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.     

A Powerful Approach to Test an Optimally Weighted Combination of Rare Variants in Admixed Populations

Population stratification has long been recognized as an issue in genetic association studies because unrecognized population stratification can lead to both false‐positive and false‐negative findings and can obscure true association signals if not appropriately corrected. This issue can be even worse in rare variant association analyses because rare variants often demonstrate stronger and potentially different patterns of stratification than common variants. To correct for population stratification in genetic association studies, we proposed a novel method to Test the effect of an Optimally Weighted combination of variants in Admixed populations (TOWA) in which the analytically derived optimal weights can be calculated from existing phenotype and genotype data. TOWA up weights rare variants and those variants that have strong associations with the phenotype. Additionally, it can adjust for the direction of the association, and allows for local ancestry difference among study subjects. Extensive simulations show that the type I error rate of TOWA is under control in the presence of population stratification and it is more powerful than existing methods. We have also applied TOWA to a real sequencing data. Our simulation studies as well as real data analysis results indicate that TOWA is a useful tool for rare variant association analyses in admixed populations.     

Genotype‐based matching to correct for population stratification in large‐scale case‐control genetic association studies

Genome‐wide association studies are helping to dissect the etiology of complex diseases. Although case‐control association tests are generally more powerful than family‐based association tests, population stratification can lead to spurious disease‐marker association or mask a true association. Several methods have been proposed to match cases and controls prior to genotyping, using family information or epidemiological data, or using genotype data for a modest number of genetic markers. Here, we describe a genetic similarity score matching (GSM) method for efficient matched analysis of cases and controls in a genome‐wide or large‐scale candidate gene association study. GSM comprises three steps: (1) calculating similarity scores for pairs of individuals using the genotype data; (2) matching sets of cases and controls based on the similarity scores so that matched cases and controls have similar genetic background; and (3) using conditional logistic regression to perform association tests. Through computer simulation we show that GSM correctly controls false‐positive rates and improves power to detect true disease predisposing variants. We compare GSM to genomic control using computer simulations, and find improved power using GSM. We suggest that initial matching of cases and controls prior to genotyping combined with careful re‐matching after genotyping is a method of choice for genome‐wide association studies. Genet. Epidemiol. 33:508–517, 2009. © 2009 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.     

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.     

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.     

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.     

Genome‐Wide Association Analysis of Imputed Rare Variants: Application to Seven Common Complex Diseases

Genome‐wide association studies have been successful in identifying loci contributing effects to a range of complex human traits. The majority of reproducible associations within these loci are with common variants, each of modest effect, which together explain only a small proportion of heritability. It has been suggested that much of the unexplained genetic component of complex traits can thus be attributed to rare variation. However, genome‐wide association study genotyping chips have been designed primarily to capture common variation, and thus are underpowered to detect the effects of rare variants. Nevertheless, we demonstrate here, by simulation, that imputation from an existing scaffold of genome‐wide genotype data up to high‐density reference panels has the potential to identify rare variant associations with complex traits, without the need for costly re‐sequencing experiments. By application of this approach to genome‐wide association studies of seven common complex diseases, imputed up to publicly available reference panels, we identify genome‐wide significant evidence of rare variant association in PRDM10 with coronary artery disease and multiple genes in the major histocompatibility complex (MHC) with type 1 diabetes. The results of our analyses highlight that genome‐wide association studies have the potential to offer an exciting opportunity for gene discovery through association with rare variants, conceivably leading to substantial advancements in our understanding of the genetic architecture underlying complex human traits.     

A Fast and Noise‐Resilient Approach to Detect Rare‐Variant Associations With Deep Sequencing Data for Complex Disorders

Next generation sequencing technology has enabled the paradigm shift in genetic association studies from the common disease/common variant to common disease/rare‐variant hypothesis. Analyzing individual rare variants is known to be underpowered; therefore association methods have been developed that aggregate variants across a genetic region, which for exome sequencing is usually a gene. The foreseeable widespread use of whole genome sequencing poses new challenges in statistical analysis. It calls for new rare‐variant association methods that are statistically powerful, robust against high levels of noise due to inclusion of noncausal variants, and yet computationally efficient. We propose a simple and powerful statistic that combines the disease‐associated P‐values of individual variants using a weight that is the inverse of the expected standard deviation of the allele frequencies under the null. This approach, dubbed as Sigma‐P method, is extremely robust to the inclusion of a high proportion of noncausal variants and is also powerful when both detrimental and protective variants are present within a genetic region. The performance of the Sigma‐P method was tested using simulated data based on realistic population demographic and disease models and its power was compared to several previously published methods. The results demonstrate that this method generally outperforms other rare‐variant association methods over a wide range of models. Additionally, sequence data on the ANGPTL family of genes from the Dallas Heart Study were tested for associations with nine metabolic traits and both known and novel putative associations were uncovered using the Sigma‐P method.     

