Biological Knowledge-Driven Analysis of Epistasis in Human GWAS with Application to Lipid Traits

Abstract

While the importance of epistasis is well established, specific gene-gene interactions have rarely been identified in human genome-wide association studies (GWAS), mainly due to the low power associated with such interaction tests. In this chapter, we integrate biological knowledge and human GWAS data to reveal epistatic interactions underlying quantitative lipid traits which are major risk factors for coronary artery disease. To increase power to detect interactions, we only tested pairs of SNPs filtered by prior biological knowledge, including GWAS results, protein-protein interactions, and pathway information. Using published GWAS results and 9,713 European Americans (EA) from the Atherosclerosis Risk in Communities (ARIC) study, we identified an interaction between HMGCR and LIPC affecting high-density lipoprotein cholesterol (HDL-C) levels. We then validated this interaction in additional EA cohorts from the Framingham Heart Study and the Multi-Ethnic Study of Atherosclerosis (MESA). We also validated the interaction in the ARIC African American sample and in the Hispanic American sample from MESA. Both HMGCR and LIPC are involved in the metabolism of lipid and lipoproteins, and LIPC itself has been associated with HDL-C. Moreover, the interaction affects HDL-C twice as much as the marginal effect of LIPC, with the effect of the two genes and their interaction combined explaining 0.8% of the variation in HDL. These results suggest the potential of the biological knowledge-driven approach to detect epistatic interactions in human GWAS, which may hold the key to exploring the role gene-gene interactions play in connecting genotype and phenotype in current and future genetic association studies.

Introduction

As of February 2013, over 1,489 publications and 8,271 single nucleotide polymorphisms (SNPs) have been collected in the catalog of genome-wide association studies (GWAS) [1]. Though these SNPs are significantly associated with human diseases and traits, most of them have a small effect and in aggregate account for a low proportion of the heritable variance [2,3,4,5,6]. Four lipid traits, total cholesterol (TC), low-density lipoprotein cholesterol (LDL-C), triglyceride (TG), and high-density lipoprotein cholesterol (HDL-C) levels, are among the most important risk factors for coronary heart disease. Recently, several meta-analyses of many GWAS, with a combined sample size of up to 100,000, have detected hundreds of loci associated with the levels of the four lipids [7,8]. However, these loci collectively only explain 25–30% of heritable variance of each lipid [7,8]. Many hypotheses have been offered to explain such missing heritability, including rare and structural variants, gene-environment interactions, epigenetics, and complex inheritance [2,3,4,5]. The missing heritability may also be partially attributed to epistatic or gene-gene interactions [9,10,11], and we seek to identify examples of pairwise SNP by SNP interaction effects on any of the four lipid levels in this study.

Since Bateson’s first discovery in 1905 that some genes suppress the effects of other genes [12], researchers have been investigating the effect of epistasis in order to better understand the complex relationship between genotype and phenotype. Studies of model organisms suggested epistasis or gene-gene interactions to be a common phenomenon [13,14,15,16], and a number of gene-gene interactions have been reported in gene mapping studies in animals, plants, and other model organisms [17,18,19,20]. However, gene-gene interactions have proven difficult to find in humans [21,22], mainly due to low statistical power caused by the small effect size, the low minor genotype frequency of the multiple-SNP combinations, the large combinatorial number of interaction tests required [14,23], and the lack of control of environmental conditions. Hence, in order to improve the power of detection of gene-gene interactions in human GWAS, many approaches have been developed to prioritize candidate genes or SNPs using biological knowledge from established GWAS hits [6,24], protein-protein interactions (PPIs) [25,26], and pathway information [27].

