Kernel-based gene–environment interaction tests for rare variants with multiple quantitative phenotypes

Xiaoqin Jin; Gang Shi

doi:10.1371/journal.pone.0275929

Abstract

Previous studies have suggested that gene–environment interactions (GEIs) between a common variant and an environmental factor can influence multiple correlated phenotypes simultaneously, that is, GEI pleiotropy, and that analyzing multiple phenotypes jointly is more powerful than analyzing phenotypes separately by using single-phenotype GEI tests. Methods to test the GEI for rare variants with multiple phenotypes are, however, lacking. In our work, we model the correlation among the GEI effects of a variant on multiple quantitative phenotypes through four kernels and propose four multiphenotype GEI tests for rare variants, which are a test with a homogeneous kernel (Hom-GEI), a test with a heterogeneous kernel (Het-GEI), a test with a projection phenotype kernel (PPK-GEI) and a test with a linear phenotype kernel (LPK-GEI). Through numerical simulations, we show that correlation among phenotypes can enhance the statistical power except for LPK-GEI, which simply combines statistics from single-phenotype GEI tests and ignores the phenotypic correlations. Among almost all considered scenarios, Het-GEI and PPK-GEI are more powerful than Hom-GEI and LPK-GEI. We apply Het-GEI and PPK-GEI in the genome-wide GEI analysis of systolic blood pressure (SBP) and diastolic blood pressure (DBP) in the UK Biobank. We analyze 18,101 genes and find that LEUTX is associated with SBP and DBP (p = 2.20×10⁻⁶) through its interaction with hemoglobin. The single-phenotype GEI test and our multiphenotype GEI tests Het-GEI and PPK-GEI are also used to evaluate the gene–hemoglobin interactions for 22 genes that were previously reported to be associated with SBP or DBP in a meta-analysis of genetic main effects. MYO1C shows nominal significance (p < 0.05) by the Het-GEI test. NOS3 shows nominal significance in DBP and MYO1C in both SBP and DBP by the single-phenotype GEI test.

Citation: Jin X, Shi G (2022) Kernel-based gene–environment interaction tests for rare variants with multiple quantitative phenotypes. PLoS ONE 17(10): e0275929. https://doi.org/10.1371/journal.pone.0275929

Editor: Mehdi Rahimi, KGUT: Graduate University of Advanced Technology, ISLAMIC REPUBLIC OF IRAN

Received: April 16, 2022; Accepted: September 26, 2022; Published: October 12, 2022

Copyright: © 2022 Jin, Shi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: This research has been conducted using the UK Biobank Resource under Application Number 44080. The genetic and phenotype datasets are available via the UK Biobank data access process. More details are available at http://www.ukbiobank.ac.uk/register-apply/.

Funding: This work was supported by the national Thousand Youth Talents Plan to GS. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Genome-wide association studies (GWASs) have identified numerous common variants associated with common diseases or phenotypes [1]. Nevertheless, a small portion of the heritabilities can be explained by the discovered common variants [2, 3]. Sequencing studies showed that some of the “missing heritability” was attributable to rare variants [4, 5]. Complex diseases are usually influenced by genetic factors, environmental factors and the interplay between them. Wang et al. showed that the interactions between SMC5 variants and alcohol consumption are associated with fasting plasma lipid levels [6]. Yang et al. demonstrated that the interactions between PDE3B variants and smoking are associated with pulmonary function [7]. Johansson et al. revealed that the interactions between NFE2L2 variants and second-hand smoke are associated with pediatric asthma risk [8]. For a long time, gene–environment interactions (GEIs) have been expected to explain some of the “missing heritability” and shed light on the genetic etiology of complex diseases [9].

Existing studies suggest that the interaction between a common variant and an environmental factor may be associated with multiple correlated phenotypes, which is called GEI pleiotropy [10]. Kilpeläinen et al. identified four loci in or near CLASP1, LHX1, SNTA1 and CNTNAP2 that are associated with three blood lipid levels: low density lipoprotein, high density lipoprotein and triglycerides through their interactions with physical activity [11]. Novel gene-sleep interactions were also identified for known lipid loci, including LPL and PCSK9 [12]. To date, all the reported GEI pleiotropies are with common variants. From a methodological perspective, Majumdar et al. showed that statistical power to detect GEI effects can be improved by analyzing multiple phenotypes jointly [10]. However, multiphenotype methods for testing GEIs with rare variants are lacking.

To the best of our knowledge, there is only one method currently available for testing GEIs with rare variants and multiple phenotypes [13]. The method consists of three steps: remove correlation among multiple phenotypes by using principal component analysis or other linear transformations; obtain p value for each transformed phenotype by testing the effects of an optimally weighted combination of GEIs for rare variants (TOW-GE) [14]; employ Fisher’s combination test (FCT) to combine the p values of multiple phenotypes. We denote the method as TOWGE-FCT in this paper. It can be expected that the degree of freedom of TOWGE-FCT would become larger with the increasing number of phenotypes, which might limit statistical power of the test.

In this work, we model the correlations among the GEI effects of a variant on multiple phenotypes by assuming four different kernel matrices, similar to those for multiphenotype tests of genetic main effects [15]. We extend the single-phenotype GEI test [16] and propose four multiphenotype GEI tests for rare variants, which are the test with homogeneous kernel (Hom-GEI), the test with heterogeneous kernel (Het-GEI), the test with projection phenotype kernel (PPK-GEI) and the test with linear phenotype kernel (LPK-GEI). We conduct simulation studies to examine the empirical distributions of the four test statistics under the null hypothesis and compare their statistical power under different scenarios. In the analysis of systolic blood pressure (SBP) and diastolic blood pressure (DBP) in the UK Biobank, we chose hemoglobin (Hb) as the environmental variable, which is known to be associated with both SBP and DBP [17, 18]. With the whole-exome sequencing data in 200,643 samples, we applied Het-GEI and PPK-GEI in the genome-wide analyses of gene-Hb interactions. We also carried out single-phenotype and multiphenotype GEI tests to evaluate the gene-Hb interactions for 22 genes that were previously reported to be associated with SBP or DBP in a meta-analysis of main genetic effects [19].

Methods

Single-phenotype GEI test

Assume that n unrelated individuals are sequenced in a gene or region with m rare variants and K quantitative phenotypes are measured. For the k-th phenotype, y_k = (y_1k, y_1k, ⋯, y_nk)^T denotes an n × 1 phenotype vector, and X = (X₁, X₂, ⋯, X_q+1) is an n × (q + 1) matrix comprised of intercept and covariate vectors with X_t = (X_1t, X_2t, ⋯, X_nt)^T, t = 1, 2, …, q+1. The first vector X₁ represents the intercept vector with elements X_i1 = 1 and i = 1, 2, ⋯, n. The other q vectors are the covariate vectors. Let G = (G₁, G₁, ⋯, G_m) be an n × m genotype matrix, in which G_j = (G_1j, G_2j, ⋯, G_nj)^T, j = 1, 2, …, m, and G_ij is the number of minor alleles. E = diag{E_i} denotes an n × n diagonal matrix of environmental measurements, and E_i is centralized and included in X as a covariate for adjusting the environmental effect. Following the single-phenotype GEI test for rare variants in rareGE [16], we consider the linear mixed model as follows: (1) where α_k = (α_k1, α_k2, ⋯, α_k(q+1))^T is a (q+1)×1 vector of covariate effects for the k-th phenotype. W = diag{w_j} is an m × m weight matrix for the m variants. The weight of the j-th variants is w_j = Beta(MAF_j, 1, 25) [20], where MAF_j is the minor allele frequency (MAF) of the j-th variants. In addition, β_k = (β_1k, β_2k, ⋯, β_mk)^T is an m × 1 vector consisting of genetic main effects for the k-th phenotype, and γ_k = (γ_1k, γ_2k, ⋯, γ_mk)^T is an m×1 vector of the interaction effects. Here, the main genetic effects β_k are assumed to be fixed and the interaction effects γ_k to be random, γ_k ~ MVN(0, σ²I_m). In addition, ε_k = (ε_1k, ε_2k, ⋯, ε_nk)^T denotes an n×1 error vector, and . The null hypothesis for testing the GEI interactions is H₀: σ² = 0. The model under the null hypothesis is (2)

Here, α_k, β_k, and can be estimated by linear regression, and the estimated mean and variance-covariance matrix of y_k are where , with Z = (X, GW). The score statistic for testing the GEI effects is (3) which is mathematically equivalent to (4) Here, is the score statistic for the j-th variant.

