Rare-variant association testing for sequencing data with the sequence kernel association test

Sequencing studies are increasingly being conducted to identify rare variants associated with complex traits. The limited power of classical single-marker association analysis for rare variants poses a central challenge in such studies. We propose the sequence kernel association test (SKAT), a supervised, flexible, computationally efficient regression method to test for association between genetic variants (common and rare) in a region and a continuous or dichotomous trait while easily adjusting for covariates. As a score-based variance-component test, SKAT can quickly calculate p values analytically by fitting the null model containing only the covariates, and so can easily be applied to genome-wide data. Using SKAT to analyze a genome-wide sequencing study of 1000 individuals, by segmenting the whole genome into 30 kb regions, requires only 7 hr on a laptop. Through analysis of simulated data across a wide range of practical scenarios and triglyceride data from the Dallas Heart Study, we show that SKAT can substantially outperform several alternative rare-variant association tests. We also provide analytic power and sample-size calculations to help design candidate-gene, whole-exome, and whole-genome sequence association studies.     

Optimal tests for rare variant effects in sequencing association studies

With development of massively parallel sequencing technologies, there is a substantial need for developing powerful rare variant association tests. Common approaches include burden and non-burden tests. Burden tests assume all rare variants in the target region have effects on the phenotype in the same direction and of similar magnitude. The recently proposed sequence kernel association test (SKAT) (Wu, M. C., and others, 2011. Rare-variant association testing for sequencing data with the SKAT. The American Journal of Human Genetics 89, 82-93], an extension of the C-alpha test (Neale, B. M., and others, 2011. Testing for an unusual distribution of rare variants. PLoS Genetics 7, 161-165], provides a robust test that is particularly powerful in the presence of protective and deleterious variants and null variants, but is less powerful than burden tests when a large number of variants in a region are causal and in the same direction. As the underlying biological mechanisms are unknown in practice and vary from one gene to another across the genome, it is of substantial practical interest to develop a test that is optimal for both scenarios. In this paper, we propose a class of tests that include burden tests and SKAT as special cases, and derive an optimal test within this class that maximizes power. We show that this optimal test outperforms burden tests and SKAT in a wide range of scenarios. The results are illustrated using simulation studies and triglyceride data from the Dallas Heart Study. In addition, we have derived sample size/power calculation formula for SKAT with a new family of kernels to facilitate designing new sequence association studies.     

Estimating Genetic Effects and Quantifying Missing Heritability Explained by Identified Rare-Variant Associations

Next-generation sequencing has led to many complex-trait rare-variant (RV) association studies. Although single-variant association analysis can be performed, it is grossly underpowered. Therefore, researchers have developed many RV association tests that aggregate multiple variant sites across a genetic region (e.g., gene), and test for the association between the trait and the aggregated genotype. After these aggregate tests detect an association, it is only possible to estimate the average genetic effect for a group of RVs. As a result of the "winner’s curse," such an estimate can be biased. Although for common variants one can obtain unbiased estimates of genetic parameters by analyzing a replication sample, for RVs it is desirable to obtain unbiased genetic estimates for the study where the association is identified. This is because there can be substantial heterogeneity of RV sites and frequencies even among closely related populations. In order to obtain an unbiased estimate for aggregated RV analysis, we developed bootstrap-sample-split algorithms to reduce the bias of the winner’s curse. The unbiased estimates are greatly important for understanding the population-specific contribution of RVs to the heritability of complex traits. We also demonstrate both theoretically and via simulations that for aggregate RV analysis the genetic variance for a gene or region will always be underestimated, sometimes substantially, because of the presence of noncausal variants or because of the presence of causal variants with effects of different magnitudes or directions. Therefore, even if RVs play a major role in the complex-trait etiologies, a portion of the heritability will remain missing, and the contribution of RVs to the complex-trait etiologies will be underestimated.     

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.     

