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

Meta-analysis of set-based multiple phenotype association test based on GWAS summary statistics from different cohorts

Genome-wide association studies (GWAS) have emerged as popular tools for identifying genetic variants that are associated with complex diseases. Standard analysis of a GWAS involves assessing the association between each variant and a disease. However, this approach suffers from limited reproducibility and difficulties in detecting multi-variant and pleiotropic effects. Although joint analysis of multiple phenotypes for GWAS can identify and interpret pleiotropic loci which are essential to understand pleiotropy in diseases and complex traits, most of the multiple phenotype association tests are designed for a single variant, resulting in much lower power, especially when their effect sizes are small and only their cumulative effect is associated with multiple phenotypes. To overcome these limitations, set-based multiple phenotype association tests have been developed to enhance statistical power and facilitate the identification and interpretation of pleiotropic regions. In this research, we propose a new method, named Meta-TOW-S, which conducts joint association tests between multiple phenotypes and a set of variants (such as variants in a gene) utilizing GWAS summary statistics from different cohorts. Our approach applies the set-based method that Tests for the effect of an Optimal Weighted combination of variants in a gene (TOW) and accounts for sample size differences across GWAS cohorts by employing the Cauchy combination method. Meta-TOW-S combines the advantages of set-based tests and multi-phenotype association tests, exhibiting computational efficiency and enabling analysis across multiple phenotypes while accommodating overlapping samples from different GWAS cohorts. To assess the performance of Meta-TOW-S, we develop a phenotype simulator package that encompasses a comprehensive simulation scheme capable of modeling multiple phenotypes and multiple variants, including noise structures and diverse correlation patterns among phenotypes. Simulation studies validate that Meta-TOW-S maintains a desirable Type I error rate. Further simulation under different scenarios shows that Meta-TOW-S can improve power compared with other existing meta-analysis methods. When applied to four psychiatric disorders summary data, Meta-TOW-S detects a greater number of significant genes.

A novel method for multiple phenotype association studies based on genotype and phenotype network

Joint analysis of multiple correlated phenotypes for genome-wide association studies (GWAS) can identify and interpret pleiotropic loci which are essential to understand pleiotropy in diseases and complex traits. Meanwhile, constructing a network based on associations between phenotypes and genotypes provides a new insight to analyze multiple phenotypes, which can explore whether phenotypes and genotypes might be related to each other at a higher level of cellular and organismal organization. In this paper, we first develop a bipartite signed network by linking phenotypes and genotypes into a Genotype and Phenotype Network (GPN). The GPN can be constructed by a mixture of quantitative and qualitative phenotypes and is applicable to binary phenotypes with extremely unbalanced case-control ratios in large-scale biobank datasets. We then apply a powerful community detection method to partition phenotypes into disjoint network modules based on GPN. Finally, we jointly test the association between multiple phenotypes in a network module and a single nucleotide polymorphism (SNP). Simulations and analyses of 72 complex traits in the UK Biobank show that multiple phenotype association tests based on network modules detected by GPN are much more powerful than those without considering network modules. The newly proposed GPN provides a new insight to investigate the genetic architecture among different types of phenotypes. Multiple phenotypes association studies based on GPN are improved by incorporating the genetic information into the phenotype clustering. Notably, it might broaden the understanding of genetic architecture that exists between diagnoses, genes, and pleiotropy.

Gene selection by incorporating genetic networks into case-control association studies

Large-scale genome-wide association studies (GWAS) have been successfully applied to a wide range of genetic variants underlying complex diseases. The network-based regression approach has been developed to incorporate a biological genetic network and to overcome the challenges caused by the computational efficiency for analyzing high-dimensional genomic data. In this paper, we propose a gene selection approach by incorporating genetic networks into case-control association studies for DNA sequence data or DNA methylation data. Instead of using traditional dimension reduction techniques such as principal component analyses and supervised principal component analyses, we use a linear combination of genotypes at SNPs or methylation values at CpG sites in a gene to capture gene-level signals. We employ three linear combination approaches: optimally weighted sum (OWS), beta-based weighted sum (BWS), and LD-adjusted polygenic risk score (LD-PRS). OWS and LD-PRS are supervised approaches that depend on the effect of each SNP or CpG site on the case-control status, while BWS can be extracted without using the case-control status. After using one of the linear combinations of genotypes or methylation values in each gene to capture gene-level signals, we regularize them to perform gene selection based on the biological network. Simulation studies show that the proposed approaches have higher true positive rates than using traditional dimension reduction techniques. We also apply our approaches to DNA methylation data and UK Biobank DNA sequence data for analyzing rheumatoid arthritis. The results show that the proposed methods can select potentially rheumatoid arthritis related genes that are missed by existing methods.

Integrating External Controls by Regression Calibration for Genome-Wide Association Study

Genome-wide association studies (GWAS) have successfully revealed many disease-associated genetic variants. For a case-control study, the adequate power of an association test can be achieved with a large sample size, although genotyping large samples is expensive. A cost-effective strategy to boost power is to integrate external control samples with publicly available genotyped data. However, the naive integration of external controls may inflate the type I error rates if ignoring the systematic differences (batch effect) between studies, such as the differences in sequencing platforms, genotype-calling procedures, population stratification, and so forth. To account for the batch effect, we propose an approach by integrating External Controls into the Association Test by Regression Calibration (iECAT-RC) in case-control association studies. Extensive simulation studies show that iECAT-RC not only can control type I error rates but also can boost statistical power in all models. We also apply iECAT-RC to the UK Biobank data for M72 Fibroblastic disorders by considering genotype calling as the batch effect. Four SNPs associated with fibroblastic disorders have been detected by iECAT-RC and the other two comparison methods, iECAT-Score and Internal. However, our method has a higher probability of identifying these significant SNPs in the scenario of an unbalanced case-control association study.

Automatic block-wise genotype-phenotype association detection based on hidden Markov model

BACKGROUND

For detecting genotype-phenotype association from case-control single nucleotide polymorphism (SNP) data, one class of methods relies on testing each genomic variant site individually. However, this approach ignores the tendency for associated variant sites to be spatially clustered instead of uniformly distributed along the genome. Therefore, a more recent class of methods looks for blocks of influential variant sites. Unfortunately, existing such methods either assume prior knowledge of the blocks, or rely on ad hoc moving windows. A principled method is needed to automatically detect genomic variant blocks which are associated with the phenotype.