Under H₀, follows a mixture of chi-square distributions with 1 degree of freedom, and λ_j are nonzero eigenvalues of the regional relationship matrix (5)

The p-value can be computed by using Kuonen’s saddlepoint approximation method [16, 21]. In the same spirit, we extend the single-phenotype GEI test for multiple phenotypes.

Kernel-based multiphenotype GEI tests

Denote y = (y₁, y₂, ⋯, y_K) as the n × K matrix of K phenotypes and A = (α₁, α₂, ⋯, α_K) as the (q+1) × K matrix of covariate effects. Let B = (β₁, β₂, ⋯, β_K) be the m × K matrix of genetic main effects and Γ = (γ₁, γ₂, ⋯, γ_K) be the m × K matrix of GEI effects. In addition, ε = (ε₁, ε₂, ⋯, ε_K) is the n × K error matrix. In light of the correlation among phenotypes, we assume ε = (ε₁, ε₂, ⋯, ε_K) ~ MVN(0, Σ), i = 1, 2, ⋯, n. Then, the mixed model for multiple phenotypes can be formulated in a matrix form as follows: (6)

Stack columns of the phenotype matrix y into a vector and columns of the error matrix ε into . We have vec(ε)~MVN(0, Σ ⊗ I_n), where ⊗ is the Kronecker product [22]. We rewrite model (6) in vector form as (7)

Assume vec(Γ)~MVN(0, σ²Σ_P ⊗ I_m), where Σ_P is a K × K kernel in the phenotype space and models the correlation among the GEI effects of a variant on multiple phenotypes. As a result, vec(y)~MVN(vec(μ), H), where μ = XA + GWB and H = σ²(Σ_P ⊗ EGWWG^T E) + Σ ⊗ I_n. The null hypothesis for testing the GEI effects with multiple phenotypes is H₀: σ² = 0, and the score statistic is (8) where and are the estimated mean and variance-covariance matrix, respectively.

The score statistic Q asymptotically follows a mixture of 1-freedom chi-square distributions and λ_j are nonzero eigenvalues of (9) where P = I_n−Z(Z^TZ)⁻¹Z^T and Z is the same as in the single-phenotype GEI test. The corresponding p-values can be computed via Kuonen’s saddlepoint method [21].

As can be seen in (8), our proposed tests depend on the kernel matrix Σ_P. Similar to [15], we use four types of kernel matrices to model the correlation among the GEI effects on multiple phenotypes.

Homogeneous kernel.

Assume that the GEI effects of a variant on multiple different phenotypes are homogeneous, implying that γ_j1 = γ_j2 = ⋯ = γ_jK. The kernel is constructed as where 1_K = (1, 1, ⋯, 1)^T is a K × 1 vector. Σ_Hom indicates the GEI effects of a variant on multiple phenotypes to be the same.

Heterogeneous kernel.

Assuming that the GEI effect sizes of a variant on multiple phenotypes are heterogeneous, the kernel is where I_K is a K × K identity matrix. Here, Σ_Het implies that the GEI effects of a variant on multiple phenotypes are independent.

Projection phenotype kernel.

Assume that the correlation among the GEI effects of a variant on multiple phenotypes can be depicted by the correlation among the phenotypes. That is, where is the estimated variance-covariance matrix of the phenotypes.

Linear phenotype kernel.

Assume that the GEI effects of a variant on multiple phenotypes equal the squared correlation among the phenotypes. That is,

Similar to the proof in [22], the test score statistic (8) is (10) which can be rewritten as (11)

Therefore, the LPK-GEI test simply combines statistics of single-phenotype GEI tests across multiple phenotypes.

Based on different choices of the kernel matrix Σ_P, we propose four multiphenotype GEI tests, which are named Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI.

Results

Numerical simulations

To evaluate the null distributions and statistical power of the four proposed tests, we carried out extensive simulation studies. Using the calibrated coalescent model implemented in COSI [23], we generated 10,000 haplotypes in a 200 kb genomic region. Parameters in the coalescent model were used to mimic the linkage disequilibrium pattern, local recombination rate and demographic history for the population of European ancestry. We randomly paired these haplotypes to form diploid genotype data of 10,000 individuals and randomly selected 5000 out of the 10,000 individuals. A subregion length of 3 kb was randomly selected from the 200 kb region to obtain the genotype data of the 5000 samples for each replicate, and 1000 replicates of genotype data were generated. Variants with MAF ≤ 0.01 were considered to be rare and used for simulations.

To evaluate null distributions of our proposed tests, four phenotypes of the 5000 unrelated individuals under the null hypothesis were generated. For the sake of simplicity, phenotypes shared the same covariate sets and were generated as follows: (12) Where y_i1, y_i2, y_i3, y_i4 are the four phenotypes for the i-th individual (i = 1, 2, …, n). For the i-th individual, sex_i is a binary covariate following a Bernoulli distribution with probability 0.5, namely, sex_i ~ Bernoulli(0.5). Both age_i and bmi_i are continuous covariates: age_i ~ N(50, 25), bmi_i ~ N(50, 25). G_ij (j = 1, 2, ⋯, m) are the coded genotypes of the simulated causal variants for individual i. Here, we assumed a proportion of causal variants θ = 0.1, 0.2, 0.3. In addition, w_j (j = 1, 2, ⋯, m) is the weight of variant j; β_j1, β_j2, β_j3, and β_j4 are the main genetic effects for phenotype 1, phenotype 2, phenotype 3 and phenotype 4, respectively, with β_j1 = 0.1, β_j2 = 0.2, β_j3 = 0.1, and β_j4 = 0.2; and l₁, l₂, l₃, and l₄ are indicator variables, with l_k = 1 when phenotype k is associated with genetic variants and l_k = 0 otherwise. Since not all of the phenotypes may be associated with the rare variants [22, 24], we considered scenarios under which pleiotropy exists or does not exist. Specifically, we assumed that the first t phenotypes were associated with the rare variants, namely, l₁ = ⋯ = l_t = 1 and l_t+1 = ⋯ = l_4-t = 0, t = 1,2,3,4. ε_ik is a random error for the i-th individual and the k-th phenotype, ε_i = (ε_i1, ε_i2, ε_i3, ε_i4)^T ~ MVN(0, Σ), where and ρ represents the correlation among different phenotypes. Three levels of correlation strength were considered: weak correlation with ρ = 0.25, moderate correlation with ρ = 0.5 and strong correlation with ρ = 0.75. For each simulation setup, 20 replicates of phenotypes and covariates were simulated based on one genotype dataset; thus, a total of 20,000 replicates of phenotypes and covariates were simulated.

