SNP Set Association Analysis for Familial Data

Genome‐wide association studies (GWAS) are a popular approach for identifying common genetic variants and epistatic effects associated with a disease phenotype. The traditional statistical analysis of such GWAS attempts to assess the association between each individual single‐nucleotide polymorphism (SNP) and the observed phenotype. Recently, kernel machine‐based tests for association between a SNP set (e.g., SNPs in a gene) and the disease phenotype have been proposed as a useful alternative to the traditional individual‐SNP approach, and allow for flexible modeling of the potentially complicated joint SNP effects in a SNP set while adjusting for covariates. We extend the kernel machine framework to accommodate related subjects from multiple independent families, and provide a score‐based variance component test for assessing the association of a given SNP set with a continuous phenotype, while adjusting for additional covariates and accounting for within‐family correlation. We illustrate the proposed method using simulation studies and an application to genetic data from the Genetic Epidemiology Network of Arteriopathy (GENOA) study.     

Robust kernel association testing (RobKAT)

Testing the association between single-nucleotide polymorphism (SNP) effects and a response is often carried out through kernel machine methods based on least squares, such as the sequence kernel association test (SKAT). However, these least-squares procedures are designed for a normally distributed conditional response, which may not apply. Other robust procedures such as the quantile regression kernel machine (QRKM) restrict the choice of the loss function and only allow inference on conditional quantiles. We propose a general and robust kernel association test with a flexible choice of the loss function, no distributional assumptions, and has SKAT and QRKM as special cases. We evaluate our proposed robust association test (RobKAT) across various data distributions through a simulation study. When errors are normally distributed, RobKAT controls type I error and shows comparable power with SKAT. In all other distributional settings investigated, our robust test has similar or greater power than SKAT. Finally, we apply our robust testing method to data from the Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) clinical trial to detect associations between selected genes including the major histocompatibility complex (MHC) region on chromosome six and neurotropic herpesvirus antibody levels in schizophrenia patients. RobKAT detected significant association with four SNP sets (HST1H2BJ, MHC, POM12L2, and SLC17A1), three of which were undetected by SKAT.     

Adjusted Sequence Kernel Association Test for Rare Variants Controlling for Cryptic and Family Relatedness

Recent progress in sequencing technologies makes it possible to identify rare and unique variants that may be associated with complex traits. However, the results of such efforts depend crucially on the use of efficient statistical methods and study designs. Although family‐based designs might enrich a data set for familial rare disease variants, most existing rare variant association approaches assume independence of all individuals. We introduce here a framework for association testing of rare variants in family‐based designs. This framework is an adaptation of the sequence kernel association test (SKAT) which allows us to control for family structure. Our adjusted SKAT (ASKAT) combines the SKAT approach and the factored spectrally transformed linear mixed models (FaST‐LMMs) algorithm to capture family effects based on a LMM incorporating the realized proportion of the genome that is identical by descent between pairs of individuals, and using restricted maximum likelihood methods for estimation. In simulation studies, we evaluated type I error and power of this proposed method and we showed that regardless of the level of the trait heritability, our approach has good control of type I error and good power. Since our approach uses FaST‐LMM to calculate variance components for the proposed mixed model, ASKAT is reasonably fast and can analyze hundreds of thousands of markers. Data from the UK twins consortium are presented to illustrate the ASKAT methodology.     

Multiple SNP Set Analysis for Genome‐Wide Association Studies Through Bayesian Latent Variable Selection

The power of genome‐wide association studies (GWAS) for mapping complex traits with single‐SNP analysis (where SNP is single‐nucleotide polymorphism) may be undermined by modest SNP effect sizes, unobserved causal SNPs, correlation among adjacent SNPs, and SNP‐SNP interactions. Alternative approaches for testing the association between a single SNP set and individual phenotypes have been shown to be promising for improving the power of GWAS. We propose a Bayesian latent variable selection (BLVS) method to simultaneously model the joint association mapping between a large number of SNP sets and complex traits. Compared with single SNP set analysis, such joint association mapping not only accounts for the correlation among SNP sets but also is capable of detecting causal SNP sets that are marginally uncorrelated with traits. The spike‐and‐slab prior assigned to the effects of SNP sets can greatly reduce the dimension of effective SNP sets, while speeding up computation. An efficient Markov chain Monte Carlo algorithm is developed. Simulations demonstrate that BLVS outperforms several competing variable selection methods in some important scenarios.     