RESULTS

In this paper, we introduce an automatic block-wise Genome-Wide Association Study (GWAS) method based on Hidden Markov model. Using case-control SNP data as input, our method detects the number of blocks associated with the phenotype and the locations of the blocks. Correspondingly, the minor allele of each variate site will be classified as having negative influence, no influence or positive influence on the phenotype. We evaluated our method using both datasets simulated from our model and datasets from a block model different from ours, and compared the performance with other methods. These included both simple methods based on the Fisher's exact test, applied site-by-site, as well as more complex methods built into the recent Zoom-Focus Algorithm. Across all simulations, our method consistently outperformed the comparisons.

CONCLUSIONS

With its demonstrated better performance, we expect our algorithm for detecting influential variant sites may help find more accurate signals across a wide range of case-control GWAS.

A fast and efficient approach for gene-based association studies of ordinal phenotypes

Many human disease conditions need to be measured by ordinal phenotypes, so analysis of ordinal phenotypes is valuable in genome-wide association studies (GWAS). However, existing association methods for dichotomous or quantitative phenotypes are not appropriate to ordinal phenotypes. Therefore, based on an aggregated Cauchy association test, we propose a fast and efficient association method to test the association between genetic variants and an ordinal phenotype. To enrich association signals of rare variants, we first use the burden method to aggregate rare variants. Then we respectively test the significance of the aggregated rare variants and other common variants. Finally, the combination of transformed variant-level P values is taken as test statistic, that approximately follows Cauchy distribution under the null hypothesis. Extensive simulation studies and analysis of GAW19 show that our proposed method is powerful and computationally fast as a gene-based method. Especially, in the presence of an extremely low proportion of causal variants in a gene, our method has better performance.

HCLC-FC: A novel statistical method for phenome-wide association studies

The emergence of genetic data coupled to longitudinal electronic medical records (EMRs) offers the possibility of phenome-wide association studies (PheWAS). In PheWAS, the whole phenome can be divided into numerous phenotypic categories according to the genetic architecture across phenotypes. Currently, statistical analyses for PheWAS are mainly univariate analyses, which test the association between one genetic variant and one phenotype at a time. In this article, we derived a novel and powerful multivariate method for PheWAS. The proposed method involves three steps. In the first step, we apply the bottom-up hierarchical clustering method to partition a large number of phenotypes into disjoint clusters within each phenotypic category. In the second step, the clustering linear combination method is used to combine test statistics within each category based on the phenotypic clusters and obtain p-values from each phenotypic category. In the third step, we propose a new false discovery rate (FDR) control approach. We perform extensive simulation studies to compare the performance of our method with that of other existing methods. The results show that our proposed method controls FDR very well and outperforms other methods we compared with. We also apply the proposed approach to a set of EMR-based phenotypes across more than 300,000 samples from the UK Biobank. We find that the proposed approach not only can well-control FDR at a nominal level but also successfully identify 1,244 significant SNPs that are reported to be associated with some phenotypes in the GWAS catalog. Our open-access tools and instructions on how to implement HCLC-FC are available at https://github.com/XiaoyuLiang/HCLCFC.

Gene-Based Association Tests Using New Polygenic Risk Scores and Incorporating Gene Expression Data

Recently, gene-based association studies have shown that integrating genome-wide association studies (GWAS) with expression quantitative trait locus (eQTL) data can boost statistical power and that the genetic liability of traits can be captured by polygenic risk scores (PRSs). In this paper, we propose a new gene-based statistical method that leverages gene-expression measurements and new PRSs to identify genes that are associated with phenotypes of interest. We used a generalized linear model to associate phenotypes with gene expression and PRSs and used a score-test statistic to test the association between phenotypes and genes. Our simulation studies show that the newly developed method has correct type I error rates and can boost statistical power compared with other methods that use either gene expression or PRS in association tests. A real data analysis figure based on UK Biobank data for asthma shows that the proposed method is applicable to GWAS.

A computationally efficient clustering linear combination approach to jointly analyze multiple phenotypes for GWAS

There has been an increasing interest in joint analysis of multiple phenotypes in genome-wide association studies (GWAS) because jointly analyzing multiple phenotypes may increase statistical power to detect genetic variants associated with complex diseases or traits. Recently, many statistical methods have been developed for joint analysis of multiple phenotypes in genetic association studies, including the Clustering Linear Combination (CLC) method. The CLC method works particularly well with phenotypes that have natural groupings, but due to the unknown number of clusters for a given data, the final test statistic of CLC method is the minimum p-value among all p-values of the CLC test statistics obtained from each possible number of clusters. Therefore, a simulation procedure needs to be used to evaluate the p-value of the final test statistic. This makes the CLC method computationally demanding. We develop a new method called computationally efficient CLC (ceCLC) to test the association between multiple phenotypes and a genetic variant. Instead of using the minimum p-value as the test statistic in the CLC method, ceCLC uses the Cauchy combination test to combine all p-values of the CLC test statistics obtained from each possible number of clusters. The test statistic of ceCLC approximately follows a standard Cauchy distribution, so the p-value can be obtained from the cumulative density function without the need for the simulation procedure. Through extensive simulation studies and application on the COPDGene data, the results demonstrate that the type I error rates of ceCLC are effectively controlled in different simulation settings and ceCLC either outperforms all other methods or has statistical power that is very close to the most powerful method with which it has been compared.

Gene-based association tests using GWAS summary statistics and incorporating eQTL

Although genome-wide association studies (GWAS) have been successfully applied to a variety of complex diseases and identified many genetic variants underlying complex diseases via single marker tests, there is still a considerable heritability of complex diseases that could not be explained by GWAS. One alternative approach to overcome the missing heritability caused by genetic heterogeneity is gene-based analysis, which considers the aggregate effects of multiple genetic variants in a single test. Another alternative approach is transcriptome-wide association study (TWAS). TWAS aggregates genomic information into functionally relevant units that map to genes and their expression. TWAS is not only powerful, but can also increase the interpretability in biological mechanisms of identified trait associated genes. In this study, we propose a powerful and computationally efficient gene-based association test, called Overall. Using extended Simes procedure, Overall aggregates information from three types of traditional gene-based association tests and also incorporates expression quantitative trait locus (eQTL) information into a gene-based association test using GWAS summary statistics. We show that after a small number of replications to estimate the correlation among the integrated gene-based tests, the p values of Overall can be calculated analytically. Simulation studies show that Overall can control type I error rates very well and has higher power than the tests that we compared with. We also apply Overall to two schizophrenia GWAS summary datasets and two lipids GWAS summary datasets. The results show that this newly developed method can identify more significant genes than other methods we compared with.

