An allelic-series rare-variant association test for candidate-gene discovery

Summary

Allelic series are of candidate therapeutic interest because of the existence of a dose-response relationship between the functionality of a gene and the degree or severity of a phenotype. We define an allelic series as a collection of variants in which increasingly deleterious mutations lead to increasingly large phenotypic effects, and we have developed a gene-based rare-variant association test specifically targeted to identifying genes containing allelic series. Building on the well-known burden test and sequence kernel association test (SKAT), we specify a variety of association models covering different genetic architectures and integrate these into a Coding-Variant Allelic-Series Test (COAST). Through extensive simulations, we confirm that COAST maintains the type I error and improves the power when the pattern of coding-variant effect sizes increases monotonically with mutational severity. We applied COAST to identify allelic-series genes for four circulating-lipid traits and five cell-count traits among 145,735 subjects with available whole-exome sequencing data from the UK Biobank. Compared with optimal SKAT (SKAT-O), COAST identified 29% more Bonferroni-significant associations with circulating-lipid traits, on average, and 82% more with cell-count traits. All of the gene-trait associations identified by COAST have corroborating evidence either from rare-variant associations in the full cohort (Genebass, n = 400,000) or from common-variant associations in the GWAS Catalog. In addition to detecting many gene-trait associations present in Genebass by using only a fraction (36.9%) of the sample, COAST detects associations, such as that between ANGPTL4 and triglycerides, that are absent from Genebass but that have clear common-variant support.

Graphical abstract

Allelic series are collections of variants that lead to a gradation of possible phenotypes. We introduce COAST (Coding-Variant Allelic-Series Test), a test that identifies genes where increasingly deleterious mutations have increasing phenotypic effects. We apply COAST to uncover genes harboring allelic series for lipid and cell-count traits in the UK Biobank.

Introduction

The term “allelic series” refers to a collection of alleles in a gene or pathway that leads to a gradation of possible phenotypes.¹ Genes demonstrating allelic series are of candidate therapeutic interest because of the existence of a dose-response relationship between the functionality of the gene and the magnitude or severity of the phenotype.² This relationship provides evidence in humans that pharmacological modulation of the implicated gene has the potential to move the target phenotype in the direction of clinical benefit. Seminal work by Plenge et al.² highlighted the opportunity for identifying such dose-response relationships preclinically from the natural genetic variation found in human populations. Such “experiments of nature” were instrumental to the development of statins² and have confirmed the role of PCSK9 in familial hypercholesterolaemia, low-density lipoprotein (LDL) cholesterol, and coronary artery disease, as reviewed by Musunuru and Kathiresan.³ Another impactful example is the allelic series in TYK2,⁴ now the basis for a successful selective inhibitor (deucravacitinib) for the treatment of psoriasis.⁵ From the standpoint of drug design, the advantage of focusing on allelic series is that modulation of the gene has already been linked with variation in phenotype, reducing the risk that an intervention targeting that gene will fail for lack of efficacy. Motivated by this paradigm, we introduce a rare-variant association test intended to identify genes with allelic series in large genotype-phenotype cohorts, such as the UK Biobank.⁶ Hereafter, by allelic series, we refer specifically to a collection of variants wherein increasingly deleterious mutations have increasingly large phenotypic effects.

Genome-wide association studies (GWASs) canonically seek to associate common genetic variants, typically those having a minor allele frequency (MAF) exceeding 1%–5%, with complex traits and diseases.⁷ The advent of whole-genome and whole-exome sequencing studies has enabled rare-variant association analysis, wherein associations are sought for variants with lower MAFs.^8,9 Because even large cohorts can have a few examples of such subjects, reliably associating phenotypes with rare variants requires specialized methodology.¹⁰ For a given effect size, the power of single-variant association tests declines precipitously with the MAF.¹¹ To overcome this limitation, rare-variant association tests typically aggregate signal within a biologically meaningful region, such as a gene.

Two major subdivisions of rare-variant association tests are burden tests and variance-component tests. Burden tests^12,13,14 associate the phenotype with a single genetic score that they form by pooling the variants in a region. These tests can differ with respect to the assignment of weights to variants but share the assumption that all rare variants in the region affect the phenotype in the same direction.¹⁰ When this is not the case, the power of burden testing is diminished. Variance-component tests, notably the sequence kernel association test (SKAT),¹⁵ relax the assumption of a common direction of effect by instead supposing that the effect sizes are random by following a distribution with mean zero and finite variance. SKAT performs well when some of the rare variants in the region are non-causal or have conflicting directions of effect, but it loses power when the genetic architecture is consonant with that assumed by the burden test. In practice, the genetic architecture of a trait is seldom known. Optimal SKAT (SKAT-O)¹⁶ adaptively combines SKAT with the burden test to provide high power for rare-variant association testing under the scenarios assumed by either of the component tests.

Several existing approaches incorporate functional annotations to generally improve power for gene-based association testing.^17,18,19 For example, STAAR¹⁹ uses annotation principal components (PCs) to upweight a variant’s probably of being causal according to the fractional rank of that variant’s annotation score in relation to those of all sequenced variants within functional categories such as epigenetic marks, conservation, and protein function. In a different vein, Regenie²⁰ and STAARpipeline²¹ allow for the definition of masks that specify which variants should be included in an association test on the basis of functional categories. However, no existing methods are specifically targeted to the identification of allelic series. We fill this gap by defining a rare-variant association test that incorporates a set of adjustable allelic-series weights to encourage rejection of the null hypothesis in cases where the expected effect of a variant on the phenotype increases monotonically with the severity of the mutation. Our approach focuses on the rare coding variants within a gene, as annotated by the Ensembl Variant Effect Predictor (VEP).²² Specifically, our test operates on three classes of variants: benign missense variants (BMVs), deleterious missense variants (DMVs), and protein-truncating variants (PTVs). Building on the burden test and SKAT, we define a variety of gene-based association models targeting different genetic architectures. These tests are aggregated into a single, omnibus, Coding-Variant Allelic-Series Test (COAST).

