On optimal pooling designs to identify rare variants through massive resequencing

The advent of next‐generation sequencing technologies has facilitated the detection of rare variants. Despite the significant cost reduction, sequencing cost is still high for large‐scale studies. In this article, we examine DNA pooling as a cost‐effective strategy for rare variant detection. We consider the optimal number of individuals in a DNA pool to detect an allele with a specific minor allele frequency (MAF) under a given coverage depth and detection threshold. We found that the optimal number of individuals in a pool is indifferent to the MAF at the same coverage depth and detection threshold. In addition, when the individual contributions to each pool are equal, the total number of individuals across different pools required in an optimal design to detect a variant with a desired power is similar at different coverage depths. When the contributions are more variable, more individuals tend to be needed for higher coverage depths. Our study provides general guidelines on using DNA pooling for more cost‐effective identifications of rare variants. Genet. Epidemiol. 35:139‐147, 2011. © 2011 Wiley‐Liss, Inc.     

Confounded by sequencing depth in association studies of rare alleles

Next‐generation DNA sequencing technologies are facilitating large‐scale association studies of rare genetic variants. The depth of the sequence read coverage is an important experimental variable in the next‐generation technologies and it is a major determinant of the quality of genotype calls generated from sequence data. When case and control samples are sequenced separately or in different proportions across batches, they are unlikely to be matched on sequencing read depth and a differential misclassification of genotypes can result, causing confounding and an increased false‐positive rate. Data from Pilot Study 3 of the 1000 Genomes project was used to demonstrate that a difference between the mean sequencing read depth of case and control samples can result in false‐positive association for rare and uncommon variants, even when the mean coverage depth exceeds 30× in both groups. The degree of the confounding and inflation in the false‐positive rate depended on the extent to which the mean depth was different in the case and control groups. A logistic regression model was used to test for association between case‐control status and the cumulative number of alleles in a collapsed set of rare and uncommon variants. Including each individual's mean sequence read depth across the variant sites in the logistic regression model nearly eliminated the confounding effect and the inflated false‐positive rate. Furthermore, accounting for the potential error by modeling the probability of the heterozygote genotype calls in the regression analysis had a relatively minor but beneficial effect on the statistical results. Genet. Epidemiol. 35: 261‐268, 2011. © 2011 Wiley‐Liss, Inc.     

Design of association studies with pooled or un‐pooled next‐generation sequencing data

Most common hereditary diseases in humans are complex and multifactorial. Large‐scale genome‐wide association studies based on SNP genotyping have only identified a small fraction of the heritable variation of these diseases. One explanation may be that many rare variants (a minor allele frequency, MAF <5%), which are not included in the common genotyping platforms, may contribute substantially to the genetic variation of these diseases. Next‐generation sequencing, which would allow the analysis of rare variants, is now becoming so cheap that it provides a viable alternative to SNP genotyping. In this paper, we present cost‐effective protocols for using next‐generation sequencing in association mapping studies based on pooled and un‐pooled samples, and identify optimal designs with respect to total number of individuals, number of individuals per pool, and the sequencing coverage. We perform a small empirical study to evaluate the pooling variance in a realistic setting where pooling is combined with exon‐capturing. To test for associations, we develop a likelihood ratio statistic that accounts for the high error rate of next‐generation sequencing data. We also perform extensive simulations to determine the power and accuracy of this method. Overall, our findings suggest that with a fixed cost, sequencing many individuals at a more shallow depth with larger pool size achieves higher power than sequencing a small number of individuals in higher depth with smaller pool size, even in the presence of high error rates. Our results provide guidelines for researchers who are developing association mapping studies based on next‐generation sequencing. Genet. Epidemiol. 34: 479–491, 2010. © 2010 Wiley‐Liss, Inc.     

