An evolutionary framework for association testing in resequencing studies

Rare variant association on unrelated individuals in case-control studies using aggregation tests: existing methods and current limitations

Over the past years, progress made in next-generation sequencing technologies and bioinformatics have sparked a surge in association studies. Especially, genome-wide association studies (GWASs) have demonstrated their effectiveness in identifying disease associations with common genetic variants. Yet, rare variants can contribute to additional disease risk or trait heterogeneity. Because GWASs are underpowered for detecting association with such variants, numerous statistical methods have been recently proposed. Aggregation tests collapse multiple rare variants within a genetic region (e.g. gene, gene set, genomic loci) to test for association. An increasing number of studies using such methods successfully identified trait-associated rare variants and led to a better understanding of the underlying disease mechanism. In this review, we compare existing aggregation tests, their statistical features and scope of application, splitting them into the five classical classes: burden, adaptive burden, variance-component, omnibus and other. Finally, we describe some limitations of current aggregation tests, highlighting potential direction for further investigations.

Evolutionary perspectives on polygenic selection, missing heritability, and GWAS

Genome-wide association studies (GWAS) have successfully identified many trait-associated variants, but there is still much we do not know about the genetic basis of complex traits. Here, we review recent theoretical and empirical literature regarding selection on complex traits to argue that "missing heritability" is as much an evolutionary problem as it is a statistical problem. We discuss empirical findings that suggest a role for selection in shaping the effect sizes and allele frequencies of causal variation underlying complex traits, and the limitations of these studies. We then use simulations of selection, realistic genome structure, and complex human demography to illustrate the results of recent theoretical work on polygenic selection, and show that statistical inference of causal loci is sharply affected by evolutionary processes. In particular, when selection acts on causal alleles, it hampers the ability to detect causal loci and constrains the transferability of GWAS results across populations. Last, we discuss the implications of these findings for future association studies, and suggest that future statistical methods to infer causal loci for genetic traits will benefit from explicit modeling of the joint distribution of effect sizes and allele frequencies under plausible evolutionary models.

The impact of rare and low-frequency genetic variants in common disease

Despite thousands of genetic loci identified to date, a large proportion of genetic variation predisposing to complex disease and traits remains unaccounted for. Advances in sequencing technology enable focused explorations on the contribution of low-frequency and rare variants to human traits. Here we review experimental approaches and current knowledge on the contribution of these genetic variants in complex disease and discuss challenges and opportunities for personalised medicine.

Tree-based quantitative trait mapping in the presence of external covariates

A central goal in biological and biomedical sciences is to identify the molecular basis of variation in morphological and behavioral traits. Over the last decade, improvements in sequencing technologies coupled with the active development of association mapping methods have made it possible to link single nucleotide polymorphisms (SNPs) and quantitative traits. However, a major limitation of existing methods is that they are often unable to consider complex, but biologically-realistic, scenarios. Previous work showed that association mapping method performance can be improved by using the evolutionary history within each SNP to estimate the covariance structure among randomly-sampled individuals. Here, we propose a method that can be used to analyze a variety of data types, such as data including external covariates, while considering the evolutionary history among SNPs, providing an advantage over existing methods. Existing methods either do so at a computational cost, or fail to model these relationships altogether. By considering the broad-scale relationships among SNPs, the proposed approach is both computationally-feasible and informed by the evolutionary history among SNPs. We show that incorporating an approximate covariance structure during analysis of complex data sets increases performance in quantitative trait mapping, and apply the proposed method to deer mice data.

Selection and explosive growth alter genetic architecture and hamper the detection of causal rare variants

The role of rare alleles in complex phenotypes has been hotly debated, but most rare variant association tests (RVATs) do not account for the evolutionary forces that affect genetic architecture. Here, we use simulation and numerical algorithms to show that explosive population growth, as experienced by human populations, can dramatically increase the impact of very rare alleles on trait variance. We then assess the ability of RVATs to detect causal loci using simulations and human RNA-seq data. Surprisingly, we find that statistical performance is worst for phenotypes in which genetic variance is due mainly to rare alleles, and explosive population growth decreases power. Although many studies have attempted to identify causal rare variants, few have reported novel associations. This has sometimes been interpreted to mean that rare variants make negligible contributions to complex trait heritability. Our work shows that RVATs are not robust to realistic human evolutionary forces, so general conclusions about the impact of rare variants on complex traits may be premature.

Association Tests for Rare Variants

Over the past few years, interest in the identification of rare variants that influence human phenotype has led to the development of many statistical methods for testing for association between sets of rare variants and binary or quantitative traits. Here, I review some of the most important ideas that underlie these methods and the most relevant issues when choosing a method for analysis. In addition to the tests for association, I review crucial issues in performing a rare variant study, from experimental design to interpretation and validation. I also discuss the many challenges of these studies, some of their limitations, and future research directions.