GEE‐Based SNP Set Association Test for Continuous and Discrete Traits in Family‐Based Association Studies

Family‐based genetic association studies of related individuals provide opportunities to detect genetic variants that complement studies of unrelated individuals. Most statistical methods for family association studies for common variants are single marker based, which test one SNP a time. In this paper, we consider testing the effect of an SNP set, e.g., SNPs in a gene, in family studies, for both continuous and discrete traits. Specifically, we propose a generalized estimating equations (GEEs) based kernel association test, a variance component based testing method, to test for the association between a phenotype and multiple variants in an SNP set jointly using family samples. The proposed approach allows for both continuous and discrete traits, where the correlation among family members is taken into account through the use of an empirical covariance estimator. We derive the theoretical distribution of the proposed statistic under the null and develop analytical methods to calculate the P‐values. We also propose an efficient resampling method for correcting for small sample size bias in family studies. The proposed method allows for easily incorporating covariates and SNP‐SNP interactions. Simulation studies show that the proposed method properly controls for type I error rates under both random and ascertained sampling schemes in family studies. We demonstrate through simulation studies that our approach has superior performance for association mapping compared to the single marker based minimum P‐value GEE test for an SNP‐set effect over a range of scenarios. We illustrate the application of the proposed method using data from the Cleveland Family GWAS Study.     

Sequence Kernel Association Test of Multiple Continuous Phenotypes

Genetic studies often collect multiple correlated traits, which could be analyzed jointly to increase power by aggregating multiple weak effects and provide additional insights into the etiology of complex human diseases. Existing methods for multiple trait association tests have primarily focused on common variants. There is a surprising dearth of published methods for testing the association of rare variants with multiple correlated traits. In this paper, we extend the commonly used sequence kernel association test (SKAT) for single‐trait analysis to test for the joint association of rare variant sets with multiple traits. We investigate the performance of the proposed method through extensive simulation studies. We further illustrate its usefulness with application to the analysis of diabetes‐related traits in the Atherosclerosis Risk in Communities (ARIC) Study. We identified an exome‐wide significant rare variant set in the gene YAP1 worthy of further investigations.     

Functional Linear Models for Association Analysis of Quantitative Traits

Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F‐distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT‐O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT‐O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study.     

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.     

A Fast Multiple‐Kernel Method With Applications to Detect Gene‐Environment Interaction

Kernel machine (KM) models are a powerful tool for exploring associations between sets of genetic variants and complex traits. Although most KM methods use a single kernel function to assess the marginal effect of a variable set, KM analyses involving multiple kernels have become increasingly popular. Multikernel analysis allows researchers to study more complex problems, such as assessing gene‐gene or gene‐environment interactions, incorporating variance‐component based methods for population substructure into rare‐variant association testing, and assessing the conditional effects of a variable set adjusting for other variable sets. The KM framework is robust, powerful, and provides efficient dimension reduction for multifactor analyses, but requires the estimation of high dimensional nuisance parameters. Traditional estimation techniques, including regularization and the “expectation‐maximization (EM)” algorithm, have a large computational cost and are not scalable to large sample sizes needed for rare variant analysis. Therefore, under the context of gene‐environment interaction, we propose a computationally efficient and statistically rigorous “fastKM” algorithm for multikernel analysis that is based on a low‐rank approximation to the nuisance effect kernel matrices. Our algorithm is applicable to various trait types (e.g., continuous, binary, and survival traits) and can be implemented using any existing single‐kernel analysis software. Through extensive simulation studies, we show that our algorithm has similar performance to an EM‐based KM approach for quantitative traits while running much faster. We also apply our method to the Vitamin Intervention for Stroke Prevention (VISP) clinical trial, examining gene‐by‐vitamin effects on recurrent stroke risk and gene‐by‐age effects on change in homocysteine level.     

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.     

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.     

Pathway analysis by adaptive combination of P‐values

It is increasingly recognized that pathway analyses—a joint test of association between the outcome and a group of single nucleotide polymorphisms (SNPs) within a biological pathway—could potentially complement single‐SNP analysis and provide additional insights for the genetic architecture of complex diseases. Building upon existing P‐value combining methods, we propose a class of highly flexible pathway analysis approaches based on an adaptive rank truncated product statistic that can effectively combine evidence of associations over different SNPs and genes within a pathway. The statistical significance of the pathway‐level test statistics is evaluated using a highly efficient permutation algorithm that remains computationally feasible irrespective of the size of the pathway and complexity of the underlying test statistics for summarizing SNP‐ and gene‐level associations. We demonstrate through simulation studies that a gene‐based analysis that treats the underlying genes, as opposed to the underlying SNPs, as the basic units for hypothesis testing, is a very robust and powerful approach to pathway‐based association testing. We also illustrate the advantage of the proposed methods using a study of the association between the nicotinic receptor pathway and cigarette smoking behaviors. Genet. Epidemiol. 33:700–709, 2009. Published 2009 Wiley‐Liss, Inc.     

