Abstract
Scalable, integrative methods to understand mechanisms that link genetic variants with phenotypes are needed. Here we derive a mathematical expression to compute PrediXcan (a gene mapping approach) results using summary data (SPrediXcan) and show its accuracy and general robustness to misspecified reference sets. We apply this framework to 44 GTEx tissues and 100+ phenotypes from GWAS and metaanalysis studies, creating a growing public catalog of associations that seeks to capture the effects of gene expression variation on human phenotypes. Replication in an independent cohort is shown. Most of the associations are tissue specific, suggesting context specificity of the trait etiology. Colocalized significant associations in unexpected tissues underscore the need for an agnostic scanning of multiple contexts to improve our ability to detect causal regulatory mechanisms. Monogenic disease genes are enriched among significant associations for related traits, suggesting that smaller alterations of these genes may cause a spectrum of milder phenotypes.
Introduction
Over the last decade, GWAS have been successful in robustly associating genetic loci to human complex traits. However, the mechanistic understanding of these discoveries is still limited, hampering the translation of the associations into actionable targets. Studies of enrichment of expression quantitative trait loci (eQTLs) among traitassociated variants^{1,2,3} show the importance of gene expression regulation. Functional class quantification showed that 80% of the common variant contribution to phenotype variability in 12 diseases can be attributed to DNAase I hypersensitivity sites, further highlighting the importance of transcript regulation in determining phenotypes^{4}.
Many transcriptome studies have been conducted where genotypes and expression levels are assayed for a large number of individuals^{5,6,7,8}. The most comprehensive transcriptome dataset, in terms of examined tissues, is the GenotypeTissue Expression Project (GTEx): a largescale effort where DNA and RNA were collected from multiple tissue samples from nearly 1000 individuals and sequenced to high coverage^{9,10}. This remarkable resource provides a comprehensive crosstissue survey of the functional consequences of genetic variation at the transcript level.
To integrate knowledge generated from these largescale transcriptome studies and shed light on disease biology, we developed PrediXcan^{11}, a genelevel association approach that tests the mediating effects of gene expression levels on phenotypes. PrediXcan is implemented on GWAS or sequencing studies (i.e., studies with genomewide interrogation of DNA variation and phenotypes). It imputes transcriptome levels with models trained in measured transcriptome datasets (e.g., GTEx). These predicted expression levels are then correlated with the phenotype in a gene association test that addresses some of the key limitations of GWAS^{11}.
Metaanalysis efforts that aggregate results from multiple GWAS have been able to identify an increasing number of associations that were not detected with smaller sample sizes^{12,13,14}. We will refer to these results as Genomewide association metaanalysis (GWAMA) results. In order to harness the power of these increased sample sizes while keeping the computational burden manageable, methods that use summary level data rather than individual level data are needed.
Methods similar to PrediXcan that estimate the association between intermediate gene expression levels and phenotypes, but use summary statistics have been reported: TWAS (summary version)^{15} and Summary Mendelian Randomization (SMR)^{16}. Another class of methods that integrate eQTL information with GWAS results are based on colocalization of eQTL and GWAS signals. Colocalized signals provide evidence of possible causal relationship between the target gene of an eQTL and the complex trait. These include RTC^{1}, Sherlock^{17}, COLOC^{18}, and more recently eCAVIAR^{19} and ENLOC^{20}.
Here we derive a mathematical expression that allows us to compute the results of PrediXcan without the need to use individuallevel data, greatly expanding its applicability. We compare with existing methods and outline a best practices framework to perform integrative gene mapping studies, which we term MetaXcan.
We apply the MetaXcan framework by first training over one million elastic net prediction models of gene expression traits, covering protein coding genes across 44 human tissues from GTEx, and then performing genelevel association tests over 100 phenotypes from 40 large metaanalysis consortia and dbGaP.
Results
Computing PrediXcan results using summary statistics
We have derived an analytic expression to compute the outcome of PrediXcan using only summary statistics from genetic association studies. Details of the derivation are shown in the Methods section. In Fig. 1a we illustrate the mechanics of SummaryPrediXcan (SPrediXcan) in relation to traditional GWAS and the individuallevel PrediXcan method^{11}.
We find high concordance between PrediXcan and SPrediXcan results indicating that in most cases, we can use the summary version without loss of power to detect associations. Figure 2 shows the comparison of PrediXcan and SPrediXcan Zscores for a simulated phenotype (under the null hypothesis), a cellular growth phenotype and two disease phenotypes: type 1 diabetes and bipolar disorder from the WTCCC Consortium^{21}; see Supplementary Notes 1, 2 and 3 for details. For the simulated phenotype, the study sets (in which GWAS is performed) and the reference set (in which LD between SNPs is computed) were African, East Asian, and European subsets from 1000 Genomes. The training set (in which prediction models are trained) was European (DGN Cohort^{5}) in all cases. The high correlation between PrediXcan and SPrediXcan demonstrates the robustness of our method to mismatches between reference and study sets. Despite the generally good concordance between the summary and individual level methods, there were a handful of false positive results with SPrediXcan much more significant than PrediXcan. This underscores the need to use closely matched LD information whenever possible. Supplementary Fig. 11 shows SPrediXcan’s performance on a phenotype simulated under the alternative hypothesis.
Notice that we are not testing here whether PrediXcan itself is robust to population differences between training and study sets. Robustness of the prediction across populations has been previously reported^{22}. We further corroborated this in Supplementary Fig. 10.
Next we compare with other summary resultbased methods such as STWAS, SMR, and COLOC.
Colocalization estimates complement PrediXcan results
One class of methods seeks to determine whether eQTL and GWAS signals are colocalized or are distinct although linked by LD. This class includes COLOC^{18}, Sherlock^{17}, and RTC^{1}, and more recently eCAVIAR^{19}, and ENLOC^{20}. Thorough comparison between these methods can be found in refs. ^{18,19}. HEIDI, the post filtering step in SMR that estimates heterogeneity of GWAS and eQTL signals, can be included in this class. We focus here on COLOC, whose quantification of the probability of five configurations complements well with SPrediXcan results.
COLOC provides the probability of five hypotheses: H0 corresponds to no eQTL and no GWAS association, H1 and H2 correspond to association with eQTL but no GWAS association or viceversa, H3 corresponds to eQTL and GWAS association but independent signals, and finally H4 corresponds to shared eQTL and GWAS association. P0, P1, P2, P3, and P4 are the corresponding probabilities for each configuration. The sum of the five probabilities is 1. The authors^{18} recommend to interpret H0, H1, and H2 as limited power; for convenience we will aggregate these three hypotheses into one event with probability 1P3P4.
