Advances and challenges in quantitative delineation of the genetic architecture of complex traits

Abstract

Background: Genome-wide association studies (GWAS) have been widely adopted in studies of human complex traits and diseases.

Results: This review surveys areas of active research: quantifying and partitioning trait heritability, fine mapping functional variants and integrative analysis, genetic risk prediction of phenotypes, and the analysis of sequencing studies that have identified millions of rare variants. Current challenges and opportunities are highlighted.

Conclusion: GWAS have fundamentally transformed the field of human complex trait genetics. Novel statistical and computational methods have expanded the scope of GWAS and have provided valuable insights on the genetic architecture underlying complex phenotypes.

Graphical abstract

Keywords

genome-wide association study / heritability / rare variants / biobank / colocalization / eQTL / polygenic risk scores / transcriptome-wide association study

1 INTRODUCTION

Genome-wide association studies (GWAS) have become an essential approach for studying complex traits and diseases. To date, 185,864 statistical associations of single nucleotide polymorphisms (SNPs) with 4,554 complex traits have been summarized in the US National Human Genome Research Institute (NHGRI)–European Bioinformatics Institute (EBI) GWAS Catalog [1] (https://www.ebi.ac.uk/gwas/, accessed May 28, 2020). The past ten years mark a transition into the post-GWAS era, during which studies have expanded both in scale and in scope, catalyzed by the biobank-scale study populations, high-throughput functional genomic data and novel analytic tools. This new phase of research activities is marked by three paradigm shifts. First, stimulated by the mounting evidence that many complex traits are highly polygenic, that is, they are influenced by a large number of genes and variants, recent GWAS have gone beyond gene-phenotype association and strived to depict the overall genetic architecture, broadly defined to include such parameters as the number of trait loci, the distribution of allelic effects, and the mode of actions of these alleles. Second, the observation that most association findings reside in non-coding regions emphasizes the urgent need for a principled framework that informs the biological processes underlying genotype-phenotype associations. Third, whereas early GWAS were powered to identify trait variants that are relatively common, the expanding cohorts and decreasing cost of sequencing have made it feasible to uncover low frequency (1%<minor allele frequency, MAF<5%) and rare variants (MAF<1%). Altogether, these studies have yielded valuable insights regarding the genetic architecture of complex phenotypes in general and have generated testable hypotheses related to the biological mechanisms underlying specific phenotypes [2]. Furthermore, the ability to predict phenotype based on an individual’s genotypes through polygenic risk scores (PRS) holds promise for implementing genomic-based medicine through disease risk stratification, prevention and intervention. This review aims to provide an overview of recent developments in analytic approaches for GWAS in these areas and to highlight challenges in translating GWAS results to biological knowledge and clinical utilities. Other important areas, such as phenome-wide association studies (PheWAS) and causal inference are reviewed elsewhere [3–6].

To set the stage, we summarize basic models and key concepts that will be used subsequently. Detailed explanations can be found in two previous reviews [7,8]. In essence, GWAS seek genomic locations where genetic variation is statistically associated with phenotypes. The vast majority of GWAS methods and analyses consider an underlying generative model, in which a quantitative phenotype (Y) is determined by the genotype of a set of causal variants, G, as well as non-genetic risk factors and covariates, X:

(1)Y=\mu +\Sigma {{\displaystyle \beta }}_m{{\displaystyle G}}_m+\gamma X+\epsilon ,

where \beta represents the allelic genetic effect. This linear additive model can be readily extended into generalized linear models for non-Gaussian phenotypes, such as dichotomized disease status [9].

Initial GWAS focused on common variants, typically referring to bi-allelic SNPs with minor allele frequency above 5% [10]. Denote G= {0,1,2} for individuals carrying 0,1, or 2 copies of the reference alleles at a SNP, respectively, the most basic yet still the most routinely performed GWAS analysis tests the statistical association between Y and G through a linear model for continuous phenotypes:

(2)Y=\mu +\beta G+\gamma X+\epsilon ,

or a logistic model (for disease status). Under this single-variant model, the statistical inference focuses on testing the null hypothesis of no association, {{\displaystyle H}}_{\mathrm{0}}:\beta =\mathrm{0}. The test is applied to each SNP in turn. To correct for multiple testing, a p-value of \mathrm{5}\times {\mathrm{10}}^{-\mathrm{8}} is considered genome-wide significant, based on a heuristic of testing one million independent tests genome-wide [11]. While multi-variants models have been developed and applied, the single-variant model remains an essential component of GWAS studies, partly owing to the ease with which summary-level statistics from this analysis can be shared across studies, usually in the form of the estimated allelic effect, the standard error and the p-value for each tested variant. Taking advantage of the much larger sample sizes available, summary-statistics-based analytic methods have been developed for conditional analysis [12], fine mapping [13–15], colocalization [16–20] and partition of heritability by functional categories [21]. Non-additive effects, representing gene-gene (GxG) interaction (also referred to as epistasis [22]) and gene-environment (GxE) interaction can be tested using a similar model that includes both the main effects and the interaction terms. For example, robust gene-sleep and gene-smoking interactions have been identified that are associated with lipid concentration [23,24]. However, genome-wide search for GxG and GxE interaction faces both computational challenges, as well as limited statistical power due to the combinatorial search space and increased multiple testing burden [25]. Instead of testing interaction between every pair of variants, several recent studies have focused on testing interactions between a variant and the rest of the genome (termed marginal epistasis [26]) or groups of genes implicated in biologically related pathways [27]. In the remaining of this review, we focus on the identifying, characterizing and interpreting the main effects of genetic loci.