In this work, we present a rare-variant association test specifically intended for the identification of genes harboring a dose-response relationship with the phenotype, and we highlight its potential for drug discovery by demonstrating its efficacy in uncovering genes with allelic series. Through extensive simulation studies, we validated that COAST controls type I error in the absence of a genotype-phenotype association and benchmarked its power in relation to that of SKAT-O¹⁰ under a variety of genetic architectures. We selected SKAT-O as the comparator because of its widespread use, computational efficiency, and direct applicability with only the data required by COAST. We note, however, that the set of genes targeted by COAST is narrower than that targeted by SKAT-O, and we are aware of no existing association test that specifically targets genes with allelic series. Using whole-exome sequencing data on up to 145,735 subjects and up to 17,225 genes from the UK Biobank, we applied COAST to identify allelic series for four circulating-lipid traits and five cell-count traits. Compared with SKAT-O, COAST identified 29% more Bonferroni-significant associations with circulating lipids, on average, and 82% more associations with cell counts. Notably, all of the additional genes detected by COAST have supporting evidence from published common- or rare-variant association studies, but not all of the rare-variant associations have previously been identified by SKAT-O applied to the full UK Biobank (Genebass).²³

Material and methods

Setting

Let Y denote a quantitative phenotype (e.g., circulating cholesterol or erythrocyte count), X denote a set of covariates (e.g., age, sex, and genetic PCs), and $G=\left(G_1,\cdots ,G_J\right)\in {\left\{\mathrm{0,1,2}\right\}}^J$ denote the additively coded genotype at the J rare coding variants within a given gene. To each variant j, assign a categorical functional annotation $A_j\in \left\{1,\cdots ,L\right\}$. For the present work, we specialize to the following $L=3$ VEP categories:

$$A_j=\{\begin{array}{cc}1\text{,}& \text{BMV,}\\ 2\text{,}& \text{DMV,}\\ 3\text{,}& \mathrm{P}\mathrm{T}\mathrm{V}\text{.}\end{array}$$

For a given subject, let $N_l$ count the total number of category l alleles present in the gene,

$$N_l=\sum _{j=1}^J\mathbb{I}\left(A_j=l\right)G_j\text{,}$$

and let $N=\left(N_1,N_2,N_3\right)$ denote the vector of category-level allele counts.

Models

Standard burden test and SKAT

Consider the standard gene-level association model:

$$\mathbb{E}\left(Y|G,X\right)=\alpha +\sum _{j=1}^J{G}_j{\beta }_j+X^{\prime }\gamma \text{.}$$

The marginal score for evaluating $H_0:{\beta }_j=0$ is $S_j={\sum }_{i=1}^N{G}_{ij}{\hat{e}}_{Y,i}$, where i indexes subjects and ${\hat{e}}_{Y,i}$ is the residual from regressing Y on X (but not G). Following Lee et al.,¹⁰ we express the standard burden test and SKAT as follows:

$$Q_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{n}}={\left[\sum _{j=1}^J{w}_{\mathrm{B},j}{S}_j\right]}^2,Q_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}}=\sum _{j=1}^J{w}_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T},j}^2{S}_j^2\text{.}$$

Different choices for the per-variant burden weight ($w_{\mathrm{B},j}$) and SKAT weight ($w_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T},j}$) provide differing powers for detecting an association. The standard burden test assigns a weight of $w_{\mathrm{B},j}=1$ to all variants within a class of interest (e.g., to PTVs), whereas the standard SKAT¹⁵ assigns weights from the beta distribution on the basis of the variant’s MAF: $w_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T},j}^2=\mathrm{b}\mathrm{e}\mathrm{t}\mathrm{a}\left({\mathrm{M}\mathrm{A}\mathrm{F}}_j;{\alpha }_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}},{\beta }_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}}\right)$. Selecting ${\alpha }_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}}={\beta }_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}}=1/2$ gives rise to inverse variance weighting $w_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T},j}^2\propto {\left\{{\mathrm{M}\mathrm{A}\mathrm{F}}_j\left(1-{\mathrm{M}\mathrm{A}\mathrm{F}}_j\right)\right\}}^{-1}$, reflecting a genetic architecture in which rarer variants have larger effects. Finally, SKAT-O is based on a convex combination of the burden and SKAT statistics¹⁶:

$$Q_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}-\mathrm{O}}=\underset{0\le \rho \le 1}{\min }\rho ·Q_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{n}}+\left(1-\rho \right)·Q_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}}\text{.}$$

Here, $\rho \in \left[\mathrm{0,1}\right]$ adaptively combines $Q_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{n}}$ and $Q_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T}}$.