Optimal unified approach for rare-variant association testing with application to small-sample case-control whole-exome sequencing studies

We propose in this paper a unified approach for testing the association between rare variants and phenotypes in sequencing association studies. This approach maximizes power by adaptively using the data to optimally combine the burden test and the nonburden sequence kernel association test (SKAT). Burden tests are more powerful when most variants in a region are causal and the effects are in the same direction, whereas SKAT is more powerful when a large fraction of the variants in a region are noncausal or the effects of causal variants are in different directions. The proposed unified test maintains the power in both scenarios. We show that the unified test corresponds to the optimal test in an extended family of SKAT tests, which we refer to as SKAT-O. The second goal of this paper is to develop a small-sample adjustment procedure for the proposed methods for the correction of conservative type I error rates of SKAT family tests when the trait of interest is dichotomous and the sample size is small. Both small-sample-adjusted SKAT and the optimal unified test (SKAT-O) are computationally efficient and can easily be applied to genome-wide sequencing association studies. We evaluate the finite sample performance of the proposed methods using extensive simulation studies and illustrate their application using the acute-lung-injury exome-sequencing data of the National Heart, Lung, and Blood Institute Exome Sequencing Project.     

A covering method for detecting genetic associations between rare variants and common phenotypes

Genome wide association (GWA) studies, which test for association between common genetic markers and a disease phenotype, have shown varying degrees of success. While many factors could potentially confound GWA studies, we focus on the possibility that multiple, rare variants (RVs) may act in concert to influence disease etiology. Here, we describe an algorithm for RV analysis, RareCover. The algorithm combines a disparate collection of RVs with low effect and modest penetrance. Further, it does not require the rare variants be adjacent in location. Extensive simulations over a range of assumed penetrance and population attributable risk (PAR) values illustrate the power of our approach over other published methods, including the collapsing and weighted-collapsing strategies. To showcase the method, we apply RareCover to re-sequencing data from a cohort of 289 individuals at the extremes of Body Mass Index distribution (NCT00263042). Individual samples were re-sequenced at two genes, FAAH and MGLL, known to be involved in endocannabinoid metabolism (187Kbp for 148 obese and 150 controls). The RareCover analysis identifies exactly one significantly associated region in each gene, each about 5 Kbp in the upstream regulatory regions. The data suggests that the RVs help disrupt the expression of the two genes, leading to lowered metabolism of the corresponding cannabinoids. Overall, our results point to the power of including RVs in measuring genetic associations.     

Links Between the Sequence Kernel Association and the Kernel-Based Adaptive Cluster Tests

Two recently developed methods for the analysis of rare variants include the sequence kernel association test (SKAT) and the kernel-based adaptive cluster test (KBAC). While SKAT represents a type of variance component score test, and KBAC computes a weighted integral representing the difference in risk between variants, they appear to be developed using different initial principles. In this note, we show in fact that the KBAC can be modified to yield a test statistic with operating characteristics more similar to SKAT. Such a development relies on U- and V-statistic theory from mathematical statistics. Some simulation studies are used to evaluate the new proposed tests.     

An optimal weighted aggregated association test for identification of rare variants involved in common diseases

The advent of next generation sequencing technologies allows one to discover nearly all rare variants in a genomic region of interest. This technological development increases the need for an effective statistical method for testing the aggregated effect of rare variants in a gene on disease susceptibility. The idea behind this approach is that if a certain gene is involved in a disease, many rare variants within the gene will disrupt the function of the gene and are associated with the disease. In this article, we present the rare variant weighted aggregate statistic (RWAS), a method that groups rare variants and computes a weighted sum of differences between case and control mutation counts. We show that our method outperforms the groupwise association test of Madsen and Browning in the disease-risk model that assumes that each variant makes an equally small contribution to disease risk. In addition, we can incorporate prior information into our method of which variants are likely causal. By using simulated data and real mutation screening data of the susceptibility gene for ataxia telangiectasia, we demonstrate that prior information has a substantial influence on the statistical power of association studies. Our method is publicly available at http://genetics.cs.ucla.edu/rarevariants.     

Testing for an unusual distribution of rare variants

Technological advances make it possible to use high-throughput sequencing as a primary discovery tool of medical genetics, specifically for assaying rare variation. Still this approach faces the analytic challenge that the influence of very rare variants can only be evaluated effectively as a group. A further complication is that any given rare variant could have no effect, could increase risk, or could be protective. We propose here the C-alpha test statistic as a novel approach for testing for the presence of this mixture of effects across a set of rare variants. Unlike existing burden tests, C-alpha, by testing the variance rather than the mean, maintains consistent power when the target set contains both risk and protective variants. Through simulations and analysis of case/control data, we demonstrate good power relative to existing methods that assess the burden of rare variants in individuals.     

