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The authors have declared that no competing interests exist.

Integration of genome-wide association studies (GWAS) and expression quantitative trait loci (eQTL) studies is needed to improve our understanding of the biological mechanisms underlying GWAS hits, and our ability to identify therapeutic targets. Gene-level association methods such as PrediXcan can prioritize candidate targets. However, limited eQTL sample sizes and absence of relevant developmental and disease context restrict our ability to detect associations. Here we propose an efficient statistical method (MultiXcan) that leverages the substantial sharing of eQTLs across tissues and contexts to improve our ability to identify potential target genes. MultiXcan integrates evidence across multiple panels using multivariate regression, which naturally takes into account the correlation structure. We apply our method to simulated and real traits from the UK Biobank and show that, in realistic settings, we can detect a larger set of significantly associated genes than using each panel separately. To improve applicability, we developed a summary result-based extension called S-MultiXcan, which we show yields highly concordant results with the individual level version when LD is well matched. Our multivariate model-based approach allowed us to use the individual level results as a gold standard to calibrate and develop a robust implementation of the summary-based extension. Results from our analysis as well as software and necessary resources to apply our method are publicly available.

We develop a new method, MultiXcan, to test the mediating role of gene expression variation on complex traits, integrating information available across multiple tissue studies. We show this approach has higher power than traditional single-tissue methods. We extend this method to use only summary-statistics from public GWAS. We apply these methods to 222 complex traits available in the UK Biobank cohort, and 109 complex traits from public GWAS and discuss the findings.

Recent technological advances allow interrogation of the genome to a high level of coverage and precision, enabling experimental studies that query the effect of genotype on both complex and molecular traits. Among these, GWAS have successfully associated genetic loci to human complex traits. GWAS meta-analyses with ever increasing sample sizes allow the detection of associated variants with smaller effect sizes [

Another approach is the study of expression quantitative trait loci (eQTLs), measuring association between genotype and gene expression. These studies provide a wealth of biological information but tend to have smaller sample sizes. A similar observation applies to QTL studies of other traits such methylation, metabolites, or protein levels.

The importance of gene expression regulation in complex traits [

Due to sharing of eQTLs across multiple tissues, we have shown the benefits of an agnostic scanning across all available tissues [

In order to aggregate evidence more efficiently, we present here a method termed MultiXcan, which tests the joint effects of gene expression variation from different tissues. Furthermore, we develop and implement a method that only needs summary statistics from a GWAS: Summary-MultiXcan (S-MultiXcan). We make our implementation publicly available to the research community in

To integrate information across tissues, MultiXcan regresses the phenotype of interest on the predicted expression of a gene in multiple tissues as follows:
_{i} is standardized predicted expression of the gene in tissue _{i} is its effect size, and

Expression predictions across tissues can be highly correlated. We predicted expression for individuals from the UK Biobank cohort using models trained on 44 GTEx tissues (as presented in [_{p50} = 0.56 (

_{j} is its effect size, _{j} is the standardized predicted gene expression for model _{j} is its effect size in the joint regression, _{j} is its effect size in the marginal regression using only prediction _{j} are error terms.

We applied MultiXcan to 222 traits from the UK Biobank cohort. The traits were chosen based on several criteria, such as availability of well-established literature, binary traits having enough cases, or potential interest for a phenome-wide study (allergy, behavioral, metabolic and anthropometric phenotypes). We used Elastic Net prediction models trained on 44 tissues from GTEx, originally presented in [

We compared three approaches for assessing the significance of a gene jointly across all tissues: 1) running PrediXcan using the most relevant tissue; 2) running PrediXcan using all tissues, one tissue at a time; 3) running MultiXcan.

Traits with more MultiXcan-significant associations | 103 |

Traits with more PrediXcan-significant associations | 21 |

Tied traits | 6 |

Traits without significant associations | 92 |

Average increase in significant associations for MultiXcan |
162.7 |

Average significant association overlap |
48.0% |

*: average performed across traits where there is at least one PrediXcan- or MultiXcan-significant association.

**: computed as

^{−30} for visualization convenience.

As an illustrative example, we examined more closely the results for self-reported high cholesterol phenotype (

To evaluate MultiXcan’s performance in different known scenarios, we simulated traits as a function of different numbers of causal tissues for each gene: a single tissue, multiple tissues, all available tissues. We executed PrediXcan, MultiXcan without PCA regularization, and MultiXcan with PCA regularization. We show proper calibration under the null hypothesis of no association in

As expected, when there is a known single causal tissue, PrediXcan with the known tissue yields more significant associations. However, when there are multiple causal tissues, MultiXcan yields more significant associations than the best single tissue PrediXcan results. In traits simulated from a single causal tissue, PrediXcan outperforms MultiXcan in 99.9% of the cases (AOV p-value < 10^{−16}). MultiXcan performs best in scenarios with multiple causal tissues (84.4% of the times when a few tissues are causal, and 99.5% when all tissues are causal; AOV p-value < 10^{−16} in both cases).