Power in the phenotypic extremes: a simulation study of power in discovery and replication of rare variants

Next‐generation sequencing technologies are making it possible to study the role of rare variants in human disease. Many studies balance statistical power with cost‐effectiveness by (a) sampling from phenotypic extremes and (b) utilizing a two‐stage design. Two‐stage designs include a broad‐based discovery phase and selection of a subset of potential causal genes/variants to be further examined in independent samples. We evaluate three parameters: first, the gain in statistical power due to extreme sampling to discover causal variants; second, the informativeness of initial (Phase I) association statistics to select genes/variants for follow‐up; third, the impact of extreme and random sampling in (Phase 2) replication. We present a quantitative method to select individuals from the phenotypic extremes of a binary trait, and simulate disease association studies under a variety of sample sizes and sampling schemes. First, we find that while studies sampling from extremes have excellent power to discover rare variants, they have limited power to associate them to phenotype—suggesting high false‐negative rates for upcoming studies. Second, consistent with previous studies, we find that the effect sizes estimated in these studies are expected to be systematically larger compared with the overall population effect size; in a well‐cited lipids study, we estimate the reported effect to be twofold larger. Third, replication studies require large samples from the general population to have sufficient power; extreme sampling could reduce the required sample size as much as fourfold. Our observations offer practical guidance for the design and interpretation of studies that utilize extreme sampling. Genet. Epidemiol. 35: 236‐246, 2011. © 2011 Wiley‐Liss, Inc.     

Resequencing of pooled DNA for detecting disease associations with rare variants

A combination of common and rare variants is thought to contribute to genetic susceptibility to complex diseases. Recently, next‐generation sequencers have greatly lowered sequencing costs, providing an opportunity to identify rare disease variants in large genetic epidemiology studies. At present, it is still expensive and time consuming to resequence large number of individual genomes. However, given that next‐generation sequencing technology can provide accurate estimates of allele frequencies from pooled DNA samples, it is possible to detect associations of rare variants using pooled DNA sequencing. Current statistical approaches to the analysis of associations with rare variants are not designed for use with pooled next‐generation sequencing data. Hence, they may not be optimal in terms of both validity and power. Therefore, we propose here a new statistical procedure to analyze the output of pooled sequencing data. The test statistic can be computed rapidly, making it feasible to test the association of a large number of variants with disease. By simulation, we compare this approach to Fisher's exact test based either on pooled or individual genotypic data. Our results demonstrate that the proposed method provides good control of the Type I error rate, while yielding substantially higher power than Fisher's exact test using pooled genotypic data for testing rare variants, and has similar or higher power than that of Fisher's exact test using individual genotypic data. Our results also provide guidelines on how various parameters of the pooled sequencing design affect the efficiency of detecting associations. Genet. Epidemiol. 34: 492–501, 2010. © 2010 Wiley‐Liss, Inc.     

Identifying Rare Variants With Optimal Depth of Coverage and Cost‐Effective Overlapping Pool Sequencing

Genome‐wide association studies have identified hundreds of genetic variants associated with complex diseases although most variants identified so far explain only a small proportion of heritability, suggesting that rare variants are responsible for missing heritability. Identification of rare variants through large‐scale resequencing becomes increasing important but still prohibitively expensive despite the rapid decline in the sequencing costs. Nevertheless, group testing based overlapping pool sequencing in which pooled rather than individual samples are sequenced will greatly reduces the efforts of sample preparation as well as the costs to screen for rare variants. Here, we proposed an overlapping pool sequencing to screen rare variants with optimal sequencing depth and a corresponding cost model. We formulated a model to compute the optimal depth for sufficient observations of variants in pooled sequencing. Utilizing shifted transversal design algorithm, appropriate parameters for overlapping pool sequencing could be selected to minimize cost and guarantee accuracy. Due to the mixing constraint and high depth for pooled sequencing, results showed that it was more cost‐effective to divide a large population into smaller blocks which were tested using optimized strategies independently. Finally, we conducted an experiment to screen variant carriers with frequency equaled 1%. With simulated pools and publicly available human exome sequencing data, the experiment achieved 99.93% accuracy. Utilizing overlapping pool sequencing, the cost for screening variant carriers with frequency equaled 1% in 200 diploid individuals dropped to at least 66% at which target sequencing region was set to 30 Mb.     

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.     

Are rare variants really independent?

Recent advances in genotyping with high‐density markers allow researchers access to genomic variants including rare ones. Linkage disequilibrium (LD) is widely used to provide insight into evolutionary history. It is also the basis for association mapping in humans and other species. Better understanding of the genomic LD structure may lead to better‐informed statistical tests that can improve the power of association studies. Although rare variant associations with common diseases (RVCD) have been extensively studied recently, there is very limited understanding, and even controversial view of LD structures among rare variants and between rare and common variants. In fact, many popular RVCD tests make the assumptions that rare variants are independent. In this report, we show that two commonly used LD measures are not capable of detecting LD when rare variants are involved. We present this argument from two perspectives, both the LD measures themselves and the computational issues associated with them. To address these issues, we propose an alternative LD measure, the polychoric correlation, that was originally designed for detecting associations among categorical variables. Using simulated as well as the 1000 Genomes data, we explore the performances of LD measures in detail and discuss their implications in association studies.     