The dramatically increased throughput, accompanied by decreased cost, of next-generation sequencing technology has enabled moderate- to large-scale sequencing-based GWAS. Initial sequencing studies focused on protein-coding regions in the genome, referred to as whole exome sequencing studies (WES) [28–30]; more recent work, however, has shifted towards whole genome sequencing (WGS), which allows unbiased interrogation of the entire genomic DNA sequence and provides the most comprehensive characterization of both protein-coding and non-coding genomic regions. These sequencing studies have markedly increased the catalogue of human genetic variation, of which a majority have low frequency (MAF<5%). Statistical methods for analyzing sequencing data and rare variants will be discussed in a subsequent section.

Linkage disequilibrium (LD) refers to the correlation of genotype between genetic variants. Physically closely located variants tend to be in strong LD, although many other factors, such as the demographic history, the local recombination rate and the age of mutation, contribute to LD structure [31]. As a result, the LD pattern varies considerably across the genome, as well as across populations at a given genomic location. LD is a double-edged sword in GWAS. On the one hand, the correlation between the biological causal variant and many non-causal variants nearby (often referred to as markers or tagSNPs) enables us to identify genomic regions, or loci, that harbor trait variants without having to sequence every base pair of the genome. Taking advantage of LD, genotyping arrays (SNP chips) have been optimized for coverage, a measure of the ability to impute variants not directly genotyped on the array on the basis of neighboring genotyped tagSNPs [32–35]. Rationale, statistical methods and reference panel resources for genotype imputation can be extensively discussed and reviewed [36–39]. On the other hand, however, LD complicates the interpretation of the association: the significant associations cannot be interpreted as causal; rather, they are proxy variants highly correlated with neighboring causal variants. In regions of high LD, it is often infeasible to distinguish between the causal and proxy variants solely based on GWAS data, even if every base is sequenced. A number of methods have been developed aiming to refine the putative causal variants by integrating external biological knowledge.

Although the covariates, X, in Eq. (2) can include any factors relevant to the phenotype, by far the most commonly adjusted covariates are designed to eliminate spurious association due to population stratification (PS). PS can occur when the study population consists of discrete subpopulations, or when study participants represent continuous variation in ancestry proportions. Both forms of PS are expected to occur in biobanks. As one of the earliest examples of genetic association due to population stratification, Knowler et al. reported an association between an HLA haplotype and type 2 diabetes in a Native American population that has experienced recent admixture with Europeans. This association arose because both the HLA haplotype and type 2 diabetes occur at higher frequency among Indigenous Amerindian populations compared to in European populations; the association disappears when stratifying on ancestry proportion [40]. As the cohort sample size increases, even more subtle population structure within a continent can give rise to spurious associations. Such a possibility was demonstrated by an association between height and a SNP near the LCT gene, rs4988235, in Europe, where both height and the allele frequency of rs4988235 vary geographically between the Northern and Southern European populations [41]. To eliminate the spurious associations, effective methods have been developed and routinely incorporated in GWAS analyses. Currently the most commonly used approaches for accounting for population structure fall into two groups. One group of methods use genotype data to infer population structure, either by explicitly modeling of discrete subpopulations and continuous variation of genetic admixture, or by using a non-model-based method such as principal component analysis (PCA). The estimated ancestry proportions or leading PCs are then included in Model (2) as fixed-effects covariates, along with other covariates relevant to the phenotype. In contrast, a second group of methods turn Model (2) into a mixed-model by introducing genetic relationship between pairs of individuals through a random effects term in the form of a genetic relationship matrix (GRM) [42–45]. Compared to methods that adjust PC or ancestry proportions, these mixed models incur a higher computational cost but enjoy the advantage of additionally accounting for population structure represented by cryptic relatedness. Both groups of methods are currently widely used in GWAS. Genomic control and LDscore are two popular methods that allow users to assess, post hoc, potential residual population stratification based on genome-wide summary-level statistics [46,47].

Heritability refers to the proportion of the phenotypic variation attributable to genetic variation. Prior to the GWAS era, the heritability of a trait was estimated using correlation between biological relatives [48,49]. Under the generative model of Eq. (1) and assuming the identity of all trait variants and their corresponding allelic effects are known, the additive (or narrow sense) heritability is defined as h^{\mathrm{2}}={\displaystyle \frac{\mathrm{var}(\Sigma {{\displaystyle \beta }}_m{{\displaystyle G}}_m)}{\mathrm{var}(Y)}}. An enigma arose in early GWAS that was referred to as missing heritability: for many traits, a striking gap exists between the pedigree-based heritability estimates and the phenotypic variance explained by the known height loci [50]. Consider adult height, a classical quantitative trait, which has an estimated heritability of 0.80 in family-based studies [51]; yet the 27 genome-wide significant SNPs ‒ discovered in a cohort of nearly 30,000 – only account for ~3.7% of the phenotypic variance [52]. As explained in the next section, through a series of elegant analyses, we now appreciate that for a wide range of traits, the heritability is not missing but simply hidden under the polygenic architecture. For dichotomous disease phenotypes, the widely-adopted liability-threshold model stipulates that the disease status is determined by a latent quantitative trait ‒ the liability – and an unobservable threshold, beyond which an individual will manifest the disease. In GWAS setting, the heritability estimate for a disease trait represents the genetic contribution to the variation in liability [53]. This quantity differs from the heritability defined based on co-occurrence of the disease in relatives [54].