Figure 3 shows ternary plots^{23} with P3, P4, and 1P3P4 as vertices. The blue region, top subtriangle, corresponds to high probability of colocalized eQTL and GWAS signals (P4). The orange region at bottom left corresponds to high probability of distinct eQTL and GWAS signals (P3). The gray region at center and bottom right corresponds to low probability of both colocalization and independent signals.
Figure 3b shows association results for all genetissue pairs with the height phenotype. We find that most associations fall in the gray, “undetermined,” region. When we restrict the plot to SPrediXcan Bonferronisignificant genes (Fig. 3c), three distinct peaks emerge in the high P4 region (P4 > 0.5, “colocalized signals”), high P3 region (P3 > 0.5, “independent signals” or “noncolocalized signals”), and “undetermined” region. Moreover, when genes with low prediction performance are excluded (Supplementary Fig. 6d) the “undetermined” peak significantly diminishes.
These clusters provide a natural way to classify significant genes and complement SPrediXcan results. Depending on false positive/false negative tradeoff choices, genes in the “independent signals” or both “independent signals” and “undetermined” can be filtered out. The proportion of colocalized associations (P4 > 0.5) ranged from 5 to 100% depending on phenotype with a median of 27.6%. The proportion of “noncolocalized” associations ranged from 0 to 77% with a median of 27.0%. Supplementary Table 1 summarizes the percentages of significant associations that fall into the different colocalization regions.
This postfiltering idea was first implemented in the SMR approach using HEIDI. Comparison of COLOC results with HEIDI is shown in Supplementary Fig. 6e to 6h.
Comparison of SPrediXcan to STWAS
Gusev et al. have proposed TranscriptomeWide Association Study based on summary statistics (STWAS), which imputes the SNP level Zscores into gene level Zscores. This is not the same as computing the results of individual level TWAS. We show (in Methods section) that the difference between the individual level and summary level TWAS is given by the factor \(\sqrt {\frac{{1  R_l^2}}{{1  R_g^2}}} \), where R_{ l } is the proportion of variance in the phenotype explained by a SNP’s allelic dosage, and R_{ g } is the proportion explained by gene expression (see Methods section). For most practical purposes we have found that this factor is very close to 1 so that if the same prediction models were used, no substantial difference between STWAS and SPrediXcan should be expected.
Figure 4a shows a diagram of SPrediXcan and STWAS. Both use SNP to phenotype associations results (Z_{ X,Y }) and prediction weights (w_{ X,Tg }) to infer the association between the gene expression level (T_{ g }) and phenotype (Y).
Figure 4b compares STWAS significance (as reported in ref. ^{24}) to SPrediXcan significance. The difference between the two approaches is mostly driven by the different prediction models: TWAS uses BSLMM^{25} whereas PrediXcan uses elastic net^{26}. BSLMM allows two components: one sparse (small set of large effect predictors) and one polygenic (all variants contribute some marginal effect to the prediction). For PrediXcan we have chosen to use a sparse model (elastic net) based on the finding that the genetic component of gene expression levels is mostly sparse^{27}.
Figure 4c shows that the COLOCestimated proportion of noncolocalized (independent) GWAS and eQTL signals is larger among TWAS significant genes than among SPrediXcan significant ones. We believe this is due to the polygenic component of BSLMM models, a wider set of SNPs increasing the chances of COLOC yielding a noncolocalized result. Figure 4d shows that, for most traits, the COLOCestimated proportion of colocalized signals is larger among SPrediXcan significant genes than STWAS significant genes.
Comparison of SPrediXcan to SMR
Zhu et al. have proposed Summary Mendelian Randomization (SMR)^{16}, a summary data based Mendelian randomization that integrates eQTL results to determine target genes of complex traitassociated GWAS loci. They derive an approximate \(\chi _1^2\) statistic (Eq 5 in ref. ^{16}) for the mediating effect of the target gene expression on the phenotype. Figure 5a depicts this mechanism.
Unfortunately, the derived statistic is not well calibrated. A QQ plot comparing the SMR statistic (under the null hypothesis of genomewide significant eQTL signal and no GWAS association) shows deflation. The sample mean of the statistic is ≈0.93 instead of 1, the expected value for the mean of a \(\chi _1^2\) random variable (see Fig. 5e, f and Methods section for details). The \(\chi ^2\) approximation is only valid in two extreme cases: when the eQTL association is much stronger than the GWAS association or vice versa, when the GWAS association is much stronger than the eQTL association (see Methods section for details).
One limitation is that the significance of the SMR statistic is the lower of the top eQTL association (genotype to expression) or the GWAS association (genotype to phenotype) as shown in Fig. 5e, f. Given the much larger sample sizes of GWAS studies, for most genes, the combined significance will be determined by the eQTL association. The combined statistic forces us to apply multiple testing correction for all genes, even those that are distant to GWAS associated loci, which is unnecessarily conservative. Keep in mind that currently both SMR and PrediXcan only use cis associations. An example may clarify this further. Let us suppose that for a given phenotype there is only one causal SNP and that the GWAS yielded a highly significant pvalue, say 10^{−50}. Let us also suppose that there is only one gene (gene A) in the vicinity (we are only using cis predictors) associated with the causal SNP with p = 10^{−5}. SMR would compute the pvalues of all genes and yield a pvalue ≈ 10^{−5} for gene A (the less significant pvalue). However, after multiple correction this gene would not be significantly associated with the phenotype. Here it is clear that we should not be adjusting for testing of all genes when we know a priori that only one is likely to produce a gene level association. In contrast, the PrediXcan pvalue would be ≈10^{−50} for gene A and would be distributed uniformly from 0 to 1 for the remaining genes. Most likely only gene A (or perhaps a handful of genes, just by chance) would be significant after Bonferroni correction. If we further correct for prediction uncertainty (here = eQTL association), a pvalue of ≈10^{−5} would remain significant since we only need to correct for the (at most) handful of genes that were Bonferroni significant for the PrediXcan pvalue.
Another potential disadvantage of this method is that only topeQTLs are used for testing the gene level association. This does not allow to aggregate the effect on the gene across multiple variants.