To evaluate the statistical power of our proposed four multiphenotype GEI tests, we simulated the four correlated phenotypes for 5000 independent individuals under the alternative hypothesis. For each of the genotype datasets, one phenotype and covariates set was simulated according to the following model: (13) where sex_i, age_i, bmi_i, G_ij, w_j, β_jk (k = 1,2,3,4), l_k (k = 1,2,3,4) and ε_i = (ε_i1, ε_i2, ε_i3, ε_i4)^T are the same as described in model (12). The body mass index (BMI) was centered and used as the environmental variate E_i. Here, γ_jk is the gene-BMI interaction effect of the j-th causal rare variant on the k-th phenotype, with γ_jk ~ N(0, 0.05)². Since the interaction effects of a variant on each phenotype were simulated independently, the gene–BMI interaction effects of a variant on multiple phenotypes are heterogeneous.

In all simulations and the analyses of the simulated data, variant weights were the density function of beta distribution with degrees of freedom of 1 and 25 evaluated at the MAF of rare variants [20] as described in the single-phenotype GEI test. We considered the gene–BMI interaction to be significant if its p-value was less than 2.5×10⁻⁶, corresponding to a correction for multiple testing in genome-wide studies of 20,000 genes. Empirical power was the portion of significant results in 1000 replicates.

Null distributions.

We examined null distributions of test statistics for Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI with causal rare variant proportion θ = 0.2 and all phenotypes associated with genetic variants. We first estimated means and residuals by performing phenotype-specific regression analyses. The variance-covariance matrix Σ was estimated by residuals from all phenotypes. Test statistics of the four tests were computed as in (8) with corresponding kernels for Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI. Using Kuonen’s saddlepoint approximation method [21], the p-values of the four test statistics were computed. Finally, we compared distributions of empirical p-values with the expected uniform distribution between 0 and 1.

The quantile-quantile (Q–Q) plots of the four multiphenotype statistics under weak (ρ = 0.25), moderate (ρ = 0.5) and strong (ρ = 0.75) correlations among phenotypes are shown in Figs 1–3, respectively. The empirical distributions of the four test statistics are aligned with their theoretical distributions, as expected.

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Fig 1. Q–Q plots of the test statistics under the null hypothesis with weak among-phenotype correlation ρ = 0.25.

The horizontal and vertical axes represent the negative log₁₀ of the expected p-values and the negative log₁₀ of the observed p-values, respectively. A: Hom-GEI; B: Het-GEI; C: PPK-GEI; D: LPK-GEI.

https://doi.org/10.1371/journal.pone.0275929.g001

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Fig 2. Q–Q plots of the test statistics under the null hypothesis with moderate among-phenotype correlation ρ = 0.5.

The horizontal and vertical axes represent the negative log₁₀ of the expected p-values and the negative log₁₀ of the observed p-values, respectively. A: Hom-GEI; B: Het-GEI; C: PPK-GEI; D: LPK-GEI.

https://doi.org/10.1371/journal.pone.0275929.g002

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Fig 3. Q–Q plots of the null distributions under the null hypothesis with strong among-phenotype correlation ρ = 0.75.

The horizontal and vertical axes represent the negative log₁₀ of the expected p-values and the negative log₁₀ of the observed p-values, respectively. A: Hom-GEI; B: Het-GEI; C: PPK-GEI; D: LPK-GEI.

https://doi.org/10.1371/journal.pone.0275929.g003

Statistical power.

The statistical power of Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI under weak, moderate and strong correlations among phenotypes are shown in Figs 4–6, respectively. In each figure, the power with three different proportions of causal variants and different numbers of associated phenotypes are presented. All four tests show improved power as the proportion of causal variants increases. This is because an increased proportion of causal variants leads to larger interaction effects under the test. Taking Fig 5D as an example, for the causal rare variant proportion θ = 0.1, Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI have powers of 0.067, 0.424, 0.431 and 0.199, respectively. For θ = 0.2, the corresponding powers are 0.145, 0.72, 0.725 and 0.428, respectively. For θ = 0.3, the power increases further to 0.278, 0.867, 0.869 and 0.608.

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Fig 4. Statistical power of Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI under weak among-phenotype correlation ρ = 0.25.

The horizontal and vertical axes represent the proportion of causal rare variants and the statistical power, respectively. A: Power when only the first phenotype is associated with interactions; B: Power when the first two phenotypes are associated with interactions; C: Power when the first three phenotypes are associated with interactions; D: Power when all four phenotypes are associated with interactions.

https://doi.org/10.1371/journal.pone.0275929.g004

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Fig 5. Statistical power of Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI under moderate among-phenotype correlation ρ = 0.5.

The horizontal and vertical axes represent the proportion of causal rare variants and the statistical power, respectively. A: Power when only the first phenotype is associated with the interactions; B: Power when the first two phenotypes are associated with the interactions; C: Power when the first three phenotypes are associated with the interactions; D: Power when all four phenotypes are associated with the interactions.

https://doi.org/10.1371/journal.pone.0275929.g005

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Fig 6. Statistical power of Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI under strong among-phenotype correlation ρ = 0.75.

The horizontal and vertical axes represent the proportion of causal rare variants and the statistical power, respectively. A: Power when only the first phenotype is associated with the interactions; B: Power when the first two phenotypes are associated with the interactions; C: Power when the first three phenotypes are associated with the interactions; D: Power when all four phenotypes are associated with the interactions.

https://doi.org/10.1371/journal.pone.0275929.g006

From Figs 4–6, we can see that the four tests provide improved power with more phenotypes associated with the interactions, which suggests that our multiphenotype analyses can exploit GEI pleiotropy effectively. For instance, in Fig 6, with the causal proportion θ = 0.2, when only the first phenotype is associated with the interactions, the powers of Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI are 0.013, 0.206, 0.292 and 0.045, respectively, as shown in Fig 6A. When the first two phenotypes are associated with the interactions, the corresponding power improves to 0.092, 0.607, 0.629 and 0.152, as shown in Fig 6B. With three phenotypes associated with the interactions, the power become even larger and are 0.173, 0.766, 0.767 and 0.252, as shown in Fig 6C. When all phenotypes are associated with the interactions, the power further increase to 0.236, 0.827, 0.828 and 0.345, as shown in Fig 6D.

We can also see from Figs 4–6 that Hom-GEI, Het-GEI and PPK-GEI have enhanced power as the correlation among phenotypes becomes stronger, but LPK-GEI suffers power loss. For instance, we observe the power of the four tests with causal proportion θ = 0.2. When the correlation among phenotypes is weak, the power values of Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI are 0.105, 0.508, 0.523 and 0.370, respectively, in Fig 4C. When the correlation is moderate, the power values are 0.104, 0.597, 0.598 and 0.311, as shown in Fig 5C. With a strong correlation, the power values are 0.173, 0.766, 0.767 and 0.252, as shown in Fig 6C. This demonstrates that Hom-GEI, Het-GEI and PPK-GEI can benefit from the increased correlations among phenotypes. However, since LPK-GEI directly combines statistics from single-phenotype GEI tests and ignores the phenotypic correlations, the increased correlation among phenotypes leads to a substantial power loss.