Tests of gene-gene interactions are not as powerful as tests of single-marker association, so a judicious strategy is essential for a successful epistasis analysis in human GWAS [11,14,15]. One fundamental limitation to the analysis of epistasis is that the statistical power of each particular test can be easily eroded by the performance of vast numbers of pairwise or higher-order interaction tests. In order to achieve a similar success for interaction analysis as one obtains with single-marker tests in GWAS, we are limited to performing a similar number of tests (~1 million), assuming the nominal per-test power to detect interaction is the same as that of a single-marker association test. This limitation prevents us from conducting an inclusive all-by-all interaction analysis in current human GWAS, which typically examines millions of SNPs. If one were to attempt all-by-all epistasis tests, the result is such reduced power that only the most exceptionally strong interactions could be detected. Therefore, we recommend epistasis analysis be done on a reduced number of SNPs, using prior biological knowledge as the simplest way to restrict SNP numbers. The selection of candidate genes or SNPs can be based on any factor(s) that the biologist or medical practitioner chooses. So long as the gene choice is not based on the tests of interactions itself, winnowing down the gene set will not inflate the type I error and can increase the power when the underlying interactions are enriched between the candidate genes or SNPs. Criteria such as SNP density, local linkage disequilibrium (LD), and data quality can further supplement primary knowledge of gene function, pathway position, connectedness to networks, etc. in selecting genes.

We illustrate the biological knowledge-driven approach with examples from analysis of large consortium cohort studies of cardiovascular disease [6]. We tested for pairwise SNP by SNP epistatic interactions affecting the level of four lipids, TC, LDL-C, TG, and HDL-C, based on prior knowledge of published GWAS hits, PPIs, and pathway information. Based on GWAS hits, we detected an interaction between HMGCR and a locus upstream of LIPC in their effect on HDL-C levels in the discovery data set from the Atherosclerosis Risk in Communities (ARIC) study. Using a locus-based replication procedure, we validated this interaction in cohorts from the Framingham Heart Study (FHS) and from the Multi-Ethnic Study of Atherosclerosis (MESA). In summary, a biological knowledge-driven approach might be crucial to the detection of epistatic interactions underlying complex traits and diseases in human GWAS.

Methods and Results

Descriptions of GWAS data

Three GWAS data sets were considered in this study, the Atherosclerosis Risk in Communities (ARIC) study, the Framingham Heart Study (FHS), and the Multi-Ethnic Study of Atherosclerosis (MESA). The ARIC study is a multi-center prospective investigation of atherosclerotic disease [28]. This analysis included 9,713 European Americans (EA) in the discovery study and 3,207 African American (AA) individuals in the validation study. The FHS is a prospective cohort study to evaluate cardiovascular disease (CVD) risk factors, which has been described in detail previously [29]. This analysis included 6,575 EA subjects in the validation study, while accounting for their familial relatedness (see Test of statistical interactions below). MESA is a prospective cohort study of individuals aged 45-84 years without clinical CVD recruited from 6 US centers [30], which is designed to study the characteristics of subclinical CVD and its progression. Participants of MESA self-reported their race or ethnicity group as EA, AA, Chinese American, or Hispanic American (HA). In total 2,685 EA, 2,588 AA and 2,174 HA individuals were included in the validation. All of the included subjects from the three GWAS studies have both genotypes and phenotypic (lipid) measurements available, as described in the following sections.

Genotype data

Genotyping of samples was obtained from the ARIC study and MESA by Affymetrix 6.0 SNP array. Affymetrix 6.0 SNP array genotyping of MESA samples and Affymetrix 500K SNP array genotyping of FHS samples were obtained from dbGaP (MESA SHARe, downloaded in May 2011; Framingham Cohort, downloaded in April 2010) [31]. Standard quality control (QC) filters were applied across each of the samples and SNPs, including: (1) exclusion of subjects with >10% missing data; (2) removing SNPs with call rates < 90%; (3) removing SNPs with minor allele frequencies (MAF) ≤ 1%; and (4) removing SNPs with Hardy-Weinberg Equilibrium (HWE) test with P < 10⁻⁶. For the SNP pairs to be tested, we also required: (1) sample size of each of the nine two-SNP combinations greater than 20 in the discovery analysis and greater than 10 in the validation study; and (2) LD measure of r² < 0.1 between the two candidate SNPs.

When necessary, untyped SNPs was imputed using IMPUTE2 [32] with HapMap3 [33] and 1000 Genomes [34] reference haplotypes, which resulted in about the same set of SNPs across the three studies. No imputation was performed in MESA HA samples due to the lack of appropriate reference haplotype panels. SNPs with information score < 0.6 were excluded and each genotype was imputed with the genotype with the highest posterior probability. When the highest posterior probability is less than 0.8, the genotype was treated as missing.