Figure 5b compares SPrediXcan (elastic net) and SMR association results. As expected, SMR pvalues tend to be less significant than SPrediXcan’s in large part due to the additional adjustment for the uncertainty in the eQTL association. Figure 5c, d show that the SMR significance is bounded by the eQTL and GWAS association strengths of the top eQTL. Figure 5g shows a comparison between SMR’s and SPrediXcan’s proportion of noncolocalization, while Fig. 5h compares proportion of colocalization, as estimated by COLOC. SMR shows a higher proportion of colocalized and independent signals. This is expected since SMR uses a more stringent eQTL association criterion so that there are few significant genes in the undetermined region.
SMR introduces a post filtering step via an approach called HEIDI, which is compared to COLOC in Fig. 3e and Supplementary Fig. 6.
MetaXcan framework
Building on SPrediXcan and existing approaches, we define a general framework (MetaXcan) to integrate eQTL information with GWAS results and map diseaseassociated genes. This evolving framework can incorporate models and methods to increase the power to detect causal genes and filter out false positives. Existing methods fit within this general framework as instances or components (Fig. 6a).
The framework starts with the training of prediction models for gene expression traits followed by a selection of highperforming models. Next, a mathematical operation is performed to compute the association between each gene and the downstream complex trait. Additional adjustment for the uncertainty in the prediction model can be added. To avoid capturing LDcontaminated associations, which can occur when expression predictor SNPs and phenotype causal SNPs are different but in LD, we use colocalization methods that estimate the probability of shared or independent signals.
PrediXcan implementations use elastic net models motivated by our observation that gene expression variation is mostly driven by sparse components^{27}. TWAS implementations have used Bayesian Sparse Linear Mixed Models^{25} (BSLMM). SMR fits into this scheme with prediction models consisting solely of the top eQTL for each gene (weights are not necessary here since only one SNP is used at a time).
For the last step, we chose COLOC to estimate the probability of colocalization of GWAS and eQTL signals. COLOC probabilities cluster more distinctly into different classes and thus, unlike other methods, suggests a natural cut off threshold at P = 0.5. Another advantage of COLOC is that for genes with low probability of colocalization, it further distinguishes distinct GWAS and eQTL signals from low power. This is a useful feature that future development of colocalization methods should also offer. SMR, on the other hand, uses its own estimate of “heterogeneity” of signals calculated by HEIDI.
Suggested association analysis pipeline

1.
Perform PrediXcan or SPrediXcan using all tissues. Use Bonferroni correction for all genetissue pairs: keep p < 0.05/number of genetissue pairs tested.

2.
Keep associations with significant prediction performance adjusting for number of PrediXcan significant genetissue pairs: keep prediction performance pvalues < 0.05/(number of significant associations from previous step).

3.
Filter out LDcontaminated associations, i.e., genetissue pairs in the “independent signal” (=”noncolocalized”) region of the ternary plot (See Fig. 3a): keep COLOC P3 < 0.5 (Blue and gray regions in Fig. 3a).

4.
If further reduction of number of genes to be taken to replication or validation is desired, keep only hits with explicit evidence of colocalization: P4 > 0.5 (Blue region in Fig. 3a).
Any choice of thresholds has some level of arbitrariness. Depending on the false positive and negative trade off, these numbers may be changed.
Gene expression variation is associated to diverse traits
We downloaded summary statistics from meta analyses of over 100 phenotypes from 40 consortia. The full list of consortia and phenotypes is shown in Supplementary Data 2. We tested association between these phenotypes and the predicted expression levels using elastic net models in 44 human tissues from GTEx as described in the Methods section, and a whole blood model from the DGN cohort presented in ref. ^{11}. We illustrate this application in Fig. 6b.
SPrediXcan’s results tend to be more significant as the genetic component of gene expression increases (larger crossvalidated prediction performance \(R^2\)). Similarly, SPrediXcan associations tend to be more significant when prediction is more reliable (pvalues of association between predicted and observed expression levels are more significant, i.e., when prediction performance pvalue is smaller). The trend is seen both when results are averaged across all tissues for a given phenotype or across all phenotypes for a given tissue, as displayed in Supplementary Figs. 14. This trend was also robust across different monotonic functions of the Zscores.
We used a Bonferroni threshold accounting for all the genetissue pairs that were tested (0.05/total number of genetissue pairs ≈2.5e7). This approach is conservative because the correlation between tissues would make the total number of independent tests smaller than the total number of genetissue pairs. Height had the largest number of significantly associated unique genes at 1686 (based on a GWAMA of 250 K individuals). Other polygenic diseases with a large number of associations include schizophrenia with 305 unique significant genes (n = 150 K individuals), lowdensity lipoprotein cholesterol (LDLC) levels with 296 unique significant genes (n = 188 K), other lipid levels, glycemic traits, and immune/inflammatory disorders such as rheumatoid arthritis and inflammatory bowel disease. For other psychiatric phenotypes, a much smaller number of significant associations was found, with eight significant genes for bipolar disorder (n = 16,731) and one for major depressive disorder (n = 18,759), probably due to smaller sample sizes, but also smaller effect sizes.
When step 2 from the suggested pipeline is applied, keeping only reliably predicted genes, we are left with 739 genes for height, 150 for schizophrenia, 117 for LDLC levels.
After step 3, which keeps genes that are without strong evidence of LDcontamination, these numbers dropped to 264 for height, 58 for schizophrenia, and 60 for LDLC levels. After step 4, which keeps only genes with strong evidence of colocalization, we find 215 genes for height, 49 for schizophrenia, and 35 for LDLC. The counts for the full set of phenotypes can be found in Supplementary Data 2.
Mostly, genomewide significant genes tend to cluster around known SNPlevel genomewide significant loci or subgenomewide significant loci. Regions with subgenomewide significant SNPs can yield genomewide significant results in SPrediXcan, because of the reduction in multiple testing and the increase in power arising from the combined effects of multiple variants. Supplementary Table 2 lists a few examples where this occurs.
The proportion of colocalized associations (P4 > 0.5) ranged from 5 to 100% depending on phenotype with a median of 27.6%. The proportion of “non colocalized” associations ranged from 0 to 77% with a median of 27.0%.
See full set of results in our online catalog (gene2pheno.org). Significant genetissue pairs are included in Supplementary Data 3. To facilitate comparison, the catalog contains all SMR results we generated and the STWAS results reported by ref. ^{24} for 30 GWAS traits and GTEx BSLMM models. Note that SMR application to 28 phenotypes was reported by ref. ^{28} using whole blood eQTL results from ref. ^{29}.