Among almost all of the considered scenarios in Figs 4–6, PPK-GEI has approximately the same or slightly larger power than Het-GEI, and the two tests outperform Hom-GEI and LPK-GEI. Hom-GEI shows the poorest power performance among all the proposed tests. This is because the phenotypes were simulated based on heterogeneous interaction effects, violating the assumption that Hom-GEI is based upon. Because the GEI effects of a variant on multiple phenotypes can hardly be homogeneous in reality, Hom-GEI may not be a good choice for real data analysis. Therefore, we choose Het-GEI and PPK-GEI for our genome-wide interaction analysis in UK Biobank.

With the proportion of causal rare variant θ = 0.1 and the among-phenotype correlation ρ = 0.5, we compared the power of our tests with the TOWGE-FCT under different numbers of phenotypes associated with the interactions, the results are shown in Fig 7. Because TOWGE-FCT is a permutation based method, which is computationally very expensive, the power results were evaluated at the significance level of 0.05. As can be observed from Fig 7 that all the five tests can provide enhanced power as more phenotypes associated with the interactions. Het-GEI, PPK-GEI and LPK-GEI tests have higher power than TOWGE-FCT, however, Hom-GEI has lower power than TOWGE-FCT. We can also see that Het-GEI and PPK-GEI tests outperform the other tests, further indicating Het-GEI and PPK-GEI to be two powerful tests. For instance, when only the first two phenotypes are associated with the interactions, the power values for Hom-GEI, Het-GEI, PPK-GEI, LPK-GEI and TOWGE-FCT are 0.177, 0.507, 0.517, 0.403 and 0.304, respectively.

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Fig 7. Statistical power of Hom-GEI, Het-GEI, PPK-GEI, LPK-GEI and TOWGE-FCT with different correlated phenotypes, ρ = 0.5, θ = 0.1.

The horizontal and vertical axes represent the number of phenotypes associated with interactions and the statistical power, respectively. The significance level is 0.05.

https://doi.org/10.1371/journal.pone.0275929.g007

Gene-Hb interaction analysis of blood pressure phenotypes in UK Biobank

UK Biobank is a prospective study that recruited approximately 500,000 volunteers aged 40 and 69 years in the United Kingdom and collected extensive genetic and phenotypic data [25, 26]. We used the whole-exome sequencing data released by UK Biobank with a total of 200,643 samples. Individuals who had withdrawn and one member in each pair with kinship larger than 0.25 measured via KING [27] were removed. We considered SBP and DBP as the blood pressure (BP) phenotypes and Hb as the environmental factor, which is known to be associated with both SBP and DBP [17, 18]. Covariates included age, age², sex, BMI and 20 principal components to adjust for population stratification. SBP and DBP averaged over multiple measurements at baseline were used. For individuals taking BP-lowering medications, 10 mm Hg and 5 mm Hg were added to the SBP and DBP, respectively [28, 29]. Phenotypes and covariates located 5 standard deviations away from their respective means were defined as outliers. Outliers or individuals with missing phenotypes or missing covariates were removed. As a result, 157,514 individuals, including 71,501 males (45.4% males) and 86,013 females (54.6% females), were included in our gene-Hb interaction analyses. BP phenotypes, age, BMI and Hb were standardized before the analysis.

We carried out genome-wide analysis on 18,101 genes from 22 autosomal chromosomes. Variants in the genotype dataset were annotated via VEP [30]. We restricted to variants annotated as stop_loss, missense_variant, start_lose, splice_donor_variant, inframe_deletion, frameshift_variant, splice_acceptor_variant, stop_gained or inframe_insertion with PolyPhen scores larger than 0.15 and Sift scores less than 0.05 [31]. Those variants with MAFs less than 3% were extracted via PLINK [32]. Genotypes were further transformed into numeric values using fcGENE [33].

For each of the 18,101 genes, we performed Het-GEI and PPK-GEI analysis of the gene-Hb interactions on SBP and DBP phenotypes. Manhattan plots of p-values from the two tests are presented in Fig 8, and QQ plots of the Het-GEI and PPK-GEI tests are shown in Fig 9. With a genome-wide significance level of 2.5×10⁻⁶, only LEUTX is significant according to the Het-GEI test (p-value = 2.2×10⁻⁶), and its p-value according to the PPK-GEI test is 7.43×10⁻⁶. If we consider a suggestive significance level at 1×10⁻⁴, twelve genes passed the threshold, whose details are presented in Table 1.

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Fig 8. Manhattan plot of genome-wide multiphenotype analysis of gene-Hb interactions in BPs.

The horizontal and vertical axes represent the genomic position and the negative log₁₀ of the p-values, respectively. A: Het-GEI; B: PPK-GEI.

https://doi.org/10.1371/journal.pone.0275929.g008

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Fig 9. Q–Q plots of genome-wide multiphenotype GEI analysis of gene-Hb interactions in BPs.

The horizontal and vertical axes represent the negative log₁₀ of the expected p-values and the negative log₁₀ of the observed p-values, respectively. A: Het-GEI; B: PPK-GEI.

https://doi.org/10.1371/journal.pone.0275929.g009

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Table 1. Genes showing suggestive evidence (p-values < 1 × 10⁻⁴) of gene-Hb interactions in the Het-GEI or PPK-GEI tests.

https://doi.org/10.1371/journal.pone.0275929.t001

Recently, Surendran et al. reported 22 genes associated with SBP or DBP in a meta-analysis of 1.3 million samples from multiple cohorts, including UK Biobank, the Million Veterans Program and deCODE [19]. For the 22 genes, we looked up our genome-wide results for the possible interactions with Hb. For comparison, we also conducted single-phenotype GEI tests using the INT-FIX function from the rareGE R package [16] for the two BP phenotypes separately. The number of rare variants involved in the analysis and p-values from the multiphenotype and single-phenotype GEI tests are provided in Table 2.

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Table 2. Multiphenotypic analyses and single-phenotype analyses of gene-Hb interactions in BP-associated genes.

https://doi.org/10.1371/journal.pone.0275929.t002

There are no significant results after correcting the multiple testing. At the nominal significance level of 0.05, only one gene, MYO1C, shows interactions with Hb for BP phenotypes by the PPK-GEI test (p-value = 0.038). With the single-phenotype GEI test, NOS3 has a p-value of 0.026 for DBP, and MYO1C has p-values of 0.018 and 0.011 for SBP and DBP, respectively.

Discussion

In this paper, we propose four statistical tests, Hom-GEI, Het-GEI, PPK-GEI and LPK-GEI, to test GEI effects with rare variants for multiple correlated quantitative phenotypes. Through simulation studies, the statistical power of the tests was investigated in terms of the proportion of causal variants, the number of phenotypes associated with interactions and the correlation strength among phenotypes. Simulation results show that all tests demonstrate improved statistical power when the proportion of causal variants or the number of associated phenotypes increases. Hom-GEI, Het-GEI and PPK-GEI benefit from correlation among phenotypes; however, the LPK-GEI test suffers power loss, especially when correlation among phenotypes is strong. This is because LPK-GEI directly combines statistics from single-phenotype GEI tests and ignores phenotype dependence. In addition, among almost all of the considered scenarios, Het-GEI and PPK-GEI have almost the same power and outperform the other two tests. Hom-GEI shows the poorest power due to its unrealistic assumption. In summary, Het-GEI and PPK-GEI are two powerful tests for investigating GEI with multiple quantitative phenotypes.

