Biases and errors on allele frequency estimation and disease association tests of next-generation sequencing of pooled samples

Next-generation sequencing is widely used to study complex diseases because of its ability to identify both common and rare variants without prior single nucleotide polymorphism (SNP) information. Pooled sequencing of implicated target regions can lower costs and allow more samples to be analyzed, thus improving statistical power for disease-associated variant detection. Several methods for disease association tests of pooled data and for optimal pooling designs have been developed under certain assumptions of the pooling process, for example, equal/unequal contributions to the pool, sequencing depth variation, and error rate. However, these simplified assumptions may not portray the many factors affecting pooled sequencing data quality, such as PCR amplification during target capture and sequencing, reference allele preferential bias, and others. As a result, the properties of the observed data may differ substantially from those expected under the simplified assumptions. Here, we use real datasets from targeted sequencing of pooled samples, together with microarray SNP genotypes of the same subjects, to identify and quantify factors (biases and errors) affecting the observed sequencing data. Through simulations, we find that these factors have a significant impact on the accuracy of allele frequency estimation and the power of association tests. Furthermore, we develop a workflow protocol to incorporate these factors in data analysis to reduce the potential biases and errors in pooled sequencing data and to gain better estimation of allele frequencies. The workflow, Psafe, is available at http://bioinformatics.med.yale.edu/group/.     

Efficient study design for next generation sequencing

Next Generation Sequencing represents a powerful tool for detecting genetic variation associated with human disease. Because of the high cost of this technology, it is critical that we develop efficient study designs that consider the trade‐off between the number of subjects (n) and the coverage depth (µ). How we divide our resources between the two can greatly impact study success, particularly in pilot studies. We propose a strategy for selecting the optimal combination of n and µ for studies aimed at detecting rare variants and for studies aimed at detecting associations between rare or uncommon variants and disease. For detecting rare variants, we find the optimal coverage depth to be between 2 and 8 reads when using the likelihood ratio test. For association studies, we find the strategy of sequencing all available subjects to be preferable. In deriving these combinations, we provide a detailed analysis describing the distribution of depth across a genome and the depth needed to identify a minor allele in an individual. The optimal coverage depth depends on the aims of the study, and the chosen depth can have a large impact on study success. Genet. Epidemiol. 35: 269‐277, 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.     

A W‐test collapsing method for rare‐variant association testing in exome sequencing data

Advancement in sequencing technology enables the study of association between complex disorder phenotypes and single‐nucleotide polymorphisms with rare mutations. However, the rare genetic variant has extremely small variance and impairs testing power of traditional statistical methods. We introduce a W‐test collapsing method to evaluate rare‐variant association by measuring the distributional differences between cases and controls through combined log of odds ratio within a genomic region. The method is model‐free and inherits chi‐squared distribution with degrees of freedom estimated from bootstrapped samples of the data, and allows for fast and accurate P‐value calculation without the need of permutations. The proposed method is compared with the Weighted‐Sum Statistic and Sequence Kernel Association Test on simulation datasets, and showed good performances and significantly faster computing speed. In the application of real next‐generation sequencing dataset of hypertensive disorder, it identified genes of interesting biological functions associated to metabolism disorder and inflammation, including the MACROD1, NLRP7, AGK, PAK6, and APBB1. The proposed method offers an efficient and effective way for testing rare genetic variants in whole exome sequencing datasets.     

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.     

gsSKAT: Rapid gene set analysis and multiple testing correction for rare‐variant association studies using weighted linear kernels

Next‐generation sequencing technologies have afforded unprecedented characterization of low‐frequency and rare genetic variation. Due to low power for single‐variant testing, aggregative methods are commonly used to combine observed rare variation within a single gene. Causal variation may also aggregate across multiple genes within relevant biomolecular pathways. Kernel‐machine regression and adaptive testing methods for aggregative rare‐variant association testing have been demonstrated to be powerful approaches for pathway‐level analysis, although these methods tend to be computationally intensive at high‐variant dimensionality and require access to complete data. An additional analytical issue in scans of large pathway definition sets is multiple testing correction. Gene set definitions may exhibit substantial genic overlap, and the impact of the resultant correlation in test statistics on Type I error rate control for large agnostic gene set scans has not been fully explored. Herein, we first outline a statistical strategy for aggregative rare‐variant analysis using component gene‐level linear kernel score test summary statistics as well as derive simple estimators of the effective number of tests for family‐wise error rate control. We then conduct extensive simulation studies to characterize the behavior of our approach relative to direct application of kernel and adaptive methods under a variety of conditions. We also apply our method to two case‐control studies, respectively, evaluating rare variation in hereditary prostate cancer and schizophrenia. Finally, we provide open‐source R code for public use to facilitate easy application of our methods to existing rare‐variant analysis results.     