Blocking Approach for Identification of Rare Variants in Family-Based Association Studies

With the advent of next-generation sequencing technology, rare variant association analysis is increasingly being conducted to identify genetic variants associated with complex traits. In recent years, significant effort has been devoted to develop powerful statistical methods to test such associations for population-based designs. However, there has been relatively little development for family-based designs although family data have been shown to be more powerful to detect rare variants. This study introduces a blocking approach that extends two popular family-based common variant association tests to rare variants association studies. Several options are considered to partition a genomic region (gene) into “independent” blocks by which information from SNVs is aggregated within a block and an overall test statistic for the entire genomic region is calculated by combining information across these blocks. The proposed methodology allows different variants to have different directions (risk or protective) and specification of minor allele frequency threshold is not needed. We carried out a simulation to verify the validity of the method by showing that type I error is well under control when the underlying null hypothesis and the assumption of independence across blocks are satisfied. Further, data from the Genetic Analysis Workshop are utilized to illustrate the feasibility and performance of the proposed methodology in a realistic setting.     

Rare-Variant Extensions of the Transmission Disequilibrium Test: Application to Autism Exome Sequence Data

Many population-based rare-variant (RV) association tests, which aggregate variants across a region, have been developed to analyze sequence data. A drawback of analyzing population-based data is that it is difficult to adequately control for population substructure and admixture, and spurious associations can occur. For RVs, this problem can be substantial, because the spectrum of rare variation can differ greatly between populations. A solution is to analyze parent-child trio data, by using the transmission disequilibrium test (TDT), which is robust to population substructure and admixture. We extended the TDT to test for RV associations using four commonly used methods. We demonstrate that for all RV-TDT methods, using proper analysis strategies, type I error is well-controlled even when there are high levels of population substructure or admixture. For trio data, unlike for population-based data, RV allele-counting association methods will lead to inflated type I errors. However type I errors can be properly controlled by obtaining p values empirically through haplotype permutation. The power of the RV-TDT methods was evaluated and compared to the analysis of case-control data with a number of genetic and disease models. The RV-TDT was also used to analyze exome data from 199 Simons Simplex Collection autism trios and an association was observed with variants in ABCA7. Given the problem of adequately controlling for population substructure and admixture in RV association studies and the growing number of sequence-based trio studies, the RV-TDT is extremely beneficial to elucidate the involvement of RVs in the etiology of complex traits.     

Sequence Kernel Association Tests for the Combined Effect of Rare and Common Variants

Recent developments in sequencing technologies have made it possible to uncover both rare and common genetic variants. Genome-wide association studies (GWASs) can test for the effect of common variants, whereas sequence-based association studies can evaluate the cumulative effect of both rare and common variants on disease risk. Many groupwise association tests, including burden tests and variance-component tests, have been proposed for this purpose. Although such tests do not exclude common variants from their evaluation, they focus mostly on testing the effect of rare variants by upweighting rare-variant effects and downweighting common-variant effects and can therefore lose substantial power when both rare and common genetic variants in a region influence trait susceptibility. There is increasing evidence that the allelic spectrum of risk variants at a given locus might include novel, rare, low-frequency, and common genetic variants. Here, we introduce several sequence kernel association tests to evaluate the cumulative effect of rare and common variants. The proposed tests are computationally efficient and are applicable to both binary and continuous traits. Furthermore, they can readily combine GWAS and whole-exome-sequencing data on the same individuals, when available, and are also applicable to deep-resequencing data of GWAS loci. We evaluate these tests on data simulated under comprehensive scenarios and show that compared with the most commonly used tests, including the burden and variance-component tests, they can achieve substantial increases in power. We next show applications to sequencing studies for Crohn disease and autism spectrum disorders. The proposed tests have been incorporated into the software package SKAT.     

Bootstrap Restricted Likelihood Ratio Test for the Detection of Rare Variants

In this paper the detection of rare variants association with continuous phenotypes of interest is investigated via the likelihood-ratio based variance component test under the framework of linear mixed models. The hypothesis testing is challenging and nonstandard, since under the null the variance component is located on the boundary of its parameter space. In this situation the usual asymptotic chisquare distribution of the likelihood ratio statistic does not necessarily hold. To circumvent the derivation of the null distribution we resort to the bootstrap method due to its generic applicability and being easy to implement. Both parametric and nonparametric bootstrap likelihood ratio tests are studied. Numerical studies are implemented to evaluate the performance of the proposed bootstrap likelihood ratio test and compare to some existing methods for the identification of rare variants. To reduce the computational time of the bootstrap likelihood ratio test we propose an effective approximation mixture for the bootstrap null distribution. The GAW17 data is used to illustrate the proposed test.     