We applied Het-GEI and PPK-GEI in the genome-wide analysis of SBP and DBP in order to detect possible gene-Hb interactions in UK Biobank. We analyzed 18,101 genes and identified LEUTX to be associated with BP phenotypes through its interaction with Hb via the Het-GEI test. At the suggestive significance level, twelve genes were identified to be associated with BP phenotypes through their interactions with Hb. LEUTX was previously reported to play a central role in embryo genome activation [34] whose role in BP regulation is unclear. Recent study of rare variants suggests that BP-associated variants are enriched in active chromatin regions of fetal tissue and potentially link fetal development to BP regulation in later life [19]. Thus, LEUTX might be associated with the BP phenotypes in a similar manner. In the analysis of 454,787 UK Biobank participants, genetic main effect of LEUTX was not associated with BP phenotypes at the nominal significance level of 0.05 [35]. However, our tests identified LEUTX to be interacted with Hb in BP phenotypes at the genome-wide significance level of 2.5×10⁻⁶ in the sample of 157,514 UK Biobank participants. We also conducted a single-phenotype GEI test and multiphenotype GEI tests to evaluate the gene-Hb interactions for 22 genes that were previously reported to be associated with SBP or DBP in a meta-analysis of genetic main effects. MYO1C shows nominal significance by the Het-GEI test. NOS3 shows nominal significance in DBP and MYO1C in SBP and DBP by the single-phenotype GEI test.

Our proposed multiphenotype GEI tests are an extension of the single-phenotype GEI test in rareGE [16]. The tests retain the desirable properties of the single-phenotype GEI test, which allows for adjusting covariates and is powerful when the GEI effects of variants act in different directions on phenotypes. Our proposed multiphenotype GEI tests, except for Hom-GEI, are more powerful than the existing multiphenotype GEI test TOWGE-FCT. Moreover, our methods are computationally less expensive. This is because that TOWGE-FCT employs permutations to evaluate p value for each transferred phenotype, however, our tests are based on asymptotic distributions and p values can be computed analytically.

Our proposed multiphenotype GEI tests have the following limitations. First, our tests have specific assumptions on the correlation structure for the GEI effects among multiple phenotypes, violating the assumption would lead to a substantial loss of power. Second, our tests assume individuals to be unrelated. Familiar correlation is not considered, and related samples must be excluded, which may substantially reduce the sample size and result in a loss of power. Third, our proposed GEI tests are for rare variants only, while both common and rare variants may contribute to complex diseases [36–38]. In future work, we plan to consider a unified test to address these issues. Finally, while we identified LEUTX to interact with Hb in BP phenotypes, the result lacks independent validation. Thus, it should be considered as being preliminary and further experiments are necessary.

Conclusion

In this paper, we modeled the correlation among the GEI effects of a variant on multiple phenotypes by using four kernels. Based on these kernels, we proposed four multiphenotype GEI tests for rare variants. The four tests retain the desirable properties of the single-phenotype GEI test and provide enhanced statistical power by analyzing multiple phenotypes simultaneously. We applied Het-GEI and PPK-GEI to test gene-Hb interactions for 18,101 genes in SBP and DBP in UK Biobank. LEUTX was associated with BP phenotypes through the interaction with Hb via the Het-GEI test. At the suggestive significance level, twelve genes were reported. Our proposed tests can be readily used to test GEIs in a variety of correlated phenotypes and hopefully contribute to the genetic studies of complex diseases.