Phenotype data

Four quantitative lipid measurements, total cholesterol (TC), LDL cholesterol (LDL-C), triglyceride (TG), and HDL cholesterol (HDL-C), were considered in the analysis. Each lipid level is measured at multiple time points and the average level per individual was used in all studies. A log transformation was applied to TG levels to normalize its distribution because of the skewness in the original distribution. Individuals self-reported to be taking lipid-lowering medications were excluded. Sex, age, age squared, body mass index (BMI) were included as covariates in all analyses. The average values for age, age squared, and BMI were also used whenever multiple measurements were available. Plate number is also included as a covariate factor in the ARIC data due to its correlation with some of the lipid levels (known as “plate effect”).

Test of statistical interactions

Statistical interactions between pairs of SNPs were tested on a quantitative trait. For each individual, let Y denote the trait of interest and G_i denote the genotype of the ith SNP (i = 1, 2). G_i is the number of copies of the reference allele, thus with possible values 0, 1, or 2. Two indicator variables, x_i and z_i, were defined for each of the two SNPs as,

$$x_i=\{\begin{array}{cc}1,\hfill & G_i=0\hfill \\ 0,\hfill & G_i=1\hfill \\ -1,\hfill & G_i=2\hfill \end{array}\phantom{\}}{z}_i=\{\begin{array}{cc}-0.5,\hfill & G_i=0\hfill \\ 0.5,\hfill & G_i=1\hfill \\ -0.5,\hfill & G_i=2\hfill \end{array}\phantom{\}}$$

Two linear models were fitted and compared for testing of interaction. The first model (M₁) included additive and dominance effect terms for each of the two SNPs without including any interaction effects between the two SNPs; The second model (M₂), on top of M₁, allows for four classic forms of epistatic interactions (additive × additive, additive × dominance, dominance × additive, and dominance × dominance), as follows:

$$Y=Z_0{\beta }_0+x_1{a}_1+z_1{d}_1+x_2{a}_2+z_2{d}_2+\epsilon$$ (M₁)

$$Y=Z_0{\beta }_0+x_1{a}_1+z_1{d}_1+x_2{a}_2+z_2{d}_2+x_1{x}_2{i}_{aa}+x_1{z}_2{i}_{ad}+z_1{x}_2{i}_{da}+z_1{z}_2{i}_{dd}+\epsilon$$ (M₂)

Here, β₀ is a vector of the intercept and possible non-genetic covariates. a_i and d_i are the additive and dominance effects of the ith SNP. i_aa, i_ad, i_da, and i_dd denote the four classic interaction effects between the two SNPs. The existence of an epistatic interaction of any combination of the four types was tested by an F-test comparing M₁ and M₂ with four degrees of freedom [6,35]. This classical test of statistical interactions is similar to the “--epistasis” option in PLINK [36], except that only additive effects and additive × additive interaction are considered, such that an F-test with one degree of freedom is performed in PLINK.

Potential population stratification was corrected by principal component (PC) approach and familial relationship in FHS was accounted for using a mixed model approach [22,37]. PC analysis was conducted using EIGENSOFT [37] and the top 10 PCs were included in the analysis as covariates to account for population stratification in ARIC and MESA samples. For FHS, a mixed model approach was first applied to account for familial relatedness and then pairwise interaction was tested on the residuals from the mixed models [22].

Locus-based validation of interactions

We sought to validate (replicate) the interactions detected in the discovery study using data from FHS, MESA and another AA sample from the ARIC study. “Validate” rather than “replicate” was used here because linked and proximate SNPs were included in the validation in addition to the original SNPs, as follows. For a significant interaction between two SNPs (e.g. A and B) in the discovery study, we perform the following possible stages of tests in the validation study: (i) Test for interaction directly between SNP A and SNP B; (ii) If the interaction is not significant in Stage (i), test for interaction between SNP A and each SNP less than 200 kb away from SNP B, and similarly between SNP B and each SNP surrounding SNP A; (iii) If no test in Stage (ii) is significant following multiple-testing correction, test for interaction between each SNP less 100kb away from A and each SNP less than 100kb away from B. Assume there are n₁ and n₂ SNPs respectively surrounding SNPs A and B, the number of statistical tests to be conducted is 1, n₁ +n₂, and n² in the three validation stages respectively. To reduce the number of tests and the cost of multiple-testing correction on power, the validation process proceeds sequentially and stops at any stage where significant results were found after multiple-testing correction.

