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.     

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.     

General Framework for Meta-analysis of Rare Variants in Sequencing Association Studies

We propose a general statistical framework for meta-analysis of gene- or region-based multimarker rare variant association tests in sequencing association studies. In genome-wide association studies, single-marker meta-analysis has been widely used to increase statistical power by combining results via regression coefficients and standard errors from different studies. In analysis of rare variants in sequencing studies, region-based multimarker tests are often used to increase power. We propose meta-analysis methods for commonly used gene- or region-based rare variants tests, such as burden tests and variance component tests. Because estimation of regression coefficients of individual rare variants is often unstable or not feasible, the proposed method avoids this difficulty by calculating score statistics instead that only require fitting the null model for each study and then aggregating these score statistics across studies. Our proposed meta-analysis rare variant association tests are conducted based on study-specific summary statistics, specifically score statistics for each variant and between-variant covariance-type (linkage disequilibrium) relationship statistics for each gene or region. The proposed methods are able to incorporate different levels of heterogeneity of genetic effects across studies and are applicable to meta-analysis of multiple ancestry groups. We show that the proposed methods are essentially as powerful as joint analysis by directly pooling individual level genotype data. We conduct extensive simulations to evaluate the performance of our methods by varying levels of heterogeneity across studies, and we apply the proposed methods to meta-analysis of rare variant effects in a multicohort study of the genetics of blood lipid levels.     

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.     

Association Studies with Imputed Variants Using Expectation-Maximization Likelihood-Ratio Tests

Genotype imputation has become standard practice in modern genetic studies. As sequencing-based reference panels continue to grow, increasingly more markers are being well or better imputed but at the same time, even more markers with relatively low minor allele frequency are being imputed with low imputation quality. Here, we propose new methods that incorporate imputation uncertainty for downstream association analysis, with improved power and/or computational efficiency. We consider two scenarios: I) when posterior probabilities of all potential genotypes are estimated; and II) when only the one-dimensional summary statistic, imputed dosage, is available. For scenario I, we have developed an expectation-maximization likelihood-ratio test for association based on posterior probabilities. When only imputed dosages are available (scenario II), we first sample the genotype probabilities from its posterior distribution given the dosages, and then apply the EM-LRT on the sampled probabilities. Our simulations show that type I error of the proposed EM-LRT methods under both scenarios are protected. Compared with existing methods, EM-LRT-Prob (for scenario I) offers optimal statistical power across a wide spectrum of MAF and imputation quality. EM-LRT-Dose (for scenario II) achieves a similar level of statistical power as EM-LRT-Prob and, outperforms the standard Dosage method, especially for markers with relatively low MAF or imputation quality. Applications to two real data sets, the Cebu Longitudinal Health and Nutrition Survey study and the Women’s Health Initiative Study, provide further support to the validity and efficiency of our proposed methods.     

Association Testing of Clustered Rare Causal Variants in Case-Control Studies

Biological evidence suggests that multiple causal variants in a gene may cluster physically. Variants within the same protein functional domain or gene regulatory element would locate in close proximity on the DNA sequence. However, spatial information of variants is usually not used in current rare variant association analyses. We here propose a clustering method (abbreviated as “CLUSTER”), which is extended from the adaptive combination of P-values. Our method combines the association signals of variants that are more likely to be causal. Furthermore, the statistic incorporates the spatial information of variants. With extensive simulations, we show that our method outperforms several commonly-used methods in many scenarios. To demonstrate its use in real data analyses, we also apply this CLUSTER test to the Dallas Heart Study data. CLUSTER is among the best methods when the effects of causal variants are all in the same direction. As variants located in close proximity are more likely to have similar impact on disease risk, CLUSTER is recommended for association testing of clustered rare causal variants in case-control studies.     