References

1. Buniello A, MacArthur JAL, Cerezo M, Harris LW, Hayhurst J, Malangone C, et al. The NHGRI-EBI GWAS Catalog of published genome-wide association studies, targeted arrays and summary statistics 2019. Nucleic Acids Res. 2019;47(D1):D1005–D1012. pmid:30445434.
- View Article
- PubMed/NCBI
- Google Scholar
2. Nolte IM, van der Most PJ, Alizadeh BZ, de Bakker PI, Boezen HM, Bruinenberg M, et al. Missing heritability: is the gap closing? An analysis of 32 complex traits in the Lifelines Cohort Study. Eur J Hum Genet. 2017;25(7):877–885. pmid:28401901.
- View Article
- PubMed/NCBI
- Google Scholar
3. López-Cortegano E, Caballero A. Inferring the Nature of Missing Heritability in Human Traits Using Data from the GWAS Catalog. Genetics. 2019;212(3):891–904. pmid:31123044.
- View Article
- PubMed/NCBI
- Google Scholar
4. Geddes L. Genetic study homes in on height’s heritability mystery. Nature. 2019;568(7753):444–445. pmid:31015700.
- View Article
- PubMed/NCBI
- Google Scholar
5. Yu C, Arcos-Burgos M, Baune BT, Arolt V, Dannlowski U, Wong ML, et al. Low-frequency and rare variants may contribute to elucidate the genetics of major depressive disorder. Transl Psychiatry. 2018;8(1):70. pmid:29581422.
- View Article
- PubMed/NCBI
- Google Scholar
6. Wang Z, Chen H, Bartz TM, Bielak LF, Chasman DI, Feitosa MF, et al. Role of Rare and Low-Frequency Variants in Gene-Alcohol Interactions on Plasma Lipid Levels. Circ Genom Precis Med. 2020;13(4):e002772. pmid:32510982.
- View Article
- PubMed/NCBI
- Google Scholar
7. Yang T, Jackson VE, Smith AV, Chen H, Bartz TM, Sitlani CM, et al. Rare and low-frequency exonic variants and gene-by-smoking interactions in pulmonary function. Sci Rep. 2021;11(1):19365. pmid:34588469.
- View Article
- PubMed/NCBI
- Google Scholar
8. Johansson E, Martin LJ, He H, Chen X, Weirauch MT, Kroner JW, et al. Second-hand smoke and NFE2L2 genotype interaction increases paediatric asthma risk and severity. Clin Exp Allergy. 2021;51(6):801–810. pmid:33382170.
- View Article
- PubMed/NCBI
- Google Scholar
9. Dahl A, Nguyen K, Cai N, Gandal MJ, Flint J, Zaitlen N. A Robust Method Uncovers Significant Context-Specific Heritability in Diverse Complex Traits. Am J Hum Genet. 2020;106(1):71–91. pmid:31901249.
- View Article
- PubMed/NCBI
- Google Scholar
10. Majumdar A, Burch KS, Haldar T, Sankararaman S, Pasaniuc B, Gauderman WJ, et al. A two-step approach to testing overall effect of gene-environment interaction for multiple phenotypes. Bioinformatics. 2021:btaa1083. pmid:33453114.
- View Article
- PubMed/NCBI
- Google Scholar
11. Kilpeläinen TO, Bentley AR, Noordam R, Sung YJ, Schwander K, Winkler TW, et al. Multi-ancestry study of blood lipid levels identifies four loci interacting with physical activity. Nat Commun. 2019;10(1):376. pmid:30670697.
- View Article
- PubMed/NCBI
- Google Scholar
12. Noordam R, Bos MM, Wang H, Winkler TW, Bentley AR, Kilpeläinen TO, et al. Multi-ancestry sleep-by-SNP interaction analysis in 126,926 individuals reveals lipid loci stratified by sleep duration. Nat Commun. 2019;10(1):5121. pmid:31719535.
- View Article
- PubMed/NCBI
- Google Scholar
13. Zhang J, Sha Q, Hao H, Zhang S, Gao XR, Wang X. Test Gene-Environment Interactions for Multiple Traits in Sequencing Association Studies. Hum Hered. 2019;84(4–5):170–196. pmid:32417835.
- View Article
- PubMed/NCBI
- Google Scholar
14. Zhao Z, Zhang J, Sha Q, Hao H. Testing gene-environment interactions for rare and/or common variants in sequencing association studies. PLoS One. 2020;15(3):e0229217. pmid:32155162.
- View Article
- PubMed/NCBI
- Google Scholar
15. Dutta D, Scott L, Boehnke M, Lee S. Multi-SKAT: General framework to test for rare-variant association with multiple phenotypes. Genet Epidemiol. 2019;43(1):4–23. pmid:30298564.
- View Article
- PubMed/NCBI
- Google Scholar
16. Chen H, Meigs JB, Dupuis J. Incorporating gene-environment interaction in testing for association with rare genetic variants. Hum Hered. 2014;78(2):81–90. pmid:25060534
- View Article
- PubMed/NCBI
- Google Scholar
17. Atsma F, Veldhuizen I, de Kort W, van Kraaij M, Pasker-de Jong P, Deinum J. Hemoglobin level is positively associated with blood pressure in a large cohort of healthy individuals. Hypertension. 2012;60(4):936–941. pmid:22949533.
- View Article
- PubMed/NCBI
- Google Scholar
18. Wang TJ, Gona P, Larson MG, Levy D, Benjamin EJ, Tofler GH, et al. Multiple biomarkers and the risk of incident hypertension. Hypertension. 2007;49(3):432–438. pmid:17242302.
- View Article
- PubMed/NCBI
- Google Scholar
19. Surendran P, Feofanova EV, Lahrouchi N, Ntalla I, Karthikeyan S, Cook J, et al. Discovery of rare variants associated with blood pressure regulation through meta-analysis of 1.3 million individuals. Nat Genet. 2020;52(12):1314–1332. pmid:33230300.
- View Article
- PubMed/NCBI
- Google Scholar
20. Wu MC, Lee S, Cai T, Li Y, Boehnke M, Lin X. Rare-variant association testing for sequencing data with the sequence kernel association test. Am J Hum Genet. 2011;89(1):82–93. pmid:21737059.
- View Article
- PubMed/NCBI
- Google Scholar
21. Kuonen D. Saddlepoint approximations for distributions of quadratic forms in normal variables. Biometrika. 1999;86(4):929–935.
- View Article
- Google Scholar
22. Wu B, Pankow JS. Sequence Kernel Association Test of Multiple Continuous Phenotypes. Genet Epidemiol. 2016;40(2):91–100. pmid:26782911.
- View Article
- PubMed/NCBI
- Google Scholar
23. Schaffner SF, Foo C, Gabriel S, Reich D, Daly MJ, Altshuler D. Calibrating a coalescent simulation of human genome sequence variation. Genome Res. 2005;15(11):1576–1583. pmid:16251467.
- View Article
- PubMed/NCBI
- Google Scholar
24. Broadaway KA, Cutler DJ, Duncan R, Moore JL, Ware EB, Jhun MA, et al. A Statistical Approach for Testing Cross-Phenotype Effects of Rare Variants. Am J Hum Genet. 2016;98(3):525–540. pmid:26942286.
- View Article
- PubMed/NCBI
- Google Scholar
25. Bycroft C, Freeman C, Petkova D, Band G, Elliott LT, Sharp K, et al. The UK Biobank resource with deep phenotyping and genomic data. Nature. 2018;562(7726):203–209. pmid:30305743.
- View Article
- PubMed/NCBI
- Google Scholar
26. Sudlow C, Gallacher J, Allen N, Beral V, Burton P, Danesh J, et al. UK biobank: an open access resource for identifying the causes of a wide range of complex diseases of middle and old age. PLoS Med. 2015;12(3):e1001779. pmid:25826379.
- View Article
- PubMed/NCBI
- Google Scholar
27. Manichaikul A, Mychaleckyj JC, Rich SS, Daly K, Sale M, Chen WM. Robust relationship inference in genome-wide association studies. Bioinformatics. 2010;26(22):2867–2873. pmid:20926424.
- View Article
- PubMed/NCBI
- Google Scholar
28. Cui JS, Hopper JL, Harrap SB. Antihypertensive treatments obscure familial contributions to blood pressure variation. Hypertension. 2003;41(2):207–210. pmid:12574083.
- View Article
- PubMed/NCBI
- Google Scholar
29. Tobin MD, Sheehan NA, Scurrah KJ, Burton PR. Adjusting for treatment effects in studies of quantitative traits: antihypertensive therapy and systolic blood pressure. Stat Med. 2005;24(19):2911–2935. pmid:16152135.
- View Article
- PubMed/NCBI
- Google Scholar
30. McLaren W, Gil L, Hunt SE, Riat HS, Ritchie GR, Thormann A, et al. The Ensembl Variant Effect Predictor. Genome Biol. 2016;17(1):122. pmid:27268795.
- View Article
- PubMed/NCBI
- Google Scholar
31. Cirulli ET, White S, Read RW, Elhanan G, Metcalf WJ, Tanudjaja F, et al. Genome-wide rare variant analysis for thousands of phenotypes in over 70,000 exomes from two cohorts. Nat Commun. 2020;11(1):542. pmid:31992710.
- View Article
- PubMed/NCBI
- Google Scholar
32. Chang CC, Chow CC, Tellier LC, Vattikuti S, Purcell SM, Lee JJ. Second-generation PLINK: rising to the challenge of larger and richer datasets. Gigascience. 2015;25;4:7. pmid:25722852.
- View Article
- PubMed/NCBI
- Google Scholar
33. Roshyara NR, Scholz M. fcGENE: a versatile tool for processing and transforming SNP datasets. PLoS One. 2014;9(7):e97589. pmid:25050709.
- View Article
- PubMed/NCBI
- Google Scholar
34. Jouhilahti EM, Madissoon E, Vesterlund L, Töhönen V, Krjutškov K, Plaza Reyes A, et al. The human PRD-like homeobox gene LEUTX has a central role in embryo genome activation. Development. 2016;143(19):3459–3469. pmid:27578796.
- View Article
- PubMed/NCBI
- Google Scholar
35. Backman JD, Li AH, Marcketta A, Sun D, Mbatchou J, Kessler MD, et al. Exome sequencing and analysis of 454,787 UK Biobank participants. Nature. 2021;599(7886):628–634. pmid:34662886.
- View Article
- PubMed/NCBI
- Google Scholar
36. Ionita-Laza I, Lee S, Makarov V, Buxbaum JD, Lin X. Sequence kernel association tests for the combined effect of rare and common variants. Am J Hum Genet. 2013;92(6):841–853. pmid:23684009.
- View Article
- PubMed/NCBI
- Google Scholar
37. Jiao S, Hsu L, Bézieau S, Brenner H, Chan AT, Chang-Claude J, et al. SBERIA: set-based gene-environment interaction test for rare and common variants in complex diseases. Genet Epidemiol. 2013;37(5):452–464. pmid:23720162.
- View Article
- PubMed/NCBI
- Google Scholar
38. Zhao G, Marceau R, Zhang D, Tzeng JY. Assessing gene-environment interactions for common and rare variants with binary traits using gene-trait similarity regression. Genetics. 2015;199(3):695–710. pmid:25585620.
- View Article
- PubMed/NCBI
- Google Scholar