2 POLYGENIC ARCHITECTURE

The polygenic genetic architecture was first articulated in a seminal paper by Visscher and colleagues, who pioneered applying a variance component approach to estimate additive heritability in GWAS studies of unrelated individuals [55]. Instead of examining the effect of each SNP individually as in Model (2), this approach estimates the chip heritability, or the total contribution by all SNPs to a trait. The main conclusion is that a large proportion of heritable variation in height and other complex phenotypes can be attributed to common genetic variation. This finding is all the more remarkable because, at the time of publication, a total of 54 genome-wide significant height loci have been reported that, together, account for a mere 5% of the phenotypic variance [52,56,57]. Thus, it provides a quantitative explanation for the missing heritability phenomenon by supporting an infinitesimal model, in which the phenotypic variation of the trait represents the aggregated effects of a large number of variants, each with modest effects [58]. It predicts that, as the sample size increases, GWAS will continue to uncover additional trait-influencing variants that fill the missing heritability gap. This prediction has been empirically validated through subsequent GWAS for height and other complex traits: in a latest meta-analysis of height totaling more than 700,000 individuals, 3290 near-independent SNPs reach genome-wide significance and together explain nearly 25% of phenotypic variance [59]. While estimating variance-component models would normally require individual-level data, it is now possible to perform this type of analysis and estimate heritability using summary-level statistics, using methods such as LD score regression [46].

The understanding of polygenic architecture has a profound impact on the design and interpretation of GWAS studies. First, the expectation that each individual variant or locus explains a tiny fraction of the phenotypic variance, and therefore a large sample size is required to uncover these loci, has incentivized the formation of consortia and the share of summary-level statistics, which enable better powered meta-analyses. Second, much effort has been devoted, bearing much fruit, characterizing the distribution of trait-loci, both with respect to physical locations and to functional categories. Extending the variance component model, Yang et al. (2011) demonstrate that, for most traits, the phenotypic variance that can be explained by GWAS SNPs on each of the 22 human chromosomes is roughly proportional to the length of the chromosomes [55]. In other words, genes influencing a given trait are scattered throughout the genome rather than clustering together. This conclusion is strengthened in Loh et al. (2015), which stipulates that more than 70% of 1-Mb genomic regions harbor at least one schizophrenia risk variant [60].

Taking the polygenic model to its extreme has inspired the recent proposal of an omnigenic model [61]. which stipulates that essentially all genes can influence a disease or trait with infinitesimal effect, but only a modest number of core genes do so directly through trait-relevant pathways while the remaining peripheral genes only affect the phenotype indirectly through perturbing the expression of the core genes. A key corollary of the omnigenic model stipulates that heritability is predominantly attributable to the peripheral genes by virtue of the sheer number of peripheral genes, while the contribution of core genes to phenotypic variance are likely low How to define core genes and how to identify these units for a specific trait awaits further development, and whether the distinction captures the complexity of the underlying process has been a subject of debate [62]. Regardless, omnigenic model serves as a timely reminder that genes and variants do not act in isolation; instead, their phenotypic consequences are dependent through tightly connected and intricately regulated networks. With expanding understanding of these networks, GWAS analyses in the next ten years will likely to shift focus from gene discovery to delineating the pathways and hierarchy among the myriads of variants that influencing a phenotype.

3 PARTITIONING OF HERITABILITY

While variants associated with a polygenic trait are distributed throughout the genome, the location of these variants with respect to genomic context is not random. The variance component model, applied to increasingly available large-scale GWAS and sequencing data (discussed in greater details in a subsequent section), has enabled informative dissection of the contributions from different types of variants to complex traits. In particular these analyses address two long-standing debates regarding the relative contributions of common versus rare variants [63], and the role of protein-coding sequences versus the non-coding genome [64].

Common vs. rare variants. Although the rationale of GWAS is rooted in the common disease-common variant hypothesis, the missing heritability problem has inspired the proposal of common disease-rare variant hypothesis, which argues that a large number of rare variants can have a substantial impact on the genetic susceptibility to common diseases [65,66]. The rare variants can be identified by genome sequencing technology. One common observation from association analysis of sequencing data is that the effect size of rare variants is generally larger than common variants [67], although this could be primarily due to a statistical power issue as the required sample size for detecting trait-associated rare variants can be significantly larger than for common variants of the equal effect size [8]. To overcome this limitation, studies have sought to quantify the aggregated contributions of common or rare variants. Take height as an example, the array based chip heritability is 0.45 with common variants [55], while the estimate based on whole genome sequencing – including both common and rare variants ‒ has reached 0.79 [68], much closer to the estimates of 0.73‒0.81 based on the twin studies [51]. The results suggest that additional heritability can be potentially explained by rare variants that are not genotyped or imputed in the array-based studies [69]. We will return to discuss statistical methods for detecting rare variant association in a later section.