A powerful association test of multiple genetic variants using a random‐effects model

There is an emerging interest in sequencing‐based association studies of multiple rare variants. Most association tests suggested in the literature involve collapsing rare variants with or without weighting. Recently, a variance‐component score test [sequence kernel association test (SKAT)] was proposed to address the limitations of collapsing method. Although SKAT was shown to outperform most of the alternative tests, its applications and power might be restricted and influenced by missing genotypes. In this paper, we suggest a new method based on testing whether the fraction of causal variants in a region is zero. The new association test, T _REM, is derived from a random‐effects model and allows for missing genotypes, and the choice of weighting function is not required when common and rare variants are analyzed simultaneously. We performed simulations to study the type I error rates and power of four competing tests under various conditions on the sample size, genotype missing rate, variant frequency, effect directionality, and the number of non‐causal rare variant and/or causal common variant. The simulation results showed that T _REM was a valid test and less sensitive to the inclusion of non‐causal rare variants and/or low effect common variants or to the presence of missing genotypes. When the effects were more consistent in the same direction, T _REM also had better power performance. Finally, an application to the Shanghai Breast Cancer Study showed that rare causal variants at the FGFR2 gene were detected by T _REM and SKAT, but T _REM produced more consistent results for different sets of rare and common variants. Copyright © 2013 John Wiley & Sons, Ltd.     

An evaluation of statistical approaches to rare variant analysis in genetic association studies

Genome‐wide association (GWA) studies have proved to be extremely successful in identifying novel common polymorphisms contributing effects to the genetic component underlying complex traits. Nevertheless, one source of, as yet, undiscovered genetic determinants of complex traits are those mediated through the effects of rare variants. With the increasing availability of large‐scale re‐sequencing data for rare variant discovery, we have developed a novel statistical method for the detection of complex trait associations with these loci, based on searching for accumulations of minor alleles within the same functional unit. We have undertaken simulations to evaluate strategies for the identification of rare variant associations in population‐based genetic studies when data are available from re‐sequencing discovery efforts or from commercially available GWA chips. Our results demonstrate that methods based on accumulations of rare variants discovered through re‐sequencing offer substantially greater power than conventional analysis of GWA data, and thus provide an exciting opportunity for future discovery of genetic determinants of complex traits. Genet. Epidemiol. 34: 188–193, 2010. © 2009 Wiley‐Liss, Inc.     

Rare variant association test with multiple phenotypes

Although genome‐wide association studies (GWAS) have now discovered thousands of genetic variants associated with common traits, such variants cannot explain the large degree of “missing heritability,” likely due to rare variants. The advent of next generation sequencing technology has allowed rare variant detection and association with common traits, often by investigating specific genomic regions for rare variant effects on a trait. Although multiple correlated phenotypes are often concurrently observed in GWAS, most studies analyze only single phenotypes, which may lessen statistical power. To increase power, multivariate analyses, which consider correlations between multiple phenotypes, can be used. However, few existing multivariant analyses can identify rare variants for assessing multiple phenotypes. Here, we propose Multivariate Association Analysis using Score Statistics (MAAUSS), to identify rare variants associated with multiple phenotypes, based on the widely used sequence kernel association test (SKAT) for a single phenotype. We applied MAAUSS to whole exome sequencing (WES) data from a Korean population of 1,058 subjects to discover genes associated with multiple traits of liver function. We then assessed validation of those genes by a replication study, using an independent dataset of 3,445 individuals. Notably, we detected the gene ZNF620 among five significant genes. We then performed a simulation study to compare MAAUSS's performance with existing methods. Overall, MAAUSS successfully conserved type 1 error rates and in many cases had a higher power than the existing methods. This study illustrates a feasible and straightforward approach for identifying rare variants correlated with multiple phenotypes, with likely relevance to missing heritability.     