Small gene expression changes associated to mild phenotypes
We reasoned that if complete knock out of monogenic disease genes cause severe forms of the disease, more moderate alterations of gene expression levels (as affected by regulatory variation in the population) could cause more moderate forms of the disease. Thus moderate alterations in expression levels of monogenic disease genes (such as those driven by eQTLs) may have an effect on related complex traits, and this effect could be captured by SPrediXcan association statistics. To test this hypothesis, we obtained genes listed in the ClinVar database^{30} for obesity, rheumatoid arthritis, diabetes, Alzheimer’s, Crohn’s disease, ulcerative colitis, agerelated macular degeneration, schizophrenia, and autism. Figure 7 displays the QQ plot for all associations and compares to those in ClinVar database. As postulated, we found enrichment of significant SPrediXcan associations for ClinVar genes for all tested phenotypes except for autism and schizophrenia. The lack of significance for autism is probably due to insufficient power: the distribution of pvalues is close to the null distribution. In contrast, for schizophrenia, many genes were found to be significant in the SPrediXcan analysis. There are several reasons that may explain this lack of enrichment: genes identified with GWAS and subsequently with SPrediXcan have rather small effect sizes, so that it would not be surprising that they were missed until very large sample sizes were aggregated; ClinVar genes may originate from rare mutations that are not well covered by our prediction models, which are based on common variation (due to limited sample sizes of eQTL studies and the minor allele frequency –MAF filter used in GWAS studies); or the mechanism of action of the schizophrenia linked ClinVar genes may be different than the alteration of expression levels. Also, the pathogenicity of some of the ClinVar entries has been questioned^{31}. The list of diseases in ClinVar used to generate the enrichment figures can be found in Supplementary Data 1, along with the corresponding association results.
Agnostic scanning across GTEx tissues improves discovery
Most genes were found to be significantly associated in a handful of tissues as illustrated in Fig. 8b. For example, for LDLC levels, liver was the most enriched tissue in significant associations as expected given known biology of this trait (See Supplementary Fig. 5). This prominent role of liver was apparent despite the smaller sample size available for building liver models (n = 97), which was less than a third of the numbers available for muscle (n = 361) or lung (n = 278).
However, in general, tissues expected to stand out as more enriched for diseases given currently known biology did not consistently do so when we looked at the average across all (significant) genes, using various measures of enrichment. For example, the enrichment in liver was less apparent for highdensity lipoprotein cholesterol (HDLC) or triglyceride levels. We find for many significant associations that the evidence is present across multiple tissues. This may be caused by a combination of context specificity and sharing of regulatory mechanism across tissues.
Next, we illustrate the challenges of identifying disease relevant tissues based on eQTL information using three genes with well established biology: C4A for schizophrenia^{32} and SORT1^{33} and PCSK9 both for LDLC and cardiovascular disease. SPrediXcan results for these genes and traits, and regulatory activity by tissue (as measured by the proportion of expression explained by the genetic component), are shown in Fig. 8a. Representative results are shown in Supplementary Tables 3, 4 and 5. Supplementary Data 4 contains the full set of MetaXcan results (i.e., association, colocalization, and HEIDI) for these genes.
SORT1 is a gene with strong evidence for a causal role in LDLC levels, and as a consequence, is likely to affect risk for cardiovascular disease^{33}. This gene is most actively regulated in liver (close to 50% of the expression level of this gene is determined by the genetic component) with the most significant SPrediXcan association in liver (pvalue ≈ 0, Z = −28.8), consistent with our prior knowledge of lipid metabolism. In this example, tissue specific results suggest a causal role of SORT1 in liver.
However, in the following example, association results across multiple tissues do not allow us to discriminate the tissue of action. C4A is a gene with strong evidence of causal effect on schizophrenia risk via excessive synaptic pruning in the brain during development^{32}. Our results show that C4A is associated with schizophrenia risk in all tissues (p < 2.5 × 10^{−7} in 36 tissue models and p < 0.05 for the remaining four tissue models).
PCSK9 is a target of several LDLC lowering drugs currently under trial to reduce cardiovascular events^{34}. The STARNET study^{35} profiled gene expression levels in cardiometabolic disease patients and showed tag SNP rs12740374 to be a strong eQTL for PCSK9 in visceral fat but not in liver. Consistent with this, our SPrediXcan results also show a highly significant association between PCSK9 and LDLC (p ≈ 10^{−13}) in visceral fat and not in liver (our training algorithm did not yield a prediction model for PCSK9, i.e., there was no evidence of regulatory activity). In our results, however, the statistical evidence is much stronger in tibial nerve (p ≈ 10^{−27}). Accordingly, in our training set (GTEx), there is much stronger evidence of regulation of this gene in tibial nerve compared to visceral fat.
Most associations highlighted here have high colocalization probabilities. See Supplementary Tables 3, 4, and 5. However, visceral fat association shows evidence of non colocalization (probability of independent signals P3 = 0.69 in LDLC). It is possible that the relevant regulatory activity in visceral adipose tissue was not detected in the GTEx samples for various reasons but it was detected in tibial nerve. Thus by looking into all tissues’ results we increase the window of opportunities where we can detect the association.
PCSK9 yields colocalized signals for LDLC levels in Tibial Nerve, Lung, and Whole blood. SORT1 shows colocalization with LDLC in liver (P4 ≈ 1) and pancreas (P4 = 0.90). C4A is colocalized with schizophrenia risk for the majority of the tissues (29/40) with a median colocalization probability of 0.82.
These examples demonstrate the power of studying regulation in a broad set of tissues and contexts and emphasize the challenges of determining causal tissues of complex traits based on insilico analysis alone. Based on these results, we recommend to scan all tissues’ models to increase the chances to detect the relevant regulatory mechanism that mediates the phenotypic association. False positives can be controlled by Bonferroni correcting for the additional tests.
Replication in an independent cohort
We used data from the Resource for Genetic Epidemiology Research on Adult Health and Aging study (GERA, phs000674.v1.p1)^{36,37}. This is a study led by the Kaiser Permanente Research Program on Genes, Environment, and Health (RPGEH) and the UCSF Institute for Human Genetics with over 100,000 participants. We downloaded the data from dbGaP and performed GWAS followed by SPrediXcan analysis of 22 conditions available in the European subset of the cohort.
