Generalization of Rare Variant Association Tests for Longitudinal Family Studies

Given the functional relevance of many rare variants, their identification is frequently critical for dissecting disease etiology. Functional variants are likely to be aggregated in family studies enriched with affected members, and this aggregation increases the statistical power to detect rare variants associated with a trait of interest. Longitudinal family studies provide additional information for identifying genetic and environmental factors associated with disease over time. However, methods to analyze rare variants in longitudinal family data remain fairly limited. These methods should be capable of accounting for different sources of correlations and handling large amounts of sequencing data efficiently. To identify rare variants associated with a phenotype in longitudinal family studies, we extended pedigree‐based burden (BT) and kernel (KS) association tests to genetic longitudinal studies. Generalized estimating equation (GEE) approaches were used to generalize the pedigree‐based BT and KS to multiple correlated phenotypes under the generalized linear model framework, adjusting for fixed effects of confounding factors. These tests accounted for complex correlations between repeated measures of the same phenotype (serial correlations) and between individuals in the same family (familial correlations). We conducted comprehensive simulation studies to compare the proposed tests with mixed‐effects models and marginal models, using GEEs under various configurations. When the proposed tests were applied to data from the Diabetes Heart Study, we found exome variants of POMGNT1 and JAK1 genes were associated with type 2 diabetes.     

Methods for Association Analysis and Meta‐Analysis of Rare Variants in Families

Advances in exome sequencing and the development of exome genotyping arrays are enabling explorations of association between rare coding variants and complex traits. To ensure power for these rare variant analyses, a variety of association tests that group variants by gene or functional unit have been proposed. Here, we extend these tests to family‐based studies. We develop family‐based burden tests, variable frequency threshold tests and sequence kernel association tests. Through simulations, we compare the performance of different tests. We describe situations where family‐based studies provide greater power than studies of unrelated individuals to detect rare variants associated with moderate to large changes in trait values. Broadly speaking, we find that when sample sizes are limited and only a modest fraction of all trait‐associated variants can be identified, family samples are more powerful. Finally, we illustrate our approach by analyzing the relationship between coding variants and levels of high‐density lipoprotein (HDL) cholesterol in 11,556 individuals from the HUNT and SardiNIA studies, demonstrating association for coding variants in the APOC3, CETP, LIPC, LIPG, and LPL genes and illustrating the value of family samples, meta‐analysis, and gene‐level tests. Our methods are implemented in freely available C++ code.     

Combining Family‐ and Population‐Based Imputation Data for Association Analysis of Rare and Common Variants in Large Pedigrees

In the last two decades, complex traits have become the main focus of genetic studies. The hypothesis that both rare and common variants are associated with complex traits is increasingly being discussed. Family‐based association studies using relatively large pedigrees are suitable for both rare and common variant identification. Because of the high cost of sequencing technologies, imputation methods are important for increasing the amount of information at low cost. A recent family‐based imputation method, Genotype Imputation Given Inheritance (GIGI), is able to handle large pedigrees and accurately impute rare variants, but does less well for common variants where population‐based methods perform better. Here, we propose a flexible approach to combine imputation data from both family‐ and population‐based methods. We also extend the Sequence Kernel Association Test for Rare and Common variants (SKAT‐RC), originally proposed for data from unrelated subjects, to family data in order to make use of such imputed data. We call this extension “famSKAT‐RC.” We compare the performance of famSKAT‐RC and several other existing burden and kernel association tests. In simulated pedigree sequence data, our results show an increase of imputation accuracy from use of our combining approach. Also, they show an increase of power of the association tests with this approach over the use of either family‐ or population‐based imputation methods alone, in the context of rare and common variants. Moreover, our results show better performance of famSKAT‐RC compared to the other considered tests, in most scenarios investigated here.     

Power of Family‐Based Association Designs to Detect Rare Variants in Large Pedigrees Using Imputed Genotypes

