Bayesian Latent Variable Collapsing Model for Detecting Rare Variant Interaction Effect in Twin Study

By analyzing more next‐generation sequencing data, researchers have affirmed that rare genetic variants are widespread among populations and likely play an important role in complex phenotypes. Recently, a handful of statistical models have been developed to analyze rare variant (RV) association in different study designs. However, due to the scarce occurrence of minor alleles in data, appropriate statistical methods for detecting RV interaction effects are still difficult to develop. We propose a hierarchical Bayesian latent variable collapsing method (BLVCM), which circumvents the obstacles by parameterizing the signals of RVs with latent variables in a Bayesian framework and is parameterized for twin data. The BLVCM can tackle nonassociated variants, allow both protective and deleterious effects, capture SNP‐SNP synergistic effect, provide estimates for the gene level and individual SNP contributions, and can be applied to both independent and various twin designs. We assessed the statistical properties of the BLVCM using simulated data, and found that it achieved better performance in terms of power for interaction effect detection compared to the Granvil and the SKAT. As proof of practical application, the BLVCM was then applied to a twin study analysis of more than 20,000 gene regions to identify significant RVs associated with low‐density lipoprotein cholesterol level. The results show that some of the findings are consistent with previous studies, and we identified some novel gene regions with significant SNP–SNP synergistic effects.     

Adjusted Sequence Kernel Association Test for Rare Variants Controlling for Cryptic and Family Relatedness

Recent progress in sequencing technologies makes it possible to identify rare and unique variants that may be associated with complex traits. However, the results of such efforts depend crucially on the use of efficient statistical methods and study designs. Although family‐based designs might enrich a data set for familial rare disease variants, most existing rare variant association approaches assume independence of all individuals. We introduce here a framework for association testing of rare variants in family‐based designs. This framework is an adaptation of the sequence kernel association test (SKAT) which allows us to control for family structure. Our adjusted SKAT (ASKAT) combines the SKAT approach and the factored spectrally transformed linear mixed models (FaST‐LMMs) algorithm to capture family effects based on a LMM incorporating the realized proportion of the genome that is identical by descent between pairs of individuals, and using restricted maximum likelihood methods for estimation. In simulation studies, we evaluated type I error and power of this proposed method and we showed that regardless of the level of the trait heritability, our approach has good control of type I error and good power. Since our approach uses FaST‐LMM to calculate variance components for the proposed mixed model, ASKAT is reasonably fast and can analyze hundreds of thousands of markers. Data from the UK twins consortium are presented to illustrate the ASKAT methodology.     

Post hoc Analysis for Detecting Individual Rare Variant Risk Associations Using Probit Regression Bayesian Variable Selection Methods in Case‐Control Sequencing Studies

Rare variants (RVs) have been shown to be significant contributors to complex disease risk. By definition, these variants have very low minor allele frequencies and traditional single‐marker methods for statistical analysis are underpowered for typical sequencing study sample sizes. Multimarker burden‐type approaches attempt to identify aggregation of RVs across case‐control status by analyzing relatively small partitions of the genome, such as genes. However, it is generally the case that the aggregative measure would be a mixture of causal and neutral variants, and these omnibus tests do not directly provide any indication of which RVs may be driving a given association. Recently, Bayesian variable selection approaches have been proposed to identify RV associations from a large set of RVs under consideration. Although these approaches have been shown to be powerful at detecting associations at the RV level, there are often computational limitations on the total quantity of RVs under consideration and compromises are necessary for large‐scale application. Here, we propose a computationally efficient alternative formulation of this method using a probit regression approach specifically capable of simultaneously analyzing hundreds to thousands of RVs. We evaluate our approach to detect causal variation on simulated data and examine sensitivity and specificity in instances of high RV dimensionality as well as apply it to pathway‐level RV analysis results from a prostate cancer (PC) risk case‐control sequencing study. Finally, we discuss potential extensions and future directions of this work.     

Adjustment for Population Stratification via Principal Components in Association Analysis of Rare Variants

For unrelated samples, principal component (PC) analysis has been established as a simple and effective approach to adjusting for population stratification in association analysis of common variants (CVs, with minor allele frequencies MAF > 5%). However, it is less clear how it would perform in analysis of low‐frequency variants (LFVs, MAF between 1% and 5%), or of rare variants (RVs, MAF < 5%). Furthermore, with next‐generation sequencing data, it is unknown whether PCs should be constructed based on CVs, LFVs, or RVs. In this study, we used the 1000 Genomes Project sequence data to explore the construction of PCs and their use in association analysis of LFVs or RVs for unrelated samples. It is shown that a few top PCs based on either CVs or LFVs could separate two continental groups, European and African samples, but those based on only RVs performed less well. When applied to several association tests in simulated data with population stratification, using PCs based on either CVs or LFVs was effective in controlling Type I error rates, while nonadjustment led to inflated Type I error rates. Perhaps the most interesting observation is that, although the PCs based on LFVs could better separate the two continental groups than those based on CVs, the use of the former could lead to overadjustment in the sense of substantial power loss in the absence of population stratification; in contrast, we did not see any problem with the use of the PCs based on CVs in all our examples.     