Baseline model

The baseline allelic-series model takes the following form:

$$\mathbb{E}\left(Y|N,X\right)=\alpha +N_1{\beta }_1+N_2{\beta }_2+N_3{\beta }_3+X^{\prime }\gamma \text{.}$$ (Equation 1)

Equation 1 is reminiscent of the standard burden model but differs in that aggregation is grouped by annotation category and a separate coefficient is allocated to each. As such, the baseline allelic-series model is not a case of the standard burden test. Equation 1 is also a count-based model, where the expected value of the phenotype increases linearly by ${\beta }_l$ for each additional category l allele. An indicator-based model replaces the category l allele count $N_l$ by an indicator that $N_l$ is non-zero:

$$\mathbb{E}\left(Y|N,X\right)=\alpha +\mathbb{I}\left(N_1>0\right){\beta }_1+\mathbb{I}\left(N_2>0\right){\beta }_2+\mathbb{I}\left(N_3>0\right){\beta }_3+X^{\prime }\gamma \text{.}$$

The indicator-based model posits a genetic architecture in which the presence or absence of category l alleles has an effect on the phenotype, but beyond the first, the number of category l alleles is immaterial. For example, the presence of any PTVs in a gene might abrogate its function, but additional PTVs beyond the first might have no effect. Under both the count and indicator models, we evaluate the null hypothesis that the rare coding variants within the gene are unrelated to the phenotype by testing $H_0:{\beta }_1={\beta }_2={\beta }_3=0$ by using a standard Wald or score test with three degrees of freedom.²⁴ Details of the Wald and score tests are provided in the supplemental material and methods.

Allelic-series sum model

The baseline model provides a test for identifying genes associated with the phenotype and allows variants belonging to different annotation categories to have differing effects. However, it is not yet tailored to the identification of allelic series. We next introduce a set of adjustable allelic-series weights, $w=\left(w_1,\dots ,w_L\right)$, one for each variant category, in order to specify the pattern of effect sizes sought. Any monotone increasing pattern corresponds to an allelic series, but as a simple default, we adopt w = (1, 2, 3). We define the allelic-series sum model as a specialization of Equation 1 under the constraint that ${\beta }_l=w_l\beta$:

$$\mathbb{E}\left(Y|N,X\right)=\alpha +\left(w_1{N}_1+w_2{N}_2+w_3{N}_3\right)\beta +X^{\prime }\gamma \text{.}$$ (Equation 2)

Equation 2 continues to allow different categories to have differing effects, but the constraint requires that the effect-size vector $\left({\beta }_1,{\beta }_2,{\beta }_3\right)$ be proportional to the allelic-series weights:

$$\left({\beta }_1,{\beta }_2,{\beta }_3\right)=\left(w_1,w_2,w_3\right)\beta \text{.}$$

Compared with Equation 1, Equation 2 reduces the number of free parameters from three to one. We evaluate the null hypothesis of no association between the gene and the phenotype by testing $H_0:\beta =0$. The allelic-series sum model is a case of the standard burden model with customized weights: $w_{\mathrm{B},j}={\sum }_{l=1}^L\mathbb{I}\left(A_j=l\right)w_l$. The baseline model might outperform the sum model for architectures where the pattern of effect size differs markedly from that sought by w, e.g., $\left({\beta }_1,{\beta }_2,{\beta }_3\right)\propto \left(\mathrm{0,0,1}\right)$. Conversely, the sum model will have better power the more nearly the prespecified allelic-series weights (w₁, w₂, w₃) are proportional to the true pattern of effect sizes $\left({\beta }_1,{\beta }_2,{\beta }_3\right)$.

Allelic-series max model

Focusing on the parenthetical term in Equation 2, we see that the allelic-series sum model aggregates the per-category allele counts (N₁, N₂, N₃) by taking a weighted sum. By using different methods of aggregation, we can construct additional allelic-series tests. The allelic-series max model aggregates via the weighted maximum:

$$\mathbb{E}\left(Y|N,X\right)=\alpha +\max \left(w_1{N}_1,w_2{N}_2,w_3{N}_3\right)\beta +X^{\prime }\gamma \text{.}$$ (Equation 3)

Equation 3, particularly the indicator version, is motivated by a genetic architecture in which the expected phenotype is determined by the most deleterious variant present. For example, the presence of a BMV might have negligible phenotypic impact in the presence of a PTV. As for the sum model, we evaluate the null hypothesis of no association by testing $H_0:\beta =0$. The allelic-series max model is not readily expressible within the standard burden framework.

Allelic-series SKAT model

The preceding tests make the burden-type assumption that all variants affect the phenotype in the same direction. The SKAT¹⁵ was introduced to allow variants to have differing directions of effect. In brief, SKAT posits that each variant $G_j$ has a separate effect ${\beta }_j$ and that these effects are drawn at random from an unspecified distribution with mean zero and variance $w_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T},j}^2{\tau }^2$, where ${\tau }^2$ is a common variance component. We evaluate the null hypothesis of no association by testing $H_0:{\tau }^2=0$. To develop an allelic-series test that allows rare variants to have differing directions of effect, we build on the existing SKAT framework but modify the SKAT weights to incorporate the allelic-series weights:

$$w_{\mathrm{S}\mathrm{K}\mathrm{A}\mathrm{T},j}^2=\frac{{\sum }_{l=1}^3\mathbb{I}\left(A_j=l\right)w_l}{{\mathrm{M}\mathrm{A}\mathrm{F}}_j\left(1-{\mathrm{M}\mathrm{A}\mathrm{F}}_j\right)}\text{.}$$ (Equation 4)

Under Equation 4, the variance of the distribution from which ${\beta }_j$ is drawn, and thus the expected magnitude of effect, is directly proportional to $w_l$ and inversely proportional to ${\mathrm{M}\mathrm{A}\mathrm{F}}_j$. In the allelic-series setting where $w_l$ increases monotonically from BMVs to DMVs to PTVs, this encodes the expectation that rarer and more deleterious variants will have larger effects on the phenotype.

