Powerful and efficient SNP-set association tests across multiple phenotypes using GWAS summary data

Abstract

Motivation

Many GWAS conducted in the past decade have identified tens of thousands of disease related variants, which in total explained only part of the heritability for most traits. There remain many more genetics variants with small effect sizes to be discovered. This has motivated the development of sequencing studies with larger sample sizes and increased resolution of genotyped variants, e.g., the ongoing NHLBI Trans-Omics for Precision Medicine (TOPMed) whole genome sequencing project. An alternative approach is the development of novel and more powerful statistical methods. The current dominating approach in the field of GWAS analysis is the “single trait single variant” association test, despite the fact that most GWAS are conducted in deeply-phenotyped cohorts with many correlated traits measured. In this paper, we aim to develop rigorous methods that integrate multiple correlated traits and multiple variants to improve the power to detect novel variants. In recognition of the difficulty of accessing raw genotype and phenotype data due to privacy and logistic concerns, we develop methods that are applicable to publicly available GWAS summary data.

Results

We build rigorous statistical models for GWAS summary statistics to motivate novel multi-trait SNP-set association tests, including variance component test, burden test and their adaptive test, and develop efficient numerical algorithms to quickly compute their analytical P-values. We implement the proposed methods in an open source R package. We conduct thorough simulation studies to verify the proposed methods rigorously control type I errors at the genome-wide significance level, and further demonstrate their utility via comprehensive analysis of GWAS summary data for multiple lipids traits and glycemic traits. We identified many novel loci that were not detected by the individual trait based GWAS analysis.

Availability and implementation

We have implemented the proposed methods in an R package freely available at http://www.github.com/baolinwu/MSKAT.

Supplementary information

Supplementary data are available at Bioinformatics online.

1 Introduction

The genome-wide association studies (GWAS) have been extremely successful identifying tens of thousands of variants associated with various human diseases and traits in the past decade (Visscher et al., 2017), and providing valuable insights into their underlying genetic architecture. However, significant gaps remain: most identified variants have small effects and in total they explained only a small part of the overall heritability for most traits (Manolio et al., 2009). This has motivated the formation of various mega-scale consortia pooling many GWAS and the ongoing large-scale whole-genome sequencing project to increase the resolution of genotyped variants. All these tremendous efforts are expected to identify more variants and further improve our understanding of the genetic architecture. Alternatively a cost-effective approach is to develop novel and powerful statistical methods that can leverage the existing GWAS data to identify novel variants. Many methods have exploited the polygenic nature of most traits and leveraged the existing GWAS with richly measured phenotypes to develop joint test of multiple traits and multiple variants. They have convincingly demonstrated their utility to identify more genetic variants (see, e.g. Broadaway et al., 2016; Ferreira and Purcell, 2009; He et al., 2013; Liu et al., 2010; Maity et al., 2012; O’Reilly et al., 2012; Seoane et al., 2014; Tang and Ferreira 2012; van der Sluis et al., 2013; Wu and Pankow 2015, 2016; Wu et al., 2010; Yang et al., 2010). A common feature of these methods is that they need raw genotype and phenotype data. However, due to various policy and privacy concerns, it is generally hard to access raw GWAS data. It has now become a common practice to share GWAS summary association statistics, which include, e.g., the SNP id, MAF, effect allele, regression coefficient and associated standard error, P-value, and sample size. Hence, it is desirable to develop novel association test methods that need only GWAS summary data (Pasaniuc and Price, 2017).

We have seen active development of such statistical methods recently. For example, Bakshi et al. (2016) proposed a method to test SNP-set association with a single trait using GWAS summary data. Stephens (2013) and Zhu et al. (2015) proposed novel methods for multi-trait association test with a single variant. Their insightful observation is that the across trait test Z-staistics have the same correlation as the traits. This has motivated using the empirical correlation matrix of Z-statistics to estimate trait correlation matrix widely adopted in most existing methods (Cichonska et al., 2016; Kwak and Pan, 2016). However, this approach implicitly assumes that majority of variants are null and hence has limitations for most traits of polygenic nature, since many variants will have effects, although small, but in aggregation they have large overall effects (as reflected in their large genetic heritability), which will convolute the empirical correlation matrix (with genetic correlation) and lead to biased estimates (see next section for more discussions). Furthermore, due to the complicated dependence across traits and variants, it is very challenging to analytically account for their dependence and efficiently and accurately calculate significance P-values for most existing joint test methods (Cichonska et al., 2016; Kwak and Pan, 2016; Van der Sluis et al., 2014). As a result, they have relied on ad hoc approach or crude Monte Carlo approximation that is computationally intensive and not scalable to genome-wide association test.