Detection of Rare Genomic Variants from Pooled Sequencing Using SPLINTER

As DNA sequencing technology has markedly advanced in recent years², it has become increasingly evident that the amount of genetic variation between any two individuals is greater than previously thought³. In contrast, array-based genotyping has failed to identify a significant contribution of common sequence variants to the phenotypic variability of common disease^4,5. Taken together, these observations have led to the evolution of the Common Disease / Rare Variant hypothesis suggesting that the majority of the "missing heritability" in common and complex phenotypes is instead due to an individual''s personal profile of rare or private DNA variants^6-8. However, characterizing how rare variation impacts complex phenotypes requires the analysis of many affected individuals at many genomic loci, and is ideally compared to a similar survey in an unaffected cohort. Despite the sequencing power offered by today''s platforms, a population-based survey of many genomic loci and the subsequent computational analysis required remains prohibitive for many investigators.To address this need, we have developed a pooled sequencing approach^1,9 and a novel software package¹ for highly accurate rare variant detection from the resulting data. The ability to pool genomes from entire populations of affected individuals and survey the degree of genetic variation at multiple targeted regions in a single sequencing library provides excellent cost and time savings to traditional single-sample sequencing methodology. With a mean sequencing coverage per allele of 25-fold, our custom algorithm, SPLINTER, uses an internal variant calling control strategy to call insertions, deletions and substitutions up to four base pairs in length with high sensitivity and specificity from pools of up to 1 mutant allele in 500 individuals. Here we describe the method for preparing the pooled sequencing library followed by step-by-step instructions on how to use the SPLINTER package for pooled sequencing analysis (http://www.ibridgenetwork.org/wustl/splinter). We show a comparison between pooled sequencing of 947 individuals, all of whom also underwent genome-wide array, at over 20kb of sequencing per person. Concordance between genotyping of tagged and novel variants called in the pooled sample were excellent. This method can be easily scaled up to any number of genomic loci and any number of individuals. By incorporating the internal positive and negative amplicon controls at ratios that mimic the population under study, the algorithm can be calibrated for optimal performance. This strategy can also be modified for use with hybridization capture or individual-specific barcodes and can be applied to the sequencing of naturally heterogeneous samples, such as tumor DNA.     

Weighted Score Tests Implementing Model-Averaging Schemes in Detection of Rare Variants in Case-Control Studies

Multi-locus effect modeling is a powerful approach for detection of genes influencing a complex disease. Especially for rare variants, we need to analyze multiple variants together to achieve adequate power for detection. In this paper, we propose several parsimonious branching model techniques to assess the joint effect of a group of rare variants in a case-control study. These models implement a data reduction strategy within a likelihood framework and use a weighted score test to assess the statistical significance of the effect of the group of variants on the disease. The primary advantage of the proposed approach is that it performs model-averaging over a substantially smaller set of models supported by the data and thus gains power to detect multi-locus effects. We illustrate these proposed approaches on simulated and real data and study their performance compared to several existing rare variant detection approaches. The primary goal of this paper is to assess if there is any gain in power to detect association by averaging over a number of models instead of selecting the best model. Extensive simulations and real data application demonstrate the advantage the proposed approach in presence of causal variants with opposite directional effects along with a moderate number of null variants in linkage disequilibrium.     

A Robust Model-free Approach for Rare Variants Association Studies Incorporating Gene-Gene and Gene-Environmental Interactions

Recently more and more evidence suggest that rare variants with much lower minor allele frequencies play significant roles in disease etiology. Advances in next-generation sequencing technologies will lead to many more rare variants association studies. Several statistical methods have been proposed to assess the effect of rare variants by aggregating information from multiple loci across a genetic region and testing the association between the phenotype and aggregated genotype. One limitation of existing methods is that they only look into the marginal effects of rare variants but do not systematically take into account effects due to interactions among rare variants and between rare variants and environmental factors. In this article, we propose the summation of partition approach (SPA), a robust model-free method that is designed specifically for detecting both marginal effects and effects due to gene-gene (G×G) and gene-environmental (G×E) interactions for rare variants association studies. SPA has three advantages. First, it accounts for the interaction information and gains considerable power in the presence of unknown and complicated G×G or G×E interactions. Secondly, it does not sacrifice the marginal detection power; in the situation when rare variants only have marginal effects it is comparable with the most competitive method in current literature. Thirdly, it is easy to extend and can incorporate more complex interactions; other practitioners and scientists can tailor the procedure to fit their own study friendly. Our simulation studies show that SPA is considerably more powerful than many existing methods in the presence of G×G and G×E interactions.     