Comparison of statistical tests for disease association with rare variants

In anticipation of the availability of next‐generation sequencing data, there is increasing interest in investigating association between complex traits and rare variants (RVs). In contrast to association studies for common variants (CVs), due to the low frequencies of RVs, common wisdom suggests that existing statistical tests for CVs might not work, motivating the recent development of several new tests for analyzing RVs, most of which are based on the idea of pooling/collapsing RVs. However, there is a lack of evaluations of, and thus guidance on the use of, existing tests. Here we provide a comprehensive comparison of various statistical tests using simulated data. We consider both independent and correlated rare mutations, and representative tests for both CVs and RVs. As expected, if there are no or few non‐causal (i.e. neutral or non‐associated) RVs in a locus of interest while the effects of causal RVs on the trait are all (or mostly) in the same direction (i.e. either protective or deleterious, but not both), then the simple pooled association tests (without selecting RVs and their association directions) and a new test called kernel‐based adaptive clustering (KBAC) perform similarly and are most powerful; KBAC is more robust than simple pooled association tests in the presence of non‐causal RVs; however, as the number of non‐causal CVs increases and/or in the presence of opposite association directions, the winners are two methods originally proposed for CVs and a new test called C‐alpha test proposed for RVs, each of which can be regarded as testing on a variance component in a random‐effects model. Interestingly, several methods based on sequential model selection (i.e. selecting causal RVs and their association directions), including two new methods proposed here, perform robustly and often have statistical power between those of the above two classes. Genet. Epidemiol. 2011. © 2011 Wiley Periodicals, Inc. 35:606‐619, 2011     

Sequence Kernel Association Test for Quantitative Traits in Family Samples

A large number of rare genetic variants have been discovered with the development in sequencing technology and the lowering of sequencing costs. Rare variant analysis may help identify novel genes associated with diseases and quantitative traits, adding to our knowledge of explaining heritability of these phenotypes. Many statistical methods for rare variant analysis have been developed in recent years, but some of them require the strong assumption that all rare variants in the analysis share the same direction of effect, and others requiring permutation to calculate the P‐values are computer intensive. Among these methods, the sequence kernel association test (SKAT) is a powerful method under many different scenarios. It does not require any assumption on the directionality of effects, and statistical significance is computed analytically. In this paper, we extend SKAT to be applicable to family data. The family‐based SKAT (famSKAT) has a different test statistic and null distribution compared to SKAT, but is equivalent to SKAT when there is no familial correlation. Our simulation studies show that SKAT has inflated type I error if familial correlation is inappropriately ignored, but has appropriate type I error if applied to a single individual per family to obtain an unrelated subset. In contrast, famSKAT has the correct type I error when analyzing correlated observations, and it has higher power than competing methods in many different scenarios. We illustrate our approach to analyze the association of rare genetic variants using glycemic traits from the Framingham Heart Study.     

Generalized Functional Linear Models for Gene‐Based Case‐Control Association Studies

By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT‐O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT‐O. In practice, it is not known whether rare variants or common variants in a gene region are disease related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT‐O on real neural tube defects and Hirschsprung's disease datasets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT‐O in the real data analysis. Our methods can be used in either gene‐disease genome‐wide/exome‐wide association studies or candidate gene analyses.     

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.     

Adaptive tests for association analysis of rare variants

In anticipation of the availability of next-generation sequencing data, there has been increasing interest in association analysis of rare variants (RVs). Owing to the extremely low frequency of a RV, single variant-based analysis and many existing tests developed for common variants may not be suitable. Hence, it is of interest to develop powerful statistical tests to assess association between complex traits and RVs with sequence data. Recently, a pooled association test based on variable thresholds (VT) was proposed and shown to be more powerful than some existing tests (Price et al. [2010] Am J Hum Genet 86:832-838). In this study, we generalize the VT test of Price et al. in several aspects. We propose a general class of adaptive tests that covers the VT test of Price et al. as a special case. In particular, we show that some of our proposed adaptive tests may substantially improve the power over the pooled association tests, including the VT test of Price et al., especially so in the presence of many neutral RVs and/or of causal RVs with opposite association directions, in which cases most of the existing pooled association tests suffer from significant loss of power. Our proposed tests are also general and flexible with the ability to incorporate weights on RVs and to adjust for covariates.     