In this paper we build rigorous statistical models and develop sound and powerful multi-trait SNP-set association test methods using GWAS summary data. We made several contributions compared to the existing methods: (i) we adopt the recently developed LD score regression approach to more accurately estimate the trait correlation matrix using the summary statistics; (ii) we develop a novel variance components test approach to motivate our proposed methods based on a rigorous multivariate normal regression model derived for the summary statistics; (iii) for the proposed tests, we derive analytical formula and develop efficient numerical algorithms to calculate their P-values accurately and efficiently without the need of resampling or permutation; (iv) we rigorously verify that our proposed methods properly control the type I errors at the genome-wide significance level through very large-scale simulation studies; and further demonstrate their utility through comprehensive analysis of GWAS summary data for multiple lipids traits and glycemic traits.

The structure of this paper is as follows. We discuss the proposed multi-trait SNP-set association test methods using GWAS summary data in Section 2. In Section 3, we investigate the performance of proposed methods through simulation studies. We conduct comprehensive analysis of GWAS summary data for multiple lipids traits and glycemic traits in Section 4. We identified many novel loci that were not detected by the current individual trait based tests. We end the paper with a discussion in Section 5. All technical details are provided in the Supplementary Materials.

2 Methods

Assume we have the GWAS summary data for K quantitative traits measured on a cohort of unrelated individuals. Denote the marginal trait correlation matrix as $\Sigma =({\sigma }_{kj})$. For simplicity of notation, consider the association test Z-statistics (standardized regression coefficient estimates) across all traits for a SNP, denoted as $(z_1,\dots ,z_K)$. Bulik-Sullivan et al. (2015) showed that $\mathbb{E}(z_k{z}_j)={\sigma }_{kj}+g_{kj}\ell$ under a polygenic model, where $\ell$ is the SNP’s average LD score (computed as the average of its LD r² with all other SNPs), and g_kj quantifies the trait genetic correlation. We can thus obtain unbiased estimate of σ_kj by regressing $z_k{z}_j$ on the LD scores, which are pre-computed using the 1 K Genomes samples (1000 Genomes Project Consortium, 2012). In contrast, the empirical correlation matrix of summary Z-statistics will produce biased estimates of Σ for polygenic traits due to the variant LD and trait genetic correlation. For simplicity of notation, we still use Σ to denote the estimated trait correlation matrix throughout the discussion.

In the following, we develop methods to test the joint association of a given set of SNPs (in a gene region or pathway) with all K traits simultaneously. Denote the association test Z-statistic as z_kj for the k-th trait and j-th SNP, $k=1,\dots ,K;j=1,\dots ,m$. Let $\mathrm{Z}=(z_{kj})$. Our null hypothesis is that $\mathrm{Z}$ have zero means.

2.1 Multi-trait SNP-set association test using GWAS summary data

Assume that the Z-statistics are derived based on genotypes coding the copies of minor alleles (i.e., the minor allele is the effect allele; if not, we switch the sign of Z-statistics). We can derive a multivariate normal regression model for the summary statistics $\mathrm{Z}$ and show that asymptotically $Var(vec(\mathrm{Z}))=R\otimes \Sigma$, where R is the m × m LD correlation matrix, $vec()$ is the vector operator stacking the columns of a matrix into a vector, and ⊗ denotes the Kronecker product.

Let $Z_j={(z_{1j},\dots ,z_{Kj})}^T$ denote the K summary Z-statistics for the j-th SNP. For a single variant, the chi-square statistic $Z_j^T{\Sigma }^{-1}{Z}_j$ can be used to test for the effect of variant j across all traits. To summarize the overall SNP-set effects, we consider $Q={\sum }_{j=1}^m{Z}_j^T{\Sigma }^{-1}{Z}_j$. Q generally has robust performance with mixed variant effects. When all variants have similar effects, we can gain more power by testing the collapsed genotype scores. We can readily check that a burden type test using GWAS summary data is $B={({\sum }_{j=1}^m{Z}_j)}^T{\Sigma }^{-1}({\sum }_{j=1}^m{Z}_j)$. We rigorously derive Q and B via a variance components test approach under the derived multivariate normal regression model for the summary statistics. We further show that under the null of no SNP-set effects, Q is distributed as the weighted sums of independent ${\chi }_K^2$ random variables, and B is a scaled ${\chi }_K^2$ random variable.