For replication, we chose Coronary Artery Disease (CAD), LDL cholesterol levels, Triglyceride levels, and schizophrenia, which had closely related phenotypes in the GERA study and had a sufficiently large number of Bonferroni significant associations in the discovery set. Analysis and replication of the type 2 diabetes phenotype can be found in ref. ^{38}. Coronary artery disease hits were compared with “Any cardiac event,” LDL cholesterol and triglyceride level signals were compared with “Dyslipidemia,” and schizophrenia was compared to “Any psychiatric event” in GERA.
High concordance between discovery and replication is shown in Fig. 9 where dyslipidemia association Zscores are compared to LDL cholesterol Zscores. The majority of genetissue pairs (92%, among the ones with Zscore magnitude greater than 2 in both sets) have concordant direction of effects in the discovery and replication sets. The high level of concordance is supportive of an omnigenic trait architecture^{39}.
Following standard practice in metaanalysis, we consider a gene to be replicated when the following three conditions are met: the pvalue in the replication set is <0.05, the direction of discovery and replication effects are the same, and the meta analyzed pvalue is Bonferroni significant with the discovery threshold.
We display summary statistics for this replication analysis in Table 1. Among the 56 genes significantly associated with CAD in the discovery set, 6 (11%) were significantly associated with “Any cardiac event” in GERA. Using “Dyslipidemia” as the closest matching phenotype, 78.5% and 43.5% of LDL and triglyceride genes replicated, respectively. Among the 285 genes associated with schizophrenia in the discovery set, 51 (21%) replicated. The low replication rate for CAD and Schizophrenia is likely due to the broad phenotype definitions in the replication.
We found no consistent replication pattern difference between colocalized and noncolocalized genes.
This is not unexpected if the LD pattern is similar between discovery and replication sets.
The full list of significant genes can be queried in gene2pheno.org.
Discussion
Here we derive a mathematical expression to compute PrediXcan results without using individual level data, which greatly expands its applicability and is robust to study and reference set mismatches. This has not been done before. TWAS, which for the individual level approach only differs from PrediXcan on the prediction model used in the implementation, has been extended to use summary level data. When Gaussian imputation is used, the relationship between individual level and summary versions of TWAS is clear. This is not the case when extended to general weights (such as BSLMM). Our mathematical derivation shows the analytic difference between them explicitly.
We also add a post filtering step, to mitigate issues with LDcontamination. Based on consistency with PrediXcan and interpretability of results, we have chosen to use COLOC for filtering. COLOC has the limitation of assuming a single causal variant, and has reduced power in the presence of multiple causal variants. However, colocalization estimation is an active area of research and improved versions or methods will be adopted in the future. We find that BSLMMbased TWAS results have a larger proportion of noncolocalized genes as estimated by COLOC. This could be due to the single variant assumption in COLOC but we believe this is rather a consequence of the polygenic component of BSLMM predictors. Given the predominantly sparse architecture of gene expression traits^{27}, we believe that adding a polygenic component unnecessarily increases the exposure to LDcontamination.
Despite the generally good concordance between the summary and individual level methods, there were a handful of false positive results with SPrediXcan much more significant than PrediXcan. This underscores the need to use closely matched LD information whenever possible.
We applied our framework to over 100 phenotypes using transcriptome prediction models trained in 44 tissues from the GTEx Consortium and generated a catalog of downstream phenotypic association results of gene expression variation, a growing resource for the community.
The enrichment of monogenic disease genes among related phenotype associations suggests that moderate alteration of expression levels as affected by common genetic variation may cause a continuum of phenotypic changes. Alternatively, a more complex interplay between common and rare variation could be taking place such as higher tolerance to loss of function mutations in lower expressing haplotypes which could induce association with predicted expression^{40}.
We are finding that most trait associations are tissue specific; i.e., they are detected in a handful of tissues. However, we also find that expected tissues given known biology do not necessarily rank among the top enriched tissues. This suggests context specificity of the pathogenic mechanism; specific developmental stage or environmental conditions may be necessary to detect the regulatory event. On the other hand, we are detecting associations in unexpected tissues which suggests a sharing of regulation across multiple tissues/contexts or perhaps novel biology that takes place in these tissues. In either case, agnostic scanning of a broad set of tissues is necessary to discover these mechanisms.
Methods
SummaryPrediXcan formula
Figure 1b shows the main analytic expression used by SummaryPrediXcan for the Zscore (Wald statistic) of the association between predicted gene expression and a phenotype. The input variables are the weights used to predict the expression of a given gene, the variance and covariances of the markers included in the prediction, and the GWAS coefficient for each marker. The last factor in the formula can be computed exactly in principle, but we would need additional information that is unavailable in typical GWAS summary statistics output such as phenotype variance and sample size. Dropping this factor from the formula does not affect the accuracy of the results as demonstrated in the close to perfect concordance between PrediXcan and SummaryPrediXcan results on the diagonal of Fig. 2a.
The approximate formula we use is:
where w_{ lg } is the weight of SNP l in the prediction of the expression of gene g; \(\hat \beta _l\) is the GWAS regression coefficients for SNP l; se(\(\hat \beta _l\)) is standard error of \(\hat \beta \), \(\hat \sigma _l\) is the estimated variance of SNP l, and \(\hat \sigma _g\) is the estimated variance of the predicted expression of gene g; and dosage and alternate allele are assumed to be the same.
The inputs are based, in general, on data from three different sources: study set (e.g., GWAS study set), expression training set (e.g., GTEx, DGN), population reference set (e.g., the training set or 1000 Genomes).
The study set is the main dataset of interest from which the genotype and phenotypes of interest are gathered. The regression coefficients and standard errors are computed based on individuallevel data from the study set or a SNPlevel metaanalysis of multiple GWAS. Training sets are the reference transcriptome datasets used for the training of the prediction models (GTEx, DGN, Framingham, etc.) thus the weights w_{ lg } are computed from this set. Training sets can also be used to generate variance and covariances of genetic markers, which will usually be different from the study sets. When individual level data are not available from the training set we use population reference sets such as 1000 Genomes data. In the most common use scenario, users will need to provide only GWAS results using their study set. The remaining parameters are precomputed, and published in PredictDB.
Association enrichment
We display the enrichment for selected phenotypes in Supplementary Fig. 5, measured as mean(Z^{2}). For visualization purposes, we selected 25 phenotypes from different categories such as anthropometric traits, cardiometabolic traits, autoimmune diseases, and psychiatric conditions (please see figure caption for the list of selected phenotypes). The simple mean of Z^{2} for all genetissue pairs in a phenotype was taken.