Recently, the “Common Disease‐Multiple Rare Variants” hypothesis has received much attention, especially with current availability of next‐generation sequencing. Family‐based designs are well suited for discovery of rare variants, with large and carefully selected pedigrees enriching for multiple copies of such variants. However, sequencing a large number of samples is still prohibitive. Here, we evaluate a cost‐effective strategy (pseudosequencing) to detect association with rare variants in large pedigrees. This strategy consists of sequencing a small subset of subjects, genotyping the remaining sampled subjects on a set of sparse markers, and imputing the untyped markers in the remaining subjects conditional on the sequenced subjects and pedigree information. We used a recent pedigree imputation method (GIGI), which is able to efficiently handle large pedigrees and accurately impute rare variants. We used burden and kernel association tests, famWS and famSKAT, which both account for family relationships and heterogeneity of allelic effect for famSKAT only. We simulated pedigree sequence data and compared the power of association tests for pseudosequence data, a subset of sequence data used for imputation, and all subjects sequenced. We also compared, within the pseudosequence data, the power of association test using best‐guess genotypes and allelic dosages. Our results show that the pseudosequencing strategy considerably improves the power to detect association with rare variants. They also show that the use of allelic dosages results in much higher power than use of best‐guess genotypes in these family‐based data. Moreover, famSKAT shows greater power than famWS in most of scenarios we considered.     

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.     

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.     

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.     

Multiple Genetic Variant Association Testing by Collapsing and Kernel Methods With Pedigree or Population Structured Data

Searching for rare genetic variants associated with complex diseases can be facilitated by enriching for diseased carriers of rare variants by sampling cases from pedigrees enriched for disease, possibly with related or unrelated controls. This strategy, however, complicates analyses because of shared genetic ancestry, as well as linkage disequilibrium among genetic markers. To overcome these problems, we developed broad classes of “burden” statistics and kernel statistics, extending commonly used methods for unrelated case‐control data to allow for known pedigree relationships, for autosomes and the X chromosome. Furthermore, by replacing pedigree‐based genetic correlation matrices with estimates of genetic relationships based on large‐scale genomic data, our methods can be used to account for population‐structured data. By simulations, we show that the type I error rates of our developed methods are near the asymptotic nominal levels, allowing rapid computation of P‐values. Our simulations also show that a linear weighted kernel statistic is generally more powerful than a weighted “burden” statistic. Because the proposed statistics are rapid to compute, they can be readily used for large‐scale screening of the association of genomic sequence data with disease status.     

Pathway‐Based Approaches for Sequencing‐Based Genome‐Wide Association Studies

For analyzing complex trait association with sequencing data, most current studies test aggregated effects of variants in a gene or genomic region. Although gene‐based tests have insufficient power even for moderately sized samples, pathway‐based analyses combine information across multiple genes in biological pathways and may offer additional insight. However, most existing pathway association methods are originally designed for genome‐wide association studies, and are not comprehensively evaluated for sequencing data. Moreover, region‐based rare variant association methods, although potentially applicable to pathway‐based analysis by extending their region definition to gene sets, have never been rigorously tested. In the context of exome‐based studies, we use simulated and real datasets to evaluate pathway‐based association tests. Our simulation strategy adopts a genome‐wide genetic model that distributes total genetic effects hierarchically into pathways, genes, and individual variants, allowing the evaluation of pathway‐based methods with realistic quantifiable assumptions on the underlying genetic architectures. The results show that, although no single pathway‐based association method offers superior performance in all simulated scenarios, a modification of Gene Set Enrichment Analysis approach using statistics from single‐marker tests without gene‐level collapsing (weighted Kolmogrov‐Smirnov [WKS]‐Variant method) is consistently powerful. Interestingly, directly applying rare variant association tests (e.g., sequence kernel association test) to pathway analysis offers a similar power, but its results are sensitive to assumptions of genetic architecture. We applied pathway association analysis to an exome‐sequencing data of the chronic obstructive pulmonary disease, and found that the WKS‐Variant method confirms associated genes previously published.     

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.     

A rare variant association test in family‐based designs and non‐normal quantitative traits

Rare variant studies are now being used to characterize the genetic diversity between individuals and may help to identify substantial amounts of the genetic variation of complex diseases and quantitative phenotypes. Family data have been shown to be powerful to interrogate rare variants. Consequently, several rare variants association tests have been recently developed for family‐based designs, but typically, these assume the normality of the quantitative phenotypes. In this paper, we present a family‐based test for rare‐variants association in the presence of non‐normal quantitative phenotypes. The proposed model relaxes the normality assumption and does not specify any parametric distribution for the marginal distribution of the phenotype. The dependence between relatives is modeled via a Gaussian copula. A score‐type test is derived, and several strategies to approximate its distribution under the null hypothesis are derived and investigated. The performance of the proposed test is assessed and compared with existing methods by simulations. The methodology is illustrated with an association study involving the adiponectin trait from the UK10K project. Copyright © 2015 John Wiley & Sons, Ltd.     