2.2 Adaptive multi-trait SNP-set association test

To combine the strength of Q and B, we consider their weighted average, $Q_{\rho }=(1-\rho )Q+\rho B$, and use the minimum p-value, $T={\min }_{\rho \in [0,1]}Pval(Q_{\rho })$, over a finite grid of ρ’s as an adaptive test statistic. We note that $Q_{\rho }$ can also be derived as a variance components test. It is very challenging to derive the null distribution of T to compute its P-value. A working solution is the crude Monte Carlo approximation, which is however too computationally intensive. We develop efficient algorithms to calculate the p-value of T without the need of resampling or permutation (See Supplementary Materials for technical details).

Next we investigate the performance of our proposed methods through numerical studies and applications. We will refer to our proposed methods as MSATS (for Multi-trait SNP-set Association Tests using Summary data) and denote B as MBT, Q as MQT, and T as MAT in the following discussion. When comparing the proposed MSATS to alternative methods, we mainly focus on computationally efficient statistical methods and do not include those computationally intensive approaches. We also view our proposed methods as a complementary approach to single trait single variant association tests. The MSATS tests are direct generalizations of the corresponding single trait GWAS summary data based SNP-set test methods (K = 1) as studied in Guo and Wu (2018). We denote the single trait burden test, sum of squares test and their adaptive test, as SBT, SQT and SAT respectively in the following discussion. We use their Bonferroni corrected p-values based on the number of traits.

3 Results

3.1 Simulations

We conducted simulation studies to evaluate the performance of the proposed methods. We consider three traits and set the trait correlation matrix: ${\Sigma }_{12}=-0.1081,{\Sigma }_{13}=-0.3579 \hspace{0.17em}\text{and}\hspace{0.17em} {\Sigma }_{23}=0.2313$, which are the outcome correlation matrix based on three lipids traits GWAS with around 100, 000 European individuals (Teslovich et al., 2010; see next section). We set R as the LD correlation matrix of 22 SNPs in the gene KLHL8.

We first evaluate the type I errors of the proposed MSATS tests. We simulate 10⁸ null summary statistics from $\mathcal{N}(0,R\otimes \Sigma )$ to estimate the type I errors at significance levels $\alpha ={10}^{-4},{10}^{-5}, \hspace{0.17em}\text{and}\hspace{0.17em} 2.5\times {10}^{-6}$. Table 1 summarizes the results. Overall we can see that all proposed tests have well-controlled type I errors.

Table 1.

Ratio of empirical type I errors divided by the significance level α estimated over 10⁸ simulations

	α	${10}^{-4}$	${10}^{-5}$	$2.5\times {10}^{-6}$
MSATS	MQT	0.98 (0.01)	0.99 (0.03)	1.00 (0.06)
	MBT	0.99 (0.01)	1.04 (0.03)	1.05 (0.06)
	MAT	0.99 (0.01)	0.97 (0.03)	0.93 (0.06)

Note: Listed within parentheses are the standard errors. MAT, MQT and MBT are the proposed multi-trait adaptive test, quadratic test and burden test, respectively.

To evaluate the power of proposed methods, we simulate 10⁵ summary statistics from $\mathcal{N}(A\otimes \Delta ,R\otimes \Sigma )$, where A is a vector of length 22 and Δ is a vector of length 3. We assume 4 SNPs with association signals by randomly setting 4 A_i as 1 or -1, and setting the rest of A as zero. Table 2 shows the estimated power at $2.5\times {10}^{-6}$ significance level under four combinations of A for four settings of Δ: two fixed values of Δ and randomly simulated Δ uniformly from $U(-3,3)$ and normally from $\mathcal{N}(0,1)$. Overall the proposed MSATS tests perform better than the single trait based tests. Among the three multi-trait tests, when we have the same effects across all 4 signal SNPs (the first and last combinations), the MBT test performs the best while MQT has the worst performance. When we have balanced mixing of positive and negative SNP effects (the third combination), not surprisingly, MBT has the worst performance since directly summing the summary statistics cancels out the overall signals, while MQT performs the best. Very interestingly, with unbalanced mixing of positive and negative SNP effects (the second combination), the adaptive test MAT truly combines the strength of both MQT and MBT and has the best performance with much improved power compared to MQT and MBT. The adaptive test MAT performs robustly across all scenarios and has the overall best performance. We have done more power simulations by varying number of signal SNPs and simulating various values of Δ, and obtained the same conclusions. The complete results are available at the Supplementary Materials.