Derivation of summaryPrediXcan formula
The goal of summaryPrediXcan is to infer the results of PrediXcan using only GWAS summary statistics. Individual level data are not needed for this algorithm. We will introduce some notations for the derivation of the analytic expressions of SPrediXcan.
Notation and preliminaries
Y is the ndimensional vector of phenotype for individuals i = 1, n. X_{ l } is the allelic dosage for SNP l. T_{ g } is the predicted expression (or estimated GREx, genetically regulated expression). w_{ lg } are weights to predict expression \(T_g = \mathop {\sum}\nolimits_{l \in {\mathrm{Model}}\,g} {w_{lg}X_l} \), derived from an independent training set.
We model the phenotype as linear functions of X_{ l } and T_{ g }
where α_{1} and α_{2} are intercepts, η and \({\it{\epsilon }}\) error terms independent of X_{ l } and T_{ g }, respectively. Let \(\hat \gamma _g\) and \(\hat \beta _l\) be the estimated regression coefficients of Y regressed on T_{ g } and X_{ l }, respectively. \(\hat \gamma _g\) is the result (effect size for gene g) we get from PrediXcan whereas \(\hat \beta _l\) is the result from a GWAS for SNP l.
We will denote as \(\widehat {{\mathrm{Var}}}\) and \(\widehat {{\mathrm{Cov}}}\) the operators that compute the sample variance and covariance, i.e.,: \(\widehat {{\mathrm{Var}}}(Y) = \hat \sigma _Y^2 = \mathop {\sum}\nolimits_{i = 1,n} {\left( {Y_i  \bar Y} \right)^2/(n  1)} \) with \(\bar Y = \mathop {\sum}\nolimits_{i = 1,n} {Y_i/n} \). Let \(\hat \sigma _l^2 = \widehat {{\mathrm{Var}}}(X_l)\), \(\hat \sigma _g^2 = \widehat {{\mathrm{Var}}}\left( {T_g} \right)\) and \({\mathrm{\Gamma }}_g = ({\bf{X}}  {\bar{\bf X}})\prime ({\bf{X}}  {\bar{\bf X}})/n\), where X′ is the p × n matrix of SNP data and \({\bar{\mathbf X}}\) is a n × p matrix where column l has the column mean of X_{ l } (p being the number of SNPs in the model for gene g, typically p ≪ n).
With this notation, our goal is to infer PrediXcan results (\(\hat \gamma _g\) and its standard error) using only GWAS results (\(\hat \beta _l\) and their standard error), estimated variances of SNPs (\(\hat \sigma _l^2\)), estimated covariances between SNPs in each gene model (Γ_{ g }), and prediction model weights w_{ lg }.
Input: \(\hat \beta _l\), se(\(\hat \beta _l\)), \(\hat \sigma _l^2\), \(\Gamma _g\), w_{ lg }. Output: \(\hat \gamma _g\)/se(\(\hat \gamma _g\)).
Next we list the properties and definitions used in the derivation
and
The proportion of variance explained by the covariate (T_{ g } or X_{ l }) can be expressed as
By definition
Thus \(\widehat {{\mathrm{Var}}}\left( {T_g} \right) = \hat \sigma _g^2\) can be computed as
where W_{ g } is the vector of \(w_{lg}\) for SNPs in the model of g. By definition, \({\mathrm{\Gamma }}_g\) is \(\widehat {{\mathrm{Var}}}({\bf{X}}_g)\), the sample covariance of X_{ g }, so that we arrive to
Calculation of regression coefficient \({\hat{\boldsymbol \gamma }}_{\boldsymbol{g}}\)
\(\hat \gamma _g\) can be expressed as
where we used the linearity of \(\widehat {\mathrm{Cov}}\) in the last step. Using Eq. (3), we arrive to
Calculation of standard error of \({\hat{\boldsymbol \gamma }}_{\boldsymbol{g}}\)
Also from the properties of linear regression we know that
In this equation, \(\hat \sigma _Y^2{\mathrm{/}}n\) is not necessarily known but can be estimated using the equation analogous to (6) for β_{ l }
Thus:
Notice that the right hand side of (8) is dependent on the SNP l while the left hand side is not. This equality will hold only approximately in our implementation since we will be using approximate values for \(\hat \sigma _l^2\), i.e., from reference population, not the actual study population.
Calculation of Zscore
To assess the significance of the association, we need to compute the ratio of the estimated effect size \(\hat \gamma _g\) and standard error se(\(\hat \gamma _g\)), or Zscore,
with which we can compute the pvalue as p = 2Φ(−Z_{g}) where Φ(.) is the normal CDF function. Thus
where we used Eqs. (5) and (6) in the second line and Eq. (8) in the last step. So
Based on results with actual and simulated data for realistic effect size ranges, we have found that the last approximation does not affect our ability to identify the association. The approximation becomes inaccurate only when the effect sizes are very large. But in these cases, the small decrease in statistical efficiency induced by the approximation is compensated by the large power to detect the larger effect sizes.
Calculation of σ _{ g } in reference set
The variance of predicted expression is computed using Eq. (4) which takes weights for each SNP in the prediction model and the correlation (LD) between the SNPs. The correlation is computed in a reference set such as 1000G or in the training set.
Expression model training
To train our prediction models, we obtained genotype data and normalized gene expression data collected by the GTEx Project. We used 44 different tissues sampled by GTEx and thus generated 44 different tissuewide models (dbGaP Accession phs000424.v6.p1). Sample sizes for different tissues range from 70 (Uterus) to 361 (Muscle—Skeletal). The models referenced in this paper make use of the GTEx Project’s V6p data, a patch to the version 6 data and makes use of improved genelevel annotation. We removed ambiguously stranded SNPs from genotype data, i.e., ref/alt pairs A/T, C/G, T/A, G/C. Genotype data was filtered to include only SNPs with MAF > 0.01. For each tissue, normalized gene expression data was adjusted for covariates such as gender, sequencing platform, the top three principal components from genotype data and top PEER Factors. The number of PEER Factors used was determined by sample size: 15 for n < 150, 30 for n between 150 and 250, and 35 for n > 250. Covariate data was provided by GTEx. For our analysis, we used proteincoding genes only.
For each genetissue pair for which we had adjusted expression data, we fit an ElasticNet model based on the genotypes of the samples for the SNPs located within 1 Mb upstream of the gene’s transcription start site and 1 Mb downstream of the transcription end site. We used the R package glmnet with mixing parameter alpha equal to 0.5, and the penalty parameter lambda was chosen through 10fold
Crossvalidation
Once we fit all models, we retained only those with qvalue less than 0.05^{41} For each tissue examined, we created a sqlite database to store the weights of the prediction models, as well as other statistics regarding model training. Supplementary Table 6 contains summary statistics on the models for each GTEx tissue. These databases have been made available for download at PredictDB.org.