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.     

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.     

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.     

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.     

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.     

Impact of genotyping errors on statistical power of association tests in genomic analyses: A case study

A key step in genomic studies is to assess high throughput measurements across millions of markers for each participant's DNA, either using microarrays or sequencing techniques. Accurate genotype calling is essential for downstream statistical analysis of genotype‐phenotype associations, and next generation sequencing (NGS) has recently become a more common approach in genomic studies. How the accuracy of variant calling in NGS‐based studies affects downstream association analysis has not, however, been studied using empirical data in which both microarrays and NGS were available. In this article, we investigate the impact of variant calling errors on the statistical power to identify associations between single nucleotides and disease, and on associations between multiple rare variants and disease. Both differential and nondifferential genotyping errors are considered. Our results show that the power of burden tests for rare variants is strongly influenced by the specificity in variant calling, but is rather robust with regard to sensitivity. By using the variant calling accuracies estimated from a substudy of a Cooperative Studies Program project conducted by the Department of Veterans Affairs, we show that the power of association tests is mostly retained with commonly adopted variant calling pipelines. An R package, GWAS.PC, is provided to accommodate power analysis that takes account of genotyping errors ( http://zhaocenter.org/software/ ).     

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.     

Haplotype Kernel Association Test as a Powerful Method to Identify Chromosomal Regions Harboring Uncommon Causal Variants

For most complex diseases, the fraction of heritability that can be explained by the variants discovered from genome‐wide association studies is minor. Although the so‐called “rare variants” (minor allele frequency [MAF] < 1%) have attracted increasing attention, they are unlikely to account for much of the “missing heritability” because very few people may carry these rare variants. The genetic variants that are likely to fill in the “missing heritability” include uncommon causal variants (MAF < 5%), which are generally untyped in association studies using tagging single‐nucleotide polymorphisms (SNPs) or commercial SNP arrays. Developing powerful statistical methods can help to identify chromosomal regions harboring uncommon causal variants, while bypassing the genome‐wide or exome‐wide next‐generation sequencing. In this work, we propose a haplotype kernel association test (HKAT) that is equivalent to testing the variance component of random effects for distinct haplotypes. With an appropriate weighting scheme given to haplotypes, we can further enhance the ability of HKAT to detect uncommon causal variants. With scenarios simulated according to the population genetics theory, HKAT is shown to be a powerful method for detecting chromosomal regions harboring uncommon causal variants.     

Rare variants association testing for a binary outcome when pooling individual level data from heterogeneous studies

Whole genome sequencing (WGS) and whole exome sequencing studies are used to test the association of rare genetic variants with health traits. Many existing WGS efforts now aggregate data from heterogeneous groups, for example, combining sets of individuals of European and African ancestries. We here investigate the statistical implications on rare variant association testing with a binary trait when combining together heterogeneous studies, defined as studies with potentially different disease proportion and different frequency of variant carriers. We study and compare in simulations the Type 1 error control and power of the naïve score test, the saddlepoint approximation to the score test, and the BinomiRare test in a range of settings, focusing on low numbers of variant carriers. We show that Type 1 error control and power patterns depend on both the number of carriers of the rare allele and on disease prevalence in each of the studies. We develop recommendations for association analysis of rare genetic variants. (1) The Score test is preferred when the case proportion in the sample is 50%. (2) Do not down‐sample controls to balance case–control ratio, because it reduces power. Rather, use a test that controls the Type 1 error. (3) Conduct stratified analysis in parallel with combined analysis. Aggregated testing may have lower power when the variant effect size differs between strata.     

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.     

Sequence Kernel Association Test for Survival Traits

Rare variant tests have been of great interest in testing genetic associations with diseases and disease‐related quantitative traits in recent years. Among these tests, the sequence kernel association test (SKAT) is an omnibus test for effects of rare genetic variants, in a linear or logistic regression framework. It is often described as a variance component test treating the genotypic effects as random. When the linear kernel is used, its test statistic can be expressed as a weighted sum of single‐marker score test statistics. In this paper, we extend the test to survival phenotypes in a Cox regression framework. Because of the anticonservative small‐sample performance of the score test in a Cox model, we substitute signed square‐root likelihood ratio statistics for the score statistics, and confirm that the small‐sample control of type I error is greatly improved. This test can also be applied in meta‐analysis. We show in our simulation studies that this test has superior statistical power except in a few specific scenarios, as compared to burden tests in a Cox model. We also present results in an application to time‐to‐obesity using genotypes from Framingham Heart Study SNP Health Association Resource.