Robust Rare Variant Association Testing for Quantitative Traits in Samples With Related Individuals

The recent development of high‐throughput sequencing technologies calls for powerful statistical tests to detect rare genetic variants associated with complex human traits. Sampling related individuals in sequencing studies offers advantages over sampling unrelated individuals only, including improved protection against sequencing error, the ability to use imputation to make more efficient use of sequence data, and the possibility of power boost due to more observed copies of extremely rare alleles among relatives. With related individuals, familial correlation needs to be accounted for to ensure correct control over type I error and to improve power. Recognizing the limitations of existing rare‐variant association tests for family data, we propose MONSTER (Minimum P‐value Optimized Nuisance parameter Score Test Extended to Relatives), a robust rare‐variant association test, which generalizes the SKAT‐O method for independent samples. MONSTER uses a mixed effects model that accounts for covariates and additive polygenic effects. To obtain a powerful test, MONSTER adaptively adjusts to the unknown configuration of effects of rare‐variant sites. MONSTER also offers an analytical way of assessing P‐values, which is desirable because permutation is not straightforward to conduct in related samples. In simulation studies, we demonstrate that MONSTER effectively accounts for family structure, is computationally efficient and compares very favorably, in terms of power, to previously proposed tests that allow related individuals. We apply MONSTER to an analysis of high‐density lipoprotein cholesterol in the Framingham Heart Study, where we are able to replicate association with three genes.     

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.     

Evaluating the Calibration and Power of Three Gene‐Based Association Tests of Rare Variants for the X Chromosome

Although genome‐wide association studies (GWAS) have identified thousands of trait‐associated genetic variants, there are relatively few findings on the X chromosome. For analysis of low‐frequency variants (minor allele frequency <5%), investigators can use region‐ or gene‐based tests where multiple variants are analyzed jointly to increase power. To date, there are no gene‐based tests designed for association testing of low‐frequency variants on the X chromosome. Here we propose three gene‐based tests for the X chromosome: burden, sequence kernel association test (SKAT), and optimal unified SKAT (SKAT‐O). Using simulated case‐control and quantitative trait (QT) data, we evaluate the calibration and power of these tests as a function of (1) male:female sample size ratio; and (2) coding of haploid male genotypes for variants under X‐inactivation. For case‐control studies, all three tests are reasonably well‐calibrated for all scenarios we evaluated. As expected, power for gene‐based tests depends on the underlying genetic architecture of the genomic region analyzed. Studies with more (haploid) males are generally less powerful due to decreased number of chromosomes. Power generally is slightly greater when the coding scheme for male genotypes matches the true underlying model, but the power loss for misspecifying the (generally unknown) model is small. For QT studies, type I error and power results largely mirror those for binary traits. We demonstrate the use of these three gene‐based tests for X‐chromosome association analysis in simulated data and sequencing data from the Genetics of Type 2 Diabetes (GoT2D) study.     

An efficient study design to test parent‐of‐origin effects in family trios

Increasing evidence has shown that genes may cause prenatal, neonatal, and pediatric diseases depending on their parental origins. Statistical models that incorporate parent‐of‐origin effects (POEs) can improve the power of detecting disease‐associated genes and help explain the missing heritability of diseases. In many studies, children have been sequenced for genome‐wide association testing. But it may become unaffordable to sequence their parents and evaluate POEs. Motivated by the reality, we proposed a budget‐friendly study design of sequencing children and only genotyping their parents through single nucleotide polymorphism array. We developed a powerful likelihood‐based method, which takes into account both sequence reads and linkage disequilibrium to infer the parental origins of children's alleles and estimate their POEs on the outcome. We evaluated the performance of our proposed method and compared it with an existing method using only genotypes, through extensive simulations. Our method showed higher power than the genotype‐based method. When either the mean read depth or the pair‐end length was reasonably large, our method achieved ideal power. When single parents’ genotypes were unavailable or parental genotypes at the testing locus were not typed, both methods lost power compared with when complete data were available; but the power loss from our method was smaller than the genotype‐based method. We also extended our method to accommodate mixed genotype, low‐, and high‐coverage sequence data from children and their parents. At presence of sequence errors, low‐coverage parental sequence data may lead to lower power than parental genotype data.     

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.     

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.     

A Comparison Study of Fixed and Mixed Effect Models for Gene Level Association Studies of Complex Traits

In association studies of complex traits, fixed‐effect regression models are usually used to test for association between traits and major gene loci. In recent years, variance‐component tests based on mixed models were developed for region‐based genetic variant association tests. In the mixed models, the association is tested by a null hypothesis of zero variance via a sequence kernel association test (SKAT), its optimal unified test (SKAT‐O), and a combined sum test of rare and common variant effect (SKAT‐C). Although there are some comparison studies to evaluate the performance of mixed and fixed models, there is no systematic analysis to determine when the mixed models perform better and when the fixed models perform better. Here we evaluated, based on extensive simulations, the performance of the fixed and mixed model statistics, using genetic variants located in 3, 6, 9, 12, and 15 kb simulated regions. We compared the performance of three models: (i) mixed models that lead to SKAT, SKAT‐O, and SKAT‐C, (ii) traditional fixed‐effect additive models, and (iii) fixed‐effect functional regression models. To evaluate the type I error rates of the tests of fixed models, we generated genotype data by two methods: (i) using all variants, (ii) using only rare variants. We found that the fixed‐effect tests accurately control or have low false positive rates. We performed simulation analyses to compare power for two scenarios: (i) all causal variants are rare, (ii) some causal variants are rare and some are common. Either one or both of the fixed‐effect models performed better than or similar to the mixed models except when (1) the region sizes are 12 and 15 kb and (2) effect sizes are small. Therefore, the assumption of mixed models could be satisfied and SKAT/SKAT‐O/SKAT‐C could perform better if the number of causal variants is large and each causal variant contributes a small amount to the traits (i.e., polygenes). In major gene association studies, we argue that the fixed‐effect models perform better or similarly to mixed models in most cases because some variants should affect the traits relatively large. In practice, it makes sense to perform analysis by both the fixed and mixed effect models and to make a comparison, and this can be readily done using our R codes and the SKAT packages.     

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

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

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.