SNPing Away at Candidate Genes

We develop regression methodology to identify subsets of single nucleotide polymorphisms (SNPs) within candidate genes related to quantitative traits and apply our methods to the simulated Genetic Analysis Workshop (GAW) 12 data set. In the data set we find 694 SNP loci with minimum allele frequencies of at least 0.01. We assume an additive casual model between these SNPs and all five quantitative traits. After initial screening using one‐way analysis of variance, we employ a computationally efficient, simulated annealing algorithm to select among all possible subsets of SNP loci, using a generalization of Mallows’ C_p as our optimality criterion. The simple transition kernel we develop evaluates new subsets in O(1), by requiring just three arithmetic operations to calculate the proposed RSS based on the Gauss‐Jordan pivot. We identify an SNP loci located at 6–5782 related to traits 2 and 3 and several sites on gene 2 related to trait 5 using a subsample of 1,000 individuals and the full data set (n = 8,250) for comparison. © 2001 Wiley‐Liss, Inc.     

Sequence Kernel Association Test for Survival Traits

Rare variant tests have been of great interest in testing genetic associations with diseases and disease‐related quantitative traits in recent years. Among these tests, the sequence kernel association test (SKAT) is an omnibus test for effects of rare genetic variants, in a linear or logistic regression framework. It is often described as a variance component test treating the genotypic effects as random. When the linear kernel is used, its test statistic can be expressed as a weighted sum of single‐marker score test statistics. In this paper, we extend the test to survival phenotypes in a Cox regression framework. Because of the anticonservative small‐sample performance of the score test in a Cox model, we substitute signed square‐root likelihood ratio statistics for the score statistics, and confirm that the small‐sample control of type I error is greatly improved. This test can also be applied in meta‐analysis. We show in our simulation studies that this test has superior statistical power except in a few specific scenarios, as compared to burden tests in a Cox model. We also present results in an application to time‐to‐obesity using genotypes from Framingham Heart Study SNP Health Association Resource.     

Conditional analysis of multiple quantitative traits based on marginal GWAS summary statistics

There has been an increasing interest in joint association testing of multiple traits for possible pleiotropic effects. However, even in the presence of pleiotropy, most of the existing methods cannot distinguish direct and indirect effects of a genetic variant, say single‐nucleotide polymorphism (SNP), on multiple traits, and a conditional analysis of a trait adjusting for other traits is perhaps the simplest and most common approach to addressing this question. However, without individual‐level genotypic and phenotypic data but with only genome‐wide association study (GWAS) summary statistics, as typical with most large‐scale GWAS consortium studies, we are not aware of any existing method for such a conditional analysis. We propose such a conditional analysis, offering formulas of necessary calculations to fit a joint linear regression model for multiple quantitative traits. Furthermore, our method can also accommodate conditional analysis on multiple SNPs in addition to on multiple quantitative traits, which is expected to be useful for fine mapping. We provide numerical examples based on both simulated and real GWAS data to demonstrate the effectiveness of our proposed approach, and illustrate possible usefulness of conditional analysis by contrasting its result differences from those of standard marginal analyses.     

A Kernel Regression Approach to Gene‐Gene Interaction Detection for Case‐Control Studies

Gene‐gene interactions are increasingly being addressed as a potentially important contributor to the variability of complex traits. Consequently, attentions have moved beyond single locus analysis of association to more complex genetic models. Although several single‐marker approaches toward interaction analysis have been developed, such methods suffer from very high testing dimensionality and do not take advantage of existing information, notably the definition of genes as functional units. Here, we propose a comprehensive family of gene‐level score tests for identifying genetic elements of disease risk, in particular pairwise gene‐gene interactions. Using kernel machine methods, we devise score‐based variance component tests under a generalized linear mixed model framework. We conducted simulations based upon coalescent genetic models to evaluate the performance of our approach under a variety of disease models. These simulations indicate that our methods are generally higher powered than alternative gene‐level approaches and at worst competitive with exhaustive SNP‐level (where SNP is single‐nucleotide polymorphism) analyses. Furthermore, we observe that simulated epistatic effects resulted in significant marginal testing results for the involved genes regardless of whether or not true main effects were present. We detail the benefits of our methods and discuss potential genome‐wide analysis strategies for gene‐gene interaction analysis in a case‐control study design.     