Prevalence estimation for monogenic autosomal recessive diseases using population-based genetic data

Genetic methods can complement epidemiological surveys and clinical registries in determining prevalence of monogenic autosomal recessive diseases. Several large population-based genetic databases, such as the NHLBI GO Exome Sequencing Project, are now publically available. By assuming Hardy-Weinberg equilibrium, the frequency of individuals homozygous in the general population for a particular pathogenic allele can be directly calculated from a sample of chromosomes where some harbor the pathogenic allele. Further assuming that the penetrance of the pathogenic allele(s) is known, the prevalence of recessive phenotypes can be determined. Such work can inform public health efforts for rare recessive diseases. A Bayesian estimation procedure has yet to be applied to the problem of estimating disease prevalence from large population-based genetic data. A Bayesian framework is developed to derive the posterior probability density of monogenic, autosomal recessive phenotypes. Explicit equations are presented for the credible intervals of these disease prevalence estimates. A primary impediment to performing accurate disease prevalence calculations is the determination of truly pathogenic alleles. This issue is discussed, but in many instances remains a significant barrier to investigations solely reliant on statistical interrogation--functional studies can provide important information for solidifying evidence of variant pathogenicity. We also discuss several challenges to these efforts, including the population structure in the sample of chromosomes, the treatment of allelic heterogeneity, and reduced penetrance of pathogenic variants. To illustrate the application of these methods, we utilized recently published genetic data collected on a large sample from the Schmiedeleut Hutterites. We estimate prevalence and calculate 95% credible intervals for 13 autosomal recessive diseases using these data. In addition, the Bayesian estimation procedure is applied to data from a central European study of hereditary fructose intolerance. The methods described herein show a viable path to robustly estimating both the expected prevalence of autosomal recessive phenotypes and corresponding credible intervals using population-based genetic databases that have recently become available. As these genetic databases increase in number and size with the advent of cost-effective next-generation sequencing, we anticipate that these methods and approaches may be helpful in recessive disease prevalence calculations, potentially impacting public health management, health economic analyses, and treatment of rare diseases.

Population genetic simulations of complex phenotypes with implications for rare variant association tests

Demographic events and natural selection alter patterns of genetic variation within populations and may play a substantial role in shaping the genetic architecture of complex phenotypes and disease. However, the joint impact of these basic evolutionary forces is often ignored in the assessment of statistical tests of association. Here, we provide a simulation-based framework for generating DNA sequences that incorporates selection and demography with flexible models for simulating phenotypic variation (sfs_coder). This tool also allows the user to perform locus-specific simulations by automatically querying annotated genomic functional elements and genetic maps. We demonstrate the effects of evolutionary forces on patterns of genetic variation by simulating recently inferred models of human selection and demography. We use these simulations to show that the demographic model and locus-specific features, such as the proportion of sites under selection, may have practical implications for estimating the statistical power of sequencing-based rare variant association tests. In particular, for some phenotype models, there may be higher power to detect rare variant associations in African populations compared to non-Africans, but power is considerably reduced in regions of the genome with rampant negative selection. Furthermore, we show that existing methods for simulating large samples based on resampling from a small set of observed haplotypes fail to recapitulate the distribution of rare variants in the presence of rapid population growth (as has been observed in several human populations).

GWAS to Sequencing: Divergence in Study Design and Analysis

The success of genome-wide association studies (GWAS) in uncovering genetic risk factors for complex traits has generated great promise for the complete data generated by sequencing. The bumpy transition from GWAS to whole-exome or whole-genome association studies (WGAS) based on sequencing investigations has highlighted important differences in analysis and interpretation. We show how the loss in power due to the allele frequency spectrum targeted by sequencing is difficult to compensate for with realistic effect sizes and point to study designs that may help. We discuss several issues in interpreting the results, including a special case of the winner's curse. Extrapolation and prediction using rare SNPs is complex, because of the selective ascertainment of SNPs in case-control studies and the low amount of information at each SNP, and naive procedures are biased under the alternative. We also discuss the challenges in tuning gene-based tests and accounting for multiple testing when genes have very different sets of SNPs. The examples we emphasize in this paper highlight the difficult road we must travel for a two-letter switch.

Multiple comparisons in genetic association studies: a hierarchical modeling approach

Multiple comparisons or multiple testing has been viewed as a thorny issue in genetic association studies aiming to detect disease-associated genetic variants from a large number of genotyped variants. We alleviate the problem of multiple comparisons by proposing a hierarchical modeling approach that is fundamentally different from the existing methods. The proposed hierarchical models simultaneously fit as many variables as possible and shrink unimportant effects towards zero. Thus, the hierarchical models yield more efficient estimates of parameters than the traditional methods that analyze genetic variants separately, and also coherently address the multiple comparisons problem due to largely reducing the effective number of genetic effects and the number of statistically "significant" effects. We develop a method for computing the effective number of genetic effects in hierarchical generalized linear models, and propose a new adjustment for multiple comparisons, the hierarchical Bonferroni correction, based on the effective number of genetic effects. Our approach not only increases the power to detect disease-associated variants but also controls the Type I error. We illustrate and evaluate our method with real and simulated data sets from genetic association studies. The method has been implemented in our freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/).