Exome-Wide Pan-Cancer Analysis of Germline Variants in 8,719 Individuals Finds Little Evidence of Rare Variant Associations

BACKGROUND

Many cancer types show considerable heritability, and extensive research has been done to identify germline susceptibility variants. Linkage studies have discovered many rare high-risk variants, and genome-wide association studies (GWAS) have discovered many common low-risk variants. However, it is believed that a considerable proportion of the heritability of cancer remains unexplained by known susceptibility variants. The "rare variant hypothesis" proposes that much of the missing heritability lies in rare variants that cannot reliably be detected by linkage analysis or GWAS. Until recently, high sequencing costs have precluded extensive surveys of rare variants, but technological advances have now made it possible to analyze rare variants on a much greater scale.

OBJECTIVES

In this study, we investigated associations between rare variants and 14 cancer types.

METHODS

We ran association tests using whole-exome sequencing data from The Cancer Genome Atlas (TCGA) and validated the findings using data from the Pan-Cancer Analysis of Whole Genomes Consortium (PCAWG).

RESULTS

We identified four significant associations in TCGA, only one of which was replicated in PCAWG (BRCA1 and ovarian cancer).

CONCLUSIONS

Our results provide little evidence in favor of the rare variant hypothesis. Much larger sample sizes may be needed to detect undiscovered rare cancer variants.

A two-stage testing strategy for detecting genes×environment interactions in association studies

Identifying gene×environment (G×E) interactions, especially when rare variants are included in genome-wide association studies, is a major challenge in statistical genetics. However, the detection of G×E interactions is very important for understanding the etiology of complex diseases. Although currently some statistical methods have been developed to detect the interactions between genes and environment, the detection of the interactions for the case of rare variants is still limited. Therefore, it is particularly important to develop a new method to detect the interactions between genes and environment for rare variants. In this study, we extend an existing method of adaptive combination of P-values (ADA) and design a novel strategy (called iSADA) for testing the effects of G×E interactions for rare variants. We propose a new two-stage test to detect the interactions between genes and environment in a certain region of a chromosome or even for the whole genome. First, the score statistic is used to test the associations between trait value and the interaction terms of genes and environment and obtain the original P-values. Then, based on the idea of the ADA method, we further construct a full test statistic via the P-values of the preliminary tests in the first stage, so that we can comprehensively test the interactions between genes and environment in the considered genome region. Simulation studies are conducted to compare our proposed method with other existing methods. The results show that the iSADA has higher power than other methods in each case. A GAW17 data set is also applied to illustrate the applicability of the new method.

Controlling for human population stratification in rare variant association studies

Population stratification is a confounder of genetic association studies. In analyses of rare variants, corrections based on principal components (PCs) and linear mixed models (LMMs) yield conflicting conclusions. Studies evaluating these approaches generally focused on limited types of structure and large sample sizes. We investigated the properties of several correction methods through a large simulation study using real exome data, and several within- and between-continent stratification scenarios. We considered different sample sizes, with situations including as few as 50 cases, to account for the analysis of rare disorders. Large samples showed that accounting for stratification was more difficult with a continental than with a worldwide structure. When considering a sample of 50 cases, an inflation of type-I-errors was observed with PCs for small numbers of controls (≤ 100), and with LMMs for large numbers of controls (≥ 1000). We also tested a novel local permutation method (LocPerm), which maintained a correct type-I-error in all situations. Powers were equivalent for all approaches pointing out that the key issue is to properly control type-I-errors. Finally, we found that power of analyses including small numbers of cases can be increased, by adding a large panel of external controls, provided an appropriate stratification correction was used.

A fast and powerful aggregated Cauchy association test for joint analysis of multiple phenotypes

BACKGROUND

Pleiotropy is a widespread phenomenon in complex human diseases. Jointly analyzing multiple phenotypes can improve power performance of detecting genetic variants and uncover the underlying genetic mechanism.

OBJECTIVE

This study aims to detect the association between genetic variants in a genomic region and multiple phenotypes.

METHODS

We develop the aggregated Cauchy association test to detect the association between rare variants in a genomic region and multiple phenotypes (abbreviated as "Multi-ACAT"). Multi-ACAT first detects the association between each rare variant and multiple phenotypes based on reverse regression and obtains variant-level p-values, then takes linear combination of transformed p-values as the test statistic which approximately follows Cauchy distribution under the null hypothesis.

RESULTS

Extensive simulation studies show that when the proportion of causal variants in a genomic region is extremely small, Multi-ACAT is more powerful than the other several methods and is robust to bi-directional effects of causal variants. Finally, we illustrate our proposed method by analyzing two phenotypes [systolic blood pressure (SBP) and diastolic blood pressure (DBP)] from Genetic Analysis Workshop 19 (GAW19).

CONCLUSION

The Multi-ACAT computes extremely fast, does not consider complex distributions of multiple correlated phenotypes, and can be applied to the case with noise phenotypes.

Test Gene-Environment Interactions for Multiple Traits in Sequencing Association Studies

MOTIVATION

The risk of many complex diseases is determined by an interplay of genetic and environmental factors. The examination of gene-environment interactions (G×Es) for multiple traits can yield valuable insights about the etiology of the disease and increase power in detecting disease-associated genes. However, the methods for testing G×Es for multiple traits are very limited.

METHOD

We developed novel approaches to test G×Es for multiple traits in sequencing association studies. We first perform a transformation of multiple traits by using either principal component analysis or standardization analysis. Then, we detect the effects of G×Es using novel proposed tests: testing the effect of an optimally weighted combination of G×Es (TOW-GE) and/or variable weight TOW-GE (VW-TOW-GE). Finally, we employ Fisher's combination test to combine the p values.

RESULTS

Extensive simulation studies show that the type I error rates of the proposed methods are well controlled. Compared to the interaction sequence kernel association test (ISKAT), TOW-GE is more powerful when there are only rare risk and protective variants; VW-TOW-GE is more powerful when there are both rare and common variants. Both TOW-GE and VW-TOW-GE are robust to directions of effects of causal G×Es. Application to the COPDGene Study demonstrates that our proposed methods are very effective.

CONCLUSIONS

Our proposed methods are useful tools in the identification of G×Es for multiple traits. The proposed methods can be used not only to identify G×Es for common variants, but also for rare variants. Therefore, they can be employed in identifying G×Es in both genome-wide association studies and next-generation sequencing data analyses.