Table 2.

Estimated test power (%) under $2.5\times {10}^{-6}$ significance level

Δ	nonzero Ai’s	MAT	MQT	MBT	SAT	SQT	SBT
(3, 2.5,-1.5)	(1, 1, 1, 1)	36.5	0.3	37.8	5.7	0.0	8.5
	(1, 1, 1, −1)	59.6	41.0	7.7	5.0	1.7	1.3
	(1, 1, −1, −1)	27.0	40.8	0.0	0.8	1.8	0.0
	(−1, −1, −1, −1)	36.1	0.3	37.3	5.4	0.0	8.2
(4, 2, 2)	(1, 1, 1, 1)	49.1	0.5	48.6	6.9	0.0	9.6
	(1, 1, 1, −1)	51.8	33.3	6.4	3.3	1.1	0.8
	(1, 1, −1, −1)	21.2	33.2	0.0	0.4	1.1	0.0
	(−1, −1, −1, −1)	49.0	0.5	48.6	6.7	0.0	9.3
$\mathcal{N}(0,1)$	(1, 1, 1, 1)	35.6	8.6	35.4	22.2	3.6	22.7
	(1, 1, 1, −1)	34.7	30.3	11.8	22.2	18.7	5.5
	(1, 1, −1, −1)	27.1	30.3	0.0	15.4	18.7	0.0
	(−1, −1, −1, −1)	35.8	8.5	35.5	22.2	3.6	22.9
$U(-3,3)$	(1, 1, 1, 1)	44.8	6.5	44.3	17.3	0.1	19.7
	(1, 1, 1, −1)	49.1	41.7	13.2	18.2	10.6	2.6
	(1, 1, −1, −1)	36.1	41.9	0.0	5.6	10.7	0.0
	(−1, −1, −1, −1)	44.8	6.4	44.3	17.1	0.1	19.5

Note: Data are simulated from $\mathcal{N}(A\otimes \Delta ,R\otimes \Sigma )$. A has 4 nonzero A_i’s with different signs. MAT, MQT and MBT are the proposed multi-trait adaptive test, quadratic test, and burden test; and SAT, SQT and SBT are the corresponding single-trait based test methods.

3.2 Application to GWAS summary data for lipids traits

We conduct a comprehensive analysis of the GWAS summary data for high-density lipoprotein cholesterol (HDL), low-density lipoprotein cholesterol (LDL), and Triglycerides (TG) conducted by the Global Lipids Consortium with around 100, 000 European individuals (Teslovich et al., 2010). The GWAS summary data are downloaded from http://csg.sph.umich.edu/abecasis/public/lipids2010. With the LD score regression approach, the estimated correlation matrix are: ${\Sigma }_{12}=-0.1081,{\Sigma }_{13}=-0.3579,{\Sigma }_{23}=0.2313$.

We first remove those SNPs with MAF <0.05 and then group all SNPs within 20 kb of a gene region into a set. For each SNP-set, we further perform LD pruning so that all pairwise LD $r^2\le 0.8$. As we view the proposed MSATS tests as a complementary approach to the traditional single variant single trait association test, and for illustrating the relative performance of different methods, we further remove those genome-wide significant SNPs ($P\le 5\times {10}^{-8}$ for any trait). In total we obtain 18 754 SNP-sets with at least two SNPs for downstream analysis. Willer et al. (2013) conducted a followup study of those promising SNPs identified by Teslovich et al. (2010) based on around 190 000 European participants. We use their summary results as partial validation in our analysis. Here we mainly focus on the results for the proposed MSATS tests. The single trait based test methods have identified much less significant genes. We list their detailed results in the Supplementary Materials.