Coding vs. non-coding variants. While coding variants often exhibit a stronger effect on the trait of interest, they only represent 1%‒2% of the genome. The remaining ~98% of the human genome is non-coding and harbors elements that dictate when, where, and how much protein-coding genes are transcribed or translated [70–73]. Among significantly associated variants from hundreds of GWAS, ~ 89% lie in non-coding regions [74]. Gusev et al. (2014) estimated the heritability of different functional categories across 11 common diseases [75]. Although protein coding regions are significantly enriched in trait-associated variants, as expected, these coding variants, together, only explain about 10% of the total heritability explained by all variants. The remaining heritability is attributed to non-coding elements such as DNaseI hypersensitivity sites, promoter and intronic regions. Specifically, for schizophrenia, coding variants are found to explain 21% of the chip heritability (11% from common variants; 10% from rare variants) while non-coding variants account for the remaining 79%. Using a summary-statistics based heritability partitioning algorithm, stratified LD score regression, Finucane et al. (2015) found strong enrichment of many non-coding functional annotation in GWAS associated regions across 17 complex diseases and traits [21].

4 INTEGRATIVE ANALYSIS FOR TRAIT MAPPING

A hallmark of GWAS is the agnostic interrogation of the entire genome. All variants are treated as equally likely to be relevant to the phenotype, a priori. However, GWAS identify statistical association, but do not reveal biologically causative genes or variants. This limitation is exacerbated by the LD between markers and by the empirical evidence that most variants implicated in GWAS do not change protein sequences; consequently, the causal variants and the mechanism of action remain unknown for most GWAS discoveries. Yet, as discussed above, variants are not created equal, a realization that has driven systematic efforts to annotate the genome based on functional and evolutionary properties, referred to as functional annotations [76–78]. Leveraging high-throughput technologies, projects such as ENCODE, Roadmap Epigenomics and Gene-Tissue-Expression (GTEx) produce catalogs of genome function at single nucleotide resolution [72,79,80]. These data open up unprecedented possibilities for elucidating the statistical associations using biological knowledge. As an example, a recent GWAS of clinically diagnosed Alzheimer’s disease (AD) and AD-by-proxy (based on parental diagnoses) integrates array-based data from 71,880 cases and 383,378 controls from four independent cohorts: Alzheimer’s disease working group of the Psychiatric Genomics Consortium (PGC-ALZ), the International Genomics of Alzheimer’s Project (IGAP), the Alzheimer’s Disease Sequencing Project (ADSP), and AD-by-proxy data from the UK Biobank (see below) [81]. The meta-analysis identified 29 risk loci, implicating 215 associated genes. These associated genes are strongly expressed in immune-related tissues and cell types (spleen, liver, and microglia) and implicate shared biology between AD and multiple health-related outcomes.

A versatile and widely adopted framework to integrate functional annotations into trait mapping introduces a hidden variable, {{\displaystyle \delta }}_m\in \{\mathrm{0},\mathrm{1}\}, which indicates if a locus, or a variant, “causally” affects the phenotype. Here the term “causal” is used loosely to mean that locus or variant explains the observed statistical association. The key insight is that both the GWAS test statistics and the annotation at a locus inform about \delta, and the two quantities are conditionally independent given \delta. In other words, P({{\displaystyle S}}_m,{{\displaystyle A}}_m|{{\displaystyle \delta }}_m)=P({{\displaystyle S}}_m|{{\displaystyle \delta }}_m)P({{\displaystyle A}}_m|{{\displaystyle \delta }}_m), where {{\displaystyle S}}_m and {{\displaystyle A}}_m generically refer to the GWAS test statistics and functional annotations, respectively. P({{\displaystyle S}}_m|{{\displaystyle \delta }}_m) is specified by the GWAS model and is assumed known under the null and alternative hypotheses; P({{\displaystyle A}}_m|{{\displaystyle \delta }}_m) describes the degree of enrichment of specific functional annotation among causative locus/variants, and can be modeled using a logistic regression for binary annotations. The model parameters representing enrichment of each annotation and {{\displaystyle \delta }}_m can be estimated using either a likelihood or a Bayesian approach [13–15]. An appealing feature of these methods is that they require only the association test statistics, thus enabling these methods to leverage the summary-level statistics from the much better powered meta-analyses. Another innovative feature of these methods is the estimation of the enrichment parameters on the basis of genome-wide data; this is in sharp contrast to previous candidate gene approaches, which rely on prior domain knowledge to choose the appropriate annotation. Therefore, these methods can consider multiple annotation features simultaneously and adaptively integrate the phenotype-specific, relevant annotations, while ignoring non-informative annotations. As an example, the analysis of Pickrell (2014) considers 450 genomic annotations that include maps of DNase-I hypersensitivity in a variety of primary cell types and cell lines [14]. Consistent with biological expectations, GWAS SNPs are depleted at repressed chromatin regions and enriched at enhancers in cell types that are plausibly related to the traits.