[ref1] 1. Buniello A, MacArthur JAL, Cerezo M, Harris LW, Hayhurst J, Malangone C, et al. The NHGRI-EBI GWAS Catalog of published genome-wide association studies, targeted arrays and summary statistics 2019. Nucleic Acids Res. 2019;47(D1):D1005–D1012. pmid:30445434.
View Article
PubMed/NCBI
Google Scholar

[2] View Article

[3] PubMed/NCBI

[4] Google Scholar

[ref2] 2. Nolte IM, van der Most PJ, Alizadeh BZ, de Bakker PI, Boezen HM, Bruinenberg M, et al. Missing heritability: is the gap closing? An analysis of 32 complex traits in the Lifelines Cohort Study. Eur J Hum Genet. 2017;25(7):877–885. pmid:28401901.
View Article
PubMed/NCBI
Google Scholar

[6] View Article

[7] PubMed/NCBI

[8] Google Scholar

[ref3] 3. López-Cortegano E, Caballero A. Inferring the Nature of Missing Heritability in Human Traits Using Data from the GWAS Catalog. Genetics. 2019;212(3):891–904. pmid:31123044.
View Article
PubMed/NCBI
Google Scholar

[10] View Article

[11] PubMed/NCBI

[12] Google Scholar

[ref4] 4. Geddes L. Genetic study homes in on height’s heritability mystery. Nature. 2019;568(7753):444–445. pmid:31015700.
View Article
PubMed/NCBI
Google Scholar

[14] View Article

[15] PubMed/NCBI

[16] Google Scholar

[ref5] 5. Yu C, Arcos-Burgos M, Baune BT, Arolt V, Dannlowski U, Wong ML, et al. Low-frequency and rare variants may contribute to elucidate the genetics of major depressive disorder. Transl Psychiatry. 2018;8(1):70. pmid:29581422.
View Article
PubMed/NCBI
Google Scholar

[18] View Article

[19] PubMed/NCBI

[20] Google Scholar

[ref6] 6. Wang Z, Chen H, Bartz TM, Bielak LF, Chasman DI, Feitosa MF, et al. Role of Rare and Low-Frequency Variants in Gene-Alcohol Interactions on Plasma Lipid Levels. Circ Genom Precis Med. 2020;13(4):e002772. pmid:32510982.
View Article
PubMed/NCBI
Google Scholar

[22] View Article

[23] PubMed/NCBI

[24] Google Scholar

[ref7] 7. Yang T, Jackson VE, Smith AV, Chen H, Bartz TM, Sitlani CM, et al. Rare and low-frequency exonic variants and gene-by-smoking interactions in pulmonary function. Sci Rep. 2021;11(1):19365. pmid:34588469.
View Article
PubMed/NCBI
Google Scholar

[26] View Article

[27] PubMed/NCBI

[28] Google Scholar

[ref8] 8. Johansson E, Martin LJ, He H, Chen X, Weirauch MT, Kroner JW, et al. Second-hand smoke and NFE2L2 genotype interaction increases paediatric asthma risk and severity. Clin Exp Allergy. 2021;51(6):801–810. pmid:33382170.
View Article
PubMed/NCBI
Google Scholar

[30] View Article

[31] PubMed/NCBI

[32] Google Scholar

[ref9] 9. Dahl A, Nguyen K, Cai N, Gandal MJ, Flint J, Zaitlen N. A Robust Method Uncovers Significant Context-Specific Heritability in Diverse Complex Traits. Am J Hum Genet. 2020;106(1):71–91. pmid:31901249.
View Article
PubMed/NCBI
Google Scholar

[34] View Article

[35] PubMed/NCBI

[36] Google Scholar

[ref10] 10. Majumdar A, Burch KS, Haldar T, Sankararaman S, Pasaniuc B, Gauderman WJ, et al. A two-step approach to testing overall effect of gene-environment interaction for multiple phenotypes. Bioinformatics. 2021:btaa1083. pmid:33453114.
View Article
PubMed/NCBI
Google Scholar

[38] View Article

[39] PubMed/NCBI

[40] Google Scholar

[ref11] 11. Kilpeläinen TO, Bentley AR, Noordam R, Sung YJ, Schwander K, Winkler TW, et al. Multi-ancestry study of blood lipid levels identifies four loci interacting with physical activity. Nat Commun. 2019;10(1):376. pmid:30670697.
View Article
PubMed/NCBI
Google Scholar

[42] View Article

[43] PubMed/NCBI

[44] Google Scholar

[ref12] 12. Noordam R, Bos MM, Wang H, Winkler TW, Bentley AR, Kilpeläinen TO, et al. Multi-ancestry sleep-by-SNP interaction analysis in 126,926 individuals reveals lipid loci stratified by sleep duration. Nat Commun. 2019;10(1):5121. pmid:31719535.
View Article
PubMed/NCBI
Google Scholar

[46] View Article

[47] PubMed/NCBI

[48] Google Scholar

[ref13] 13. Zhang J, Sha Q, Hao H, Zhang S, Gao XR, Wang X. Test Gene-Environment Interactions for Multiple Traits in Sequencing Association Studies. Hum Hered. 2019;84(4–5):170–196. pmid:32417835.
View Article
PubMed/NCBI
Google Scholar

[50] View Article

[51] PubMed/NCBI

[52] Google Scholar

[ref14] 14. Zhao Z, Zhang J, Sha Q, Hao H. Testing gene-environment interactions for rare and/or common variants in sequencing association studies. PLoS One. 2020;15(3):e0229217. pmid:32155162.
View Article
PubMed/NCBI
Google Scholar

[54] View Article

[55] PubMed/NCBI

[56] Google Scholar

[ref15] 15. Dutta D, Scott L, Boehnke M, Lee S. Multi-SKAT: General framework to test for rare-variant association with multiple phenotypes. Genet Epidemiol. 2019;43(1):4–23. pmid:30298564.
View Article
PubMed/NCBI
Google Scholar

[58] View Article

[59] PubMed/NCBI

[60] Google Scholar

[ref16] 16. Chen H, Meigs JB, Dupuis J. Incorporating gene-environment interaction in testing for association with rare genetic variants. Hum Hered. 2014;78(2):81–90. pmid:25060534
View Article
PubMed/NCBI
Google Scholar

[62] View Article

[63] PubMed/NCBI

[64] Google Scholar

[ref17] 17. Atsma F, Veldhuizen I, de Kort W, van Kraaij M, Pasker-de Jong P, Deinum J. Hemoglobin level is positively associated with blood pressure in a large cohort of healthy individuals. Hypertension. 2012;60(4):936–941. pmid:22949533.
View Article
PubMed/NCBI
Google Scholar

[66] View Article

[67] PubMed/NCBI

[68] Google Scholar

[ref18] 18. Wang TJ, Gona P, Larson MG, Levy D, Benjamin EJ, Tofler GH, et al. Multiple biomarkers and the risk of incident hypertension. Hypertension. 2007;49(3):432–438. pmid:17242302.
View Article
PubMed/NCBI
Google Scholar

[70] View Article

[71] PubMed/NCBI

[72] Google Scholar

[ref19] 19. Surendran P, Feofanova EV, Lahrouchi N, Ntalla I, Karthikeyan S, Cook J, et al. Discovery of rare variants associated with blood pressure regulation through meta-analysis of 1.3 million individuals. Nat Genet. 2020;52(12):1314–1332. pmid:33230300.
View Article
PubMed/NCBI
Google Scholar