Rare Variants Association Analysis in Large-Scale Sequencing Studies at the Single Locus Level

Genetic association analyses of rare variants in next-generation sequencing (NGS) studies are fundamentally challenging due to the presence of a very large number of candidate variants at extremely low minor allele frequencies. Recent developments often focus on pooling multiple variants to provide association analysis at the gene instead of the locus level. Nonetheless, pinpointing individual variants is a critical goal for genomic researches as such information can facilitate the precise delineation of molecular mechanisms and functions of genetic factors on diseases. Due to the extreme rarity of mutations and high-dimensionality, significances of causal variants cannot easily stand out from those of noncausal ones. Consequently, standard false-positive control procedures, such as the Bonferroni and false discovery rate (FDR), are often impractical to apply, as a majority of the causal variants can only be identified along with a few but unknown number of noncausal variants. To provide informative analysis of individual variants in large-scale sequencing studies, we propose the Adaptive False-Negative Control (AFNC) procedure that can include a large proportion of causal variants with high confidence by introducing a novel statistical inquiry to determine those variants that can be confidently dispatched as noncausal. The AFNC provides a general framework that can accommodate for a variety of models and significance tests. The procedure is computationally efficient and can adapt to the underlying proportion of causal variants and quality of significance rankings. Extensive simulation studies across a plethora of scenarios demonstrate that the AFNC is advantageous for identifying individual rare variants, whereas the Bonferroni and FDR are exceedingly over-conservative for rare variants association studies. In the analyses of the CoLaus dataset, AFNC has identified individual variants most responsible for gene-level significances. Moreover, single-variant results using the AFNC have been successfully applied to infer related genes with annotation information.     

A Powerful and Adaptive Association Test for Rare Variants

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

Discovery of Rare Variants via Sequencing: Implications for the Design of Complex Trait Association Studies

There is strong evidence that rare variants are involved in complex disease etiology. The first step in implicating rare variants in disease etiology is their identification through sequencing in both randomly ascertained samples (e.g., the 1,000 Genomes Project) and samples ascertained according to disease status. We investigated to what extent rare variants will be observed across the genome and in candidate genes in randomly ascertained samples, the magnitude of variant enrichment in diseased individuals, and biases that can occur due to how variants are discovered. Although sequencing cases can enrich for casual variants, when a gene or genes are not involved in disease etiology, limiting variant discovery to cases can lead to association studies with dramatically inflated false positive rates.     

A Powerful Pathway-Based Adaptive Test for Genetic Association with Common or Rare Variants

In spite of the success of genome-wide association studies (GWASs), only a small proportion of heritability for each complex trait has been explained by identified genetic variants, mainly SNPs. Likely reasons include genetic heterogeneity (i.e., multiple causal genetic variants) and small effect sizes of causal variants, for which pathway analysis has been proposed as a promising alternative to the standard single-SNP-based analysis. A pathway contains a set of functionally related genes, each of which includes multiple SNPs. Here we propose a pathway-based test that is adaptive at both the gene and SNP levels, thus maintaining high power across a wide range of situations with varying numbers of the genes and SNPs associated with a trait. The proposed method is applicable to both common variants and rare variants and can incorporate biological knowledge on SNPs and genes to boost statistical power. We use extensively simulated data and a WTCCC GWAS dataset to compare our proposal with several existing pathway-based and SNP-set-based tests, demonstrating its promising performance and its potential use in practice.     