LD between neighboring markers presents a thorny issue in jointly modeling GWAS and functional enrichment. Intuitively this is because the causality indicator, {{\displaystyle \delta }}_m, affects the association statistic at SNP m, as well as neighboring SNPs through LD. This problem is especially challenging because a GWAS region may harbor more than one causative variant and because summary-level statistics do not convey the LD pattern. A number of methods have made significant progress through two strategies: first, the LD between SNPs can be approximated by using an external reference population, such as individuals of matching ethnicity from the 1000 genomes project [82], and second, explicitly modeling the multivariate test statistic of all SNPs at each locus, R, whose mean depends on the vector of hidden causative indicators and whose covariance depends the approximate LD matrix computed on the external reference population [83–85]. However, applications of these methods to integrate high-dimensional annotation features face computational challenges; methods that improve statistical and computational efficiency and biological interpretability are under active development.

In the methods reviewed thus far, the annotation variables are assumed to be observed. These variables often indicate specific attributes, such as “non-synonymous variant” or “repressed chromatin in hepatocyte”. A special class of annotations are derived from large-scale expression-QTL (eQTL) experiments, which use gene expression, measured by microarray or through RNA-seq, as phenotype [86,87]. These studies, such as GTEx, are building an ever-expanding compendium of variants that affect RNA abundance in a variety of human tissues [80,88]. The decreasing cost of single-cell RNA sequencing will enable the characterization of gene expression at cell-type resolution in the near future. The trove of eQTL datasets present unprecedented opportunity for elucidating biological actions underlying GWAS associations, as empirical evidence demonstrates that a significant proportion of GWAS SNPs fall on or close to eQTLs [88]. Thus, the enrichment approaches described above can be applied with annotations indicating if a variant is an eQTL in a specific tissue. However, integrating eQTL evidence as annotation also presents unique challenges. Like GWAS, eQTL studies identify statistical associations and thus face the same limitations: causal regulatory variants may not reach statistical significance due to insufficient statistical power, and the precise regulatory variants are not unambiguously identified due to LD. These unique challenges have inspired the so-called colocalization methods, which aim to determine if the same set of variants give rise to the observed association with both gene expression and GWAS phenotypes [16–20]. Applications of these methods have not only refined putative causal variants underlying GWAS hits, but have also pointed to candidate tissues in which the actions of these eQTL variants may take place. Fully accounting for the LD pattern in GWAS and eQTL studies and jointly modeling eQTLs from multiple tissues will further enhance colocalization analysis but these remain open problems.

In parallel to colocalization analysis, the ability to systematically interrogate the regulatory wiring of gene expression through eQTL studies has inspired the transcriptome-wide association study (TWAS) framework [89–92]. These methods consist of three steps: first, for every gene, a genotype-to-expression prediction model is built using the eQTL data; second, these predictive models are applied to genotype data in a GWAS, predicting the unmeasured gene expression levels in GWAS individuals; last, the association between the predicted gene expression levels and the GWAS phenotype is tested, in a model similar to Eq. (2), but substituting genotype with the expression of a single gene. The improved statistical power of TWAS are due to two factors: first, for genes whose RNA expression is associated with the GWAS trait, TWAS leverages biological insight to aggregate the effects of multiple variants into a single variable, whose association with the trait is expected to be stronger than the corresponding association between the trait and each variant individually. Second, testing at the gene level dramatically reduces the multiple testing burden; thus, while a GWAS typically corrects for one million tests, the transcriptome-wide significance level for TWAS is based on testing 20,000 genes. Despite its considerable success, two open challenges in TWAS invite novel methodology. First, the predictive accuracy of expression is low for many genes, and it is reasonable to expect that the power of TWAS can be substantially improved with a more accurate gene expression prediction model. The prediction will improve as the eQTL sample increases; at the same time, novel ideas such as UTMOST have shown promise by leveraging information across multiple tissues [90]. Second, an appealing feature of TWAS is interpretability: TWAS implicitly assume that the genetic effect on a phenotype is mediated through gene expression, and therefore genes identified in TWAS hint at the functional pathways and biological processes. However, expression-phenotype association can arise without bona fide biological causality as explained in [93]. Statistical frameworks that facilitate rigorous interpretation of TWAS association and estimation of causal effects are under active development [94].

5 GENETIC RISK PREDICTION AND POLYGENIC RISK SCORE

An initial expectation of GWAS was that variants identified through these studies could be used to predict an individual’s genetic predisposition for various complex diseases. Polygenic risk score (PRS), which aggregates genetic risk variants into a single score to predict disease, can be computed at birth and, in combination with other non-genetic risk factors, has the potential to guide the prevention, diagnosis, and treatment of diseases, as well as for life planning. It should be emphasized that the risks of most complex traits are influenced by an array of non-genetic factors, and therefore PRS alone cannot be expected to achieve accurate prediction at the individual level. Nonetheless, recent work has demonstrated remarkable success using genome-wide PRS for population-level risk stratification: for coronary artery disease (CAD), PRS identified 8% of the population with at least three-fold elevated risk; as a comparison, rare monogenic mutations in familial hypercholesterolemia, which confers comparable risk for CAD, has a prevalence of 0.4% of the population [95]. Likewise, even though the current PRS for schizophrenia does not achieve the sensitivity and specificity for it to be used for individual prediction, the odds ratios of manifesting the disease between individuals in the top and bottom decile range between 7‒20 in three large cohorts [96].