At the Bonferroni corrected SNP-set significance level $2.67\times {10}^{-6}$, the proposed MSATS tests identified a total of 237 significant genes. Figure 1 shows the Venn diagram comparing the number of significant genes identified by the proposed tests. The MBT identified 101 significant genes, MQT identified 191 significant genes, and MAT identified 218 significant genes. The adaptive test MAT captured the majority of significant SNP-sets identified by MQT and MBT, and it further identified five additional significant genes which were not identified by MQT and MBT. Table 3 shows the MSATS test p-values for these five genes and the minimum p-value across all SNPs in the gene and all traits from Teslovich et al. (2010) and Willer et al. (2013). Among them four genes harbor genome-wide significant SNPs in the meta analysis of Willer et al. (2013). The novel gene ANUBL1 has been implicated in lipids metabolism (Demetz et al., 2014; Burkhardt et al., 2015).

Fig. 1.

Venn diagram of number of significant genes identified by proposed MSATS tests for the three lipids traits

Table 3.

Significant genes identified only by MAT, missed by MQT and MBT

Gene	MQT	MBT	MAT	minP-2010	minP-2013
ANUBL1	1.57e-05	3.71e-06	1.72e-06	5.36e-07	2.28e-06
CCDC18	4.70e-06	4.36e-06	1.57e-06	4.10e-07	3.56e-10
CTSA	3.10e-06	6.68e-05	9.62e-07	3.37e-21	3.98e-36
LCAT	3.82e-06	6.45e-06	2.40e-06	1.22e-31	3.30e-52
SPI1	1.68e-05	1.36e-05	1.07e-06	3.30e-15	1.40e-31

Note: We listed the MSATS test P-values and the minimum P-value across all SNPs in the gene and all traits from Teslovich et al. (2010) study (denoted as minP-2010) and Willer et al. (2013) study (denoted as minP-2013).

Among the 237 significant genes, 209 genes harbored genome-wide significant SNPs from the meta-analysis results of Willer et al. (2013); and 45 of them were “novel” genes in the sense that the meta-analysis of Teslovich et al. (2010) did not identify any significant SNPs in these 45 genes. Table 4 lists 10 representative genes identified by the proposed tests. The Supplementary Materials listed the detailed information for all identified genes.

Table 4.

Some “novel” significant genes

Gene	MQT	MBT	MAT	minP-2010	minP-2013
NIPSNAP3B	1.89e-07	5.66e-03	4.84e-07	7.71e-07	1.63e-18
RAB11B	9.18e-08	1.10e-06	7.75e-08	6.63e-08	6.66e-18
ZDHHC18	3.77e-08	2.77e-09	3.51e-09	6.11e-07	9.74e-16
NUDC	2.34e-07	1.15e-06	1.85e-07	1.40e-07	2.00e-15
OBP2B	4.76e-09	6.08e-06	6.75e-09	1.15e-07	4.32e-15
MIR148A	1.59e-10	2.01e-08	6.03e-11	7.93e-07	3.95e-14
GPR61	2.92e-07	2.12e-04	4.97e-07	6.35e-08	5.60e-14
GPN2	1.62e-06	2.22e-04	2.20e-06	1.40e-07	1.44e-13
NR0B2	5.38e-08	5.26e-07	3.31e-08	1.40e-07	1.44e-13
LRRC36	1.17e-07	5.36e-02	1.66e-07	1.67e-07	1.05e-12

We listed MSATS test P-values and the minimum P-value across all SNPs in the gene and all traits from Teslovich et al. (2010) study (denoted as minP-2010) and Willer et al. (2013) study (denoted as minP-2013).

In total we identified 27 novel genes: they did not harbor any significant SNPs in Teslovich et al. (2010) and Willer et al. (2013). Table 5 summarizes their information. For each novel gene, we listed the MSATS test P-values together with the minimum P-value of all SNPs in the gene across all traits for both studies.

Table 5.