Evaluating empirical bounds on complex disease genetic architecture

The genetic architecture of human diseases governs the success of genetic mapping and the future of personalized medicine. Although numerous studies have queried the genetic basis of common disease, contradictory hypotheses have been advocated about features of genetic architecture (for example, the contribution of rare versus common variants). We developed an integrated simulation framework, calibrated to empirical data, to enable the systematic evaluation of such hypotheses. For type 2 diabetes (T2D), two simple parameters--(i) the target size for causal mutation and (ii) the coupling between selection and phenotypic effect--define a broad space of architectures. Whereas extreme models are excluded by the combination of epidemiology, linkage and genome-wide association studies, many models remain consistent, including those where rare variants explain either little (<25%) or most (>80%) of T2D heritability. Ongoing sequencing and genotyping studies will further constrain the space of possible architectures, but very large samples (for example, >250,000 unselected individuals) will be required to localize most of the heritability underlying T2D and other traits characterized by these models.

Combined genotype and haplotype tests for region-based association studies

Background

Although single-SNP analysis has proven to be useful in identifying many disease-associated loci, region-based analysis has several advantages. Empirically, it has been shown that region-based genotype and haplotype approaches may possess much higher power than single-SNP statistical tests. Both high quality haplotypes and genotypes may be available for analysis given the development of next generation sequencing technologies and haplotype assembly algorithms.

Results

As generally it is unknown whether genotypes or haplotypes are more relevant for identifying an association, we propose to use both of them with the purpose of preserving high power under both genotype and haplotype disease scenarios. We suggest two approaches for a combined association test and investigate the performance of these two approaches based on a theoretical model, population genetics simulations and analysis of a real data set.

Conclusions

Based on a theoretical model, population genetics simulations and analysis of a central corneal thickness (CCT) Genome Wide Association Study (GWAS) data set we have shown that combined genotype and haplotype approach has a high potential utility for applications in association studies.

Bayesian detection of causal rare variants under posterior consistency

Identification of causal rare variants that are associated with complex traits poses a central challenge on genome-wide association studies. However, most current research focuses only on testing the global association whether the rare variants in a given genomic region are collectively associated with the trait. Although some recent work, e.g., the Bayesian risk index method, have tried to address this problem, it is unclear whether the causal rare variants can be consistently identified by them in the small-n-large-P situation. We develop a new Bayesian method, the so-called Bayesian Rare Variant Detector (BRVD), to tackle this problem. The new method simultaneously addresses two issues: (i) (Global association test) Are there any of the variants associated with the disease, and (ii) (Causal variant detection) Which variants, if any, are driving the association. The BRVD ensures the causal rare variants to be consistently identified in the small-n-large-P situation by imposing some appropriate prior distributions on the model and model specific parameters. The numerical results indicate that the BRVD is more powerful for testing the global association than the existing methods, such as the combined multivariate and collapsing test, weighted sum statistic test, RARECOVER, sequence kernel association test, and Bayesian risk index, and also more powerful for identification of causal rare variants than the Bayesian risk index method. The BRVD has also been successfully applied to the Early-Onset Myocardial Infarction (EOMI) Exome Sequence Data. It identified a few causal rare variants that have been verified in the literature.

A unified mixed-effects model for rare-variant association in sequencing studies

For rare-variant association analysis, due to extreme low frequencies of these variants, it is necessary to aggregate them by a prior set (e.g., genes and pathways) in order to achieve adequate power. In this paper, we consider hierarchical models to relate a set of rare variants to phenotype by modeling the effects of variants as a function of variant characteristics while allowing for variant-specific effect (heterogeneity). We derive a set of two score statistics, testing the group effect by variant characteristics and the heterogeneity effect. We make a novel modification to these score statistics so that they are independent under the null hypothesis and their asymptotic distributions can be derived. As a result, the computational burden is greatly reduced compared with permutation-based tests. Our approach provides a general testing framework for rare variants association, which includes many commonly used tests, such as the burden test [Li and Leal, 2008] and the sequence kernel association test [Wu et al., 2011], as special cases. Furthermore, in contrast to these tests, our proposed test has an added capacity to identify which components of variant characteristics and heterogeneity contribute to the association. Simulations under a wide range of scenarios show that the proposed test is valid, robust, and powerful. An application to the Dallas Heart Study illustrates that apart from identifying genes with significant associations, the new method also provides additional information regarding the source of the association. Such information may be useful for generating hypothesis in future studies.

Population genetics of rare variants and complex diseases

OBJECTIVES

Identifying drivers of complex traits from the noisy signals of genetic variation obtained from high-throughput genome sequencing technologies is a central challenge faced by human geneticists today. We hypothesize that the variants involved in complex diseases are likely to exhibit non-neutral evolutionary signatures. Uncovering the evolutionary history of all variants is therefore of intrinsic interest for complex disease research. However, doing so necessitates the simultaneous elucidation of the targets of natural selection and population-specific demographic history.

METHODS

Here we characterize the action of natural selection operating across complex disease categories, and use population genetic simulations to evaluate the expected patterns of genetic variation in large samples. We focus on populations that have experienced historical bottlenecks followed by explosive growth (consistent with many human populations), and describe the differences between evolutionarily deleterious mutations and those that are neutral.

RESULTS

Genes associated with several complex disease categories exhibit stronger signatures of purifying selection than non-disease genes. In addition, loci identified through genome-wide association studies of complex traits also exhibit signatures consistent with being in regions recurrently targeted by purifying selection. Through simulations, we show that population bottlenecks and rapid growth enable deleterious rare variants to persist at low frequencies just as long as neutral variants, but low-frequency and common variants tend to be much younger than neutral variants. This has resulted in a large proportion of modern-day rare alleles that have a deleterious effect on function and that potentially contribute to disease susceptibility.