Allelic-series omnibus test

We have now defined several burden-type tests and a SKAT-based test. Which test is best powered for a particular gene-phenotype pair will depend upon which best approximates the true genetic architecture. Moreover, for a given phenotype, a single test is unlikely to be optimal for all genes given that the genetic architecture can vary from gene to gene. To obviate the need for deciding among tests, we apply each of the preceding tests and then combine their p values via the Cauchy combination method introduced by Liu and Xie,²⁵ a strategy that has also been applied by ACAT-V,²⁶ STAAR,¹⁹ and SAIGE-GENE+.²⁷ Given M p values $\left({\mathrm{p}}_1,\dots ,{\mathrm{p}}_M\right)$, the omnibus test statistic is defined by

$$Q_{\mathrm{o}\mathrm{m}\mathrm{n}\mathrm{i}}=\sum _{m=1}^M{w}_{\mathrm{o}\mathrm{m}\mathrm{n}\mathrm{i},m}\tan \left\{\pi \left(0.5-{\mathrm{p}}_m\right)\right\}\text{,}$$ (Equation 5)

where the omnibus weights w_omni,m are selected to give burden-type and SKAT-type tests equal weight. Finally, the omnibus p value is given by

$${\mathrm{p}}_{\mathrm{o}\mathrm{m}\mathrm{n}\mathrm{i}}=\frac{1}{2}-\frac{1}{\pi }\arctan \left(\frac{Q_{\mathrm{o}\mathrm{m}\mathrm{n}\mathrm{i}}}{{\sum }_{m=1}^M{w}_{\mathrm{o}\mathrm{m}\mathrm{n}\mathrm{i},m}}\right)\text{.}$$

We refer to the omnibus test and its associated p value as the COAST. By default, COAST includes M = 7 tests: six allelic-series burden tests ({base, sum, max} × {count, indicator}) with weight w_omni,m = 1/12 and one allelic-series SKAT with weight w_omni,m = 1/2. Optionally, SKAT-O applied to all variants or SKAT-O applied to PTVs only can be included in the omnibus test. Using an omnibus statistic makes COAST robust in the sense that it will have power to detect an association if any of the component models is powered to detect the association.²⁶

Simulation methods

Our simulation studies considered sample sizes of 1,000, 5,000, 10,000, and 50,000. We simulated rare variants in linkage equilibrium to have a minimum minor allele count (MAC) of 1 and a maximum empirical MAF of 1%. We assigned variants annotations of BMV, DMV, or PTV in a 5:4:1 ratio to emulate the empirical frequencies of BMVs, DMVs, and PTVs across all 17,225 genes in our UK Biobank analyses, which were 51.6%, 39.9%, and 8.5%, respectively. We also conducted simulation studies by using real APOB genotypes and VEP annotations from randomly selected UK Biobank participants. For each subject, covariates were simulated to represent age, sex, and three genetic PCs; 10% of phenotypic variation was explained by age, 10% was explained by sex, and 20% was explained by the three genetic PCs collectively. For type I error simulations, genotype had no effect on the phenotype. For power simulations, phenotypes were generated under multiple genetic architectures. Each simulated gene contained 10² variants. A random subset of these variants, between 25% and 100%, were selected as causal. The effect size of non-causal variants was zeroed out. We simulated burden phenotypes from the {baseline, sum, max} models by varying the generative effect sizes (β₁, β₂, β₃). We simulated the sum and max phenotypes by fixing β = 1 and varying the generative weights (w₁, w₂, w₃). For SKAT phenotypes, the effect size of variant j was generated as ${\beta }_j=r_j{\gamma }_j{\sum }_{l=1}^3\mathbb{I}\left(A_j=l\right){\beta }_l$. Here, r_j is a random sign, ${\gamma }_j\sim \mathrm{\Gamma }\left(\alpha ,\alpha \right)$ is a positive random scalar with $\mathbb{E}\left({\gamma }_j\right)=1$ and $\mathbb{V}\left({\gamma }_j\right)={\alpha }^{-1}$ (α = 1 for simplicity), and the term ${\sum }_{l=1}^3\mathbb{I}\left(A_j=l\right){\beta }_l$ incorporates an additional fixed scalar that depends on the variant’s annotation. Note that the sum and max architectures are not compatible with a SKAT phenotype.

Preparation of UK Biobank data

Whole-exome sequencing data

Variants in the UK Biobank whole-exome sequencing variant call set (n = 200,000²⁸) were filtered out if they were located >100 bp away from the exome-capture regions, within the ENCODE black list,²⁹ or within low-complexity regions.³⁰ We further filtered to autosomal, biallelic variants meeting the following criteria: allele balance fractions ≤ 0.1 (homozygous) or ≥ 0.25 (heterozygous), call rate ≥ 0.95, mean depth (DP) of 12 ≤ DP < 200, mean genotype quality (GQ) ≥ 20, Hardy-Weinberg equilibrium p > 1 × 10⁻⁶, and inbreeding coefficient (F) > −0.3. Variants were annotated by VEP v96²² with the following transcript consequences (for any transcript of a gene): splice acceptor variant, splice donor variant, stop gained, or frameshift variant for PTVs and missense variant, in-frame deletion, in-frame insertion, stop lost, start lost, or protein-altering variant for missense variants. Missense variants were annotated as damaging (DMV) if they were predicted to be probably damaging or possibly damaging by PolyPhen2³¹ and deleterious or deleterious low confidence by SIFT.³² Missense variants were annotated as benign (BMV) if they were predicted to be benign by PolyPhen2 and tolerated or tolerated low confidence by SIFT.^33,34 We further filtered PTVs to remove low-confidence loss of function by LOFTEE.³⁵