Rare‐variant association tests in longitudinal studies,with an application to the Multi‐Ethnic Study of Atherosclerosis (MESA)

Over the past few years, an increasing number of studies have identified rare variants that contribute to trait heritability. Due to the extreme rarity of some individual variants, gene‐based association tests have been proposed to aggregate the genetic variants within a gene, pathway, or specific genomic region as opposed to a one‐at‐a‐time single variant analysis. In addition, in longitudinal studies, statistical power to detect disease susceptibility rare variants can be improved through jointly testing repeatedly measured outcomes, which better describes the temporal development of the trait of interest. However, usual sandwich/model‐based inference for sequencing studies with longitudinal outcomes and rare variants can produce deflated/inflated type I error rate without further corrections. In this paper, we develop a group of tests for rare‐variant association based on outcomes with repeated measures. We propose new perturbation methods such that the type I error rate of the new tests is not only robust to misspecification of within‐subject correlation, but also significantly improved for variants with extreme rarity in a study with small or moderate sample size. Through extensive simulation studies, we illustrate that substantially higher power can be achieved by utilizing longitudinal outcomes and our proposed finite sample adjustment. We illustrate our methods using data from the Multi‐Ethnic Study of Atherosclerosis for exploring association of repeated measures of blood pressure with rare and common variants based on exome sequencing data on 6,361 individuals.     

A Unified Mixed‐Effects Model for Rare‐Variant Association in Sequencing Studies

For rare‐variant association analysis, due to extreme low frequencies of these variants, it is necessary to aggregate them by a prior set (e.g., genes and pathways) in order to achieve adequate power. In this paper, we consider hierarchical models to relate a set of rare variants to phenotype by modeling the effects of variants as a function of variant characteristics while allowing for variant‐specific effect (heterogeneity). We derive a set of two score statistics, testing the group effect by variant characteristics and the heterogeneity effect. We make a novel modification to these score statistics so that they are independent under the null hypothesis and their asymptotic distributions can be derived. As a result, the computational burden is greatly reduced compared with permutation‐based tests. Our approach provides a general testing framework for rare variants association, which includes many commonly used tests, such as the burden test [Li and Leal, 2008] and the sequence kernel association test [Wu et al., 2011], as special cases. Furthermore, in contrast to these tests, our proposed test has an added capacity to identify which components of variant characteristics and heterogeneity contribute to the association. Simulations under a wide range of scenarios show that the proposed test is valid, robust, and powerful. An application to the Dallas Heart Study illustrates that apart from identifying genes with significant associations, the new method also provides additional information regarding the source of the association. Such information may be useful for generating hypothesis in future studies.     

Gene‐based genetic association test with adaptive optimal weights

It is well known that using proper weights for genetic variants is crucial in enhancing the power of gene‐ or pathway‐based association tests. To increase the power, we propose a general approach that adaptively selects weights among a class of weight families and apply it to the popular sequencing kernel association test. Through comprehensive simulation studies, we demonstrate that the proposed method can substantially increase power under some conditions. Applications to real data are also presented. This general approach can be extended to all current set‐based rare variant association tests whose performances depend on variant's weight assignment.     

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.     

Family‐Based Rare Variant Association Analysis: A Fast and Efficient Method of Multivariate Phenotype Association Analysis

Family‐based designs have been repeatedly shown to be powerful in detecting the significant rare variants associated with human diseases. Furthermore, human diseases are often defined by the outcomes of multiple phenotypes, and thus we expect multivariate family‐based analyses may be very efficient in detecting associations with rare variants. However, few statistical methods implementing this strategy have been developed for family‐based designs. In this report, we describe one such implementation: the multivariate family‐based rare variant association tool (mFARVAT). mFARVAT is a quasi‐likelihood‐based score test for rare variant association analysis with multiple phenotypes, and tests both homogeneous and heterogeneous effects of each variant on multiple phenotypes. Simulation results show that the proposed method is generally robust and efficient for various disease models, and we identify some promising candidate genes associated with chronic obstructive pulmonary disease. The software of mFARVAT is freely available at http://healthstat.snu.ac.kr/software/mfarvat/ , implemented in C++ and supported on Linux and MS Windows.     