Detecting association of rare and common variants by testing an optimally weighted combination of variants

Next-generation sequencing technology will soon allow sequencing the whole genome of large groups of individuals, and thus will make directly testing rare variants possible. Currently, most of existing methods for rare variant association studies are essentially testing the effect of a weighted combination of variants with different weighting schemes. Performance of these methods depends on the weights being used and no optimal weights are available. By putting large weights on rare variants and small weights on common variants, these methods target at rare variants only, although increasing evidence shows that complex diseases are caused by both common and rare variants. In this paper, we analytically derive optimal weights under a certain criterion. Based on the optimal weights, we propose a Variable Weight Test for testing the effect of an Optimally Weighted combination of variants (VW-TOW). VW-TOW aims to test the effects of both rare and common variants. VW-TOW is applicable to both quantitative and qualitative traits, allows covariates, can control for population stratification, and is robust to directions of effects of causal variants. Extensive simulation studies and application to the Genetic Analysis Workshop 17 (GAW17) data show that VW-TOW is more powerful than existing ones either for testing effects of both rare and common variants or for testing effects of rare variants only.     

A Rare Variant Association Test Based on Combinations of Single‐Variant Tests

Next generation sequencing technologies make direct testing rare variant associations possible. However, the development of powerful statistical methods for rare variant association studies is still underway. Most of existing methods are burden and quadratic tests. Recent studies show that the performance of each of burden and quadratic tests depends strongly upon the underlying assumption and no test demonstrates consistently acceptable power. Thus, combined tests by combining information from the burden and quadratic tests have been proposed recently. However, results from recent studies (including this study) show that there exist tests that can outperform both burden and quadratic tests. In this article, we propose three classes of tests that include tests outperforming both burden and quadratic tests. Then, we propose the optimal combination of single‐variant tests (OCST) by combining information from tests of the three classes. We use extensive simulation studies to compare the performance of OCST with that of burden, quadratic and optimal single‐variant tests. Our results show that OCST either is the most powerful test or has similar power with the most powerful test. We also compare the performance of OCST with that of the two existing combined tests. Our results show that OCST has better power than the two combined tests.     

Association testing for next-generation sequencing data using score statistics

The advances in sequencing technology have made large-scale sequencing studies for large cohorts feasible. Often, the primary goal for large-scale studies is to identify genetic variants associated with a disease or other phenotypes. Even when deep sequencing is performed, there will be many sites where there is not enough data to call genotypes accurately. Ignoring the genotype classification uncertainty by basing subsequent analyses on called genotypes leads to a loss in power. Additionally, using called genotypes can lead to spurious association signals. Some methods taking the uncertainty of genotype calls into account have been proposed; most require numerical optimization which for large-scale data is not always computationally feasible. We show that using a score statistic for the joint likelihood of observed phenotypes and observed sequencing data provides an attractive approach to association testing for next-generation sequencing data. The joint model accounts for the genotype classification uncertainty via the posterior probabilities of the genotypes given the observed sequencing data, which gives the approach higher power than methods based on called genotypes. This strategy remains computationally feasible due to the use of score statistics. As part of the joint likelihood, we model the distribution of the phenotypes using a generalized linear model framework, which works for both quantitative and discrete phenotypes. Thus, the method presented here is applicable to case-control studies as well as mapping of quantitative traits. The model allows additional covariates that enable correction for confounding factors such as population stratification or cohort effects.     

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.     

Using extreme phenotype sampling to identify the rare causal variants of quantitative traits in association studies

Variants identified in recent genome-wide association studies based on the common-disease common-variant hypothesis are far from fully explaining the hereditability of complex traits. Rare variants may, in part, explain some of the missing hereditability. Here, we explored the advantage of the extreme phenotype sampling in rare-variant analysis and refined this design framework for future large-scale association studies on quantitative traits. We first proposed a power calculation approach for a likelihood-based analysis method. We then used this approach to demonstrate the potential advantages of extreme phenotype sampling for rare variants. Next, we discussed how this design can influence future sequencing-based association studies from a cost-efficiency (with the phenotyping cost included) perspective. Moreover, we discussed the potential of a two-stage design with the extreme sample as the first stage and the remaining nonextreme subjects as the second stage. We demonstrated that this two-stage design is a cost-efficient alternative to the one-stage cross-sectional design or traditional two-stage design. We then discussed the analysis strategies for this extreme two-stage design and proposed a corresponding design optimization procedure. To address many practical concerns, for example measurement error or phenotypic heterogeneity at the very extremes, we examined an approach in which individuals with very extreme phenotypes are discarded. We demonstrated that even with a substantial proportion of these extreme individuals discarded, an extreme-based sampling can still be more efficient. Finally, we expanded the current analysis and design framework to accommodate the CMC approach where multiple rare-variants in the same gene region are analyzed jointly.     