Comparison of Statistical Tests for Association between Rare Variants and Binary Traits

Genome-wide association studies have found thousands of common genetic variants associated with a wide variety of diseases and other complex traits. However, a large portion of the predicted genetic contribution to many traits remains unknown. One plausible explanation is that some of the missing variation is due to the effects of rare variants. Nonetheless, the statistical analysis of rare variants is challenging. A commonly used method is to contrast, within the same region (gene), the frequency of minor alleles at rare variants between cases and controls. However, this strategy is most useful under the assumption that the tested variants have similar effects. We previously proposed a method that can accommodate heterogeneous effects in the analysis of quantitative traits. Here we extend this method to include binary traits that can accommodate covariates. We use simulations for a variety of causal and covariate impact scenarios to compare the performance of the proposed method to standard logistic regression, C-alpha, SKAT, and EREC. We found that i) logistic regression methods perform well when the heterogeneity of the effects is not extreme and ii) SKAT and EREC have good performance under all tested scenarios but they can be computationally intensive. Consequently, it would be more computationally desirable to use a two-step strategy by (i) selecting promising genes by faster methods and ii) analyzing selected genes using SKAT/EREC. To select promising genes one can use (1) regression methods when effect heterogeneity is assumed to be low and the covariates explain a non-negligible part of trait variability, (2) C-alpha when heterogeneity is assumed to be large and covariates explain a small fraction of trait's variability and (3) the proposed trend and heterogeneity test when the heterogeneity is assumed to be non-trivial and the covariates explain a large fraction of trait variability.     

Joint rare variant association test of the average and individual effects for sequencing studies

For many complex traits, single nucleotide polymorphisms (SNPs) identified from genome-wide association studies (GWAS) only explain a small percentage of heritability. Next generation sequencing technology makes it possible to explore unexplained heritability by identifying rare variants (RVs). Existing tests designed for RVs look for optimal strategies to combine information across multiple variants. Many of the tests have good power when the true underlying associations are either in the same direction or in opposite directions. We propose three tests for examining the association between a phenotype and RVs, where two of them jointly consider the common association across RVs and the individual deviations from the common effect. On one hand, similar to some of the best existing methods, the individual deviations are modeled as random effects to borrow information across multiple RVs. On the other hand, unlike the existing methods which pool individual effects towards zero, we pool them towards a possibly non-zero common effect by adding a pooled variant into the model. The common effect and the individual effects are jointly tested. We show through extensive simulations that at least one of the three tests proposed here is the most powerful or very close to being the most powerful in various settings of true models. This is appealing in practice because the direction and size of the true effects of the associated RVs are unknown. Researchers can apply the developed tests to improve power under a wide range of true models.     

RET mutational spectrum in Hirschsprung disease: evaluation of 601 Chinese patients

Rare (RVs) and common variants of the RET gene contribute to Hirschsprung disease (HSCR; congenital aganglionosis). While RET common variants are strongly associated with the commonest manifestation of the disease (males; short-segment aganglionosis; sporadic), rare coding sequence (CDS) variants are more frequently found in the lesser common and more severe forms of the disease (females; long/total colonic aganglionosis; familial).Here we present the screening for RVs in the RET CDS and intron/exon boundaries of 601 Chinese HSCR patients, the largest number of patients ever reported. We identified 61 different heterozygous RVs (50 novel) distributed among 100 patients (16.64%). Those include 14 silent, 29 missense, 5 nonsense, 4 frame-shifts, and one in-frame amino-acid deletion in the CDS, two splice-site deletions, 4 nucleotide substitutions and a 22-bp deletion in the intron/exon boundaries and 1 single-nucleotide substitution in the 5' untranslated region. Exonic variants were mainly clustered in RET the extracellular domain. RET RVs were more frequent among patients with the most severe phenotype (24% vs. 15% in short-HSCR). Phasing RVs with the RET HSCR-associated haplotype suggests that RVs do not underlie the undisputable association of RET common variants with HSCR. None of the variants were found in 250 Chinese controls.     