CONCLUSIONS

The key question for sequencing-based association studies of complex traits is how to distinguish between deleterious and benign genetic variation. We used population genetic simulations to uncover patterns of genetic variation that distinguish these two categories, especially derived allele age, thereby providing inroads into novel methods for characterizing rare genetic variation driving complex diseases.

Marbled inflation from population structure in gene-based association studies with rare variants

Accurate genetic association studies are crucial for the detection and the validation of disease determinants. One of the main confounding factors that affect accuracy is population stratification, and great efforts have been extended for the past decade to detect and to adjust for it. We have now efficient solutions for population stratification adjustment for single-SNP (where SNP is single-nucleotide polymorphisms) inference in genome-wide association studies, but it is unclear whether these solutions can be effectively applied to rare variation studies and in particular gene-based (or set-based) association methods that jointly analyze multiple rare and common variants. We examine here, both theoretically and empirically, the performance of two commonly used approaches for population stratification adjustment-genomic control and principal component analysis-when used on gene-based association tests. We show that, different from single-SNP inference, genes with diverse composition of rare and common variants may suffer from population stratification to various extent. The inflation in gene-level statistics could be impacted by the number and the allele frequency spectrum of SNPs in the gene, and by the gene-based testing method used in the analysis. As a consequence, using a universal inflation factor as a genomic control should be avoided in gene-based inference with sequencing data. We also demonstrate that caution needs to be exercised when using principal component adjustment because the accuracy of the adjusted analyses depends on the underlying population substructure, on the way the principal components are constructed, and on the number of principal components used to recover the substructure.

Properties and modeling of GWAS when complex disease risk is due to non-complementing, deleterious mutations in genes of large effect

Current genome-wide association studies (GWAS) have high power to detect intermediate frequency SNPs making modest contributions to complex disease, but they are underpowered to detect rare alleles of large effect (RALE). This has led to speculation that the bulk of variation for most complex diseases is due to RALE. One concern with existing models of RALE is that they do not make explicit assumptions about the evolution of a phenotype and its molecular basis. Rather, much of the existing literature relies on arbitrary mapping of phenotypes onto genotypes obtained either from standard population-genetic simulation tools or from non-genetic models. We introduce a novel simulation of a 100-kilobase gene region, based on the standard definition of a gene, in which mutations are unconditionally deleterious, are continuously arising, have partially recessive and non-complementing effects on phenotype (analogous to what is widely observed for most Mendelian disorders), and are interspersed with neutral markers that can be genotyped. Genes evolving according to this model exhibit a characteristic GWAS signature consisting of an excess of marginally significant markers. Existing tests for an excess burden of rare alleles in cases have low power while a simple new statistic has high power to identify disease genes evolving under our model. The structure of linkage disequilibrium between causative mutations and significantly associated markers under our model differs fundamentally from that seen when rare causative markers are assumed to be neutral. Rather than tagging single haplotypes bearing a large number of rare causative alleles, we find that significant SNPs in a GWAS tend to tag single causative mutations of small effect relative to other mutations in the same gene. Our results emphasize the importance of evaluating the power to detect associations under models that are genetically and evolutionarily motivated.

Current GWA studies typically only explain a small fraction of heritable variation in complex traits, resulting in speculation that a large fraction of variation in such traits may be due to rare alleles of large effect (RALE). The most parsimonious evolutionary mechanism that results in an inverse relationship between the frequency and effect size of causative alleles is an equilibrium between newly arising deleterious mutations and selection eliminating those mutations, resulting in an inverse relation between effect size and average frequency. This assumption is not built into many current models of RALE and, as a result, power calculations may be misleading. We use forward population genetic simulations to explore the ability of GWAS to detect genes in which unconditionally deleterious, partially recessive mutations arise each generation. Our model is based on the standard definition of a gene as a region within which loss-of-function mutations fail to complement, consistent with the multi-allelic basis for Mendelian disorders. Our model predicts that it may not be uncommon for single genes evolving under our model to contribute upwards of 5% to variation in a complex trait, and that such genes could be routinely detected via modified GWAS approaches.

Family-based association tests for sequence data, and comparisons with population-based association tests

Recent advances in high-throughput sequencing technologies make it increasingly more efficient to sequence large cohorts for many complex traits. We discuss here a class of sequence-based association tests for family-based designs that corresponds naturally to previously proposed population-based tests, including the classical Burden and variance-component tests. This framework allows for a direct comparison between the powers of sequence-based association tests with family- vs population-based designs. We show that for dichotomous traits using family-based controls results in similar power levels as the population-based design (although at an increased sequencing cost for the family-based design), while for continuous traits (in random samples, no ascertainment) the population-based design can be substantially more powerful. A possible disadvantage of population-based designs is that they can lead to increased false-positive rates in the presence of population stratification, while the family-based designs are robust to population stratification. We show also an application to a small exome-sequencing family-based study on autism spectrum disorders. The tests are implemented in publicly available software.