Testing gene-environment interactions for rare and/or common variants in sequencing association studies

The risk of many complex diseases is determined by a complex interplay of genetic and environmental factors. Advanced next generation sequencing technology makes identification of gene-environment (GE) interactions for both common and rare variants possible. However, most existing methods focus on testing the main effects of common and/or rare genetic variants. There are limited methods developed to test the effects of GE interactions for rare variants only or rare and common variants simultaneously. In this study, we develop novel approaches to test the effects of GE interactions of rare and/or common risk, and/or protective variants in sequencing association studies. We propose two approaches: 1) testing the effects of an optimally weighted combination of GE interactions for rare variants (TOW-GE); 2) testing the effects of a weighted combination of GE interactions for both rare and common variants (variable weight TOW-GE, VW-TOW-GE). Extensive simulation studies based on the Genetic Analysis Workshop 17 data show that the type I error rates of the proposed methods are well controlled. Compared to the existing interaction sequence kernel association test (ISKAT), TOW-GE is more powerful when there are GE interactions' effects for rare risk and/or protective variants; VW-TOW-GE is more powerful when there are GE interactions' effects for both rare and common risk and protective variants. Both TOW-GE and VW-TOW-GE are robust to the directions of effects of causal GE interactions. We demonstrate the applications of TOW-GE and VW-TOW-GE using an imputed data from the COPDGene Study.

RAINBOW: Haplotype-based genome-wide association study using a novel SNP-set method

Difficulty in detecting rare variants is one of the problems in conventional genome-wide association studies (GWAS). The problem is closely related to the complex gene compositions comprising multiple alleles, such as haplotypes. Several single nucleotide polymorphism (SNP) set approaches have been proposed to solve this problem. These methods, however, have been rarely discussed in connection with haplotypes. In this study, we developed a novel SNP-set method named "RAINBOW" and applied the method to haplotype-based GWAS by regarding a haplotype block as a SNP-set. Combining haplotype block estimation and SNP-set GWAS, haplotype-based GWAS can be conducted without prior information of haplotypes. We prepared 100 datasets of simulated phenotypic data and real marker genotype data of Oryza sativa subsp. indica, and performed GWAS of the datasets. We compared the power of our method, the conventional single-SNP GWAS, the conventional haplotype-based GWAS, and the conventional SNP-set GWAS. Our proposed method was shown to be superior to these in three aspects: (1) controlling false positives; (2) in detecting causal variants without relying on the linkage disequilibrium if causal variants were genotyped in the dataset; and (3) it showed greater power than the other methods, i.e., it was able to detect causal variants that were not detected by the others, primarily when the causal variants were located very close to each other, and the directions of their effects were opposite. By using the SNP-set approach as in this study, we expect that detecting not only rare variants but also genes with complex mechanisms, such as genes with multiple causal variants, can be realized. RAINBOW was implemented as an R package named "RAINBOWR" and is available from CRAN (https://cran.r-project.org/web/packages/RAINBOWR/index.html) and GitHub (https://github.com/KosukeHamazaki/RAINBOWR).

A general statistic to test an optimally weighted combination of common and/or rare variants

Both genome-wide association study and next-generation sequencing data analyses are widely employed to identify disease susceptible common and/or rare genetic variants. Rare variants generally have large effects though they are hard to detect due to their low frequencies. Currently, many existing statistical methods for rare variants association studies employ a weighted combination scheme, which usually puts subjective weights or suboptimal weights based on some adhoc assumptions (e.g., ignoring dependence between rare variants). In this study, we analytically derived optimal weights for both common and rare variants and proposed a general and novel approach to test association between an optimally weighted combination of variants (G-TOW) in a gene or pathway for a continuous or dichotomous trait while easily adjusting for covariates. Results of the simulation studies show that G-TOW has properly controlled type I error rates and it is the most powerful test among the methods we compared when testing effects of either both rare and common variants or rare variants only. We also illustrate the effectiveness of G-TOW using the Genetic Analysis Workshop 17 (GAW17) data. Additionally, we applied G-TOW and other competitive methods to test disease-associated genes in real data of schizophrenia. The G-TOW has successfully verified genes FYN and VPS39 which are associated with schizophrenia reported in existing publications. Both of these genes are missed by the weighted sum statistic and the sequence kernel association test. Simulation study and real data analysis indicate that G-TOW is a powerful test.

A gene based approach to test genetic association based on an optimally weighted combination of multiple traits

There is increasing evidence showing that pleiotropy is a widespread phenomenon in complex diseases for which multiple correlated traits are often measured. Joint analysis of multiple traits could increase statistical power by aggregating multiple weak effects. Existing methods for multiple trait association tests usually study each of the multiple traits separately and then combine the univariate test statistics or combine p-values of the univariate tests for identifying disease associated genetic variants. However, ignoring correlation between phenotypes may cause power loss. Additionally, the genetic variants in one gene (including common and rare variants) are often viewed as a whole that affects the underlying disease since the basic functional unit of inheritance is a gene rather than a genetic variant. Thus, results from gene level association tests can be more readily integrated with downstream functional and pathogenic investigation, whereas many existing methods for multiple trait association tests only focus on testing a single common variant rather than a gene. In this article, we propose a statistical method by Testing an Optimally Weighted Combination of Multiple traits (TOW-CM) to test the association between multiple traits and multiple variants in a genomic region (a gene or pathway). We investigate the performance of the proposed method through extensive simulation studies. Our simulation studies show that the proposed method has correct type I error rates and is either the most powerful test or comparable with the most powerful tests. Additionally, we illustrate the usefulness of TOW-CM based on a COPDGene study.

Joint Analysis of Multiple Phenotypes in Association Studies based on Cross-Validation Prediction Error

In genome-wide association studies (GWAS), joint analysis of multiple phenotypes could have increased statistical power over analyzing each phenotype individually to identify genetic variants that are associated with complex diseases. With this motivation, several statistical methods that jointly analyze multiple phenotypes have been developed, such as O’Brien’s method, Trait-based Association Test that uses Extended Simes procedure (TATES), multivariate analysis of variance (MANOVA), and joint model of multiple phenotypes (MultiPhen). However, the performance of these methods under a wide range of scenarios is not consistent: one test may be powerful in some situations, but not in the others. Thus, one challenge in joint analysis of multiple phenotypes is to construct a test that could maintain good performance across different scenarios. In this article, we develop a novel statistical method to test associations between a genetic variant and Multiple Phenotypes based on cross-validation Prediction Error (MultP-PE). Extensive simulations are conducted to evaluate the type I error rates and to compare the power performance of MultP-PE with various existing methods. The simulation studies show that MultP-PE controls type I error rates very well and has consistently higher power than the tests we compared in all simulation scenarios. We conclude with the recommendation for the use of MultP-PE for its good performance in association studies with multiple phenotypes.