Quality control

We performed sample-level quality control (QC) by using 104,616 high-confidence variants that passed the above filtering criteria, had a minor allele count ≥ 5, and were linkage disequilibrium (LD) pruned to r² < 0.05. To mitigate confounding due to population structure, we first filtered samples to unrelated individuals without sex chromosome aneuploidy; within ±7 standard deviations of the mean of the first six genotype PCs³⁶; with a self-reported ethnic background of White British, Irish, or White; and with a call rate ≥ 0.95, mean DP ≥ 19, and mean GQ ≥ 47.5. We regressed the top 20 genetic PCs from the following sample QC metrics and removed samples that were >4 median absolute deviations (MADs) from the median for any of the following metrics: number of SNPs, number of heterozygous variants, number of homozygous alternate variants, number of insertions, number of deletions, number of transitions, number of transversions, the ratio between the number of transitions and transversions, the ratio between the number of heterozygous and homozygous alternate variants, and the ratio between the number of insertions and deletions.³⁵ The sample size after filtering was 145,753. All data preprocessing was performed in Hail 0.2.37 (see web resources).

Association analysis

Processed whole-exome sequencing data were restricted to BMVs, DMVs, and PTVs with a sample MAF ≤ 1%. Following Liu and Xie²⁵ and Zhou et al.,²⁷ we collapsed ultra-rare variants (those with a sample MAC ≤ 10) into a single pseudo-marker separately for each gene × variant category. Genes were required to have at least three distinct rare variants (including the pseudo-marker) for inclusion in the genome-wide screen; 17,225 genes passed this threshold. The circulating-lipid phenotypes analyzed included LDL and high-density lipoprotein (HDL) (UK Biobank field IDs 30780 and 30760, respectively), triglycerides (30870), and total cholesterol (30690). The cell-count phenotypes included erythrocytes (30010), leukocytes (30000), lymphocytes (30120), neutrophils (30140), and thrombocytes (30080). In all cases, we transformed the phenotype to normality by applying the rank-based inverse normal transformation (INT).³⁷ Covariates included age (to degree 3), genetic sex, age × sex interaction (to degree 3), 20 genetic PCs, and an indicator for being among the first 50,000 exomes sequenced. We performed association analyses by using the COAST function from the AllelicSeries R package (v0.0.2) and the SKAT function from the SKAT R package (v2.2.5) (see web resources).

Overlap analysis

For each trait of interest, common-variant associations were obtained from the NHGRI-EBI GWAS Portal³⁸ (see web resources) and filtered to those having p > 5 × 10⁻⁸. Rare-variant associations from both putative loss-of-function (pLoF) variants and missense variants, including low-confidence pLoF variants and in-frame insertions or deletions, were obtained from the Genebass Portal²³ (see web resources). Associations were filtered to those that were Bonferroni significant according to the number of genes with non-missing p values, and the union of significant associations from the pLoF and missense analyses was taken.

Results

Simulation studies

We performed simulation studies to evaluate the type I error (validity) and power of the proposed COAST. Across sample sizes ranging from 1,000 to 50,000, the p values from COAST were uniformly distributed under the null hypothesis of no association (Figure 1A). The distribution was uniform both as applied to real genotypes from APOB (133 variants: 79 BMVs, 48 DMVs, and 6 PTVs; Figures 1 and S1) and as applied to simulated genotypes in linkage equilibrium (BMVs, DMVs, and PTVs in a 5:4:1 ratio; Figure S2). Empirical demonstration that the type I error is controlled genome-wide is provided by the analyses of permuted phenotypes in Figures S9 and S13. Across sample sizes, the distribution of p values from COAST was comparable to that of SKAT-O (Figure S3). Expected χ² statistics for COAST and its components are presented in Figure S4. COAST is slightly conservative for larger p values (which are not of interest) but well calibrated in the tails, a known consequence of Cauchy combination’s higher accuracy for smaller p values.²⁵ Overall, these findings support the validity of COAST, and its components, for genome-wide analyses.

Figure 1.

Type I error and power of the coding-variant allelic-series test (COAST)

(A) Observed vs. expected quantiles of −log₁₀(p) for COAST applied to null phenotypes at various sample sizes with real genotypes from APOB. Adherence to the dashed 45° line indicates that the observed p values are uniformly distributed. Results are from 10⁶ simulation replicates at each sample size.

(B and C) Power across various genetic architectures at sample size n = 10⁴ with simulated genotypes. Genes included 10² variants with a BMV/DMV/PTV ratio of 5:4:1. Each subplot corresponds to a different genetic architecture generated via Equation 1. The tuple in the heading denotes the relative effect sizes (β₁, β₂, β₃) of BMVs, DMVs, and PTVs. The allelic-series weights remained fixed at w = (1, 2, 3). For the burden phenotype, the effect sizes of all variants were in the same direction, whereas for the SKAT phenotype, the magnitude and direction of effect were randomized. Each bar aggregates results from 10⁴ simulation replicates.