A hybrid likelihood model for sequence-based disease association studies

In the past few years, case-control studies of common diseases have shifted their focus from single genes to whole exomes. New sequencing technologies now routinely detect hundreds of thousands of sequence variants in a single study, many of which are rare or even novel. The limitation of classical single-marker association analysis for rare variants has been a challenge in such studies. A new generation of statistical methods for case-control association studies has been developed to meet this challenge. A common approach to association analysis of rare variants is the burden-style collapsing methods to combine rare variant data within individuals across or within genes. Here, we propose a new hybrid likelihood model that combines a burden test with a test of the position distribution of variants. In extensive simulations and on empirical data from the Dallas Heart Study, the new model demonstrates consistently good power, in particular when applied to a gene set (e.g., multiple candidate genes with shared biological function or pathway), when rare variants cluster in key functional regions of a gene, and when protective variants are present. When applied to data from an ongoing sequencing study of bipolar disorder (191 cases, 107 controls), the model identifies seven gene sets with nominal p-values0.05, of which one MAPK signaling pathway (KEGG) reaches trend-level significance after correcting for multiple testing.

Inexpensive, high-throughput sequencing has transformed the field of case-control association studies. For the first time, it may be possible to identify the genetic underpinnings of complex diseases, by sequencing the DNA of hundreds (even thousands) of cases and controls and comparing patterns of DNA sequence variation. However, complex diseases are likely to be caused by many variants, some of which are very rare. Taken one at a time, the association between variant and disease phenotype may not be detectable by current statistical methods. One strategy is to identify regions where important variants occur by “collapsing” variants into groups. Here, we present a new collapsing approach, capable of detecting subtle genetic differences between cases and controls. We show, in extensive simulations and using a benchmark set of genes involved in human triglyceride levels, that the approach is potentially more powerful than existing methods. We apply the new method to an ongoing sequencing study of bipolar cases and controls and identify a set of genes found in neuronal synapses, which may be implicated in bipolar disorder.

Comparison of similarity-based tests and pooling strategies for rare variants

Background

As several rare genomic variants have been shown to affect common phenotypes, rare variants association analysis has received considerable attention. Several efficient association tests using genotype and phenotype similarity measures have been proposed in the literature. The major advantages of similarity-based tests are their ability to accommodate multiple types of DNA variations within one association test, and to account for the possible interaction within a region. However, not much work has been done to compare the performance of similarity-based tests on rare variants association scenarios, especially when applied with different rare variants pooling strategies.

Results

Based on the population genetics simulations and analysis of a publicly-available sequencing data set, we compared the performance of four similarity-based tests and two rare variants pooling strategies. We showed that weighting approach outperforms collapsing under the presence of strong effect from rare variants and under the presence of moderate effect from common variants, whereas collapsing of rare variants is preferable when common variants possess a strong effect. We also demonstrated that the difference in statistical power between the two pooling strategies may be substantial. The results also highlighted consistently high power of two similarity-based approaches when applied with an appropriate pooling strategy.

Conclusions

Population genetics simulations and sequencing data set analysis showed high power of two similarity-based tests and a substantial difference in power between the two pooling strategies.

Quantitative trait locus analysis for next-generation sequencing with the functional linear models

BACKGROUND

Although in the past few years we have witnessed the rapid development of novel statistical methods for association studies of qualitative traits using next generation sequencing (NGS) data, only a few statistics are proposed for testing the association of rare variants with quantitative traits. The quantitative trait locus (QTL) analysis of rare variants remains challenging. Analysis from low dimensional data to high dimensional genomic data demands changes in statistical methods from multivariate data analysis to functional data analysis.

METHODS

We propose a functional linear model (FLM) as a general principle for developing novel and powerful QTL analysis methods designed for resequencing data. By simulations we calculated the type I error rates and evaluated the power of the FLM and other eight existing statistical methods, even in the presence of both positive and negative signs of effects.

RESULTS

Since the FLM retains all of the genetic information in the data and explores the merits of both variant-by-variant and collective analysis and overcomes their limitation, the FLM has a much higher power than other existing statistics in all the scenarios considered. To evaluate its performance further, the FLM was applied to association analysis of six quantitative traits in the Dallas Heart Study, and RNA-seq eQTL analysis with genetic variation in the low coverage resequencing data of the 1000 Genomes Project. Real data analysis showed that the FLM had much smaller p values to identify significantly associated variants than other existing methods.

CONCLUSIONS

The FLM is expected to open a new route for QTL analysis.

An exponential combination procedure for set-based association tests in sequencing studies

State-of-the-art next-generation-sequencing technologies can facilitate in-depth explorations of the human genome by investigating both common and rare variants. For the identification of genetic factors that are associated with disease risk or other complex phenotypes, methods have been proposed for jointly analyzing variants in a set (e.g., all coding SNPs in a gene). Variants in a properly defined set could be associated with risk or phenotype in a concerted fashion, and by accumulating information from them, one can improve power to detect genetic risk factors. Many set-based methods in the literature are based on statistics that can be written as the summation of variant statistics. Here, we propose taking the summation of the exponential of variant statistics as the set summary for association testing. From both Bayesian and frequentist perspectives, we provide theoretical justification for taking the sum of the exponential of variant statistics because it is particularly powerful for sparse alternatives-that is, compared with the large number of variants being tested in a set, only relatively few variants are associated with disease risk-a distinctive feature of genetic data. We applied the exponential combination gene-based test to a sequencing study in anticancer pharmacogenomics and uncovered mechanistic insights into genes and pathways related to chemotherapeutic susceptibility for an important class of oncologic drugs.