Gene-based sequential burden association test

Detecting the association between a set of variants and a phenotype of interest is the first and important step in genetic and genomic studies. Although it attracted a large amount of attention in the scientific community and several related statistical approaches have been proposed in the literature, powerful and robust statistical tests are still highly desired and yet to be developed in this area. In this paper, we propose a powerful and robust association test, which combines information from each individual single-nucleotide polymorphisms based on sequential independent burden tests. We compare the proposed approach with some popular tests through a comprehensive simulation study and real data application. Our results show that, in general, the new test is more powerful; the gain in detecting power can be substantial in many situations, compared to other methods.

A modified association test for rare and common variants based on affected sib-pair design

Current genome-wide association analysis has identified a great number of rare and common variants associated with common complex traits, however, more effective approaches for detecting associations between rare and common variants with common diseases are still demanded. Approaches for detecting rare variant association analysis will compromise the power when detecting the effects of rare and common variants simultaneously. In this paper, we extend an existing method of testing for rare variant association based on affected sib pairs (TOW-sib) and propose a variable weight test for rare and common variants association based on affected sib pairs (abbreviated as VW-TOWsib). The VW-TOWsib can be used to achieve the purpose of detecting the association of rare and common variants with complex diseases. Simulation results in various scenarios show that our proposed method is more powerful than existing methods for detecting effects of rare and common variants. At the same time, the VW-TOWsib also performs well as a method for rare variant association analysis.

Family-based association tests for rare variants with censored traits

We propose a set of family-based burden and kernel tests for censored traits (FamBAC and FamKAC). Here, censored traits refer to time-to-event outcomes, for instance, age-at-onset of a disease. To model censored traits in family-based designs, we used the frailty model, which incorporated not only fixed genetic effects of rare variants in a region of interest but also random polygenic effects shared within families. We first partitioned genotype scores of rare variants into orthogonal between- and within-family components, and then derived their corresponding efficient score statistics from the frailty model. Finally, FamBAC and FamKAC were constructed by aggregating the weighted efficient scores of the within-family components across rare variants and subjects. FamBAC collapsed rare variants within subject first to form a burden test that followed a chi-squared distribution; whereas FamKAC was a variant component test following a mixture of chi-squared distributions. For FamKAC, p-values can be computed by permutation tests or for computational efficiency by approximation methods. Through simulation studies, we showed that type I error was correctly controlled by FamBAC for various variant weighting schemes (0.0371 to 0.0527). However, FamKAC type I error rates based on approximation methods were deflated (max 0.0376) but improved by permutation tests. Our simulations also demonstrated that burden test FamBAC had higher power than kernel test FamKAC when high proportion (e.g. ≥ 80%) of causal variants had effects in the same direction. In contrast, when the effects of causal variants on the censored trait were in mixed directions, FamKAC outperformed FamBAC and had comparable or higher power than an existing method, RVFam. Our proposed framework has the flexibility to accommodate general nuclear families, and can be used to analyze sequence data for censored traits such as age-at-onset of a complex disease of interest.

Joint analysis of multiple phenotypes in association studies using allele-based clustering approach for non-normal distributions

In the study of complex diseases, several correlated phenotypes are usually measured. There is also increasing evidence showing that testing the association between a single-nucleotide polymorphism (SNP) and multiple-dependent phenotypes jointly is often more powerful than analyzing only one phenotype at a time. Therefore, developing statistical methods to test for genetic association with multiple phenotypes has become increasingly important. In this paper, we develop an Allele-based Clustering Approach (ACA) for the joint analysis of multiple non-normal phenotypes in association studies. In ACA, we consider the alleles at a SNP of interest as a dependent variable with two classes, and the correlated phenotypes as predictors to predict the alleles at the SNP of interest. We perform extensive simulation studies to evaluate the performance of ACA and compare the power of ACA with the powers of Adaptive Fisher's Combination test, Trait-based Association Test that uses Extended Simes procedure, Fisher's Combination test, the standard MANOVA, and the joint model of Multiple Phenotypes. Our simulation studies show that the proposed method has correct type I error rates and is much more powerful than other methods for some non-normal distributions.

Methods to evaluate rare variants gene-age interaction for triglycerides

Triglycerides are an important measure of heart health. Although more than 90 genes have been found to be associated to lipids, they only explain 12 to 15% of the variance in lipid levels. Evidence suggests that age may interact with the genetic effect on lipid levels. Existing methods to detect the main effect of rare variants cannot be readily applied for testing the gene environment interaction effect of rare variants, as those methods either have unstable results or inflated Type I error rates when the main effect exists. To overcome these difficulties, we developed two statistical methods: testing of optimally weighted combination of single-nucleotide polymorphism (SNP) environment interaction (TOW-SE) and a variable weight TOW-SE (VW-TOW-SE) to test the gene environment interaction effect of rare variants by grouping SNPs into biologically meaningful SNP-sets (SNPs in a gene or pathway) to improve power and interpretability. The proposed methods can be applied to either continuous or binary environmental variables, and to either continuous or binary outcomes. Simulation studies show that Type I error rates of the proposed methods are under control. Comparing the two methods with the existing interaction sequence kernel association test (iSKAT), the VW-TOW-SE is the most powerful test and the TOW-SE is the second most powerful test when gene environment interaction effect exists for both rare and common variants. The three tests were applied to the GAW20 simulated data, among the five regions in which the main effect of common SNPs was simulated and the gene–age interaction effect was not included. As expected, none of the tests indicated positive results.

Methods and results from the genome-wide association group at GAW20

BACKGROUND

This paper summarizes the contributions from the Genome-wide Association Study group (GWAS group) of the GAW20. The GWAS group contributions focused on topics such as association tests, phenotype imputation, and application of empirical kinships. The goals of the GWAS group contributions were varied. A real or a simulated data set based on the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) study was employed by different methods. Different outcomes and covariates were considered, and quality control procedures varied throughout the contributions.

RESULTS

The consideration of heritability and family structure played a major role in some contributions. The inclusion of family information and adaptive weights based on data were found to improve power in genome-wide association studies. It was proven that gene-level approaches are more powerful than single-marker analysis. Other contributions focused on the comparison between pedigree-based kinship and empirical kinship matrices, and investigated similar results in heritability estimation, association mapping, and genomic prediction. A new approach for linkage mapping of triglyceride levels was able to identify a novel linkage signal.