Figures 1B and 1C compare the power to detect genes harboring allelic series between COAST and SKAT-O applied either to all variants (SKAT-O ALL, including BMVs, DMVs, and PTVs) or to PTVs only (SKAT-O PTV). The weights of COAST were fixed at w = (1, 2, 3). Various genetic architectures are generated from Equation 1 with different choices for (β₁, β₂, β₃), as indicated by the tuple in each panel heading. Note that for all architectures save BASE, COAST is applied with misspecified weights.

For all methods, the power to detect an association increased with the proportion of causal variants in the gene. However, the rank ordering of tests by power was insensitive to the causal proportion. For the burden phenotype in Figure 1B, COAST was uniformly more powerful than SKAT-O ALL and was superseded only by SKAT-O PTV in the case of a PTV-only architecture. Intuitively, the power advantage of COAST declined with the L₁ distance of the generative effect sizes from those specified by the allelic-series weights (Figure S8). For the SKAT phenotype in Figure 1C, COAST was most powerful in cases of allelic-series architectures, but SKAT-O PTV performed best in the case of a PTV-only phenotype, and SKAT-O ALL performed best in the case of a uniform phenotype, meaning that the variant annotation was uninformative as to the expected effect size. It is noteworthy that the only architectures for which COAST did not achieve the best power are those that do not exhibit a dose-response relationship (as indicated by the weight tuple). Overall, these findings suggest that although COAST loses some power when its weights do not match the true pattern of effective sizes, COAST is generally well powered for the task of detecting genes with allelic series.

To disentangle the contribution of the allelic-series weights from model synthesis provided by the omnibus test, Figure S7 compares the power among COAST, SKAT-O ALL with allelic-series weights, and SKAT-O ALL with standard weights. For burden phenotypes, the COAST omnibus test was substantially more powerful than SKAT-O with allelic-series weights, whereas for SKAT phenotypes, the COAST omnibus test and SKAT-O with allelic-series weights were similarly powerful, although the latter achieved a slight power advantage. In addition, SKAT-O with allelic-series weights was uniformly more powerful than SKAT-O with standard weights for allelic-series architectures. At genes empirically found to harbor allelic series, the COAST omnibus test was consistently more powerful than SKAT-O with allelic-series weights, which in turn outperformed SKAT-O with standard weights (Figure S18). In practice, whether a gene-phenotype pair follows a burden or SKAT architecture is seldom known. Therefore, having an omnibus test (i.e., COAST) that is considerably more powerful in one case (i.e., burden) and comparably powerful in the other case (i.e., SKAT) is desirable.

Application to circulating-lipid phenotypes

As our first case study, we applied COAST and SKAT-O to identify genes associated with the following circulating-lipid phenotypes: cholesterol, HDL, LDL, and triglycerides. Figure 2 presents the number of Bonferroni-significant genes identified by COAST and SKAT-O. On average, COAST identified 29% more significant associations than SKAT-O ALL and 3.3 times more associations than SKAT-O PTV (Table S1). Across the union of genes declared significant by any association test, the average χ² statistic of COAST was 24% higher than that of SKAT-O ALL and 2.3 times higher than that of SKAT-O PTV (Table S2). Among 43 total associations, 9 (21%) were unique to COAST, 33 (77%) were in common, and 1 (2%) was unique to SKAT-O ALL (Figure S10). The uniform quantile-quantile plots in Figure S9 evince no inflation of the type I error.

Figure 2.

Number and significance of genes significantly associated with circulating-lipid phenotypes

(A) Number of significantly associated genes by phenotype and association test.

(B) Average χ² across the union of genes considered Bonferroni significant by any association test. Error bars indicate 95% confidence intervals for the expected χ² statistic.

Taking cholesterol as an example, we performed a downsampling analysis in which we selected nested subsets of 25%, 50%, and 75% of the total sample and performed association analysis on each (Figure S11). At all sample sizes, COAST identified more Bonferroni-significant associations than SKAT-O. Using only 50% of the sample, COAST recovered the same number of associations as SKAT-O ALL in the full sample.

The mirrored Manhattan plots in Figure 3 show that the signals identified by COAST and SKAT-O ALL were generally concordant, although several additional associations crossed the Bonferroni threshold under COAST. Manhattan plots for COAST stratified by trait are available in Figure S12. Tables S3 and S4 assess the extent to which the gene-trait associations identified by COAST and SKAT-O have existing support from rare variants (Genebass) or common variants (GWAS Catalog). All gene-trait associations have support from Genebass and/or the GWAS Catalog, and most have support from both. Many well-known gene-trait associations—for example, those between APOB (p = 3.8 × 10⁻¹⁸⁵) and PCSK9 (p = 5.5 × 10⁻⁶⁸) and LDL, between ABCA1 (p = 1.3 × 10⁻¹²¹) and HDL, and between ANGPTL3 (p = 1.0 × 10⁻⁵⁴) and triglycerides—appear as positive controls. It should be noted that although most of the associations reported here are already present in Genebass, the sample size of this analysis is only 36.9% of that of Genebass (145,735 vs. 394,841). The two genes, both associated with triglycerides, that were identified by COAST but were not present in Genebass were ANGPTL4 (p = 6.7 × 10⁻¹⁴) and A1CF (p = 3.4 × 10⁻⁷).

Figure 3.

Mirrored Manhattan plots for lipid phenotypes

(Top) COAST.

(Bottom) SKAT-O applied to all rare coding variants (SKAT-O ALL).