Prioritize SNP pairs using biological knowledge

Though only pairwise interactions are considered, the total number of possible interaction tests across 2.5 million SNPs is still huge, at more than 3×10¹² tests. Due to the severe reduction in power entailed by stringent multiple-testing correction for such a large number of tests, it is crucial to restrict the total number of tests for the whole study. Therefore, through the following three strategies, we aimed to reduce the total number of interaction tests and to enrich interaction signals in the fewer number of tests considered.

1. Lipid GWAS results

In total, 95 genetic loci have been recently reported to be associated with TC, LDL-C, TG, or HDL-C in a GWAS meta-analysis [7]. We considered 125 SNPs in the 95 loci and tested each pair of SNPs on TC, LDL-C, TG, and HDL-C in the discovery sample of 9,713 EAs from the ARIC study. The 125 SNPs have been previously associated with any of the four lipid levels [7]. Using this approach, we tested ~7,748 pairwise interactions for each trait. We identified one significant interaction affecting LDL-C levels and one interaction on HDL-C. The interaction on LDL-C was between rs2247056 and rs1030431 (P_c = 0.03 after Bonferroni correction). Both rs2247056 and rs1030431 were marginally associated with LDL-C, TG, and TC [7,38]. We then performed fine mapping analysis in the two loci surrounding the two SNPs to find the most significant interaction to be between rs2853928 and rs1993453 (P_c = 0.01). We tried to validate this interaction on LDL-C in additional replication samples from ARIC, FHS, and MESA, but had no success.

The interaction on HDL-C was between rs12916 and rs1532085 (P_c = 0.008) in the discovery study and was successfully validated in the replication samples (Table 1). To further explore the interaction between the two loci, we tested interaction between each SNP surrounding rs12916 and each SNP surrounding rs1532085 within a 100 kb distance. While many of these SNP pairs show significant interactions due to LD, the strongest signal was between rs3846662 and rs2043085 (P_c = 0.002). SNP rs3846662, located in the intron of gene HMGCR, has been previously associated with TC and LDL-C [7,39], but not with HDL-C. Rs3846662 has also been shown in vitro to be associated with a 2.2-fold change in HMGCR expression [40] and affect alternative splicing of exon 13 [41]. The other SNP, rs2043085, has been found to be marginally associated with HDL-C [7]. Rs2043085 is located upstream of LIPC and associated with the expression of the gene [6]. On top of the marginal effects, the interaction between the two SNPs affects HDL-C twice as much as the effect of LIPC alone: While on average individuals with TT genotype at rs2043085 show an increase of 2.63 mg/dl in HDL-C, subject with TT at rs2043085 and AA at rs3846662 exhibits an average increase of 5.72 mg/dl. The linear model with these two SNPs and their interaction has an r² value of 0.8%, meaning that these two SNPs and their interaction combined explain a 0.8% of phenotypic variation in HDL-C. Using the locus-based validation procedure, the interaction between rs3846662 and rs2043085 on HDL-C was successfully validated in Stage (ii) for MESA EA samples and in Stage (iii) for FHS EA, MESA HA and ARIC AA cohorts (Table 1). It did not validate significantly after multiple-testing correction for the MESA AA sample with a smaller sample size.

Table 1. Significant interactions affecting HDL-C levels validated in multiple population cohorts.