Meta‐Analysis of Rare Variant Association Tests in Multiethnic Populations

Several methods have been proposed to increase power in rare variant association testing by aggregating information from individual rare variants (MAF < 0.005). However, how to best combine rare variants across multiple ethnicities and the relative performance of designs using different ethnic sampling fractions remains unknown. In this study, we compare the performance of several statistical approaches for assessing rare variant associations across multiple ethnicities. We also explore how different ethnic sampling fractions perform, including single‐ethnicity studies and studies that sample up to four ethnicities. We conducted simulations based on targeted sequencing data from 4,611 women in four ethnicities (African, European, Japanese American, and Latina). As with single‐ethnicity studies, burden tests had greater power when all causal rare variants were deleterious, and variance component‐based tests had greater power when some causal rare variants were deleterious and some were protective. Multiethnic studies had greater power than single‐ethnicity studies at many loci, with inclusion of African Americans providing the largest impact. On average, studies including African Americans had as much as 20% greater power than equivalently sized studies without African Americans. This suggests that association studies between rare variants and complex disease should consider including subjects from multiple ethnicities, with preference given to genetically diverse groups.     

A Novel Test for Testing the Optimally Weighted Combination of Rare and Common Variants Based on Data of Parents and Affected Children

With the development of sequencing technologies, the direct testing of rare variant associations has become possible. Many statistical methods for detecting associations between rare variants and complex diseases have recently been developed, most of which are population‐based methods for unrelated individuals. A limitation of population‐based methods is that spurious associations can occur when there is a population structure. For rare variants, this problem can be more serious, because the spectrum of rare variation can be very different in diverse populations, as well as the current nonexistence of methods to control for population stratification in population‐based rare variant associations. A solution to the problem of population stratification is to use family‐based association tests, which use family members to control for population stratification. In this article, we propose a novel test for Testing the Optimally Weighted combination of variants based on data of Parents and Affected Children (TOW‐PAC). TOW‐PAC is a family‐based association test that tests the combined effect of rare and common variants in a genomic region, and is robust to the directions of the effects of causal variants. Simulation studies confirm that, for rare variant associations, family‐based association tests are robust to population stratification although population‐based association tests can be seriously confounded by population stratification. The results of power comparisons show that the power of TOW‐PAC increases with an increase of the number of affected children in each family and TOW‐PAC based on multiple affected children per family is more powerful than TOW based on unrelated individuals.     

Flexible and Robust Methods for Rare‐Variant Testing of Quantitative Traits in Trios and Nuclear Families

Most rare‐variant association tests for complex traits are applicable only to population‐based or case‐control resequencing studies. There are fewer rare‐variant association tests for family‐based resequencing studies, which is unfortunate because pedigrees possess many attractive characteristics for such analyses. Family‐based studies can be more powerful than their population‐based counterparts due to increased genetic load and further enable the implementation of rare‐variant association tests that, by design, are robust to confounding due to population stratification. With this in mind, we propose a rare‐variant association test for quantitative traits in families; this test integrates the QTDT approach of Abecasis et al. [Abecasis et al., 2000a ] into the kernel‐based SNP association test KMFAM of Schifano et al. [Schifano et al., 2012 ]. The resulting within‐family test enjoys the many benefits of the kernel framework for rare‐variant association testing, including rapid evaluation of P‐values and preservation of power when a region harbors rare causal variation that acts in different directions on phenotype. Additionally, by design, this within‐family test is robust to confounding due to population stratification. Although within‐family association tests are generally less powerful than their counterparts that use all genetic information, we show that we can recover much of this power (although still ensuring robustness to population stratification) using a straightforward screening procedure. Our method accommodates covariates and allows for missing parental genotype data, and we have written software implementing the approach in R for public use.     

Gene‐based segregation method for identifying rare variants in family‐based sequencing studies

Whole‐exome sequencing using family data has identified rare coding variants in Mendelian diseases or complex diseases with Mendelian subtypes, using filters based on variant novelty, functionality, and segregation with the phenotype within families. However, formal statistical approaches are limited. We propose a gene‐based segregation test (GESE) that quantifies the uncertainty of the filtering approach. It is constructed using the probability of segregation events under the null hypothesis of Mendelian transmission. This test takes into account different degrees of relatedness in families, the number of functional rare variants in the gene, and their minor allele frequencies in the corresponding population. In addition, a weighted version of this test allows incorporating additional subject phenotypes to improve statistical power. We show via simulations that the GESE and weighted GESE tests maintain appropriate type I error rate, and have greater power than several commonly used region‐based methods. We apply our method to whole‐exome sequencing data from 49 extended pedigrees with severe, early‐onset chronic obstructive pulmonary disease (COPD) in the Boston Early‐Onset COPD study (BEOCOPD) and identify several promising candidate genes. Our proposed methods show great potential for identifying rare coding variants of large effect and high penetrance for family‐based sequencing data. The proposed tests are implemented in an R package that is available on CRAN ( https://cran.r-project.org/web/packages/GESE/ ).