Pooled Sequencing of Candidate Genes Implicates Rare Variants in the Development of Asthma Following Severe RSV Bronchiolitis in Infancy

Severe infection with respiratory syncytial virus (RSV) during infancy is strongly associated with the development of asthma. To identify genetic variation that contributes to asthma following severe RSV bronchiolitis during infancy, we sequenced the coding exons of 131 asthma candidate genes in 182 European and African American children with severe RSV bronchiolitis in infancy using anonymous pools for variant discovery, and then directly genotyped a set of 190 nonsynonymous variants. Association testing was performed for physician-diagnosed asthma before the 7^th birthday (asthma) using genotypes from 6,500 individuals from the Exome Sequencing Project (ESP) as controls to gain statistical power. In addition, among patients with severe RSV bronchiolitis during infancy, we examined genetic associations with asthma, active asthma, persistent wheeze, and bronchial hyperreactivity (methacholine PC₂₀) at age 6 years. We identified four rare nonsynonymous variants that were significantly associated with asthma following severe RSV bronchiolitis, including single variants in ADRB2, FLG and NCAM1 in European Americans (p = 4.6x10^-4, 1.9x10^-13 and 5.0x10^-5, respectively), and NOS1 in African Americans (p = 2.3x10^-11). One of the variants was a highly functional nonsynonymous variant in ADRB2 (rs1800888), which was also nominally associated with asthma (p = 0.027) and active asthma (p = 0.013) among European Americans with severe RSV bronchiolitis without including the ESP. Our results suggest that rare nonsynonymous variants contribute to the development of asthma following severe RSV bronchiolitis in infancy, notably in ADRB2. Additional studies are required to explore the role of rare variants in the etiology of asthma and asthma-related traits following severe RSV bronchiolitis.     

Fine-Scale Patterns of Population Stratification Confound Rare Variant Association Tests

Advances in next-generation sequencing technology have enabled systematic exploration of the contribution of rare variation to Mendelian and complex diseases. Although it is well known that population stratification can generate spurious associations with common alleles, its impact on rare variant association methods remains poorly understood. Here, we performed exhaustive coalescent simulations with demographic parameters calibrated from exome sequence data to evaluate the performance of nine rare variant association methods in the presence of fine-scale population structure. We find that all methods have an inflated spurious association rate for parameter values that are consistent with levels of differentiation typical of European populations. For example, at a nominal significance level of 5%, some test statistics have a spurious association rate as high as 40%. Finally, we empirically assess the impact of population stratification in a large data set of 4,298 European American exomes. Our results have important implications for the design, analysis, and interpretation of rare variant genome-wide association studies.     

An Exponential Combination Procedure for Set-Based Association Tests in Sequencing Studies

State-of-the-art next-generation-sequencing technologies can facilitate in-depth explorations of the human genome by investigating both common and rare variants. For the identification of genetic factors that are associated with disease risk or other complex phenotypes, methods have been proposed for jointly analyzing variants in a set (e.g., all coding SNPs in a gene). Variants in a properly defined set could be associated with risk or phenotype in a concerted fashion, and by accumulating information from them, one can improve power to detect genetic risk factors. Many set-based methods in the literature are based on statistics that can be written as the summation of variant statistics. Here, we propose taking the summation of the exponential of variant statistics as the set summary for association testing. From both Bayesian and frequentist perspectives, we provide theoretical justification for taking the sum of the exponential of variant statistics because it is particularly powerful for sparse alternatives—that is, compared with the large number of variants being tested in a set, only relatively few variants are associated with disease risk—a distinctive feature of genetic data. We applied the exponential combination gene-based test to a sequencing study in anticancer pharmacogenomics and uncovered mechanistic insights into genes and pathways related to chemotherapeutic susceptibility for an important class of oncologic drugs.