CONCLUSIONS

This summary paper reports on promising statistical approaches and findings of the members of the GWAS group applied on real and simulated data which encompass the current topics of epigenetic and pharmacogenomics.

ADAPTIVE-WEIGHT BURDEN TEST FOR ASSOCIATIONS BETWEEN QUANTITATIVE TRAITS AND GENOTYPE DATA WITH COMPLEX CORRELATIONS

High-throughput sequencing has often been used to screen samples from pedigrees or with population structure, producing genotype data with complex correlations rendered from both familial relation and linkage disequilibrium. With such data, it is critical to account for these genotypic correlations when assessing the contribution of variants by gene or pathway. Recognizing the limitations of existing association testing methods, we propose Adaptive-weight Burden Test (ABT), a retrospective, mixed-model test for genetic association of quantitative traits on genotype data with complex correlations. This method makes full use of genotypic correlations across both samples and variants, and adopts "data-driven" weights to improve power. We derive the ABT statistic and its explicit distribution under the null hypothesis, and demonstrate through simulation studies that it is generally more powerful than the fixed-weight burden test and family-based SKAT in various scenarios, controlling for the type I error rate. Further investigation reveals the connection of ABT with kernel tests, as well as the adaptability of its weights to the direction of genetic effects. The application of ABT is illustrated by a whole genome analysis of genes with common and rare variants associated with fasting glucose from the NHLBI "Grand Opportunity" Exome Sequencing Project.

Testing an optimally weighted combination of common and/or rare variants with multiple traits

Recently, joint analysis of multiple traits has become popular because it can increase statistical power to identify genetic variants associated with complex diseases. In addition, there is increasing evidence indicating that pleiotropy is a widespread phenomenon in complex diseases. Currently, most of existing methods test the association between multiple traits and a single genetic variant. However, these methods by analyzing one variant at a time may not be ideal for rare variant association studies because of the allelic heterogeneity as well as the extreme rarity of rare variants. In this article, we developed a statistical method by testing an optimally weighted combination of variants with multiple traits (TOWmuT) to test the association between multiple traits and a weighted combination of variants (rare and/or common) in a genomic region. TOWmuT is robust to the directions of effects of causal variants and is applicable to different types of traits. Using extensive simulation studies, we compared the performance of TOWmuT with the following five existing methods: gene association with multiple traits (GAMuT), multiple sequence kernel association test (MSKAT), adaptive weighting reverse regression (AWRR), single-TOW, and MANOVA. Our results showed that, in all of the simulation scenarios, TOWmuT has correct type I error rates and is consistently more powerful than the other five tests. We also illustrated the usefulness of TOWmuT by analyzing a whole-genome genotyping data from a lung function study.

A Zoom-Focus algorithm (ZFA) to locate the optimal testing region for rare variant association tests

Motivation

Increasing amounts of whole exome or genome sequencing data present the challenge of analysing rare variants with extremely small minor allele frequencies. Various statistical tests have been proposed, which are specifically configured to increase power for rare variants by conducting the test within a certain bin, such as a gene or a pathway. However, a gene may contain from several to thousands of markers, and not all of them are related to the phenotype. Combining functional and non-functional variants in an arbitrary genomic region could impair the testing power.

Results

We propose a Zoom-Focus algorithm (ZFA) to locate the optimal testing region within a given genomic region. It can be applied as a wrapper function in existing rare variant association tests to increase testing power. The algorithm consists of two steps. In the first step, Zooming, a given genomic region is partitioned by an order of two, and the best partition is located. In the second step, Focusing, the boundaries of the zoomed region are refined. Simulation studies showed that ZFA substantially increased the statistical power of rare variants' tests, including the SKAT, SKAT-O, burden test and the W-test. The algorithm was applied on real exome sequencing data of hypertensive disorder, and identified biologically relevant genetic markers to metabolic disorders that were undetectable by a gene-based method. The proposed algorithm is an efficient and powerful tool to enhance the power of association study for whole exome or genome sequencing data.

Availability and Implementation

The ZFA software is available at: http://www2.ccrb.cuhk.edu.hk/statgene/software.html.

Contact

maggiew@cuhk.edu.hk or bzee@cuhk.edu.hk.

Supplementary information

Supplementary data are available at Bioinformatics online.

Advances in the Genetics of Hypertension: The Effect of Rare Variants

Worldwide, hypertension still represents a serious health burden with nine million people dying as a consequence of hypertension-related complications. Essential hypertension is a complex trait supported by multifactorial genetic inheritance together with environmental factors. The heritability of blood pressure (BP) is estimated to be 30-50%. A great effort was made to find genetic variants affecting BP levels through Genome-Wide Association Studies (GWAS). This approach relies on the "common disease-common variant" hypothesis and led to the identification of multiple genetic variants which explain, in aggregate, only 2-3% of the genetic variance of hypertension. Part of the missing genetic information could be caused by variants too rare to be detected by GWAS. The use of exome chips and Next-Generation Sequencing facilitated the discovery of causative variants. Here, we report the advances in the detection of novel rare variants, genes, and/or pathways through the most promising approaches, and the recent statistical tests that have emerged to handle rare variants. We also discuss the need to further support rare novel variants with replication studies within larger consortia and with deeper functional studies to better understand how new genes might improve patient care and the stratification of the response to antihypertensive treatments.

Association analysis of rare and common variants with multiple traits based on variable reduction method

Pleiotropy, the effect of one variant on multiple traits, is widespread in complex diseases. Joint analysis of multiple traits can improve statistical power to detect genetic variants and uncover the underlying genetic mechanism. Currently, a large number of existing methods target one common variant or only rare variants. Increasing evidence shows that complex diseases are caused by common and rare variants. Here we propose a region-based method to test both rare and common variant associated multiple traits based on variable reduction method (abbreviated as MULVR). However, in the presence of noise traits, the MULVR method may lose power, so we propose the MULVR-O method, which jointly analyses the optimal number of traits associated with genetic variants by the MULVR method, to guard against the effect of noise traits. Extensive simulation studies show that our proposed method (MULVR-O) is applied to not only multiple quantitative traits but also qualitative traits, and is more powerful than several other comparison methods in most scenarios. An application to the two genes (SHBG and CHRM3) and two phenotypes (systolic blood pressure and diastolic blood pressure) from the GAW19 dataset illustrates that our proposed methods (MULVR and MULVR-O) are feasible and efficient as a region-based method.

