Rare‐variant association tests in longitudinal studies,with an application to the Multi‐Ethnic Study of Atherosclerosis (MESA)

Over the past few years, an increasing number of studies have identified rare variants that contribute to trait heritability. Due to the extreme rarity of some individual variants, gene‐based association tests have been proposed to aggregate the genetic variants within a gene, pathway, or specific genomic region as opposed to a one‐at‐a‐time single variant analysis. In addition, in longitudinal studies, statistical power to detect disease susceptibility rare variants can be improved through jointly testing repeatedly measured outcomes, which better describes the temporal development of the trait of interest. However, usual sandwich/model‐based inference for sequencing studies with longitudinal outcomes and rare variants can produce deflated/inflated type I error rate without further corrections. In this paper, we develop a group of tests for rare‐variant association based on outcomes with repeated measures. We propose new perturbation methods such that the type I error rate of the new tests is not only robust to misspecification of within‐subject correlation, but also significantly improved for variants with extreme rarity in a study with small or moderate sample size. Through extensive simulation studies, we illustrate that substantially higher power can be achieved by utilizing longitudinal outcomes and our proposed finite sample adjustment. We illustrate our methods using data from the Multi‐Ethnic Study of Atherosclerosis for exploring association of repeated measures of blood pressure with rare and common variants based on exome sequencing data on 6,361 individuals.     

Detection of Mendelian Consistent Genotyping Errors in Pedigrees

Detection of genotyping errors is a necessary step to minimize false results in genetic analysis. This is especially important when the rate of genotyping errors is high, as has been reported for high‐throughput sequence data. To detect genotyping errors in pedigrees, Mendelian inconsistent (MI) error checks exist, as do multi‐point methods that flag Mendelian consistent (MC) errors for sparse multi‐allelic markers. However, few methods exist for detecting MC genotyping errors, particularly for dense variants on large pedigrees. Here, we introduce an efficient method to detect MC errors even for very dense variants (e.g., SNPs and sequencing data) on pedigrees that may be large. Our method first samples inheritance vectors (IVs) using a moderately sparse but informative set of markers using a Markov chain Monte Carlo‐based sampler. Using sampled IVs, we considered two test statistics to detect MC genotyping errors: the percentage of IVs inconsistent with observed genotypes (A1) or the posterior probability of error configurations (A2). Using simulations, we show that this method, even with the simpler A1 statistic, is effective for detecting MC genotyping errors in dense variants, with sensitivity almost as high as the theoretical best sensitivity possible. We also evaluate the effectiveness of this method as a function of parameters, when including the observed pattern for genotype, density of framework markers, error rate, allele frequencies, and number of sampled inheritance vectors. Our approach provides a line of defense against false findings based on the use of dense variants in pedigrees.     

Hierarchical Bayesian Model for Rare Variant Association Analysis Integrating Genotype Uncertainty in Human Sequence Data

Next‐generation sequencing (NGS) has led to the study of rare genetic variants, which possibly explain the missing heritability for complex diseases. Most existing methods for rare variant (RV) association detection do not account for the common presence of sequencing errors in NGS data. The errors can largely affect the power and perturb the accuracy of association tests due to rare observations of minor alleles. We developed a hierarchical Bayesian approach to estimate the association between RVs and complex diseases. Our integrated framework combines the misclassification probability with shrinkage‐based Bayesian variable selection. It allows for flexibility in handling neutral and protective RVs with measurement error, and is robust enough for detecting causal RVs with a wide spectrum of minor allele frequency (MAF). Imputation uncertainty and MAF are incorporated into the integrated framework to achieve the optimal statistical power. We demonstrate that sequencing error does significantly affect the findings, and our proposed model can take advantage of it to improve statistical power in both simulated and real data. We further show that our model outperforms existing methods, such as sequence kernel association test (SKAT). Finally, we illustrate the behavior of the proposed method using a Finnish low‐density lipoprotein cholesterol study, and show that it identifies an RV known as FH North Karelia in LDLR gene with three carriers in 1,155 individuals, which is missed by both SKAT and Granvil.     