In its simplest form, PRS is defined as the weighted sum of risk alleles with the weights given by the allelic effects, {\mathrm{\Sigma }}_{m=\mathrm{1}}^M{{\displaystyle \beta }}_m{{\displaystyle G}}_m. For a quantitative trait, PRS can be interpreted as the predicted deviation of an individual from the population mean. For the risk of dichotomous disease outcomes, PRS can be thought of as the predicted deviation, from the population mean, on the liability scale. Building PRS is fundamentally a high-dimensional prediction problem, in which the number of predictors (genetic variants) far exceeds the number of training individuals. Several additional features pose challenges for PRS. First, LD creates complex correlation structure between variants in physical proximity, and multiple variants in a region may contribute to the genetic risk. Second, the polygenic architecture suggests that the true PRS depends on thousands, if not more, of risk variants; hence methods favoring extremely sparse models are not optimal. This hypothesis is supported by the empirical evidence that the prediction improves when many variants not reaching the genome-wide significance level are included in the PRS [97]. Lastly, while typical prediction algorithms assume availability of individual-level genotype and phenotype data, it is desirable to exploit the wealth of existing GWAS summary-level statistics, for which individual-level data is not available.

A simple PRS algorithm is referred to “P+T,” which selects a set of independent SNPs by pruning correlated SNPs (P) and thresholding based on the single-variant association p-value (T) [97,98]. Specifically, SNPs are clumped based on LD and pruned to keep only the most significant SNP in each clump. SNPs with p-values exceeding a pre-specified threshold are kept and the estimated allelic effects are plugged-in to compute PRS. The tuning parameters, the LD threshold for clumping and the p-value threshold for retaining risk variants, are chosen through a validation dataset. P+T is intuitive and easy to implement on summary level-statistics: clumping can be based on the LD pattern in a publicly available dataset, such as the 1000 Genomes project, while thresholding and the computing of PRS do not require individual-level data. However, the performance of P+T is compromised by two limitations: first, in regions of high LD, the clumping step necessarily selects only one SNP even if multiple risk variants independently contribute to the disease risk; second, since the same dataset is used to select SNPs and to estimate allelic effects, the allelic effects tend to be overestimated due to the phenomenon of “winner’s curse” [99]. Subsequent research has tackled these problems through frequentist [100], empirical Bayes [101,102] and Bayesian [103–105] approaches. Additionally, several efforts have developed tools for, and demonstrated the benefits of, integrating functional annotation information [106,107] and leveraging shared genetic architecture of correlated phenotypes [108,109].

6 BIOBANK-SCALE DATA

The decreasing costs and increasing throughput of genomic technologies have propelled comprehensive genomic characterization of ultra-large cohorts, many of which are biobank repositories [110]. These biobanks host a rich catalog of phenotypes through participants’ survey response or electronic medical record [111]. For example, UK Biobank is a recently established cohort, in which more than 500,000 participants are genotyped at more than 820,000 SNP [112]. At the time of recruitment, an assortment of demographic, normal variation and health-related phenotypes was recorded for each participant; these participants are followed-up prospectively through linked health records. Summary statistics for more than 4,000 phenotypes are publicly available [113], facilitating integration of the UK biobank resource not only into studies of individual traits, but also characterization of shared genetic determinism between traits (pleiotropy) through PheWAS [4]. The sheer size of biobank data poses computational challenges when applying existing analysis methods. For example, the standard implementation of linear mixed model used to account for population stratification and sample relatedness requires computations of O(MN²) or O(M²N) (where M and N denote the number of SNPs and of individuals, respectively). One approach, implemented in the GENESIS package, generates a sparse, block-diagonal, GRM, which effectively reduces both the computational time and the memory requirement [114,115]. Alternatively, BOLT-LMM and SAIGE circumvent the need to compute and to perform the spectral decomposition on a GRM, by using preconditioned conjugate gradient to solve a linear systems of mixed-model equations [116–118]. In addition, these methods reduce the memory use by compactly storing raw genotypes instead of calculating and storing the GRM. Another issue arises in Biobank and EHR studies is that binary disease phenotypes often feature highly unbalanced case-control ratios. For such phenotypes, statistical significance based on the asymptotic approximations of the logistic regression may be inaccurate [119]. A number of methods, including SAIGE, ameliorate the problem by implementing a saddlepoint approximation for calibrating the score test statistics.