Three ways of combining genotyping and resequencing in case-control association studies

We describe three statistical results that we have found to be useful in case-control genetic association testing. All three involve combining the discovery of novel genetic variants, usually by sequencing, with genotyping methods that recognize previously discovered variants. We first consider expanding the list of known variants by concentrating variant-discovery in cases. Although the naive inclusion of cases-only sequencing data would create a bias, we show that some sequencing data may be retained, even if controls are not sequenced. Furthermore, for alleles of intermediate frequency, cases-only sequencing with bias-correction entails little if any loss of power, compared to dividing the same sequencing effort among cases and controls. Secondly, we investigate more strongly focused variant discovery to obtain a greater enrichment for disease-related variants. We show how case status, family history, and marker sharing enrich the discovery set by increments that are multiplicative with penetrance, enabling the preferential discovery of high-penetrance variants. A third result applies when sequencing is the primary means of counting alleles in both cases and controls, but a supplementary pooled genotyping sample is used to identify the variants that are very rare. We show that this raises no validity issues, and we evaluate a less expensive and more adaptive approach to judging rarity, based on group-specific variants. We demonstrate the important and unusual caveat that this method requires equal sample sizes for validity. These three results can be used to more efficiently detect the association of rare genetic variants with disease.     

Testing for Treatment Effects on Subsets of Endpoints

Multiple endpoints are tested to assess an overall treatment effect and also to identify which endpoints or subsets of endpoints contributed to treatment differences. The conventional p‐value adjustment methods, such as single‐step, step‐up, or step‐down procedures, sequentially identify each significant individual endpoint. Closed test procedures can also detect individual endpoints that have effects via a step‐by‐step closed strategy. This paper proposes a global‐based statistic for testing an a priori number, say, r of the k endpoints, as opposed to the conventional approach of testing one (r = 1) endpoint. The proposed test statistic is an extension of the single‐step p‐value‐based statistic based on the distribution of the smallest p‐value. The test maintains strong control of the FamilyWise Error (FWE) rate under the null hypothesis of no difference in any (sub)set of r endpoints among all possible combinations of the k endpoints. After rejecting the null hypothesis, the individual endpoints in the sets that are rejected can be tested further, using a univariate test statistic in a second step, if desired. However, the second step test only weakly controls the FWE. The proposed method is illustrated by application to a psychosis data set.     

Family-Based Association Test Using Both Common and Rare Variants and Accounting for Directions of Effects for Sequencing Data

Current family-based association tests for sequencing data were mainly developed for identifying rare variants associated with a complex disease. As the disease can be influenced by the joint effects of common and rare variants, common variants with modest effects may not be identified by the methods focusing on rare variants. Moreover, variants can have risk, neutral, or protective effects. Association tests that can effectively select groups of common and rare variants that are likely to be causal and consider the directions of effects have become important. We developed the Ordered Subset - Variable Threshold - Pedigree Disequilibrium Test (OVPDT), a combination of three algorithms, for association analysis in family sequencing data. The ordered subset algorithm is used to select a subset of common variants based on their relative risks, calculated using only parental mating types. The variable threshold algorithm is used to search for an optimal allele frequency threshold such that rare variants below the threshold are more likely to be causal. The PDT statistics from both rare and common variants selected by the two algorithms are combined as the OVPDT statistic. A permutation procedure is used in OVPDT to calculate the p-value. We used simulations to demonstrate that OVPDT has the correct type I error rates under different scenarios and compared the power of OVPDT with two other family-based association tests. The results suggested that OVPDT can have more power than the other tests if both common and rare variants have effects on the disease in a region.     

A new testing strategy to identify rare variants with either risk or protective effect on disease

Rapid advances in sequencing technologies set the stage for the large-scale medical sequencing efforts to be performed in the near future, with the goal of assessing the importance of rare variants in complex diseases. The discovery of new disease susceptibility genes requires powerful statistical methods for rare variant analysis. The low frequency and the expected large number of such variants pose great difficulties for the analysis of these data. We propose here a robust and powerful testing strategy to study the role rare variants may play in affecting susceptibility to complex traits. The strategy is based on assessing whether rare variants in a genetic region collectively occur at significantly higher frequencies in cases compared with controls (or vice versa). A main feature of the proposed methodology is that, although it is an overall test assessing a possibly large number of rare variants simultaneously, the disease variants can be both protective and risk variants, with moderate decreases in statistical power when both types of variants are present. Using simulations, we show that this approach can be powerful under complex and general disease models, as well as in larger genetic regions where the proportion of disease susceptibility variants may be small. Comparisons with previously published tests on simulated data show that the proposed approach can have better power than the existing methods. An application to a recently published study on Type-1 Diabetes finds rare variants in gene IFIH1 to be protective against Type-1 Diabetes.