Online Catalog and SMR, COLOC, TWAS
Supplementary Data 2 shows the list of GWA/GWAMA studies we considered in this analysis. We applied SPrediXcan to these studies using the transcriptome models trained on GTEx studies for patched version 6. For simplicity, SPrediXcan only considers those SNPs that have a matching set of alleles in the prediction model, and adjusts the dosages (2 dosage) if the alleles are swapped.
To make the results of this study broadly accessible, we built a Postgre SQL relational database to store SPrediXcan results, and serve them via a web application http://gene2pheno.org.
We also applied SMR^{16} to the same set of GWAMA studies, using the GTEx eQTL associations. We downloaded version 0.66 of the software from the SMR website, and ran it using the default parameters. We converted the GWAMA and GTEx eQTL studies to SMR input formats. In order to have SMR compute the colocalization test, for those few GWAMA studies where allele frequency was not reported, we filled in with frequencies from the 1000 Genomes Project^{42} as an approximation. We also used the 1000 Genomes genotype data as reference panel for SMR.
Next we ran COLOC^{18} (as downloaded from the Comprehensive R Archive Network) over the same set of GWAMA and eQTL studies. We used the Approximate Bayes Factor colocalization analysis, with effect sizes, their standard errors, allele frequencies and sample sizes as arguments. When the frequency information was missing from the GWAS, we filled in with data from the 1000 Genomes Project.
For comparison purposes, we have also included the results of the application of SummaryTWAS to 30 traits publicly shared by the authors^{24}.
Comparison with TWAS
Formal similarity with TWAS can be made more explicit by rewriting SPrediXcan formula in matrix form. With the following notation and definitions
and correlation matrix of SNPs in the model for gene g
\({\mathrm{\Sigma }}_g = {\mathrm{diag}}\left( {\frac{1}{{\hat \sigma _1}}, \ldots ,\frac{1}{{\hat \sigma _p}}} \right) \cdot {\mathrm{\Gamma }}_g \cdot {\mathrm{diag}}\left( {\frac{1}{{\hat \sigma _1}}, \ldots ,\frac{1}{{\hat \sigma _p}}} \right)\)
it is quite straightforward to write the numerator in (1) and (11) as
\({\tilde{\bf W}}_g \cdot {\bf{Z}}_{\mathrm{SNPs}}\) and in the denominator, the variance of the predicted expression level of gene g, as
Thus
This equation has the same form as the TWAS expression if we use the scaled weight vector \({\tilde{\mathbf W}}_g\) instead of W_{ g }. SummaryTWAS imputes the Zscore for the genelevel result assuming that under the null hypothesis, the Zscores are normally distributed with the same correlation structure as the SNPs; whereas in SPrediXcan we compute the results of PrediXcan using summary statistics. Thus, STWAS and SPrediXcan yield equivalent mathematical expressions (after setting the factor \(\sqrt {\frac{{(1  R_l^2)}}{{(1  R_g^2)}}} \approx 1\)).
SummaryPrediXcan with only top eQTL as predictor
The SPrediXcan formula when only the top eQTL is used to predict the expression level of a gene can be expressed as
where Z_{1} is the GWAS Zscore of the top eQTL in the model for gene. Thus
Comparison with SMR
SMR quantifies the strength of the association between expression levels of a gene and complex traits with T_{SMR} using the following function of the eQTL and GWAS Zscore statistics
Here \(Z_{{\mathrm{eQTL}}}\) is the Zscore (=effect size/standard error) of the association between SNP and gene expression, and \(Z_{{\mathrm{GWAS}}}\) is the Zscore of the association between SNP and trait.
This SMR statistic (T_{SMR}) is not a \(\chi _1^2\) random variable as assumed in ref. ^{16}. To prove this, we performed simulations following those described in ref. ^{16}. We generated 10^{5} pairs of values for \(Z_{{\mathrm{GWAS}}}^2\) and \(Z_{{\mathrm{eQTL}}}^2\). \(Z_{{\mathrm{GWAS}}}^2\) was sampled from a \(\chi _1^2\) distribution. \(Z_{{\mathrm{eQTL}}}^2\) was sampled from a noncentral \(\chi _1^2\) distribution with parameter λ = 29 (a value chosen to mimic results from^{29}, see ref. ^{16}). Only pairs with eQTLs satisfying genomewide significance (p < 5 × 10^{−8}) were kept. We performed a QQ plot and observed deflation when comparing to random values sampled from a \(\chi _1^2\) distribution (Fig. 5e). This simulation was repeated 1000 times, and we observed a mean of T_{SMR} close to 0.93 (Fig. 5f).
Only in two extreme cases, the chisquare approximation holds, when \(Z_{{\mathrm{eQTL}}} \gg Z_{{\mathrm{GWAS}}}\) or \(Z_{{\mathrm{eQTL}}} \ll Z_{{\mathrm{GWAS}}}\). In these extremes, we can apply Taylor expansions to find an interpretable form of the SMR statistic.
If \(Z_{{\mathrm{eQTL}}} \gg Z_{{\mathrm{GWAS}}}\), i.e., the eQTL association is much more significant than the GWAS association,
so that for large enough \(Z_{{\mathrm{eQTL}}}^2\) relative to \(Z_{{\mathrm{GWAS}}}^2\),
using Eq. 12. Thus, in this case, the SMR statistic is slightly smaller than the (top eQTL based) SPrediXcan \(\chi _1\)square. This reduced significance is accounting for the uncertainty in the eQTL association. As the evidence for eQTL association grows, the denominator \(Z_{\mathrm{eQTL}}^2\) increases and the difference tends to 0.
On the other extreme when the GWAS association is much stronger than the eQTLs, \(Z_{{\mathrm{eQTL}}} \ll Z_{{\mathrm{GWAS}}}\),
so that analogously
In both extremes, the SMR statistic significance is approximately equal to the less significant of the two statistics GWAS or eQTL, albeit strictly smaller.
In between the two extremes, the right distribution must be computed using numerical methods. When we look at the empirical distribution of the SMR statistic’s pvalue against the GWAS and eQTL (top eQTL for the gene) pvalues, we find the ceiling of the SMR statistic is maintained as shown in Fig. 5e, f.