PhredEM: a phred‐score‐informed genotype‐calling approach for next‐generation sequencing studies

A fundamental challenge in analyzing next‐generation sequencing (NGS) data is to determine an individual's genotype accurately, as the accuracy of the inferred genotype is essential to downstream analyses. Correctly estimating the base‐calling error rate is critical to accurate genotype calls. Phred scores that accompany each call can be used to decide which calls are reliable. Some genotype callers, such as GATK and SAMtools, directly calculate the base‐calling error rates from phred scores or recalibrated base quality scores. Others, such as SeqEM, estimate error rates from the read data without using any quality scores. It is also a common quality control procedure to filter out reads with low phred scores. However, choosing an appropriate phred score threshold is problematic as a too high threshold may lose data, while a too low threshold may introduce errors. We propose a new likelihood‐based genotype‐calling approach that exploits all reads and estimates the per‐base error rates by incorporating phred scores through a logistic regression model. The approach, which we call PhredEM, uses the expectation–maximization (EM) algorithm to obtain consistent estimates of genotype frequencies and logistic regression parameters. It also includes a simple, computationally efficient screening algorithm to identify loci that are estimated to be monomorphic, so that only loci estimated to be nonmonomorphic require application of the EM algorithm. Like GATK, PhredEM can be used together with a linkage‐disequilibrium‐based method such as Beagle, which can further improve genotype calling as a refinement step. We evaluate the performance of PhredEM using both simulated data and real sequencing data from the UK10K project and the 1000 Genomes project. The results demonstrate that PhredEM performs better than either GATK or SeqEM, and that PhredEM is an improved, robust, and widely applicable genotype‐calling approach for NGS studies. The relevant software is freely available.     

Testing for Rare Variant Associations in the Presence of Missing Data

For studies of genetically complex diseases, many association methods have been developed to analyze rare variants. When variant calls are missing, naïve implementation of rare variant association (RVA) methods may lead to inflated type I error rates as well as a reduction in power. To overcome these problems, we developed extensions for four commonly used RVA tests. Data from the National Heart Lung and Blood Institute‐Exome Sequencing Project were used to demonstrate that missing variant calls can lead to increased false‐positive rates and that the extended RVA methods control type I error without reducing power. We suggest a combined strategy of data filtering based on variant and sample level missing genotypes along with implementation of these extended RVA tests.     

Meta‐Analysis of Sequencing Studies With Heterogeneous Genetic Associations

Recent advances in sequencing technologies have made it possible to explore the influence of rare variants on complex diseases and traits. Meta‐analysis is essential to this exploration because large sample sizes are required to detect rare variants. Several methods are available to conduct meta‐analysis for rare variants under fixed‐effects models, which assume that the genetic effects are the same across all studies. In practice, genetic associations are likely to be heterogeneous among studies because of differences in population composition, environmental factors, phenotype and genotype measurements, or analysis method. We propose random‐effects models which allow the genetic effects to vary among studies and develop the corresponding meta‐analysis methods for gene‐level association tests. Our methods take score statistics, rather than individual participant data, as input and thus can accommodate any study designs and any phenotypes. We produce the random‐effects versions of all commonly used gene‐level association tests, including burden, variable threshold, and variance‐component tests. We demonstrate through extensive simulation studies that our random‐effects tests are substantially more powerful than the fixed‐effects tests in the presence of moderate and high between‐study heterogeneity and achieve similar power to the latter when the heterogeneity is low. The usefulness of the proposed methods is further illustrated with data from National Heart, Lung, and Blood Institute Exome Sequencing Project (NHLBI ESP). The relevant software is freely available.     