[74] View Article

[75] PubMed/NCBI

[76] Google Scholar

[ref20] 20. Wu MC, Lee S, Cai T, Li Y, Boehnke M, Lin X. Rare-variant association testing for sequencing data with the sequence kernel association test. Am J Hum Genet. 2011;89(1):82–93. pmid:21737059.
View Article
PubMed/NCBI
Google Scholar

[78] View Article

[79] PubMed/NCBI

[80] Google Scholar

[ref21] 21. Kuonen D. Saddlepoint approximations for distributions of quadratic forms in normal variables. Biometrika. 1999;86(4):929–935.
View Article
Google Scholar

[82] View Article

[83] Google Scholar

[ref22] 22. Wu B, Pankow JS. Sequence Kernel Association Test of Multiple Continuous Phenotypes. Genet Epidemiol. 2016;40(2):91–100. pmid:26782911.
View Article
PubMed/NCBI
Google Scholar

[85] View Article

[86] PubMed/NCBI

[87] Google Scholar

[ref23] 23. Schaffner SF, Foo C, Gabriel S, Reich D, Daly MJ, Altshuler D. Calibrating a coalescent simulation of human genome sequence variation. Genome Res. 2005;15(11):1576–1583. pmid:16251467.
View Article
PubMed/NCBI
Google Scholar

[89] View Article

[90] PubMed/NCBI

[91] Google Scholar

[ref24] 24. Broadaway KA, Cutler DJ, Duncan R, Moore JL, Ware EB, Jhun MA, et al. A Statistical Approach for Testing Cross-Phenotype Effects of Rare Variants. Am J Hum Genet. 2016;98(3):525–540. pmid:26942286.
View Article
PubMed/NCBI
Google Scholar

[93] View Article

[94] PubMed/NCBI

[95] Google Scholar

[ref25] 25. Bycroft C, Freeman C, Petkova D, Band G, Elliott LT, Sharp K, et al. The UK Biobank resource with deep phenotyping and genomic data. Nature. 2018;562(7726):203–209. pmid:30305743.
View Article
PubMed/NCBI
Google Scholar

[97] View Article

[98] PubMed/NCBI

[99] Google Scholar

[ref26] 26. Sudlow C, Gallacher J, Allen N, Beral V, Burton P, Danesh J, et al. UK biobank: an open access resource for identifying the causes of a wide range of complex diseases of middle and old age. PLoS Med. 2015;12(3):e1001779. pmid:25826379.
View Article
PubMed/NCBI
Google Scholar

[101] View Article

[102] PubMed/NCBI

[103] Google Scholar

[ref27] 27. Manichaikul A, Mychaleckyj JC, Rich SS, Daly K, Sale M, Chen WM. Robust relationship inference in genome-wide association studies. Bioinformatics. 2010;26(22):2867–2873. pmid:20926424.
View Article
PubMed/NCBI
Google Scholar

[105] View Article

[106] PubMed/NCBI

[107] Google Scholar

[ref28] 28. Cui JS, Hopper JL, Harrap SB. Antihypertensive treatments obscure familial contributions to blood pressure variation. Hypertension. 2003;41(2):207–210. pmid:12574083.
View Article
PubMed/NCBI
Google Scholar

[109] View Article

[110] PubMed/NCBI

[111] Google Scholar

[ref29] 29. Tobin MD, Sheehan NA, Scurrah KJ, Burton PR. Adjusting for treatment effects in studies of quantitative traits: antihypertensive therapy and systolic blood pressure. Stat Med. 2005;24(19):2911–2935. pmid:16152135.
View Article
PubMed/NCBI
Google Scholar

[113] View Article

[114] PubMed/NCBI

[115] Google Scholar

[ref30] 30. McLaren W, Gil L, Hunt SE, Riat HS, Ritchie GR, Thormann A, et al. The Ensembl Variant Effect Predictor. Genome Biol. 2016;17(1):122. pmid:27268795.
View Article
PubMed/NCBI
Google Scholar

[117] View Article

[118] PubMed/NCBI

[119] Google Scholar

[ref31] 31. Cirulli ET, White S, Read RW, Elhanan G, Metcalf WJ, Tanudjaja F, et al. Genome-wide rare variant analysis for thousands of phenotypes in over 70,000 exomes from two cohorts. Nat Commun. 2020;11(1):542. pmid:31992710.
View Article
PubMed/NCBI
Google Scholar

[121] View Article

[122] PubMed/NCBI

[123] Google Scholar

[ref32] 32. Chang CC, Chow CC, Tellier LC, Vattikuti S, Purcell SM, Lee JJ. Second-generation PLINK: rising to the challenge of larger and richer datasets. Gigascience. 2015;25;4:7. pmid:25722852.
View Article
PubMed/NCBI
Google Scholar

[125] View Article

[126] PubMed/NCBI

[127] Google Scholar

[ref33] 33. Roshyara NR, Scholz M. fcGENE: a versatile tool for processing and transforming SNP datasets. PLoS One. 2014;9(7):e97589. pmid:25050709.
View Article
PubMed/NCBI
Google Scholar

[129] View Article

[130] PubMed/NCBI

[131] Google Scholar

[ref34] 34. Jouhilahti EM, Madissoon E, Vesterlund L, Töhönen V, Krjutškov K, Plaza Reyes A, et al. The human PRD-like homeobox gene LEUTX has a central role in embryo genome activation. Development. 2016;143(19):3459–3469. pmid:27578796.
View Article
PubMed/NCBI
Google Scholar

[133] View Article

[134] PubMed/NCBI

[135] Google Scholar

[ref35] 35. Backman JD, Li AH, Marcketta A, Sun D, Mbatchou J, Kessler MD, et al. Exome sequencing and analysis of 454,787 UK Biobank participants. Nature. 2021;599(7886):628–634. pmid:34662886.
View Article
PubMed/NCBI
Google Scholar

[137] View Article

[138] PubMed/NCBI

[139] Google Scholar

[ref36] 36. Ionita-Laza I, Lee S, Makarov V, Buxbaum JD, Lin X. Sequence kernel association tests for the combined effect of rare and common variants. Am J Hum Genet. 2013;92(6):841–853. pmid:23684009.
View Article
PubMed/NCBI
Google Scholar

[141] View Article

[142] PubMed/NCBI

[143] Google Scholar

[ref37] 37. Jiao S, Hsu L, Bézieau S, Brenner H, Chan AT, Chang-Claude J, et al. SBERIA: set-based gene-environment interaction test for rare and common variants in complex diseases. Genet Epidemiol. 2013;37(5):452–464. pmid:23720162.
View Article
PubMed/NCBI
Google Scholar

[145] View Article

[146] PubMed/NCBI

[147] Google Scholar

[ref38] 38. Zhao G, Marceau R, Zhang D, Tzeng JY. Assessing gene-environment interactions for common and rare variants with binary traits using gene-trait similarity regression. Genetics. 2015;199(3):695–710. pmid:25585620.
View Article
PubMed/NCBI
Google Scholar

[149] View Article

[150] PubMed/NCBI

[151] Google Scholar

Figures

Abstract

Introduction

Methods

Single-phenotype GEI test

Kernel-based multiphenotype GEI tests

Homogeneous kernel.

Heterogeneous kernel.

Projection phenotype kernel.

Linear phenotype kernel.

Results

Numerical simulations

Null distributions.

Statistical power.

Gene-Hb interaction analysis of blood pressure phenotypes in UK Biobank

Discussion

Conclusion

References