GERA imputation
Genotype files were obtained from dbGaP, and updated to release 35 of the probe annotations published by Affymetrix via PLINK^{43}. Probes were filtered out that had a minor allele frequency of <0.01, were missing in >10% of subjects, or did not fit HardyWeinberg equilibrium. Subjects were dropped that had an unexpected level of heterozygosity (F>0.05). Finally the HRC1000Gcheckbim.pl script (http://www.well.ox.ac.uk/~wrayner/tools/) was used to perform some final filtering and split data by chromosome. Phasing (via eagle v2.3^{44}) and imputation against the HRC r1.1 2016 panel^{45} (via minimac3) were carried out by the Michigan Imputation Server^{46}.
GERA GWAS and MetaXcan Application
European samples had been split into ten groups during imputation to ease the computational burden on the Michigan server, so after obtaining the imputed .vcf files, we used the software PLINK^{43} to convert the genotype files into the PLINK binary file format and merge the ten groups of samples together, while dropping any variants not found in all sample groups. For the association analysis, we performed a logistic regression using PLINK, and following QC practices from ref. ^{14} we filtered out individuals with genotype missingness >0.03 and filtered out variants with minor allele frequency <0.01, missingness >0.05, out of HardyWeinberg equilibrium significant at 1e6, or had imputation quality <0.8. We used gender and the first ten genetic principal components as obtained from dbGaP as covariates. Following all filtering, our analysis included 61,444 European samples with 7,120,064 variants. MetaXcan was then applied to these GWAS results, using the 45 prediction models (GTEx and DGN).
Code Availability
We make our software publicly available on a GitHub repository: https://github.com/hakyimlab/MetaXcan. A short working example can be found on the GitHub page; more extensive documentation can be found on the project’s wiki page.
Data availability
The underlying GWAS results used in this analysis were downloaded from publicly available resources listed in Supplementary Data 2. The relevant GTEx gene expression data was obtained from dbGAP using accession phs000424.v6.p1. The GERA study was downloaded from dbGAP using accession number phs000674.v2.p2. WTCCC data was downloaded from WTCCC EGA european genomephenome archive.
The list of ClinVar genes was downloaded from https://www.ncbi.nlm.nih.gov/clinvar/. TWAS results published in ref. ^{24} were used. Prediction model weights and covariances for different tissues are available from the predictdb.org resource. The results of MetaXcan applied to the 44 human tissues and a broad set of phenotypes can be queried in gene2pheno.org, and we make the full data set of results available via the public GitHub repository https://github.com/hakyimlab/MetaXcan.
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Acknowledgements
We acknowledge the following US National Institutes of Health grants: R01MH107666 (H.K.I.), T32 MH020065 (K.P.S.), R01 MH101820 (GTEx), P30 DK20595 (Diabetes Research and Training Center), F31 DK101202 (J.M.T.), P50 DA037844 (Rat Genomics), and P50 MH094267 (Conte). H.E.W. was supported in part by startup funds from the Loyola University Chicago.
The GenotypeTissue Expression (GTEx) Project was supported by the Common Fund of the Office of the Director of the National Institutes of Health. Additional funds were provided by the NCI, NHGRI, NHLBI, NIDA, NIMH, and NINDS. Donors were enrolled at Biospecimen Source Sites funded by NCI SAICFrederick, Inc. (SAICF) subcontracts to the National Disease Research Interchange (10XS170), Roswell Park Cancer Institute (10XS171), and Science Care, Inc. (X10S172). The Laboratory, Data Analysis, and Coordinating Center (LDACC) was funded through a contract (HHSN268201000029C) to the Broad Institute, Inc. Biorepository operations were funded through an SAICF subcontract to the Van Andel Institute (10ST1035). Additional data repository and project management were provided by SAICF (HHSN261200800001E). The Brain Bank was supported by a supplements to the University of Miami grants DA006227 and DA033684 and to contract N01MH000028. Statistical Methods development grants were made to the University of Geneva (MH090941 and MH101814), the University of Chicago (MH090951, MH090937, MH101820, and MH101825), the University of North Carolina—Chapel Hill (MH090936 and MH101819), the Harvard University (MH090948), the Stanford University (MH101782), the Washington University St Louis (MH101810), and the University of Pennsylvania (MH101822). The data used for the analyses described in this manuscript were obtained from dbGaP accession number phs000424.v6.p1 on 06/17/2016.
This study makes use of data generated by the Wellcome Trust CaseControl Consortium. A full list of the investigators who contributed to the generation of the data is available from www.wtccc.org.uk. Funding for the project was provided by the Wellcome Trust under award 076113 and 085475.
This work was completed in part with resources provided by the University of Chicago Research Computing Center, Bionimbus^{47}, and the Center for Research Informatics. The Center for Research Informatics is funded by the Biological Sciences Division at the University of Chicago with additional funding provided by the Institute for Translational Medicine, CTSA grant number UL1 TR000430 from the National Institutes of Health.
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A.N.B. contributed to SPrediXcan software developmentl; executed SPredixCan runs on the GWAS traits; developed framework for comparing PrediXcan and SPrediXcan in simulated, cellular and WTCCC phenotypes; ran COLOC and SMR; developed gene2pheno.org database and web dashboard; contributed to the main text, supplement, figures, and analyses. S.P.D. performed the GTEx model training; ran the GERA GWAS; contributed to the main text. J.M.T. contributed to the main text. J.Z. contributed to the figures and predictdb.org resource. E.S.T. contributed to SPrediXcan software. H.E.W. contributed to the main text and analysis. K.P.S. ran PrediXcan on WTCCC data and contributed to the analysis. R.B. contributed to the main text and figures. T.G. ran imputation of GERA genotypes. T.L.E. contributed to the analysis. L.M.H. contributed to the main text. E.A.S. contributed to the main text. D.L.N. contributed to the main text and analysis. N.J.C. contributed to the analysis. H.K.I. conceived the method, supervised the project, performed analysis, contributed to the main text, supplement, and figures. The GTEx consortium authors contributed in the collection, gathering, and processing of GTEx study data used for training transcriptome prediction models and running COLOC and SMR.
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Barbeira, A.N., Dickinson, S.P., Bonazzola, R. et al. Exploring the phenotypic consequences of tissue specific gene expression variation inferred from GWAS summary statistics. Nat Commun 9, 1825 (2018). https://doi.org/10.1038/s41467018036211
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DOI: https://doi.org/10.1038/s41467018036211
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