7 GENOME SEQUENCING STUDIES

Genome sequencing technology has extended the coverage of GWAS beyond array-based studies of common variants [120]. Sequencing-based GWAS studies have the advantage to investigate low frequency (1%< MAF<5%) and rare (MAF<1%) variants, which are not practical to be directly and comprehensively measured in array-based studies (Fig.1). Data generated from genome sequencing can also serve as a reference panel to impute unmeasured variants in array-based studies to expand the existing GWAS studies to study rare variants, although the imputation accuracy for rare variants is lower than for common variants [121–124]. Therefore, sequencing-based GWAS are particularly effective for characterizing the contribution of rare variants to complex phenotypes. However, the large number of variants, of which a majority have very low minor allele frequencies, poses analytic challenges. The current release of UK Biobank interrogated the exomes of 49,960 individuals, revealing more than four million variants [125]. As WGS replaces WES and more individuals are sequenced, the number of variants increases accordingly. The Alzheimer’s Disease Sequencing Project (ADSP) Discovery Extension Study performed whole genomes sequencing in 3085 individuals of diverse genetic ancestry and identified ~85 million variants [126]. Likewise, more than 400 million single-nucleotide and insertion/deletion variants have been detected in the 53,581 genome sequences generated by the multi-ethnic Trans-Omics for Precision Medicine (TOPMed) program [127,128].

When the minor allele is very rare, single-variant association test used for analyzing common variants (Eq. (2)) suffers from low statistical power. To improve power, gene-based methods, such as burden and dispersion tests, aggregate rare variants in a gene or region [124,129–132]. Many computational techniques described above for single variant analysis have been extended to gene/region-based analysis of sequencing studies [30,118,133]. For exome sequencing data, the coding region of a gene serves as a natural unit for grouping variants. In whole genome sequencing studies, however, such an approach would leave out a large number of non-coding variants. Currently, most WGS studies adopt a heuristic strategy of sliding window: a gene-based test is applied to rare variants within a contiguous window of fixed width. Bonferroni correction is used to account for multiple testing [134,135]. This strategy is suboptimal because the test statistics are correlated due to window overlap. Moreover, the optimal window size is often unknown, and misspecification may lead to loss of statistical power. An alternative approach is to group variants by annotation, such as chromatin states, genomic context (coding, intron, promoter, UTR, and intergenic) or regulatory functions (e.g., predicted enhancers, transcription factor binding and DNase-hypersensitive sites) [136]. A limitation of such approaches is that the choice of categories for testing is subjective. Recently, data-driven screening strategies, at the genome-wide scale, have been proposed to dynamically choose the window size and localize the windows in which association signals reside [137,138]. To account for the linkage disequilibrium among genetic variants and window overlap, Monte Carlo simulations can be used to establish an empirical significant threshold, which controls for the genome-wise type I error rate [118]. Alternatively, He et al. (2019) proposed an analytical estimate of the significance threshold for WGS window-based analysis using extreme-value distribution (e.g., the Gumbel distribution) [119].

In addition to the single nucleotide variants, WGS have enabled the characterization of a broad range of structure variations (SVs), which refers to sequence variation larger than 50 base pairs (bp) in size and includes copy number variants (CNVs), mobile element insertions (MEIs), inversions, and complex rearrangements. Although SVs are abundant in the genome and can have pronounced phenotypic impact through disrupting coding sequence or regulation, they are difficult to genotype by array-based platforms. Recent studies have developed accurate SV calling algorithms using WGS data [139–141], as well as have identified SVs associated with gene expression and complex traits [142,143].

8 GENERALIZABILITY OF GWAS RESULTS ACROSS POPULATIONS AND MULTI-ETHNIC STUDIES

Until recently, our knowledge regarding complex traits has been derived primarily from populations of European ancestry. A survey published in 2019 reveals that minority populations remain severely under-represented in GWAS studies: among studies curated by the NHGRI-EBI GWAS Catalog, over 78% of the participants are Europeans; in contrast, the two largest US minority groups, African Americans and Hispanic Americans, constitute over 25% of the population but less than 5% of GWAS participants [144]. There is no doubt that GWAS cohorts with expanded genetic diversity is a priority for all individuals to benefit from the fruit of genomic medicine. Yet analyzing multi-ethnic GWAS poses special analytic challenges. Population stratification is a particular concern because a number of minority populations, such as the African American and the Hispanic populations have experienced recent genetic admixture, which acts as a confounder and may give rise to spurious genotype-phenotype association. Methods for correcting PS was discussed in an earlier section.