MSATS test P-values for 27 novel genes

Gene	MQT	MBT	MAT	minP-2010	minP-2013
ACADS	3.44e-02	1.48e-06	5.12e-06	3.87e-04	1.29e-03
ACHE	4.13e-02	1.37e-08	2.86e-08	9.53e-05	4.30e-05
ANUBL1	1.57e-05	3.71e-06	1.72e-06	5.36e-07	2.28e-06
AURKB	1.12e-06	1.77e-06	1.74e-06	3.01e-07	2.46e-07
BACE1	3.81e-07	8.44e-02	4.65e-07	1.59e-05	5.69e-08
CBFB	1.52e-06	8.28e-01	4.59e-06	2.70e-07	5.66e-08
CD320	8.43e-02	1.44e-07	4.89e-07	1.79e-03	1.19e-04
CENPA	7.82e-03	3.51e-07	5.40e-07	1.01e-03	1.02e-05
CSH2	1.92e-01	2.36e-06	4.35e-06	3.43e-03	1.45e-02
ETNK1	1.20e-06	1.15e-01	1.88e-06	4.93e-07	1.42e-06
GH1	8.52e-01	8.13e-14	1.55e-13	5.35e-03	4.17e-03
KIAA1949	2.05e-07	2.53e-02	5.90e-07	1.65e-06	3.41e-06
MAFB	2.28e-06	1.61e-01	5.35e-06	1.78e-05	4.65e-07
NICN1	1.18e-01	2.85e-07	3.90e-07	7.46e-03	9.85e-03
NPEPPS	6.87e-09	4.39e-01	1.28e-08	1.15e-07	1.36e-06
NSUN5	9.29e-06	7.82e-09	2.83e-08	9.58e-05	5.95e-07
OR8J1	1.36e-03	2.52e-06	3.36e-06	8.21e-07	1.73e-06
RABEP2	2.14e-02	1.04e-37	1.75e-37	4.39e-03	7.40e-05
RNF39	1.85e-06	8.31e-02	3.79e-06	5.62e-05	1.05e-06
SFN	2.48e-08	1.31e-07	1.25e-08	1.66e-06	2.30e-06
SFRS16	2.02e-11	2.01e-02	5.85e-11	2.74e-07	8.91e-08
SNORD19	2.78e-03	2.58e-09	6.19e-09	6.74e-04	9.75e-05
SPCS1	2.86e-03	1.70e-09	4.13e-09	7.26e-04	9.75e-05
TPPP3	1.70e-07	4.79e-02	2.40e-07	5.84e-07	3.90e-07
TRIM50	9.39e-06	1.58e-08	2.02e-08	9.58e-05	8.12e-08
TRIP6	3.86e-02	1.42e-06	2.88e-06	2.97e-05	4.30e-05
ZDHHC1	7.54e-07	5.42e-03	1.22e-06	5.84e-07	3.90e-07

We listed MSATS test P-values and the minimum P-value across all SNPs in the gene and all traits from Teslovich et al. (2010) study (denoted as minP-2010) and Willer et al. (2013) study (denoted as minP-2013).