Smoothed functional principal component analysis for testing association of the entire allelic spectrum of genetic variation

Fast and cheaper next-generation sequencing technologies will generate unprecedentedly massive and highly dimensional genetic variation data that allow nearly complete evaluation of genetic variation including both common and rare variants. There are two types of association tests: variant-by-variant test and group test. The variant-by-variant test is designed to test the association of common variants, while the group test is suitable to collectively test the association of multiple rare variants. We propose here a smoothed functional principal component analysis (SFPCA) statistic as a general approach for testing association of the entire allelic spectrum of genetic variation (both common and rare variants), which utilizes the merits of both variant-by-variant analysis and group tests. By intensive simulations, we demonstrate that the SFPCA statistic has the correct type 1 error rates and much higher power than the existing methods to detect association of (1) common variants, (2) rare variants, (3) both common and rare variants and (4) variants with opposite directions of effects. To further evaluate its performance, the SFPCA statistic is applied to ANGPTL4 sequence and six continuous phenotypes data from the Dallas Heart Study as an example for testing association of rare variants and a GWAS of schizophrenia data as an example for testing association of common variants. The results show that the SFPCA statistic has much smaller P-values than many existing statistics in both real data analysis examples.

Haplotype-based methods for detecting uncommon causal variants with common SNPs

Detecting uncommon causal variants (minor allele frequency [MAF] < 5%) is difficult with commercial single-nucleotide polymorphism (SNP) arrays that are designed to capture common variants (MAF > 5%). Haplotypes can provide insights into underlying linkage disequilibrium (LD) structure and can tag uncommon variants that are not well tagged by common variants. In this work, we propose a wei-SIMc-matching test that inversely weights haplotype similarities with the estimated standard deviation of haplotype counts to boost the power of similarity-based approaches for detecting uncommon causal variants. We then compare the power of the wei-SIMc-matching test with that of several popular haplotype-based tests, including four other similarity-based tests, a global score test for haplotypes (global), a test based on the maximum score statistic over all haplotypes (max), and two newly proposed haplotype-based tests for rare variant detection. With systematic simulations under a wide range of LD patterns, the results show that wei-SIMc-matching and global are the two most powerful tests. Among these two tests, wei-SIMc-matching has reliable asymptotic P-values, whereas global needs permutations to obtain reliable P-values when the frequencies of some haplotype categories are low or when the trait is skewed. Therefore, we recommend wei-SIMc-matching for detecting uncommon causal variants with surrounding common SNPs, in light of its power and computational feasibility.

Scan-statistic approach identifies clusters of rare disease variants in LRP2, a gene linked and associated with autism spectrum disorders, in three datasets

Cluster-detection approaches, commonly used in epidemiology and astronomy, can be applied in the context of genetic sequence data for the identification of genetic regions significantly enriched with rare disease-risk variants (DRVs). Unlike existing association tests for sequence data, the goal of cluster-detection methods is to localize significant disease mutation clusters within a gene or region of interest. Here, we focus on a chromosome 2q replicated linkage region that is associated with autism spectrum disorder (ASD) and that has been sequenced in three independent datasets. We found that variants in one gene, LRP2, residing on 2q are associated with ASD in two datasets (the combined variable-threshold-test p value is 1.2 × 10(-5)). Using a cluster-detection method, we show that in the discovery and replication datasets, variants associated with ASD cluster preponderantly in 25 kb windows (adjusted p values are p(1) = 0.003 and p(2) = 0.002), and the two windows are highly overlapping. Furthermore, for the third dataset, a 25 kb region similar to those in the other two datasets shows significant evidence of enrichment of rare DRVs. The region implicated by all three studies is involved in ligand binding, suggesting that subtle alterations in either LRP2 expression or LRP2 primary sequence modulate the uptake of LRP2 ligands. BMP4 is a ligand of particular interest given its role in forebrain development, and modest changes in BMP4 binding, which binds to LRP2 near the mutation cluster, might subtly affect development and could lead to autism-associated phenotypes.

A unified framework for detecting rare variant quantitative trait associations in pedigree and unrelated individuals via sequence data

OBJECTIVES

There is great interest to sequence unrelated or pedigree samples for detecting rare variant quantitative trait associations. In order to reduce the cost of sequencing and improve power, many studies sequence selected samples with extreme traits. Existing methods for detecting rare variant associations were developed for unrelated samples. Methods are needed to analyze (selected or randomly ascertained) pedigree samples.

METHODS

We propose a unified framework of modeling extreme trait genetic associations (MEGA) with rare variants. Using MEGA and appropriate permutation algorithms, many rare variant tests can be extended to family data. As an application, we compared study designs using both sib-pairs and unrelated individuals. Extensive simulations were carried out using realistic population genetic and complex trait models.

RESULTS

It is demonstrated that when extreme sampling is implemented within equal-sized cohorts of unrelated individuals or sib-pairs, analyzing unrelated individuals is consistently more powerful than studying sib-pairs. A higher portion of rare variants can be identified through sequencing unrelated samples compared to sibs. Alternatively, if samples are ascertained using fixed thresholds from an infinite-sized population, sequencing one sib with the most extreme trait from each extreme concordant sib-pair is consistently the most powerful design.