Population Genetics Identifies Challenges in Analyzing Rare Variants

Geneticists have, for years, understood the nature of genome‐wide association studies using common genomic variants. Recently, however, focus has shifted to the analysis of rare variants. This presents potential problems for researchers, as rare variants do not always behave in the same way common variants do, sometimes rendering decades of solid intuition moot. In this paper, we present examples of the differences between common and rare variants. We show why one must be significantly more careful about the origin of rare variants, and how failing to do so can lead to highly inflated type I error. We then explain how to best avoid such concerns with careful understanding and study design. Additionally, we demonstrate that a seemingly low error rate in next‐generation sequencing can dramatically impact the false‐positive rate for rare variants. This is due to the fact that rare variants are, by definition, seen infrequently, making it hard to distinguish between errors and real variants. Compounding this problem is the fact that the proportion of errors is likely to get worse, not better, with increasing sample size. One cannot simply scale their way up in order to solve this problem. Understanding these potential pitfalls is a key step in successfully identifying true associations between rare variants and diseases.     

A Variational Bayes Discrete Mixture Test for Rare Variant Association

Recently, many statistical methods have been proposed to test for associations between rare genetic variants and complex traits. Most of these methods test for association by aggregating genetic variations within a predefined region, such as a gene. Although there is evidence that “aggregate” tests are more powerful than the single marker test, these tests generally ignore neutral variants and therefore are unable to identify specific variants driving the association with phenotype. We propose a novel aggregate rare‐variant test that explicitly models a fraction of variants as neutral, tests associations at the gene‐level, and infers the rare‐variants driving the association. Simulations show that in the practical scenario where there are many variants within a given region of the genome with only a fraction causal our approach has greater power compared to other popular tests such as the Sequence Kernel Association Test (SKAT), the Weighted Sum Statistic (WSS), and the collapsing method of Morris and Zeggini (MZ). Our algorithm leverages a fast variational Bayes approximate inference methodology to scale to exome‐wide analyses, a significant computational advantage over exact inference model selection methodologies. To demonstrate the efficacy of our methodology we test for associations between von Willebrand Factor (VWF) levels and VWF missense rare‐variants imputed from the National Heart, Lung, and Blood Institute's Exome Sequencing project into 2,487 African Americans within the VWF gene. Our method suggests that a relatively small fraction (～10%) of the imputed rare missense variants within VWF are strongly associated with lower VWF levels in African Americans.     

Adjusting for Population Stratification in a Fine Scale With Principal Components and Sequencing Data

Population stratification is of primary interest in genetic studies to infer human evolution history and to avoid spurious findings in association testing. Although it is well studied with high‐density single nucleotide polymorphisms (SNPs) in genome‐wide association studies (GWASs), next‐generation sequencing brings both new opportunities and challenges to uncovering population structures in finer scales. Several recent studies have noticed different confounding effects from variants of different minor allele frequencies (MAFs). In this paper, using a low‐coverage sequencing dataset from the 1000 Genomes Project, we compared a popular method, principal component analysis (PCA), with a recently proposed spectral clustering technique, called spectral dimensional reduction (SDR), in detecting and adjusting for population stratification at the level of ethnic subgroups. We investigated the varying performance of adjusting for population stratification with different types and sets of variants when testing on different types of variants. One main conclusion is that principal components based on all variants or common variants were generally most effective in controlling inflations caused by population stratification; in particular, contrary to many speculations on the effectiveness of rare variants, we did not find much added value with the use of only rare variants. In addition, SDR was confirmed to be more robust than PCA, especially when applied to rare variants.     

PreCimp: Pre‐collapsing imputation approach increases imputation accuracy of rare variants in terms of collapsed variables

Imputation is widely used for obtaining information about rare variants. However, one issue concerning imputation is the low accuracy of imputed rare variants as the inaccurate imputed rare variants may distort the results of region‐based association tests. Therefore, we developed a pre‐collapsing imputation method (PreCimp) to improve the accuracy of imputation by using collapsed variables. Briefly, collapsed variables are generated using rare variants in the reference panel, and a new reference panel is constructed by inserting pre‐collapsed variables into the original reference panel. Following imputation analysis provides the imputed genotypes of the collapsed variables. We demonstrated the performance of PreCimp on 5,349 genotyped samples using a Korean population specific reference panel including 848 samples of exome sequencing, Affymetrix 5.0, and exome chip. PreCimp outperformed a traditional post‐collapsing method that collapses imputed variants after single rare variant imputation analysis. Compared with the results of post‐collapsing method, PreCimp approach was shown to relatively increase imputation accuracy about 3.4–6.3% when dosage r² is between 0.6 and 0.8, 10.9–16.1% when dosage r² is between 0.4 and 0.6, and 21.4 ～ 129.4% when dosage r² is below 0.4.     