Detecting association of rare and common variants based on cross‐validation prediction error

Despite the extensive discovery of disease‐associated common variants, much of the genetic contribution to complex traits remains unexplained. Rare variants may explain additional disease risk or trait variability. Although sequencing technology provides a supreme opportunity to investigate the roles of rare variants in complex diseases, detection of these variants in sequencing‐based association studies presents substantial challenges. In this article, we propose novel statistical tests to test the association between rare and common variants in a genomic region and a complex trait of interest based on cross‐validation prediction error (PE). We first propose a PE method based on Ridge regression. Based on PE, we also propose another two tests PE‐WS and PE‐TOW by testing a weighted combination of variants with two different weighting schemes. PE‐WS is the PE version of the test based on the weighted sum statistic (WS) and PE‐TOW is the PE version of the test based on the optimally weighted combination of variants (TOW). Using extensive simulation studies, we are able to show that (1) PE‐TOW and PE‐WS are consistently more powerful than TOW and WS, respectively, and (2) PE is the most powerful test when causal variants contain both common and rare variants.     

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.     

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 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.     

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.     

Functional Linear Models for Association Analysis of Quantitative Traits

Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F‐distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT‐O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT‐O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study.     

Leveraging population information in family‐based rare variant association analyses of quantitative traits

Confounding due to population substructure is always a concern in genetic association studies. Although methods have been proposed to adjust for population stratification in the context of common variation, it is unclear how well these approaches will work when interrogating rare variation. Family‐based association tests can be constructed that are robust to population stratification. For example, when considering a quantitative trait, a linear model can be used that decomposes genetic effects into between‐ and within‐family components and a test of the within‐family component is robust to population stratification. However, this within‐family test ignores between‐family information potentially leading to a loss of power. Here, we propose a family‐based two‐stage rare‐variant test for quantitative traits. We first construct a weight for each variant within a gene, or other genetic unit, based on score tests of between‐family effect parameters. These weights are then used to combine variants using score tests of within‐family effect parameters. Because the between‐family and within‐family tests are orthogonal under the null hypothesis, this two‐stage approach can increase power while still maintaining validity. Using simulation, we show that this two‐stage test can significantly improve power while correctly maintaining type I error. We further show that the two‐stage approach maintains the robustness to population stratification of the within‐family test and we illustrate this using simulations reflecting samples composed of continental and closely related subpopulations.     

SBERIA: Set‐Based Gene‐Environment Interaction Test for Rare and Common Variants in Complex Diseases

Identification of gene‐environment interaction (G × E) is important in understanding the etiology of complex diseases. However, partially due to the lack of power, there have been very few replicated G × E findings compared to the success in marginal association studies. The existing G × E testing methods mainly focus on improving the power for individual markers. In this paper, we took a different strategy and proposed a set‐based gene‐environment interaction test (SBERIA), which can improve the power by reducing the multiple testing burdens and aggregating signals within a set. The major challenge of the signal aggregation within a set is how to tell signals from noise and how to determine the direction of the signals. SBERIA takes advantage of the established correlation screening for G × E to guide the aggregation of genotypes within a marker set. The correlation screening has been shown to be an efficient way of selecting potential G × E candidate SNPs in case‐control studies for complex diseases. Importantly, the correlation screening in case‐control combined samples is independent of the interaction test. With this desirable feature, SBERIA maintains the correct type I error level and can be easily implemented in a regular logistic regression setting. We showed that SBERIA had higher power than benchmark methods in various simulation scenarios, both for common and rare variants. We also applied SBERIA to real genome‐wide association studies (GWAS) data of 10,729 colorectal cancer cases and 13,328 controls and found evidence of interaction between the set of known colorectal cancer susceptibility loci and smoking.     