CONCLUSIONS

MEGA will play an important role in the analysis of sequence-based genetic association studies.

Host genes important to HIV replication and evolution

Recent years have seen a significant increase in understanding of the host genetic and genomic determinants of susceptibility to HIV-1 infection and disease progression, driven in large part by candidate gene studies, genome-wide association studies, genome-wide transcriptome analyses, and large-scale in vitro genome screens. These studies have identified common variants in some host loci that clearly influence disease progression, characterized the scale and dynamics of gene and protein expression changes in response to infection, and provided the first comprehensive catalogs of genes and pathways involved in viral replication. Experimental models of AIDS and studies in natural hosts of primate lentiviruses have complemented and in some cases extended these findings. As the relevant technology continues to progress, the expectation is that such studies will increase in depth (e.g., to include host whole exome and whole genome sequencing) and in breadth (in particular, by integrating multiple data types).

Next-generation sequencing approaches for genetic mapping of complex diseases

The advent of next generation sequencing technologies has opened new possibilities in the analysis of human disease. In this review we present the main next-generation sequencing technologies, with their major contributions and possible applications to the study of the genetic etiology of complex diseases.

A powerful test for multiple rare variants association studies that incorporates sequencing qualities

Next-generation sequencing data will soon become routinely available for association studies between complex traits and rare variants. Sequencing data, however, are characterized by the presence of sequencing errors at each individual genotype. This makes it especially challenging to perform association studies of rare variants, which, due to their low minor allele frequencies, can be easily perturbed by genotype errors. In this article, we develop the quality-weighted multivariate score association test (qMSAT), a new procedure that allows powerful association tests between complex traits and multiple rare variants under the presence of sequencing errors. Simulation results based on quality scores from real data show that the qMSAT often dominates over current methods, that do not utilize quality information. In particular, the qMSAT can dramatically increase power over existing methods under moderate sample sizes and relatively low coverage. Moreover, in an obesity data study, we identified using the qMSAT two functional regions (MGLL promoter and MGLL 3′-untranslated region) where rare variants are associated with extreme obesity. Due to the high cost of sequencing data, the qMSAT is especially valuable for large-scale studies involving rare variants, as it can potentially increase power without additional experimental cost. qMSAT is freely available at http://qmsat.sourceforge.net/.

Finding disease variants in Mendelian disorders by using sequence data: methods and applications

Many sequencing studies are now underway to identify the genetic causes for both Mendelian and complex traits. Via exome-sequencing, genes harboring variants implicated in several Mendelian traits have already been identified. The underlying methodology in these studies is a multistep algorithm based on filtering variants identified in a small number of affected individuals and depends on whether they are novel (not yet seen in public resources such as dbSNP), shared among affected individuals, and other external functional information on the variants. Although intuitive, these filter-based methods are nonoptimal and do not provide any measure of statistical uncertainty. We describe here a formal statistical approach that has several distinct advantages: (1) it provides fast computation of approximate p values for individual genes, (2) it adjusts for the background variation in each gene, (3) it allows for incorporation of functional or linkage-based information, and (4) it accommodates designs based on both affected relative pairs and unrelated affected individuals. We show via simulations that the proposed approach can be used in conjunction with the existing filter-based methods to achieve a substantially better ranking of a gene relevant for disease when compared to currently used filter-based approaches, this is especially so in the presence of disease locus heterogeneity. We revisit recent studies on three Mendelian diseases and show that the proposed approach results in the implicated gene being ranked first in all studies, and approximate p values of 10(-6) for the Miller Syndrome gene, 1.0 × 10(-4) for the Freeman-Sheldon Syndrome gene, and 3.5 × 10(-5) for the Kabuki Syndrome gene.

Hierarchical generalized linear models for multiple groups of rare and common variants: jointly estimating group and individual-variant effects

Complex diseases and traits are likely influenced by many common and rare genetic variants and environmental factors. Detecting disease susceptibility variants is a challenging task, especially when their frequencies are low and/or their effects are small or moderate. We propose here a comprehensive hierarchical generalized linear model framework for simultaneously analyzing multiple groups of rare and common variants and relevant covariates. The proposed hierarchical generalized linear models introduce a group effect and a genetic score (i.e., a linear combination of main-effect predictors for genetic variants) for each group of variants, and jointly they estimate the group effects and the weights of the genetic scores. This framework includes various previous methods as special cases, and it can effectively deal with both risk and protective variants in a group and can simultaneously estimate the cumulative contribution of multiple variants and their relative importance. Our computational strategy is based on extending the standard procedure for fitting generalized linear models in the statistical software R to the proposed hierarchical models, leading to the development of stable and flexible tools. The methods are illustrated with sequence data in gene ANGPTL4 from the Dallas Heart Study. The performance of the proposed procedures is further assessed via simulation studies. The methods are implemented in a freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/).