One caveat is that the simulation does not cover cases when the prediction in the single tissue has low quality. In such an scenario, borrowing information from other tissues will still be beneficial.

To expand the applicability of our method to massive sample sizes and to studies where individual level data are not available, we extend our method to use summary results rather than individual-level data. We call this extension Summary-MultiXcan (S-MultiXcan).

We infer the joint estimates of effect sizes of predicted expression on phenotype (

^{2} statistics ends up being equivalent to the omnibus test.

As with the individual level approach, the correlation between tissues leads to numerical problems (due to near singular covariance matrices that need to be inverted). We address this by using a pseudo inverse approach which, in a nutshell, uses singular value decomposition (SVD) of the covariance matrix to keep only the components of large variation. This is analogous to the PCA regularization used for the individual level approach. Thus we test for significance using

A robust implementation for calculating predicted expression correlation is critical to avoid unnecessary false positive results. In principle, it is possible to simply calculate the correlation between tissues using predicted expression in a reference set. However, we found that this approach can lead to large differences between the individual level data results (our gold standard) and the summary level ones when SNPs from the reference set are missing in the GWAS results. An example of this is shown in

This figure compares S-MultiXcan to MultiXcan in four UK Biobank phenotypes. GTEx individuals were used as a reference panel for estimating expression correlation in the study population. The summary data-based method shows a good level of agreement with the individual-based method. In cases where the LD-structure between reference and study cohorts is mismatched, the summary-based method becomes less accurate. For example in Asthma, two genes are overestimated; however it tends to be conservative for most genes.

Traits with more S-MultiXcan-significant associations | 102 |

Traits with more S-PrediXcan-significant associations | 22 |

Tied traits | 14 |

Traits without significant associations | 84 |

Average increase in significant associations for S-MultiXcan |
125.5 |

Average significant association overlap |
50.0% |

*: average performed across traits where there is at least one PrediXcan- or MultiXcan-significant association.

**: computed as

To reduce false positives due to LD misspecification when dealing with GWAS summary statistics, we discard any significant association result for a gene if the best single tissue result has p-value greater than 10^{−4} (“suspicious associations”). In other words, we keep significant associations if at least one single gene-tissue pair association is borderline significant or better (10^{−5} is the Bonferroni threshold for a typical tissue model). This is rather conservative since it is possible that evidence with modest significance from weakly correlated tissues can lead to very significant combined association when their effects get aggregated. For example among Bonferroni significant genes in the individual level analysis, a median of 8.3% across traits (IQR = 5.7%) have the most significant marginal (PrediXcan) p-value greater than 10^{−4}. We list the number of such genes for each of the 222 UK Biobank traits in

We applied S-MultiXcan to 109 traits on publicly available GWAS, chosen with a similar criteria as UK Biobank’s traits. Like the individual level method, we observed S-MultiXcan to detect more associations than S-PrediXcan in most cases (average detection increase 10), as shown in

We display a summarized comparison between S-MultiXcan and S-PrediXcan in

We examine below the biological relevance of a few of the genes detected by our new method that was missed when using one tissue at a time (S-PrediXcan).

For example, in the Early Growth Genetics (EGG) Consortium’s Body-Mass Index (BMI) study, S-MultiXcan detects three genes not significant in S-PrediXcan: ^{−6}, tied to childhood obesity [^{−10}; embryogenesis [^{−09}, circadian cycle processes and psychological disorders [

In the CARDIoGRAM+C4D Coronary Artery Disease (CAD) study, S-MultiXcan detected 12 associations not significant in S-PrediXcan. The top result was ^{−9}), related to arsenic metabolism; interestingly, environmental and toxicological studies link arsenic exposure and ^{−6}, [^{−6}, [^{−7}, a gene for chloride channel activity); ^{−7}, recently linked to pulmonary conditions, [^{−07}, from the disintegrin and metalloproteinase family, linked to atherosclerosis [

The list of significant S-MultiXcan and S-PrediXcan results for all traits can be found in

Motivated by the widespread sharing of regulatory processes across tissues [

We found high concordance, in general, between the individual level and summary version with the latter slightly more conservative. As any method relying on a reference panel, S-MultiXcan may be inaccurate when the study population has a different LD structure than the reference panel. We attempted to address this by flagging results where none of the marginal associations reached a somewhat arbitrary threshold of 10^{−4}. This is far from perfect. To take full advantage of summary results and summary-based methods, reference sets that are the closest to the study population should be used. This also stresses the need to generate representative reference LD datasets for a wide variety of populations.

