Progress in methods for rare variant association

Empirical studies and evolutionary theory support a role for rare variants in the etiology of complex traits. Given this motivation and increasing affordability of whole-exome and whole-genome sequencing, methods for rare variant association have been an active area of research for the past decade. Here, we provide a survey of the current literature and developments from the Genetics Analysis Workshop 19 (GAW19) Collapsing Rare Variants working group. In particular, we present the generalized linear regression framework and associated score statistic for the 2 major types of methods: burden and variance components methods. We further show that by simply modifying weights within these frameworks we arrive at many of the popular existing methods, for example, the cohort allelic sums test and sequence kernel association test. Meta-analysis techniques are also described. Next, we describe the 6 contributions from the GAW19 Collapsing Rare Variants working group. These included development of new methods, such as a retrospective likelihood for family data, a method using genomic structure to compare cases and controls, a haplotype-based meta-analysis, and a permutation-based method for combining different statistical tests. In addition, one contribution compared a mega-analysis of family-based and population-based data to meta-analysis. Finally, the power of existing family-based methods for binary traits was compared. We conclude with suggestions for open research questions.     

Optimal tests for rare variant effects in sequencing association studies

With development of massively parallel sequencing technologies, there is a substantial need for developing powerful rare variant association tests. Common approaches include burden and non-burden tests. Burden tests assume all rare variants in the target region have effects on the phenotype in the same direction and of similar magnitude. The recently proposed sequence kernel association test (SKAT) (Wu, M. C., and others, 2011. Rare-variant association testing for sequencing data with the SKAT. The American Journal of Human Genetics 89, 82-93], an extension of the C-alpha test (Neale, B. M., and others, 2011. Testing for an unusual distribution of rare variants. PLoS Genetics 7, 161-165], provides a robust test that is particularly powerful in the presence of protective and deleterious variants and null variants, but is less powerful than burden tests when a large number of variants in a region are causal and in the same direction. As the underlying biological mechanisms are unknown in practice and vary from one gene to another across the genome, it is of substantial practical interest to develop a test that is optimal for both scenarios. In this paper, we propose a class of tests that include burden tests and SKAT as special cases, and derive an optimal test within this class that maximizes power. We show that this optimal test outperforms burden tests and SKAT in a wide range of scenarios. The results are illustrated using simulation studies and triglyceride data from the Dallas Heart Study. In addition, we have derived sample size/power calculation formula for SKAT with a new family of kernels to facilitate designing new sequence association studies.     

Adaptive ridge regression for rare variant detection

It is widely believed that both common and rare variants contribute to the risks of common diseases or complex traits and the cumulative effects of multiple rare variants can explain a significant proportion of trait variances. Advances in high-throughput DNA sequencing technologies allow us to genotype rare causal variants and investigate the effects of such rare variants on complex traits. We developed an adaptive ridge regression method to analyze the collective effects of multiple variants in the same gene or the same functional unit. Our model focuses on continuous trait and incorporates covariate factors to remove potential confounding effects. The proposed method estimates and tests multiple rare variants collectively but does not depend on the assumption of same direction of each rare variant effect. Compared with the Bayesian hierarchical generalized linear model approach, the state-of-the-art method of rare variant detection, the proposed new method is easy to implement, yet it has higher statistical power. Application of the new method is demonstrated using the well-known data from the Dallas Heart Study.     

The empirical power of rare variant association methods: results from sanger sequencing in 1,998 individuals

The role of rare genetic variation in the etiology of complex disease remains unclear. However, the development of next-generation sequencing technologies offers the experimental opportunity to address this question. Several novel statistical methodologies have been recently proposed to assess the contribution of rare variation to complex disease etiology. Nevertheless, no empirical estimates comparing their relative power are available. We therefore assessed the parameters that influence their statistical power in 1,998 individuals Sanger-sequenced at seven genes by modeling different distributions of effect, proportions of causal variants, and direction of the associations (deleterious, protective, or both) in simulated continuous trait and case/control phenotypes. Our results demonstrate that the power of recently proposed statistical methods depend strongly on the underlying hypotheses concerning the relationship of phenotypes with each of these three factors. No method demonstrates consistently acceptable power despite this large sample size, and the performance of each method depends upon the underlying assumption of the relationship between rare variants and complex traits. Sensitivity analyses are therefore recommended to compare the stability of the results arising from different methods, and promising results should be replicated using the same method in an independent sample. These findings provide guidance in the analysis and interpretation of the role of rare base-pair variation in the etiology of complex traits and diseases.     