Optimum designs for next-generation sequencing to discover rare variants for common complex disease

Recent advances in next-generation sequencing technologies make it affordable to search for rare and functional variants for common complex diseases systematically. We investigated strategies for enriching rare variants in the samples selected for sequencing so as to optimize the power for their discovery. In particular, we investigated the roles of alternative sources of enrichment in families through computer simulations. We showed that linkage information, extreme phenotype, and nonrandom ascertainment, such as multiply affected families, constitute different sources for enriching rare and functional variants in a sequencing study design. Linkage is well known to have limited power for detecting small genetic effects, and hence not considered to be a powerful tool for discovering variants for common complex diseases. However, those families with some degree of family-specific linkage evidence provide an effective sampling strategy to sub-select the most linkage-informative families for sequencing. Compared with selecting subjects with extreme phenotypes, linkage evidence performs better with larger families, while extreme-phenotype method is more efficient with smaller families. Families with multiple affected siblings were found to provide the largest enrichment of rare variants. Finally, we showed that combined strategies, such as selecting linkage-informative families from multiply affected families, provide much higher enrichment of rare functional variants than either strategy alone.     

SimPEL: Simulation‐based power estimation for sequencing studies of low‐prevalence conditions

Power estimations are important for optimizing genotype‐phenotype association study designs. However, existing frameworks are designed for common disorders, and thus ill‐suited for the inherent challenges of studies for low‐prevalence conditions such as rare diseases and infrequent adverse drug reactions. These challenges include small sample sizes and the need to leverage genetic annotation resources in association analyses for the purpose of ranking potential causal genes. We present SimPEL, a simulation‐based program providing power estimations for the design of low‐prevalence condition studies. SimPEL integrates the usage of gene annotation resources for association analyses. Customizable parameters, including the penetrance of the putative causal allele and the employed pathogenic scoring system, allow SimPEL to realistically model a large range of study designs. To demonstrate the effects of various parameters on power, we estimated the power of several simulated designs using SimPEL and captured power trends in agreement with observations from current literature on low‐frequency condition studies. SimPEL, as a tool, provides researchers studying low‐frequency conditions with an intuitive and highly flexible avenue for statistical power estimation. The platform‐independent “batteries included” executable and default input files are available at https://github.com/precisionomics/SimPEL .     

Streamlined analysis of pooled genotype data in SNP-based association studies

Several groups have developed methods for estimating allele frequencies in DNA pools as a fast and cheap way for detecting allelic association between genetic markers and disease. To obtain accurate estimates of allele frequencies, a correction factor k for the degree to which measurement of allele-specific products is biased is generally applied. Factor k is usually obtained as the ratio of the two allele-specific signals in samples from heterozygous individuals, a step that can significantly impair throughput and increase cost. We have systematically investigated the properties of k through the use of empirical and simulated data. We show that for the dye terminator primer extension genotyping method we have applied, the correction factor k is substantially influenced by the dye terminators incorporated, but also by the terminal 3' base of the extension primer. We also show that the variation in k is large enough to result in unacceptable error rates if association studies are conducted without regard to k. We show that the impact of ignoring k can be neutralized by applying a correction factor k(max) that can be easily derived, but this at the potential cost of an increase in type I error. Finally, based upon observed distributions for k we derive a method allowing the estimation of the probability pooled data reflects significant differences in the allele frequencies between the subjects comprising the pools. By controlling the error rates in the absence of knowledge of the appropriate SNP-specific correction factors, each approach enhances the performance of DNA pooling, while considerably streamlining the method by reducing time and cost.     

A comparison study of multivariate fixed models and Gene Association with Multiple Traits (GAMuT) for next‐generation sequencing

In this paper, extensive simulations are performed to compare two statistical methods to analyze multiple correlated quantitative phenotypes: (1) approximate F‐distributed tests of multivariate functional linear models (MFLM) and additive models of multivariate analysis of variance (MANOVA), and (2) Gene Association with Multiple Traits (GAMuT) for association testing of high‐dimensional genotype data. It is shown that approximate F‐distributed tests of MFLM and MANOVA have higher power and are more appropriate for major gene association analysis (i.e., scenarios in which some genetic variants have relatively large effects on the phenotypes); GAMuT has higher power and is more appropriate for analyzing polygenic effects (i.e., effects from a large number of genetic variants each of which contributes a small amount to the phenotypes). MFLM and MANOVA are very flexible and can be used to perform association analysis for (i) rare variants, (ii) common variants, and (iii) a combination of rare and common variants. Although GAMuT was designed to analyze rare variants, it can be applied to analyze a combination of rare and common variants and it performs well when (1) the number of genetic variants is large and (2) each variant contributes a small amount to the phenotypes (i.e., polygenes). MFLM and MANOVA are fixed effect models that perform well for major gene association analysis. GAMuT can be viewed as an extension of sequence kernel association tests (SKAT). Both GAMuT and SKAT are more appropriate for analyzing polygenic effects and they perform well not only in the rare variant case, but also in the case of a combination of rare and common variants. Data analyses of European cohorts and the Trinity Students Study are presented to compare the performance of the two methods.