Via simulations, we show that MultiXcan is properly calibrated under the null hypothesis of no associations. This is reassuring, but it is possible that in real data there are hidden confounders that we did not capture in our simulations. For example, significant association results might arise due to LD contamination, i.e. when causal variants for the trait and expression are different but in LD with each other, inducing a spurious correlation between the predicted expression and the trait. This is a complex problem that we are currently working to address. In Barbeira et al [_{colocalized} > 0.5. A similar strategy may be applied for MultiXcan by restricting the analysis to gene-tissue pairs with high colocalization probability in the marginal analysis.

In practice, we emphasize the need to further validate the significant associations with additional replication and experimental follow-up.

Importantly, we provide compelling examples where using multiple tissues rather than picking one considered to be relevant for the phenotype increases the list of candidate causal genes. In our simulations, we found that only when the single causal tissue is known and the regulatory mechanism is captured perfectly by predicted expression in that tissue, using PrediXcan with that tissue yields more significant associations than MultiXcan. This scenario is unlikely to occur in practice. Therefore, in general, we recommend jointly scanning of all tissues in addition to focusing on a few tissues selected based on prior knowledge.

We make our software publicly available on a GitHub repository:

This study uses de-identified genotype and phenotype data from public repositories including dbGaP, EGA, and UK Biobank. Our study has been determined to be non-human subject research by the University of Chicago’s IRB protocol number IRB16-0921.

In the following, we shall denote scalar quantities by italicized lower-case letter (e.g. _{i} is the

Let us consider a GWAS study of

Let:

_{l} is the

_{j} be the standardization of

In our application, different genes have different numbers of available tissue models trained on GTEx data, ranging up to

MultiXcan consists of fitting a linear regression of the phenotype on predicted expression from multiple tissue models jointly:
_{j} is an _{j} is the effect size for the predicted gene expression _{j}, and _{j}.

The high degree of eQTL sharing between different tissues induces a high correlation between predicted expression levels. In order to avoid collinearity issues and numerical instability, we decompose the predicted expression matrix into principal components and keep only the eigenvectors of non negligible variance. To select the number of components, we used a condition number threshold of _{i} is an eigenvalue of the matrix ^{t}

Lastly, we use an F-test to quantify the significance of the joint fit.

We use Bonferroni correction to determine the significance threshold. For MultiXcan, we use the total number of genes with a prediction model in at least one tissue, which yields a threshold approximately at 0.05/17500 ∼ 2.9 × 10^{−6}. For PrediXcan across all tissues, we use the total number of gene-tissue pairs, which yields a threshold approximately at 0.05/200, 000 ∼ 2.5 × 10^{−7}. Since the tested hypotheses are not independent, Bonferroni correction is overly conservative, as can be seen when counting the number of associations via FDR in

UK Biobank genotype data for 487, 409 individuals was downloaded and processed in the Bionimbus Protected Data Cloud (PDC

We computed gene expression on all individuals using 44 models trained on GTEx release v6p (presented in [

To allow for uniform correction of unwanted variation, we treated all traits as quantitative and adjusted for the same covariates reported in [

On most continuous phenotypes, there were between 300, 000 and 400, 000 individuals with available data determined by the intersection of covariates and traits. For the case of self reported diseases, we found a number of cases ranging from a few hundreds (i.e. Acne) to 50, 000 (i.e. High Cholesterol).

We have demonstrated that S-PrediXcan can accurately infer PrediXcan results from GWAS Summary Statistics and LD information from a reference panel [

Summary-MultiXcan (S-MultiXcan) infers the individual-level MultiXcan results, using univariate S-PrediXcan results and LD information from a reference panel. It consists of the following steps:

Computation of single tissue association results with S-PrediXcan.

Estimation of the correlation matrix of predicted gene expression for the models using the Linkage Disequilibrium (LD) information from a reference panel (typically GTEx or 1000 Genomes [

Discarding components of smallest variation from this correlation matrix to avert collinearity and numerical problems (Singular Value Decomposition, analogue to PC analysis in individual-level data).

Estimation of joint effects from the univariate (single-tissue) results and expression correlation.

Discarding suspicious results, suspect to be false positives arising from LD-structure mismatch.