Rare variants, common markers: synthetic association and beyond

The phenomenon of synthetic association raises the possibility that common variant genetic markers may be coupled with functional rare variants sufficiently often to allow the rare variants to be tagged by the common ones. Using human exome sequence data from the 1000 Genomes Project, two investigative teams in Group 12 of Genetic Analysis Workshop 17 found that stochastic coupling between rare and common variants does occur, although perhaps not sufficiently often that we can expect common variant signals to reflect synthetic association; other teams considered methods for detecting association using both rare and common variants. Common themes were that synthetic association is more apparent in population strata (ancestral or familial) and that careful selection of the unit of analysis (gene, gene network, or other genomic subset) is likely to be crucial to the discovery of rare variants that contribute to risk of disease.     

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.     

A Novel Statistic for Global Association Testing Based on Penalized Regression

Natural genetic structures like genes may contain multiple variants that work as a group to determine a biologic outcome. The effect of rare variants, mutations occurring in less than 5% of samples, is hypothesized to be explained best as groups collectively associated with a biologic function. Therefore, it is important to develop powerful association tests to identify a true association between an outcome of interest and a group of variants, in particular a group with many rare variants. In this article we first delineate a novel penalized regression‐based global test for the association between sets of variants and a disease phenotype. Next, we use Genetic Analysis Workshop 18 (GAW18) data to assess the power of the new global association test to capture a relationship between an aggregated group of variants and a simulated hypertension status. Rare variant only, common variant only, and combined variant groups are studied. The power values are compared to those obtained from eight well‐regarded global tests (Score, Sum, SSU, SSUw, UminP, aSPU, aSPUw, and sequence kernel association test (SKAT)) that do not use penalized regression and a set of tests using either the SSU or score statistics and least absolute shrinkage and selection operator penalty (LASSO) logistic regression. Association testing of rare variants with our method was the top performer when there was low linkage disequilibrium (LD) between and within causal variants. This was similarly true when simultaneously testing rare and common variants in low LD scenarios. Finally, our method was able to provide meaningful variant‐specific association information.     

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.     

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.     

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.     

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/ ).     

Haplotype sharing transmission/disequilibrium tests that allow for genotyping errors

The present study introduces new Haplotype Sharing Transmission/Disequilibrium Tests (HS-TDTs) that allow for random genotyping errors. We evaluate the type I error rate and power of the new proposed tests under a variety of scenarios and perform a power comparison among the proposed tests, the HS-TDT and the single-marker TDT. The results indicate that the HS-TDT shows a significant increase in type I error when applied to data in which either Mendelian inconsistent trios are removed or Mendelian inconsistent markers are treated as missing genotypes, and the magnitude of the type I error increases both with an increase in sample size and with an increase in genotyping error rate. The results also show that a simple strategy, that is, merging each rare haplotype to a most similar common haplotype, can control the type I error inflation for a wide range of genotyping error rates, and after merging rare haplotypes, the power of the test is very similar to that without merging the rare haplotypes. Therefore, we conclude that a simple strategy may make the HS-TDT robust to genotyping errors. Our simulation results also show that this strategy may also be applicable to other haplotype-based TDTs.     

Is It Rare or Common?

Many genome‐wide association studies (GWAS) have signals with unknown etiology. This paper addresses the question—is such an association signal caused by rare or common variants that lead to increased disease risk? For a genomic region implicated by a GWAS, we use single nucleotide polymorphism (SNP) data in a case‐control setting to predict how many common or rare variants there are, using a Bayesian analysis. Our objective is to compute posterior probabilities for configurations of rare and/or common variants. We use an extension of coalescent trees—the ancestral recombination graphs—to model the genealogical history of the samples based on marker data. As we expect SNPs to be in linkage disequilibrium with common disease variants, we can expect the trees to reflect the type of variants. To demonstrate the application, we apply our method to candidate gene sequencing data from a German case‐control study on nonsyndromic cleft lip with or without cleft palate. Genet. Epidemiol. 36:419‐429, 2012. © 2012 Wiley Periodicals, Inc.