Figure 4 presents the pattern of effect sizes among genes significantly associated with lipid phenotypes by either COAST or SKAT-O. With a few exceptions, the mean effect-size magnitude increases monotonically from BMVs to DMVs to PTVs (e.g., association between PCSK9 and cholesterol). The two genes associated with triglycerides by COAST but not present in Genebass (ANGPTL4 and A1CF) both had a monotonically increasing pattern of effect sizes. The one gene (APOE) associated with LDL by SKAT-O but not by COAST had an anti-allelic-series pattern, meaning that the effect-size magnitude decreased monotonically from BMVs to DMVs to PTVs. COAST retains some power to identify genes containing a partial allelic series. For example, the association between LDLR and cholesterol was significant, but whereas the effect size increased from BMVs to DMVs, it declined from DMVs to PTVs. We return to this point in the discussion.

Figure 4.

Effect-size patterns among genes significantly associated with lipid traits

Effect sizes were estimated by standard linear regression. Each bar represents the mean effect size for variants within a gene and variant category. Error bars represent 95% confidence intervals for the mean effect-size magnitude. The absence of an error bar indicates that there are not enough variants for estimating a standard error.

Application to cell-count phenotypes

As a second case study, we applied COAST and SKAT-O to a collection of cell-count phenotypes: erythrocytes, leukocytes, lymphocytes, neutrophils, and thrombocytes (platelets). The uniform quantile-quantile plots in Figure S13 again demonstrate control of the type I error. For all cell-count traits, COAST identified more Bonferroni-significant associations than SKAT-O (Figure 5): 82% more than SKAT-O ALL and 6.3 times more than SKAT-O PTV (Table S5). Across the union of genes declared significant by any association test, the average χ² statistic of COAST was 37% higher than that of SKAT-O ALL and 4.8 times higher than that of SKAT-O PTV (Table S6).

Figure 5.

Number and significance of genes significantly associated with cell-count phenotypes

(A) Number of significantly associated genes by phenotype and association test.

(B) Average χ² across the union of genes considered Bonferroni significant by any association test. Error bars indicate 95% confidence intervals for the expected χ² statistic.

Among 61 total associations, 25 (41%) were unique to COAST, 33 (54%) were in common, and 3 (5%) were unique to SKAT-O ALL (Figure S14). All associations except one (that between TNXB and thrombocytes, identified only by SKAT-O ALL) had common-variant support from the GWAS Catalog, rare-variant support from Genebass, or both (Tables S7 and S8). One gene, DOK2 (p = 4.8 × 10⁻⁷), associated with lymphocytes by COAST, did not previously reach significance in Genebass, although its association with missense variants was suggestive (p = 7.6 × 10⁻⁶). Many well-known gene-trait associations, including those between HBB (p = 1.2 × 10⁻⁸) and erythrocytes, between CXCR2 (p = 2.6 × 10⁻⁴¹) and neutrophils, and between JAK2 (p = 2.2 × 10⁻⁸⁶) and thrombocytes, were recapitulated (Figures S15 and S16).

For cell-count traits, the pattern of effect sizes among genes identified by COAST did not always increase monotonically, although there were many such examples: the associations between SH2B3 and erythrocytes, S1PR2 and leukocytes, SBNO2 and lymphocytes, and JAK2 and thrombocytes (Figure S17). Among genes identified as significant by SKAT-O ALL but not COAST, none had an allelic-series pattern of effect sizes. Figure 6 compares the average χ² statistics of COAST and SKAT-O at genes empirically found to harbor allelic series for both lipid and cell-count traits. A gene was identified as containing an empirical allelic series if it was significantly associated with the trait by any association test and if the mean effect size increased monotonically from BMVs to DMVs to PTVs. Such genes are the intended targets of COAST, and COAST had the best power to uncover such genes.

Figure 6.

Average χ² statistic at genes empirically found to harbor allelic series

A gene was identified as containing an empirical allelic series if it was significantly associated with the trait by any association test and if the mean effect size increased monotonically from BMVs to DMVs to PTVs. Note that the mean effect size is subject to estimation error. The number of allelic series represented in each panel is denoted by G. No panel is shown for neutrophils because no genes with a strictly monotonic pattern of effect sizes were identified. Error bars indicate 95% confidence intervals for the expected χ² statistic.

Discussion

We have developed a rare-variant association test (COAST) tailored to identifying genes containing allelic series: genes wherein increasingly deleterious mutations have increasingly large phenotypic effects. In simulation studies, COAST controlled the type I error and tended to improve power when the pattern of effect sizes increased monotonically from BMVs to DMVs to PTVs. In applications to circulating-lipid and cell-count phenotypes from the UK Biobank, COAST consistently identified more Bonferroni-significant associations than SKAT-O and did so at a higher level of significance. In all cases, the additional genes detected by COAST have supporting evidence from Genebass and/or the GWAS Catalog, mitigating the risk that these associations are spurious. Empirically, in many cases the pattern of effect sizes for genes identified by COAST increased monotonically, and for genes where the pattern of effect sizes was monotonic, COAST provided the greatest power.

COAST is not intended to be a replacement for existing rare-variant associations tests, such as SKAT-O,¹⁶ ACAT-V,²⁶ STAAR,¹⁹ or SAIGE-GENE+.²⁷ These methods seek to identify the existence of a gene-trait association in general and place no prior on what form that relationship should take. In contrast, COAST is tailored to the identification of genes that harbor a dose-response relationship between the functionality of the gene and the magnitude or severity of the phenotype. As such, the collection of genes targeted by COAST is only a subset of that targeted by existing methods. Empirically, the effect sizes of genes identified by COAST did not always increase monotonically in mutational severity. Part of this is most likely due to uncertainty in estimating the effect sizes of individual rare variants, but it is also due in part to the fact that COAST retains power to detect gene-trait associations that follow a partial allelic-series pattern. In practice, when the goal of an analysis is to identify high-confidence allelic series, the initial results of COAST might require post hoc filtering to remove those genes whose effect-size patterns do not increase monotonically.