Replication strategies for rare variant complex trait association studies via next-generation sequencing

There is solid evidence that complex traits can be caused by rare variants. Next-generation sequencing technologies are powerful tools for mapping rare variants. Confirmation of significant findings in stage 1 through replication in an independent stage 2 sample is necessary for association studies. For gene-based mapping of rare variants, two replication strategies are possible: (1) variant-based replication, wherein only variants from nucleotide sites uncovered in stage 1 are genotyped and followed-up and (2) sequence-based replication, wherein the gene region is sequenced in the replication sample and both known and novel variants are tested. The efficiency of the two strategies is dependent on the proportions of causative variants discovered in stage 1 and sequencing/genotyping errors. With rigorous population genetic and phenotypic models, it is demonstrated that sequence-based replication is consistently more powerful. However, the power gain is small (1) for large-scale studies with thousands of individuals, because a large fraction of causative variant sites can be observed and (2) for small- to medium-scale studies with a few hundred samples, because a large proportion of the locus population attributable risk can be explained by the uncovered variants. Therefore, genotyping can be a temporal solution for replicating genetic studies if stage 1 and 2 samples are drawn from the same population. However, sequence-based replication is advantageous if the stage 1 sample is small or novel variants discovery is also of interest. It is shown that currently attainable levels of sequencing error only minimally affect the comparison, and the advantage of sequence-based replication remains.     

Reconsidering association testing methods using single-variant test statistics as alternatives to pooling tests for sequence data with rare variants

Association tests that pool minor alleles into a measure of burden at a locus have been proposed for case-control studies using sequence data containing rare variants. However, such pooling tests are not robust to the inclusion of neutral and protective variants, which can mask the association signal from risk variants. Early studies proposing pooling tests dismissed methods for locus-wide inference using nonnegative single-variant test statistics based on unrealistic comparisons. However, such methods are robust to the inclusion of neutral and protective variants and therefore may be more useful than previously appreciated. In fact, some recently proposed methods derived within different frameworks are equivalent to performing inference on weighted sums of squared single-variant score statistics. In this study, we compared two existing methods for locus-wide inference using nonnegative single-variant test statistics to two widely cited pooling tests under more realistic conditions. We established analytic results for a simple model with one rare risk and one rare neutral variant, which demonstrated that pooling tests were less powerful than even Bonferroni-corrected single-variant tests in most realistic situations. We also performed simulations using variants with realistic minor allele frequency and linkage disequilibrium spectra, disease models with multiple rare risk variants and extensive neutral variation, and varying rates of missing genotypes. In all scenarios considered, existing methods using nonnegative single-variant test statistics had power comparable to or greater than two widely cited pooling tests. Moreover, in disease models with only rare risk variants, an existing method based on the maximum single-variant Cochran-Armitage trend chi-square statistic in the locus had power comparable to or greater than another existing method closely related to some recently proposed methods. We conclude that efficient locus-wide inference using single-variant test statistics should be reconsidered as a useful framework for devising powerful association tests in sequence data with rare variants.     