(Regenerated from Ref [6] )

Test Stage	Cohort	SNP 1				SNP 2				P c c
		rsID	Chr	Posa	Geneb	rsID	Chr	Posa	Geneb
Discovery	ARIC EA	rs12916	5	74656539	HMGCR (3’ UTR)	rs1532085	15	58683366	40.8k U LIPC	0.008
Fine Mapping	ARIC EA	rs3846662	5	74651084	HMGCR (Intron)	rs2043085	15	58680954	43.2k U LIPC	0.002
Validation	MESA EA	rs3846662	5	74651084	HMGCR (Intron)	rs1973688	15	58582540	141.6k U LIPC	0.006
Validation	FHS EA	rs55727654	5	74651864	HMGCR (Intron)	rs473422	15	58666341	57.8k U LIPC	0.002
Validation	MESA HA	rs1423527	5	74602699	30.3k U HMGCR	rs7163280	15	58718340	5.8k U LIPC	0.04
Validation	ARIC AA	rs3761743	5	74685520	27.6k D HMGCR	rs567838	15	58736623	LIPC (Intron)	0.004

^aBuild 37.1 (GRCh37)

^bU = upstream of; D = downstream of

^cP-value after Bonferroni correction

2. Protein-protein interactions (PPIs)

Over 3,000 high-confidence human PPIs were carefully assembled [42]. For each gene pair indicated by a PPI, we exhaustively tested all pairwise interactions between each SNP in the first gene and each SNP in the second one. Suppose n₁ and n₂ are the numbers of SNPs in the first and second genes respectively, the number of possible pairwise interactions is n₁ × n₂. To map SNPs to genes, gene information (hg18) was obtained from the UCSC genome browser [43] and we considered all SNPs located between 5 kb upstream and 5 kb downstream of a gene. For each of the four lipid traits, we performed ~6 million pairwise interaction tests according to the ~3,000 PPIs, which, however, resulted in no significant interactions following multiple-testing correction.

3. Lipid pathway information

We hypothesized that possible gene-gene interactions are enriched between genes in the lipid related pathways. To test this hypothesis, we used the metabolism of lipids and lipoproteins pathway as an example. There are a total of 228 genes in this pathway [44] and 12,716 SNPs are mapped to the 228 genes. We tested all pairwise interactions among the 12,716 SNPs, resulting in a total of ~27 million interaction tests for each lipid trait. Hence, it is not surprising that we found nothing significant after multiple-testing correction. However, there is a deviation in the QQ plot of the P values for interactions underlying TC levels. The interaction between rs4804546 and rs914196 is the strongest, though not significant following correction for the ~27 million tests (P_c = 0.14). The interaction is between two genes, CARM1 and AGPAT3, from the metabolism of lipids and lipoproteins pathway. Gene AGPAT3 has been associated with the level of phospholipid [45], and CARM1 has not been found to be associated with any lipid levels.

Notes

To ensure accuracy and power, quality control is of crucial importance in genetic association studies, as well as in epistasis analysis [46,47]. Non-normality and outliers in the distribution of the phenotypes can potentially lead to false positive interactions with very small P values, particularly when the individuals carrying the minor multi-SNP genotype incidentally are also outliers in phenotype. When both outliers and low-frequency SNPs exist in the data, the chance of false positives will be greatly increased. Therefore, a minor multi-SNP genotype frequency filter (20 in discovery and 10 in validation in this study) is necessary when testing for interactions, much like the MAF filtering in typical GWAS.

While the interaction we identified was replicated in multi-ethnic populations, it has a small effect size, which is about the same magnitude as the marginal effect discovered in GWAS for complex diseases and traits. If this is the case for general epistatic interactions, we will have even lower power for detecting epistasis than marginal associations, which also explains why so few interactions have been detected and replicated in human GWAS.

Note that the interaction we detected in this study was validated in part by proximate SNPs, thus indicating the power of integrating information from a genomic region surrounding the target SNPs, like a gene-based test for marginal associations. Recently, a series of gene-based interaction testing methods have been developed in the literature [48,49,50,51,52], which can be employed to increase power of detecting and replicating interactions.

In this study, we detected significant interactions after multiple-testing correction only in < 10k tests guided by GWAS results, but found nothing significant in 6 million and 27 million tests respectively using PPI and pathway information. By noticing that the discovery study is already powerful with a sample size of ~10k, multiple measurements of the phenotypic values, and a genome-wide 1 million SNP genotyping, we only afford to perform <10k tests. In conclusion, a small-scale biological knowledge-driven study with higher enrichment of putative signals may hold the key to identifying gene-gene interactions underlying complex diseases or traits in current and future human association studies.