Sequence Kernel Association Test for Quantitative Traits in Family Samples

A large number of rare genetic variants have been discovered with the development in sequencing technology and the lowering of sequencing costs. Rare variant analysis may help identify novel genes associated with diseases and quantitative traits, adding to our knowledge of explaining heritability of these phenotypes. Many statistical methods for rare variant analysis have been developed in recent years, but some of them require the strong assumption that all rare variants in the analysis share the same direction of effect, and others requiring permutation to calculate the P‐values are computer intensive. Among these methods, the sequence kernel association test (SKAT) is a powerful method under many different scenarios. It does not require any assumption on the directionality of effects, and statistical significance is computed analytically. In this paper, we extend SKAT to be applicable to family data. The family‐based SKAT (famSKAT) has a different test statistic and null distribution compared to SKAT, but is equivalent to SKAT when there is no familial correlation. Our simulation studies show that SKAT has inflated type I error if familial correlation is inappropriately ignored, but has appropriate type I error if applied to a single individual per family to obtain an unrelated subset. In contrast, famSKAT has the correct type I error when analyzing correlated observations, and it has higher power than competing methods in many different scenarios. We illustrate our approach to analyze the association of rare genetic variants using glycemic traits from the Framingham Heart Study.     

Kernel Approach for Modeling Interaction Effects in Genetic Association Studies of Complex Quantitative Traits

The etiology of complex traits likely involves the effects of genetic and environmental factors, along with complicated interaction effects between them. Consequently, there has been interest in applying genetic association tests of complex traits that account for potential modification of the genetic effect in the presence of an environmental factor. One can perform such an analysis using a joint test of gene and gene‐environment interaction. An optimal joint test would be one that remains powerful under a variety of models ranging from those of strong gene‐environment interaction effect to those of little or no gene‐environment interaction effect. To fill this demand, we have extended a kernel machine based approach for association mapping of multiple SNPs to consider joint tests of gene and gene‐environment interaction. The kernel‐based approach for joint testing is promising, because it incorporates linkage disequilibrium information from multiple SNPs simultaneously in analysis and permits flexible modeling of interaction effects. Using simulated data, we show that our kernel machine approach typically outperforms the traditional joint test under strong gene‐environment interaction models and further outperforms the traditional main‐effect association test under models of weak or no gene‐environment interaction effects. We illustrate our test using genome‐wide association data from the Grady Trauma Project, a cohort of highly traumatized, at‐risk individuals, which has previously been investigated for interaction effects.     

Sequence Kernel Association Analysis of Rare Variant Set Based on the Marginal Regression Model for Binary Traits

Recent sequencing efforts have focused on exploring the influence of rare variants on the complex diseases. Gene level based tests by aggregating information across rare variants within a gene have become attractive to enrich the rare variant association signal. Among them, the sequence kernel association test (SKAT) has proved to be a very powerful method for jointly testing multiple rare variants within a gene. In this article, we explore an alternative SKAT. We propose to use the univariate likelihood ratio statistics from the marginal model for individual variants as input into the kernel association test. We show how to compute its significance P‐value efficiently based on the asymptotic chi‐square mixture distribution. We demonstrate through extensive numerical studies that the proposed method has competitive performance. Its usefulness is further illustrated with application to associations between rare exonic variants and type 2 diabetes (T2D) in the Atherosclerosis Risk in Communities (ARIC) study. We identified an exome‐wide significant rare variant set in the gene ZZZ3 worthy of further investigations.     

Gene,region and pathway level analyses in whole‐genome studies

In the setting of genome‐wide association studies, we propose a method for assigning a measure of significance to pre‐defined sets of markers in the genome. The sets can be genes, conserved regions, or groups of genes such as pathways. Using the proposed methods and algorithms, evidence for association between a particular functional unit and a disease status can be obtained not just by the presence of a strong signal from a SNP within it, but also by the combination of several simultaneous weaker signals that are not strongly correlated. This approach has several advantages. First, moderately strong signals from different SNPs are combined to obtain a much stronger signal for the set, therefore increasing power. Second, in combination with methods that provide information on untyped markers, it leads to results that can be readily combined across studies and platforms that might use different SNPs. Third, the results are easy to interpret, since they refer to functional sets of markers that are likely to behave as a unit in their phenotypic effect. Finally, the availability of gene‐level P‐values for association is the first step in developing methods that integrate information from pathways and networks with genome‐wide association data, and these can lead to a better understanding of the complex traits genetic architecture. The power of the approach is investigated in simulated and real datasets. Novel Crohn's disease associations are found using the WTCCC data. Genet. Epidemiol. 34: 222–231, 2010. © 2009 Wiley‐Liss, Inc.