Joint rare variant association test of the average and individual effects for sequencing studies

For many complex traits, single nucleotide polymorphisms (SNPs) identified from genome-wide association studies (GWAS) only explain a small percentage of heritability. Next generation sequencing technology makes it possible to explore unexplained heritability by identifying rare variants (RVs). Existing tests designed for RVs look for optimal strategies to combine information across multiple variants. Many of the tests have good power when the true underlying associations are either in the same direction or in opposite directions. We propose three tests for examining the association between a phenotype and RVs, where two of them jointly consider the common association across RVs and the individual deviations from the common effect. On one hand, similar to some of the best existing methods, the individual deviations are modeled as random effects to borrow information across multiple RVs. On the other hand, unlike the existing methods which pool individual effects towards zero, we pool them towards a possibly non-zero common effect by adding a pooled variant into the model. The common effect and the individual effects are jointly tested. We show through extensive simulations that at least one of the three tests proposed here is the most powerful or very close to being the most powerful in various settings of true models. This is appealing in practice because the direction and size of the true effects of the associated RVs are unknown. Researchers can apply the developed tests to improve power under a wide range of true models.     

Family-based association tests for genomewide association scans

With millions of single-nucleotide polymorphisms (SNPs) identified and characterized, genomewide association studies have begun to identify susceptibility genes for complex traits and diseases. These studies involve the characterization and analysis of very-high-resolution SNP genotype data for hundreds or thousands of individuals. We describe a computationally efficient approach to testing association between SNPs and quantitative phenotypes, which can be applied to whole-genome association scans. In addition to observed genotypes, our approach allows estimation of missing genotypes, resulting in substantial increases in power when genotyping resources are limited. We estimate missing genotypes probabilistically using the Lander-Green or Elston-Stewart algorithms and combine high-resolution SNP genotypes for a subset of individuals in each pedigree with sparser marker data for the remaining individuals. We show that power is increased whenever phenotype information for ungenotyped individuals is included in analyses and that high-density genotyping of just three carefully selected individuals in a nuclear family can recover >90% of the information available if every individual were genotyped, for a fraction of the cost and experimental effort. To aid in study design, we evaluate the power of strategies that genotype different subsets of individuals in each pedigree and make recommendations about which individuals should be genotyped at a high density. To illustrate our method, we performed genomewide association analysis for 27 gene-expression phenotypes in 3-generation families (Centre d'Etude du Polymorphisme Humain pedigrees), in which genotypes for ~860,000 SNPs in 90 grandparents and parents are complemented by genotypes for ~6,700 SNPs in a total of 168 individuals. In addition to increasing the evidence of association at 15 previously identified cis-acting associated alleles, our genotype-inference algorithm allowed us to identify associated alleles at 4 cis-acting loci that were missed when analysis was restricted to individuals with the high-density SNP data. Our genotype-inference algorithm and the proposed association tests are implemented in software that is available for free.     

Nonlinear tests for genomewide association studies

As millions of single-nucleotide polymorphisms (SNPs) have been identified and high-throughput genotyping technologies have been rapidly developed, large-scale genomewide association studies are soon within reach. However, since a genomewide association study involves a large number of SNPs it is therefore nearly impossible to ensure a genomewide significance level of 0.05 using the available statistics, although the multiple-test problems can be alleviated, but not sufficiently, by the use of tagging SNPs. One strategy to circumvent the multiple-test problem associated with genome-wide association tests is to develop novel test statistics with high power. In this report, we introduce several nonlinear tests, which are based on nonlinear transformation of allele or haplotype frequencies. We investigate the power of the nonlinear test statistics and demonstrate that under certain conditions, some nonlinear test statistics have much higher power than the standard chi2-test statistic. Type I error rates of the nonlinear tests are validated using simulation studies. We also show that a class of similarity measure-based test statistics is based on the quadratic function of allele or haplotype frequencies, and thus they belong to nonlinear tests. To evaluate their performance, the nonlinear test statistics are also applied to three real data sets. Our study shows that nonlinear test statistics have great potential in association studies of complex diseases.     