A novel method to test associations between a weighted combination of phenotypes and genetic variants

Many complex diseases like diabetes, hypertension, metabolic syndrome, et cetera, are measured by multiple correlated phenotypes. However, most genome-wide association studies (GWAS) focus on one phenotype of interest or study multiple phenotypes separately for identifying genetic variants associated with complex diseases. Analyzing one phenotype or the related phenotypes separately may lose power due to ignoring the information obtained by combining phenotypes, such as the correlation between phenotypes. In order to increase statistical power to detect genetic variants associated with complex diseases, we develop a novel method to test a weighted combination of multiple phenotypes (WCmulP). We perform extensive simulation studies as well as real data (COPDGene) analysis to evaluate the performance of the proposed method. Our simulation results show that WCmulP has correct type I error rates and is either the most powerful test or comparable to the most powerful test among the methods we compared. WCmulP also has an outstanding performance for identifying single-nucleotide polymorphisms (SNPs) associated with COPD-related phenotypes.

Adaptive combination of Bayes factors as a powerful method for the joint analysis of rare and common variants

Multi-marker association tests can be more powerful than single-locus analyses because they aggregate the variant information within a gene/region. However, combining the association signals of multiple markers within a gene/region may cause noise due to the inclusion of neutral variants, which usually compromises the power of a test. To reduce noise, the “adaptive combination of P-values” (ADA) method removes variants with larger P-values. However, when both rare and common variants are considered, it is not optimal to truncate variants according to their P-values. An alternative summary measure, the Bayes factor (BF), is defined as the ratio of the probability of the data under the alternative hypothesis to that under the null hypothesis. The BF quantifies the “relative” evidence supporting the alternative hypothesis. Here, we propose an “adaptive combination of Bayes factors” (ADABF) method that can be directly applied to variants with a wide spectrum of minor allele frequencies. The simulations show that ADABF is more powerful than single-nucleotide polymorphism (SNP)-set kernel association tests and burden tests. We also analyzed 1,109 case-parent trios from the Schizophrenia Trio Genomic Research in Taiwan. Three genes on chromosome 19p13.2 were found to be associated with schizophrenia at the suggestive significance level of 5 × 10⁻⁵.

A Powerful Variant-Set Association Test Based on Chi-Square Distribution

Detecting the association between a set of variants and a given phenotype has attracted a large amount of attention in the scientific community, although it is a difficult task. Recently, several related statistical approaches have been proposed in the literature; powerful statistical tests are still highly desired and yet to be developed in this area. In this paper, we propose a powerful test that combines information from each individual single nucleotide polymorphism (SNP) based on principal component analysis without relying on the eigenvalues associated with the principal components. We compare the proposed approach with some popular tests through a simulation study and real data applications. Our results show that, in general, the new test is more powerful than its competitors considered in this study; the gain in detecting power can be substantial in many situations.

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.

A novel statistical method for rare-variant association studies in general pedigrees

Both population-based and family-based designs are commonly used in genetic association studies to identify rare variants that underlie complex diseases. For any type of study design, the statistical power will be improved if rare variants can be enriched in the samples. Family-based designs, with ascertainment based on phenotype, may enrich the sample for causal rare variants and thus can be more powerful than population-based designs. Therefore, it is important to develop family-based statistical methods that can account for ascertainment. In this paper, we develop a novel statistical method for rare-variant association studies in general pedigrees for quantitative traits. This method uses a retrospective view that treats the traits as fixed and the genotypes as random, which allows us to account for complex and undefined ascertainment of families. We then apply the newly developed method to the Genetic Analysis Workshop 19 data set and compare the power of the new method with two other methods for general pedigrees. The results show that the newly proposed method increases power in most of the cases we consider, more than the other two methods.

A Nonparametric Regression Approach to Control for Population Stratification in Rare Variant Association Studies

Recently, there is increasing interest to detect associations between rare variants and complex traits. Rare variant association studies usually need large sample sizes due to the rarity of the variants, and large sample sizes typically require combining information from different geographic locations within and across countries. Although several statistical methods have been developed to control for population stratification in common variant association studies, these methods are not necessarily controlling for population stratification in rare variant association studies. Thus, new statistical methods that can control for population stratification in rare variant association studies are needed. In this article, we propose a principal component based nonparametric regression (PC-nonp) approach to control for population stratification in rare variant association studies. Our simulations show that the proposed PC-nonp can control for population stratification well in all scenarios, while existing methods cannot control for population stratification at least in some scenarios. Simulations also show that PC-nonp's robustness to population stratification will not reduce power. Furthermore, we illustrate our proposed method by using whole genome sequencing data from genetic analysis workshop 18 (GAW18).

Testing rare variants for hypertension using family-based tests with different weighting schemes

Next-generation sequencing technology makes directly testing rare variants possible. However, existing statistical methods to detect common variants may not be optimal for testing rare variants because of allelic heterogeneity as well as the extreme rarity of individual variants. Recently, several statistical methods to detect associations of rare variants were developed, including population-based and family-based methods. Compared with population-based methods, family-based methods have more power and can prevent bias induced by population substructure. Both population-based and family-based methods for rare variant association studies are essentially testing the effect of a weighted combination of variants or its function. How to model the weights is critical for the testing power because the number of observations for any given rare variant is small and the multiple-test correction is more stringent for rare variants. We propose 4 weighting schemes for the family-based rare variants test (FBAT-v) to test for the effects of both rare and common variants across the genome. Applying FBAT-v with the proposed weighting schemes on the Genetic Analysis Workshop 19 family data indicates that the power of FBAT-v can be comparatively enhanced in most circumstances.

Poisson Approximation-Based Score Test for Detecting Association of Rare Variants

Genome-wide association study (GWAS) has achieved great success in identifying genetic variants, but the nature of GWAS has determined its inherent limitations. Under the common disease rare variants (CDRV) hypothesis, the traditional association analysis methods commonly used in GWAS for common variants do not have enough power for detecting rare variants with a limited sample size. As a solution to this problem, pooling rare variants by their functions provides an efficient way for identifying susceptible genes. Rare variant typically have low frequencies of minor alleles, and the distribution of the total number of minor alleles of the rare variants can be approximated by a Poisson distribution. Based on this fact, we propose a new test method, the Poisson Approximation-based Score Test (PAST), for association analysis of rare variants. Two testing methods, namely, ePAST and mPAST, are proposed based on different strategies of pooling rare variants. Simulation results and application to the CRESCENDO cohort data show that our methods are more powerful than the existing methods.