COAST identified several gene-trait associations that are not present in Genebass but that garner support from the GWAS Catalog: those between ANGPTL4 and triglycerides, A1CF and triglycerides, and DOK2 and lymphocytes. A low-frequency coding variant (rs116843064) in ANGPTL4 was associated with HDL and triglycerides among 42,000 individuals of European ancestry (outside of the UK Biobank)³⁹ and among 66,000 individuals of multiple ancestries (outside of the UK Biobank).⁴⁰ A meta-analysis of 50,000 individuals associated rs116843064 with fasting triglyceride levels.⁴¹ A candidate-gene study associated rare inactivating mutations in ANGPTL4 with reduced levels of fasting triglycerides and reduced odds of coronary artery disease.⁴² Consistent with that work, 25 of the 27 ANGPTL4 rare variants considered in the present study, including all PTVs, were marginally associated with decreased triglyceride levels. A low-frequency coding variant (rs41274050) in A1CF was associated with triglycerides and total cholesterol in over 300,000 individuals of various ancestries, and the association was validated experimentally in a mouse model.⁴³ A large trans-ethnic analysis of 750,000 individuals, including those in the UK Biobank, identified a low-frequency coding variant (rs56094005) in DOK2 as being associated with lymphocyte count, in addition to monocytes, neutrophils, and platelets.^44,45

COAST has several limitations and opportunities for extension. The current implementation incorporates only rare coding variants annotated as BMVs, DMVs, or PTVs. Although a clear ordering exists among the expected phenotypic impacts of these variant categories, in other cases the effect of a variant on gene function is complex and difficult to predict.⁴⁶ One potential extension of COAST is to assign a continuous measure of mutational severity to all of a gene’s variants, including non-coding variants. Possible choices for the severity metric include the CADD,^47,48 MACIE,⁴⁹ or annotation PC^19,50 scores. The continuous metric could then be cut into a finite number of intervals, and the variants could be categorized accordingly. These intervals of mutational severity would replace the current categorization into BMVs, DMVs, and PTVs. Open questions include what metric to use for measuring mutational severity and how to discretize it. Alternatively, the idea of categorizing could be discarded, and models could be defined to allow the expected value of the phenotype to vary continuously with, for example, the total value of the mutational-severity metric aggregated across all rare variants within the gene.

We view the allelic-series weights as hyperparameters that specify the pattern of effect sizes sought. The default values of (w₁, w₂, w₃) = (1, 2, 3) for BMVs, DMVs, and PTVs specify a monotonically increasing pattern. However, any choice of weights such that $w_1\le w_2\le w_3$ suffices to tailor COAST to detecting genes containing allelic series. In general, the optimal weighting scheme will depend on the genetic architecture of a given gene-trait pair. Nevertheless, a weighting scheme that is informed by the expected distribution of effect sizes for a particular phenotype is likely to improve power. For example, data from a single large biobank might be split into training and evaluation sets. COAST with default weights could be run on the training data, and a collection of candidate allelic series could be identified. Among the candidate allelic series, the average effect sizes of BMVs, DMVs, and PTVs could be calculated. These average effect sizes would then serve as the weights (w₁, w₂, w₃) when COAST is applied to the evaluation data. Improving power by learning the allelic-series weights empirically is a promising direction for future research.

Although COAST does not consider the effects of common variants, many prominent examples of allelic series have supporting evidence from both rare and common variants. For example, cholesterol levels are associated with common non-coding variants in a locus near ANGPTL3⁵¹ and with rare loss-of-function variants in the same gene.^3,52 Additionally, both a common missense variant and rare PTVs in SLC30A8 are independently associated with type 2 diabetes.⁵³ Extending COAST to include common-variant effects would increase the power to detect allelic series that have both rare- and common-variant support.

Finally, a single gene can have a dose-response relationship with multiple related traits. For example, APOB was significantly associated with cholesterol, HDL, LDL, and triglycerides by COAST. In such cases, a multivariate outcome model, such as a linear mixed-effects model, can improve power by simultaneously estimating the effects of rare variants on multiple correlated traits. Mixed-effects modeling would also enable the analysis of genetically related individuals, for example, by including a random intercept with covariance proportional to the genetic relatedness matrix.^54,55 Alternatively, COAST can be extended to non-quantitative phenotypes, such as binary, count, or time-to-event phenotypes, by generalizing the constituent models to generalized linear models or Cox proportional hazards models. These extensions are under active development.

Published: July 25, 2023

Web resources

• AllelicSeries, https://CRAN.R-project.org/package=AllelicSeries

• Genebass, https://app.genebass.org/

• GWAS Catalog, https://www.ebi.ac.uk/gwas/

• Hail, https://github.com/hail-is/hail

• R, https://www.R-project.org/

• SKAT, https://CRAN.R-project.org/package=SKAT

Data and code availability

This work used genotypes and phenotypes from the UK Biobank (https://www.ukbiobank.ac.uk/), accessed pursuant to approved application number 51766. The coding-variant allelic-series test was implemented in the AllelicSeries R package, which is available on CRAN (see web resources).