively detected ANGPTL 4 and ANGPTL 3 associated with obesity, FANOVA was able to identify both genes associated with obesity.

TARV: tree-based analysis of rare variants identifying risk modifying variants in CTNNA2 and CNTNAP2 for alcohol addiction

Since the development of next generation sequencing (NGS) technology, researchers have been extending their efforts on genome-wide association studies (GWAS) from common variants to rare variants to find the missing inheritance. Although various statistical methods have been proposed to analyze rare variants data, they generally face difficulties for complex disease models involving multiple genes. In this paper, we propose a tree-based analysis of rare variants (TARV) that adopts a nonparametric disease model and is capable of exploring gene-gene interactions. We found that TARV outperforms the sequence kernel association test (SKAT) in most of our simulation scenarios, and by notable margins in some cases. By applying TARV to the study of addiction: genetics and environment (SAGE) data, we successfully detected gene CTNNA2 and its 43 specific variants that increase the risk of alcoholism in women, with an odds ratio (OR) of 1.94. This gene has not been detected in the SAGE data. Post hoc literature search also supports the role of CTNNA2 as a likely risk gene for alcohol addiction. In addition, we also detected a plausible protective gene CNTNAP2, whose 97 rare variants can reduce the risk of alcoholism in women, with an OR of 0.55. These findings suggest that TARV can be effective in dissecting genetic variants for complex diseases using rare variants data.

Longitudinal analysis is more powerful than cross-sectional analysis in detecting genetic association with neuroimaging phenotypes

Most existing genome-wide association analyses are cross-sectional, utilizing only phenotypic data at a single time point, e.g. baseline. On the other hand, longitudinal studies, such as Alzheimer's Disease Neuroimaging Initiative (ADNI), collect phenotypic information at multiple time points. In this article, as a case study, we conducted both longitudinal and cross-sectional analyses of the ADNI data with several brain imaging (not clinical diagnosis) phenotypes, demonstrating the power gains of longitudinal analysis over cross-sectional analysis. Specifically, we scanned genome-wide single nucleotide polymorphisms (SNPs) with 56 brain-wide imaging phenotypes processed by FreeSurfer on 638 subjects. At the genome-wide significance level P < 1.8 x 10(9)) or a less stringent level (e.g. P < 10(7)), longitudinal analysis of the phenotypic data from the baseline to month 48 identified more SNP-phenotype associations than cross-sectional analysis of only the baseline data. In particular, at the genome-wide significance level, both SNP rs429358 in gene APOE and SNP rs2075650 in gene TOMM40 were confirmed to be associated with various imaging phenotypes in multiple regions of interests (ROIs) by both analyses, though longitudinal analysis detected more regional phenotypes associated with the two SNPs and indicated another significant SNP rs439401 in gene APOE. In light of the power advantage of longitudinal analysis, we advocate its use in current and future longitudinal neuroimaging studies.

A powerful and adaptive association test for rare variants

This article focuses on conducting global testing for association between a binary trait and a set of rare variants (RVs), although its application can be much broader to other types of traits, common variants (CVs), and gene set or pathway analysis. We show that many of the existing tests have deteriorating performance in the presence of many nonassociated RVs: their power can dramatically drop as the proportion of nonassociated RVs in the group to be tested increases. We propose a class of so-called sum of powered score (SPU) tests, each of which is based on the score vector from a general regression model and hence can deal with different types of traits and adjust for covariates, e.g., principal components accounting for population stratification. The SPU tests generalize the sum test, a representative burden test based on pooling or collapsing genotypes of RVs, and a sum of squared score (SSU) test that is closely related to several other powerful variance component tests; a previous study (Basu and Pan 2011) has demonstrated good performance of one, but not both, of the Sum and SSU tests in many situations. The SPU tests are versatile in the sense that one of them is often powerful, although its identity varies with the unknown true association parameters. We propose an adaptive SPU (aSPU) test to approximate the most powerful SPU test for a given scenario, consequently maintaining high power and being highly adaptive across various scenarios. We conducted extensive simulations to show superior performance of the aSPU test over several state-of-the-art association tests in the presence of many nonassociated RVs. Finally we applied the SPU and aSPU tests to the GAW17 mini-exome sequence data to compare its practical performance with some existing tests, demonstrating their potential usefulness.