Joint Analysis of Multiple Traits in Rare Variant Association Studies

The joint analysis of multiple traits has recently become popular since it can increase statistical power to detect genetic variants and there is increasing evidence showing that pleiotropy is a widespread phenomenon in complex diseases. Currently, the majority of existing methods for the joint analysis of multiple traits test association between one common variant and multiple traits. However, the variant-by-variant methods for common variant association studies may not be optimal for rare variant association studies due to the allelic heterogeneity as well as the extreme rarity of individual variants. Current statistical methods for rare variant association studies are for one single trait only. In this paper, we propose an adaptive weighting reverse regression (AWRR) method to test association between multiple traits and rare variants in a genomic region. AWRR is robust to the directions of effects of causal variants and is also robust to the directions of association of traits. Using extensive simulation studies, we compare the performance of AWRR with canonical correlation analysis (CCA), Single-TOW, and the weighted sum reverse regression (WSRR). Our results show that, in all of the simulation scenarios, AWRR is consistently more powerful than CCA. In most scenarios, AWRR is more powerful than Single-TOW and WSRR.

Joint Analysis of Multiple Traits Using "Optimal" Maximum Heritability Test

The joint analysis of multiple traits has recently become popular since it can increase statistical power to detect genetic variants and there is increasing evidence showing that pleiotropy is a widespread phenomenon in complex diseases. Currently, most of existing methods use all of the traits for testing the association between multiple traits and a single variant. However, those methods for association studies may lose power in the presence of a large number of noise traits. In this paper, we propose an “optimal” maximum heritability test (MHT-O) to test the association between multiple traits and a single variant. MHT-O includes a procedure of deleting traits that have weak or no association with the variant. Using extensive simulation studies, we compare the performance of MHT-O with MHT, Trait-based Association Test uses Extended Simes procedure (TATES), SUM_SCORE and MANOVA. Our results show that, in all of the simulation scenarios, MHT-O is either the most powerful test or comparable to the most powerful test among the five tests we compared.

Detecting the Common and Individual Effects of Rare Variants on Quantitative Traits by Using Extreme Phenotype Sampling

Next-generation sequencing technology has made it possible to detect rare genetic variants associated with complex human traits. In recent literature, various methods specifically designed for rare variants are proposed. These tests can be broadly classified into burden and nonburden tests. In this paper, we take advantage of the burden and nonburden tests, and consider the common effect and the individual deviations from the common effect. To achieve robustness, we use two methods of combining p-values, Fisher's method and the minimum-p method. In rare variant association studies, to improve the power of the tests, we explore the advantage of the extreme phenotype sampling. At first, we dichotomize the continuous phenotypes before analysis, and the two extremes are treated as two different groups representing a dichotomous phenotype. We next compare the powers of several methods based on extreme phenotype sampling and random sampling. Extensive simulation studies show that our proposed methods by using extreme phenotype sampling are the most powerful or very close to the most powerful one in various settings of true models when the same sample size is used.

Detecting association of rare and common variants by adaptive combination of P-values

Genome-wide association studies (GWAS) can detect common variants associated with diseases. Next generation sequencing technology has made it possible to detect rare variants. Most of association tests, including burden tests and nonburden tests, mainly target rare variants by upweighting rare variant effects and downweighting common variant effects. But there is increasing evidence that complex diseases are caused by both common and rare variants. In this paper, we extend the ADA method (adaptive combination of P-values; Lin et al., 2014) for rare variants only and propose a RC-ADA method (common and rare variants by adaptive combination of P-values). Our proposed method combines the per-site P-values with the weights based on minor allele frequencies (MAFs). The RC-ADA is robust to directions of effects of causal variants and inclusion of a high proportion of neutral variants. The performance of the RC-ADA method is compared with several other association methods. Extensive simulation studies show that the RC-ADA method is more powerful than other association methods over a wide range of models.

Permutation testing in the presence of polygenic variation

This article discusses problems with and solutions to performing valid permutation tests for quantitative trait loci in the presence of polygenic effects. Although permutation testing is a popular approach for determining statistical significance of a test statistic with an unknown distribution--for instance, the maximum of multiple correlated statistics or some omnibus test statistic for a gene, gene-set, or pathway--naive application of permutations may result in an invalid test. The risk of performing an invalid permutation test is particularly acute in complex trait mapping where polygenicity may combine with a structured population resulting from the presence of families, cryptic relatedness, admixture, or population stratification. I give both analytical derivations and a conceptual understanding of why typical permutation procedures fail and suggest an alternative permutation-based algorithm, MVNpermute, that succeeds. In particular, I examine the case where a linear mixed model is used to analyze a quantitative trait and show that both phenotype and genotype permutations may result in an invalid permutation test. I provide a formula that predicts the amount of inflation of the type 1 error rate depending on the degree of misspecification of the covariance structure of the polygenic effect and the heritability of the trait. I validate this formula by doing simulations, showing that the permutation distribution matches the theoretical expectation, and that my suggested permutation-based test obtains the correct null distribution. Finally, I discuss situations where naive permutations of the phenotype or genotype are valid and the applicability of the results to other test statistics.

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.

Longitudinal data analysis for genetic studies in the whole-genome sequencing era

The analysis of whole-genome sequence (WGS) data using longitudinal phenotypes offers a potentially rich resource for the examination of the genetic variants and their covariates that affect complex phenotypes over time. We summarize eight contributions to the Genetic Analysis Workshop 18, which applied a diverse array of statistical genetic methods to analyze WGS data in combination with data from genome-wide association studies (GWAS) from up to four different time points on blood pressure phenotypes. The common goal of these analyses was to develop and apply appropriate methods that utilize longitudinal repeated measures to potentially increase the analytic efficiency of WGS and GWAS data. These diverse methods can be grouped into two categories, based on the way they model dependence structures: (1) linear mixed-effects (LME) models, where the random effect terms in the linear models are used to capture the dependence structures; and (2) variance-components models, where the dependence structures are constructed directly based on multiple components of variance-covariance matrices for the multivariate Gaussian responses. Despite the heterogeneous nature of these analytical methods, the group came to the following conclusions: (1) the use of repeat measurements can gain power to identify variants associated with the phenotype; (2) the inclusion of family data may correct genotyping errors and allow for more accurate detection of rare variants than using unrelated individuals only; and (3) fitting mixed-effects and variance-components models for longitudinal data presents computational challenges. The challenges and computational burden demanded by WGS data were addressed in the eight contributions.