Comparison of regression methods for phenology

Several methods exist for investigation of the relationship between records and weather data. These can be broadly classified into models that attempt to incorporate information about underlying biological processes, such as those based on the concept of thermal time, and linear regression methods. The latter are less driven by the biology but have the advantages of ease of use and flexibility. Regression can be used where there is no obvious mechanistic model or to suggest the form of a mechanistic or empirical model where there are several to choose from. Stepwise regression is commonly used in phenology. However, it requires aggregation of the weather records, resulting in loss of information. Penalised signal regression (PSR) was recently introduced to overcome this weakness. Here, we introduce a further method to the phenology context called fusion, which is a sparse version of PSR. In this paper, we compare the performance of these three regression methods based on simulations from two types of mechanistic models, the spring warming and sequential models. Given a suitable choice of temperature days as regression covariates, PSR and fusion performed better than stepwise regression for the spring warming model and PSR performed best for the sequential model. However, if a large number of redundant temperature days were included as covariates, the performance of PSR fell off whilst fusion was quite robust to this change. For this reason, it is best to use PSR and fusion methods in tandem, and to vary the number of covariates included.     

Generalized genomic distance-based regression methodology for multilocus association analysis

Large-scale, multilocus genetic association studies require powerful and appropriate statistical-analysis tools that are designed to relate genotype and haplotype information to phenotypes of interest. Many analysis approaches consider relating allelic, haplotypic, or genotypic information to a trait through use of extensions of traditional analysis techniques, such as contingency-table analysis, regression methods, and analysis-of-variance techniques. In this work, we consider a complementary approach that involves the characterization and measurement of the similarity and dissimilarity of the allelic composition of a set of individuals' diploid genomes at multiple loci in the regions of interest. We describe a regression method that can be used to relate variation in the measure of genomic dissimilarity (or "distance") among a set of individuals to variation in their trait values. Weighting factors associated with functional or evolutionary conservation information of the loci can be used in the assessment of similarity. The proposed method is very flexible and is easily extended to complex multilocus-analysis settings involving covariates. In addition, the proposed method actually encompasses both single-locus and haplotype-phylogeny analysis methods, which are two of the most widely used approaches in genetic association analysis. We showcase the method with data described in the literature. Ultimately, our method is appropriate for high-dimensional genomic data and anticipates an era when cost-effective exhaustive DNA sequence data can be obtained for a large number of individuals, over and above genotype information focused on a few well-chosen loci.     

Robust tests for matched case-control genetic association studies

Background

Infectious disease of livestock continues to be a cause of substantial economic loss and has adverse welfare consequences in both the developing and developed world. New solutions to control disease are needed and research focused on the genetic loci determining variation in immune-related traits has the potential to deliver solutions. However, identifying selectable markers and the causal genes involved in disease resistance and vaccine response is not straightforward. The aims of this study were to locate regions of the bovine genome that control the immune response post immunisation. 195 F2 and backcross Holstein Charolais cattle were immunised with a 40-mer peptide derived from foot-and-mouth disease virus (FMDV). T cell and antibody (IgG1 and IgG2) responses were measured at several time points post immunisation. All experimental animals (F0, F1 and F2, n = 982) were genotyped with 165 microsatellite markers for the genome scan.

Results

Considerable variability in the immune responses across time was observed and sire, dam and age had significant effects on responses at specific time points. There were significant correlations within traits across time, and between IgG1 and IgG2 traits, also some weak correlations were detected between T cell and IgG2 responses. The whole genome scan detected 77 quantitative trait loci (QTL), on 22 chromosomes, including clusters of QTL on BTA 4, 5, 6, 20, 23 and 25. Two QTL reached 5% genome wide significance (on BTA 6 and 24) and one on BTA 20 reached 1% genome wide significance.

Conclusions

A proportion of the variance in the T cell and antibody response post immunisation with an FDMV peptide has a genetic component. Even though the antigen was relatively simple, the humoral and cell mediated responses were clearly under complex genetic control, with the majority of QTL located outside the MHC locus. The results suggest that there may be specific genes or loci that impact on variation in both the primary and secondary immune responses, whereas other loci may be specifically important for early or later phases of the immune response. Future fine mapping of the QTL clusters identified has the potential to reveal the causal variations underlying the variation in immune response observed.