A Generalized Genetic Random Field Method for the Genetic Association Analysis of Sequencing Data

With the advance of high‐throughput sequencing technologies, it has become feasible to investigate the influence of the entire spectrum of sequencing variations on complex human diseases. Although association studies utilizing the new sequencing technologies hold great promise to unravel novel genetic variants, especially rare genetic variants that contribute to human diseases, the statistical analysis of high‐dimensional sequencing data remains a challenge. Advanced analytical methods are in great need to facilitate high‐dimensional sequencing data analyses. In this article, we propose a generalized genetic random field (GGRF) method for association analyses of sequencing data. Like other similarity‐based methods (e.g., SIMreg and SKAT), the new method has the advantages of avoiding the need to specify thresholds for rare variants and allowing for testing multiple variants acting in different directions and magnitude of effects. The method is built on the generalized estimating equation framework and thus accommodates a variety of disease phenotypes (e.g., quantitative and binary phenotypes). Moreover, it has a nice asymptotic property, and can be applied to small‐scale sequencing data without need for small‐sample adjustment. Through simulations, we demonstrate that the proposed GGRF attains an improved or comparable power over a commonly used method, SKAT, under various disease scenarios, especially when rare variants play a significant role in disease etiology. We further illustrate GGRF with an application to a real dataset from the Dallas Heart Study. By using GGRF, we were able to detect the association of two candidate genes, ANGPTL3 and ANGPTL4, with serum triglyceride.     

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 Weighted U‐Statistic for Genetic Association Analyses of Sequencing Data

With advancements in next‐generation sequencing technology, a massive amount of sequencing data is generated, which offers a great opportunity to comprehensively investigate the role of rare variants in the genetic etiology of complex diseases. Nevertheless, the high‐dimensional sequencing data poses a great challenge for statistical analysis. The association analyses based on traditional statistical methods suffer substantial power loss because of the low frequency of genetic variants and the extremely high dimensionality of the data. We developed a Weighted U Sequencing test, referred to as WU‐SEQ, for the high‐dimensional association analysis of sequencing data. Based on a nonparametric U‐statistic, WU‐SEQ makes no assumption of the underlying disease model and phenotype distribution, and can be applied to a variety of phenotypes. Through simulation studies and an empirical study, we showed that WU‐SEQ outperformed a commonly used sequence kernel association test (SKAT) method when the underlying assumptions were violated (e.g., the phenotype followed a heavy‐tailed distribution). Even when the assumptions were satisfied, WU‐SEQ still attained comparable performance to SKAT. Finally, we applied WU‐SEQ to sequencing data from the Dallas Heart Study (DHS), and detected an association between ANGPTL 4 and very low density lipoprotein cholesterol.     

Extracting Actionable Information From Genome Scans

Genome‐wide association studies discovered numerous genetic variants significantly associated with various phenotypes. However, significant signals explain only a small portion of the variation in many traits. One explanation is that missing variation is found in “suggestive signals,” i.e., variants with reasonably small P‐values. However, it is not clear how to capture this information and use it optimally to design and analyze future studies. We propose to extract the available information from a genome scan by accurately estimating the means of univariate statistics. The means are estimated by: (i) computing the sum of squares (SS) of a genome scan's univariate statistics, (ii) using SS to estimate the expected SS for the means (SSM) of univariate statistics, and (iii) constructing accurate soft threshold (ST) estimators for means of univariate statistics by requiring that the SS of these estimators equals the SSM. When compared to competitors, ST estimators explain a substantially higher fraction of the variability in true means. The accuracy of proposed estimators can be used to design two‐tier follow‐up studies in which regions close to variants having ST‐estimated means above a certain threshold are sequenced at high coverage and the rest of the genome is sequenced at low coverage. This follow‐up approach reduces the sequencing burden by at least an order of magnitude when compared to a high coverage sequencing of the whole genome. Finally, we suggest ways in which ST methodology can be used to improve signal detection in future sequencing studies and to perform general statistical model selection.