Comparison of statistical approaches to rare variant analysis for quantitative traits

With recent advances in technology, deep sequencing data will be widely used to further the understanding of genetic influence on traits of interest. Therefore not only common variants but also rare variants need to be better used to exploit the new information provided by deep sequencing data. Recently, statistical approaches for analyzing rare variants in genetic association studies have been proposed, but many of them were designed only for dichotomous outcomes. We compare the type I error and power of several statistical approaches applicable to quantitative traits for collapsing and analyzing rare variant data within a defined gene region. In addition to comparing methods that consider only rare variants, such as indicator, count, and data-adaptive collapsing methods, we also compare methods that incorporate the analysis of common variants along with rare variants, such as CMC and LASSO regression. We find that the three methods used to collapse rare variants perform similarly in this simulation setting where all risk variants were simulated to have effects in the same direction. Further, we find that incorporating common variants is beneficial and using a LASSO regression to choose which common variants to include is most useful when there is are few common risk variants compared to the total number of risk variants.

Association tests for rare and common variants based on genotypic and phenotypic measures of similarity between individuals

Genome-wide association studies have helped us identify thousands of common variants associated with several widespread complex diseases. However, for most traits, these variants account for only a small fraction of phenotypic variance or heritability. Next-generation sequencing technologies are being used to identify additional rare variants hypothesized to have higher effect sizes than the already identified common variants, and to contribute significantly to the fraction of heritability that is still unexplained. Several pooling strategies have been proposed to test the joint association of multiple rare variants, because testing them individually may not be optimal. Within a gene or genomic region, if there are both rare and common variants, testing their joint association may be desirable to determine their synergistic effects. We propose new methods to test the joint association of several rare and common variants with binary and quantitative traits. Our association test for quantitative traits is based on genotypic and phenotypic measures of similarity between pairs of individuals. For the binary trait or case-control samples, we recently proposed an association test based on the genotypic similarity between individuals. Here, we develop a modified version of this test for rare variants. Our tests can be used for samples taken from multiple subpopulations. The power of our test statistics for case-control samples and quantitative traits was evaluated using the GAW17 simulated data sets. Type I error rates for the proposed tests are well controlled. Our tests are able to identify some of the important causal genes in the GAW17 simulated data sets.

Computational and statistical approaches to analyzing variants identified by exome sequencing

New sequencing technology has enabled the identification of thousands of single nucleotide polymorphisms in the exome, and many computational and statistical approaches to identify disease-association signals have emerged.

A general framework for detecting disease associations with rare variants in sequencing studies

Biological and empirical evidence suggests that rare variants account for a large proportion of the genetic contributions to complex human diseases. Recent technological advances in high-throughput sequencing platforms have made it possible for researchers to generate comprehensive information on rare variants in large samples. We provide a general framework for association testing with rare variants by combining mutation information across multiple variant sites within a gene and relating the enriched genetic information to disease phenotypes through appropriate regression models. Our framework covers all major study designs (i.e., case-control, cross-sectional, cohort and family studies) and all common phenotypes (e.g., binary, quantitative, and age at onset), and it allows arbitrary covariates (e.g., environmental factors and ancestry variables). We derive theoretically optimal procedures for combining rare mutations and construct suitable test statistics for various biological scenarios. The allele-frequency threshold can be fixed or variable. The effects of the combined rare mutations on the phenotype can be in the same direction or different directions. The proposed methods are statistically more powerful and computationally more efficient than existing ones. An application to a deep-resequencing study of drug targets led to a discovery of rare variants associated with total cholesterol. The relevant software is freely available.

Incorporating model uncertainty in detecting rare variants: the Bayesian risk index

We are interested in investigating the involvement of multiple rare variants within a given region by conducting analyses of individual regions with two goals: (1) to determine if regional rare variation in aggregate is associated with risk; and (2) conditional upon the region being associated, to identify specific genetic variants within the region that are driving the association. In particular, we seek a formal integrated analysis that achieves both of our goals. For rare variants with low minor allele frequencies, there is very little power to statistically test the null hypothesis of equal allele or genotype counts for each variant. Thus, genetic association studies are often limited to detecting association within a subset of the common genetic markers. However, it is very likely that associations exist for the rare variants that may not be captured by the set of common markers. Our framework aims at constructing a risk index based on multiple rare variants within a region. Our analytical strategy is novel in that we use a Bayesian approach to incorporate model uncertainty in the selection of variants to include in the index as well as the direction of the associated effects. Additionally, the approach allows for inference at both the group and variant-specific levels. Using a set of simulations, we show that our methodology has added power over other popular rare variant methods to detect global associations. In addition, we apply the approach to sequence data from the WECARE Study of second primary breast cancers.

Study designs for identification of rare disease variants in complex diseases: the utility of family-based designs

The recent progress in sequencing technologies makes possible large-scale medical sequencing efforts to assess the importance of rare variants in complex diseases. The results of such efforts depend heavily on the use of efficient study designs and analytical methods. We introduce here a unified framework for association testing of rare variants in family-based designs or designs based on unselected affected individuals. This framework allows us to quantify the enrichment in rare disease variants in families containing multiple affected individuals and to investigate the optimal design of studies aiming to identify rare disease variants in complex traits. We show that for many complex diseases with small values for the overall sibling recurrence risk ratio, such as Alzheimer's disease and most cancers, sequencing affected individuals with a positive family history of the disease can be extremely advantageous for identifying rare disease variants. In contrast, for complex diseases with large values of the sibling recurrence risk ratio, sequencing unselected affected individuals may be preferable.