To derive the multivariate regression (

More specifically, we want to obtain the multivariate regression coefficient estimates for _{j} (_{j} is the marginal regression error term with variance

First, notice that the solution to the multivariate regression in _{j}. Please note that, since the _{j} are standardized, then

From (

To compute the variance of the estimated effect sizes (

As the genotypes from most GWAS are typically unavailable, we must use a reference panel to compute ^{t} _{ij} are the elements of the covariance matrix

We restrict the computation to using only SNPS in the intersection between reference panel and GWAS. Failing to do so may lead to inaccurate inference of predicted expression covariance, typically underestimating correlation, leading to false positives as can be seen in

Given the high degree of correlation among many of the prediction models, ^{t} ^{+} the pseudo-inverse for any matrix

To quantify significance of the inferred multi-tissue gene-level association, we use the fact that the regression coefficient estimates follow (approximately) a multivariate normal distribution: _{j}/_{j}). We have used

In practice, we will use the SVD pseudo-inverse ^{+} as explained in the previous section, and a ^{2}-test:

109 public GWAS and GWAS meta-analysis summary statistics data sets were downloaded and analyzed with S-PrediXcan and S-MultiXcan, using the 44 prediction models from GTEx tissues in release version 6p. The list of traits and their Consortium/publication information is available in

A type 1 Diabetes study from the Wellcome Trust Case-Control Consortium [

Prediction Models were obtained from

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Significant results included in

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We observe a high degree of predicted expression correlation, in agreement with recent publications on the high degree of mechanism sharing across tissues [

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There is a satisfactory agreement between the individual-level and the summary-level versions of MultiXcan in UK Biobank traits.

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Here we use a simulated trait, generated from a standard normal distribution as the phenotype. We perform MultiXcan, regressing the simulated phenotype on predicted expression for 17,435 genes in 1,000 individuals from the UK Biobank. As described in the Methods, we drop principal components of small variation to avoid multi collinearity. We keep the number of principal components so that the condition number of the covariance matrix of the predicted expression across tissues (ratio of the maximum and minimum eigenvalues) is below 30.

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For each gene, we simulate traits as different combinations of predicted expression from multiple tissues in one thousand individuals from the UK Biobank. We add a noise term from the normal distribution with variance chosen so that 1% of the total variance in the trait is explained by predicted expression. For each trait, we show results from running MultiXcan with no regularization, MultiXcan with regularization (condition number < 30), PrediXcan with ‘best’ single tissue (either the single causal tissue or most significant p-value in each gene). For a trait with specific causal tissues, we also show MultiXcan using only them.

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For each gene, we simulate traits as different combinations of predicted expression from multiple tissues in one thousand individuals from the UK Biobank. We add a noise term from the normal distribution with variance chosen so that 1% of the total variance in the trait is explained by predicted expression. The top panel shows traits generated from the combination of 5 brain tissues (Cerebellum, Cerebellar Hemisphere, Hippocampus, Cortex, Frontal Cortex BA9; top panel), and the bottom panel a combination of all available tissues. These traits were analyzed through MultiXcan both with PCA regularization and without regularization. The lines correspond to smoothed conditional means, and the gray area displays the confidence intervals. We observe that PCA regularization has increased power over no regularization with larger effect as the number of included tissues increases. When the number of causal tissues is small (“5 Brains”), significance decreases when more tissue models are available, and the regularized and unregularized MultiXcan perform similarly. This is expected since extra uninformative components add noise and reduce power. Conversely, when all tissues are causal, significance increases as we increase the number of included tissues. Regularized MultiXcan achieves higher significance than unregularized MultiXcan.

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Using simulated traits in two scenarios (5 brain causal tissues and all causal tissues, as described in the Supplementary Note), we display MultiXcan’s significance distribution for different PCA regularization thresholds. In both scenarios the significance remains relatively constant for all thresholds tested. More stringent regularization thresholds achieve slightly higher significance. We consider the threshold of 30 to be a conservative choice.

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The number of FDR-significant associations are shown for PrediXcan using both a single tissue and all tissues, and MultiXcan. Using ^{−4} we observe a similar number of detections as when performing traditional multiple-testing correction at 0.05/

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A scatter plot of association significance between MultiXcan and S-MultiXcan is shown for the Wellcome Trust Case-Control Type 1 Diabetes study. The left plot uses the covariance matrix computed from predicted expression in a reference panel (GTEx). The right plot uses predicted expression covariance taking into account missing SNPs (i.e.: using only SNPs in the intersection between reference panel and the GWAS study). We observe that using expression predicted in the reference panel without correction leads to false positives and negatives, as the inferred covariance is inaccurate.

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This research has been conducted using the UK Biobank Resource under Application Number 19526. We used data from the GTEx project (dbGap accession number phs000424.v6.p1).

This study makes use of data generated by the Wellcome Trust Case Control Consortium. A full list of the investigators who contributed to the generation of the data is available from

We used data from the Resource for Genetic Epidemiology Research on Adult Health and Aging study (GERA, phs000674.v1.p1). 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.

This research benefited from the use of credits from the National Institutes of Health (NIH) Cloud Credits Model Pilot, a component of the NIH Big Data to Knowledge (BD2K) program.