Some identified novel genes have been reported to be significantly associated with lipids traits or harbor some genome-wide significant SNPs in some recent GWAS. For example, MAFB is close to a significant SNP identified in a LDL GWAS (Kathiresan et al., 2009), and it has been shown to increase LDL cholesterol levels by negatively regulating the LDL receptor transcription activity (Petersen et al., 2004). Through cis-eQTL analysis, Yao et al. (2015) showed that the SNP rs7206971 in NPEPPS is genome-wide significantly associated with LDL cholesterol. In a GWAS meta-analysis, Postmus et al. (2014) showed that the SNP rs445925 (0.1Mb upstream of SFRS16 on chromosome 19) is significantly associated with LDL response after statin treatment. The SNP rs2240466, which is close to NSUN5, was found genome-wide significantly associated with TG (Aulchenko et al., 2009; Folkersen et al., 2010). TPPP3 is a protein coding gene which was found to be a signal for HDL in the analysis of Charlesworth et al. (2009). Andreassen et al. (2015) showed that three of the identified novel genes (CBFB, ETNK1, KIAA1949) contained risk SNPs shared between the immune-mediated diseases and TG or HDL. In addition, several identified novel genes have been reported to be involved in some diseases or traits which are strongly related to the lipids traits. For example, coronary artery disease (CAD) is a common disease showing strong relationship with lipids traits (Nair et al., 2009; Wilson, 1990). Weng et al. (2016) found that RNF39 might cause those genes involved in cardio-dysfunction to contribute to risk of nonobstructive CAD in Caucasian women, while the SNP rs2301753 in RNF39 can reduce the likelihood of nonobstructive CAD. For NICN1, LeBlanc et al. (2015) showed that it might have some eQTL effect on CAD in the blood tissue. Waist-to-hip ratio (WHR) was shown to be significantly correlated with serum lipids concentrations (especially HDL concentration) in obese women (Komiya and Masuda, 1989). ZDHHC1 has been found to be significantly associated with WHR in women of both African and European ancestry (Ng et al., 2017). Similarly, the SNP rs6784615 near SNORD19 was also associated with WHR (Heid et al., 2010). ACADS is the plausible candidate gene underlying total-cholesterol quantitative trait loci on Chromesome 5 in male mice, and this finding provided insight into the genetic mechanisms of plasma lipid metabolism (Suto and Kojima, 2017). Hietaniemi et al. (2005) found that the GH1 was associated with LDL cholesterol. SPCS1 is a protein coding gene, and Suzuki et al. (2013) found that it participated in the assembly of Hepatitics C Virus (HCV) which was associated with cholesterol and lipoproteins (Felmlee et al., 2013). For the RABEP2 gene, copy number variations of a genomic region including this gene have been associated with severe obesity which is a common risk factor of HDL (Bochukova et al., 2010). Micale et al. (2008) showed that TRIM50 encoded an E3 ubiquitin ligase, and research has shown that E3 ubiquitin ligase IDOL induced the degradation of the low density lipoprotein receptor (Hong et al., 2010) and helped control cholesterol (Brown and Hsieh, 2016). Another protein coding gene BACE1 was found to play an important role in linking lipids to Alzheimer’s Disease (Di Paolo and Kim, 2011) and interact with scaffolding proteins of lipid rafts (Hattori et al., 2006). All these evidences suggest that these identified novel genes are likely to be associated with lipids. Further research is needed on the possible roles of these identified SNPs/genes.

3.3 Application to GWAS summary data for glycemic traits

We also jointly analyze the GWAS meta-analysis summary data for the fasting glucose, fasting insulin, indices of β-cell function and insulin resistance conducted by the MAGIC consortium with 46, 186 non-diabetic European participants (Dupuis et al., 2010). We follow the previous procedure to process the summary data. Figure 2 shows the Venn diagram comparing the number of significant genes identified by the proposed tests. The MSATS tests identified a total of 19 significant genes, and 11 of them are novel genes. They perform better than the single trait based tests. The adaptive test MAT is the most powerful. We provide detailed analysis results at the Supplementary Materials.

Fig. 2.

Venn diagram of number of significant genes identified by the proposed MSATS tests for the four glycemic traits

4 Discussion

Various multi-trait testing methods have been developed along the line of Stephens (2013) and Zhu et al. (2015), though generally they require computing-intensive Monte Carlo or MCMC sampling (see, e.g., Shim et al., 2015; Zhu and Stephens, 2017). Our proposed methods provide an alternative approach with extreme scalability and robust performance. In the same spirit as these existing approaches, the proposed methods need only the publicly available GWAS summary statistics without the need to access raw genotype and phenotype data. We expect that these newly developed GWAS summary data based joint testing methods can potentially identify more novel variants and shed more lights into the underlying disease mechanism.

We note that the Bayesian modeling is an alternative and very useful approach (see, e.g., Shim et al., 2015; Zhu and Stephens, 2017). Compared to frequentist approach, they are often more flexible to accommodate various useful outside information (e.g., as a form of informative prior) and can easily account for the complicated dependence across traits and variants. For example, Zhu and Stephens (2017) recently developed a novel approach to simultaneously model the summary statistics across all variants. However, a potential drawback is that they often need intensive MCMC sampling to make inferences, which partially hinders their applicability, especially when we prototype different methods and want to make quick inferences on millions of variants or tens of thousands of SNP-sets. Therefore there is a pressing need to develop powerful, flexible, yet efficient statistical methods that are built on rigorous statistical models and can integrate various information. Our developed methods showcase that novel integration of multiple related traits and variants can identify more novel variants.

Throughout the discussions, we have mainly focused on multiple GWAS summary data from the same cohort. The proposed methods can be readily extended to GWAS with partially overlapped samples (see Supplementary Materials). We have implemented the proposed methods in an R package publicly available online.