A second challenge faced by GWAS in minority populations is that because the power of discovering genotype-phenotype association depends on sample size, far fewer trait loci have been identified in non-European populations. Likewise, the under-representation of non- European participants hinders the inference of causal variants and the estimation of allelic effects in these populations. Therefore, although nearly all analytic strategies described above are applicable to any population, they are less effective for minority populations. Importantly, several studies have demonstrated that polygenic risk scores do not transfer well across ethnicities; in other words, the approach that uses European GWAS results to select risk variants and to estimate their allelic effects yields polygenic risk scores with poorer predictive accuracy when applied to non-European populations. Multiple factors contribute to this phenomenon. First, trait loci and risk variants that contribute substantially to the phenotypic variation in a minority population may be entirely missed in a European GWAS if the causal variants are rare, not well tagged by markers on the genotyping array, or have weak effects in the study cohort. Consider the example of APOL1: two African-ancestry-specific risk variants in this gene confer increased risk for specific forms of kidney diseases; the risk alleles are virtually absent in all populations with no African ancestry [145]. Thus, despite an odds ratio of 7.3 for hypertension-attributed end-stage kidney disease, the association could not have been identified in a European GWAS. Second, heterogeneity in allelic effects among populations is well documented. As an example, multiple studies support a causal role of the APOE\epsilon \mathrm{4} allele that increases the risks for Alzheimer’s disease and coronary artery disease across ethnicities [146]. Yet the magnitudes of effects, for both diseases, are higher in East Asians than in Europeans and African Americans [147]. Therefore, PRS built based on European GWAS, which uses the allelic effects estimated in Europeans, would not generalize accurately to East Asian individuals. Lastly, even when a risk variant occurs in all populations and exerts identical allelic effects, the SNPs used in PRS are often tag SNPs and not the causal variants. Therefore, a PRS model built using European cohorts selects SNPs based on the LD pattern in Europeans. As the LD structure differs between populations, these SNPs are often not optimal tags for the causal variants in non-European populations; in other words, tagging SNPs selected based on European GWAS are expected to be poorer surrogates in non-European populations on average, leading to reduced predictive accuracy. For the same reasons, integrative analyses‒such as determining colocalization of a GWAS association in a minority population and eQTL evidence ‒ are hampered because eQTL and other-omics studies have also been conducted predominantly in European populations. To fill this gap, concerted efforts are underway to expand the diversity in GWAS cohort. Consortia such as the Human Heredity and Health in Africa (H3Africa) focus on establishing infrastructure for genomic studies in historically under-represented populations [148]. Multi-ethnic cohorts offer opportunities to minority-specific and trans-ethnic GWAS for a variety of diseases and phenotypes, examples of such cohorts include ALL of Us Research Program, Resource for Genetic Epidemiology Research on Aging (GERA) [149], the Population Architecture using Genomics and Epidemiology (PAGE) Consortium [150] and the Million Veterans Program [151]. In addition to these large-scale genotyping and sequencing efforts, the TOPMed program aims to systematically assay the methylome, transcriptome, proteome and metabolome in under-represented minority populations, which will enable the characterization of biological processes that underlie complex phenotypes in a population-specific context [127,128].

Complementary to the resource-building efforts, a number of analytic innovations have been proposed to ameliorate the challenges posed by the limited existing minority genomic resources. A key insight motivating these statistical approaches is the empirical evidence supporting a model that, for many complex phenotypes, a considerable fraction – but not all ‒ of trait loci are shared across populations [152,153]. Therefore, a comprehensive, and population-aware, delineation of the genetic architecture underlying a phenotype of interest can benefit from borrowing information across populations. Such trans-ethnic approaches, however, must be adapted for the phenotype and population under study and acknowledge minority-specific genetic component. Coram et al. proposed an empirical Bayes approach, XPEB, which improves the power of GWAS in a minority populations by explicitly modeling and estimating shared genetic architecture [154]. Distinct from meta-analysis approaches, which treat all populations symmetrically, XPEB focuses on one minority population and treats information from other populations as auxiliary. It is adaptive in the sense that the method automatically assesses the relevance of the auxiliary information, and only ‘borrows’ information across ethnicities when empirical evidence supports substantial overlap. Furthermore, XPEB acknowledges, and has power to detect, population-specific biomolecules. This is in contrast to conventional meta-analysis approaches whose goal is to improve the overall mapping power but at a sacrifice of detecting minority-specific association. Applied to an African American lipid GWAS data, XPEB more than quadrupled the discoveries compared to the standard single-population approach. Furthermore, XPEB estimated that, for matching lipid traits,>95% loci overlap between EU and AA; at the same time African-specific lipids loci are identified. In a follow-up paper, these authors proposed a trans-ethnic approach for improving PRS for minority individuals [155]. Novel methods that more precisely account for population-specific disease loci, rare variants and LD structure are needed to maximize the value of the rich multi-omics and phenotypic data that are being generated in diverse populations.

9 SUMMARY AND CONCLUSIONS

During the past ten years, GWAS have not only successfully identified abundant loci that underly a variety of traits and diseases but have also provided fundamental insights into the genetic architecture of complex phenotypes. Critical to these successes are novel statistical and computational approaches. Figure 2 provides an overview of major areas discussed in this review. Much of recent advances in understanding the genetic architecture of complex traits have benefitted from the open sharing of GWAS summary-level statistics from the single-variant analysis (Fig. 2A). Methods based on mixed-effects models have enabled the estimation of heritability of a trait, as well as partitioning the heritability based on attributes of the genomic regions (Fig. 2B). Integrating the GWAS summary-statistics with prior biological annotation or functional genomic data can substantially refine the associated genomic regions, although precisely identifying causal variant(s) underlying the statistical association remains challenging (Fig. 2C). Lastly, the predictive accuracy of PRS has continued to improve, owing to the expanding GWAS cohorts (Fig. 2D). We anticipate that GWAS in the next ten years will feature participants with more extensive phenotypes and representing increasing genetic diversity. Furthermore, fueled by technological advancement, molecular phenotypes, such as epigenetics marks and gene expression, are systematically characterized in GWAS cohorts. In the near future, it may be possible to assess these molecular phenotypes across tissues and even at a single cell resolution. Exploiting this data explosion, innovation in statistical and computational strategies have the potential to elucidate the biological functions underlying the genotype-phenotype associations and to inform disease risk or intervention.

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