A multi-tissue mendelian randomization method based on eQTL data for mapping tissue-specific disease genes

Abstract

Tissue-specific gene expression is critical in complex disease etiology, but traditional transcriptome-wide Mendelian Randomization (TWMR) often overlooks tissue heterogeneity and is constrained by limited valid instrumental variables (IVs) per tissue. We propose Multi-Tissue TWMR (MT-TWMR), which selects cis-eQTLs with consistent effects across tissues as IVs and estimates tissue-specific causal effects via a penalized regression model combining L1 regularization for sparsity with a weighted tissue-difference penalty based on tissue similarity to enable cross-tissue information sharing. Simulations under varying IV numbers, pleiotropy levels, and tissue counts showed MT-TWMR consistently achieved higher power, lower root mean square error, and better type I error control than existing univariate and multivariable MR methods, particularly when IVs were scarce. Applied to major depressive disorder and primary hypertension, MT-TWMR identified 28 and 57 causal genes respectively, with enriched signals in biologically relevant tissues and strong colocalization and pathway evidence. MT-TWMR offers an effective and interpretable framework for integrating multi-tissue eQTL data to construct tissue-specific disease gene maps.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-026-06451-x.

Introduction

In evidence-based medicine, establishing causality is crucial for formulating intervention strategies. Generally, the gold standard for determining causal relationships is the Randomized Controlled Trial (RCT), which investigates the effect of specific factors on outcomes by randomly assigning subjects to control and experimental groups [1]. However, conducting RCTs in practice is often highly challenging, requiring substantial resources, and is sometimes nearly impossible due to ethical concerns [2]. In such cases, alternative methods must be employed, among which Mendelian Randomization (MR) is a widely used approach [3]. MR utilizes genetic variants as instrumental variables (IVs) to provide valuable assessments of the causal effect of an exposure on an outcome [4–6]. In MR studies, genetic variants are analogous to the group assignments in RCTs, enabling the inference of causal effects of exposures on outcomes through the analysis of associations between genetic variants, exposures, and outcomes [7].

In recent years, Mendelian randomization (MR) has advanced rapidly and been widely applied across research fields. Beyond two-sample MR using complex traits as exposures, multi-omics data such as genomics and proteomics have been used to treat biomolecular features as exposures, enabling causal analyses with complex diseases [8]. The Genotype-Tissue Expression (GTEx) database provides extensive multi-tissue expression quantitative trait loci (eQTL) data [9], supporting the construction of gene expression–disease maps and promoting transcriptome-wide MR (TWMR) as an important approach. TWMR uses eQTL and genome-wide association study (GWAS) summary statistics to identify potential risk genes [10–12], offering deeper mechanistic insights than traditional MR by elucidating molecular-level causal relationships between gene expression and phenotypes [13]. However, traditional TWMR still faces challenges [14, 15]. eQTL studies have limited sample sizes, leading to few available instruments per tissue [16]; eQTLs often show tissue-specific effects on complex diseases [9], and deleterious variants are typically restricted to a few tissues due to strong selection [17], while the disease-relevant tissues may be unknown [18]. As a result, genetic effects in multi-tissue MR are often sparse and highly tissue-specific [19]. If instruments are from tissues unrelated to the disease, horizontal pleiotropy from other tissues may bias estimates [15], and cross-tissue correlations in eQTL expression may introduce confounding [20]. As illustrated in Fig. 1, accurately identifying tissue-specific risk genes is particularly challenging when the number of valid instruments is small.

Fig. 1.

Common causes of estimation bias

Recently, Yihao Lu, Ke Xu, et al. proposed mintMR, a multi-context multivariable integrative MR method extending traditional TWMR [21]. It models tissue-specific disease associations via multi-view learning to extract latent patterns and refine non-zero effect probabilities. Its multi-view learning framework is specifically built to exploit correlations among traits, making it particularly advantageous when multiple molecular trait datasets are available. However, mintMR requires at least two molecular trait datasets, is primarily designed for gene expression and molecular traits as exposures, may not outperform traditional methods with sufficient IVs, and remains unsuitable when IVs are fewer than variables due to unresolved identifiability issues. These challenges motivated us to develop Multi-Tissue Transcriptome-Wide Mendelian Randomization (MT-TWMR), which simultaneously assesses gene expression as a risk exposure across multiple tissues using multi-tissue eQTL data from GTEx. For each gene, we select eQTLs significant in at least two tissues with non-zero, directionally consistent effects as IVs. To address tissue specificity and sparsity, we incorporate the Least Absolute Shrinkage and Selection Operator (Lasso) [22] and a weighted tissue-difference network penalty exploiting inter-tissue associations [18], encouraging similar coefficients among correlated tissues. This improves capture of cross-tissue causal patterns, predictive accuracy, and robustness, enabling sparse, tissue-specific risk gene identification in multi-tissue MR.

We conducted simulations to assess MT-TWMR under various scenarios, showing clear advantages in accuracy, robustness, and detection of tissue-specific causal signals compared with existing methods. Applied to real data, MT-TWMR identified multiple genes for major depressive disorder with brain-specific expression consistent with known neurobiological mechanisms, and tissue-specific genes for primary hypertension linked to blood pressure regulation and cardiovascular function. These results validate the method’s effectiveness and provide new insights into disease mechanisms, with the resulting tissue-specific gene maps offering a valuable resource for studying disease etiology and guiding precision, tissue-targeted interventions.

Method

Mendelian randomization assumptions

This study is based on the core assumptions of Mendelian randomization (MR): (1) the genetic variants used as instrumental variables (IVs) are robustly associated with the exposure (gene expression; relevance assumption); (2) the IVs are independent of unmeasured confounders of the exposure–outcome relationship (independence assumption); and (3) the IVs influence the outcome only through the exposure, with no direct or alternative pathways (exclusion restriction assumption). Additionally, we assume a linear causal effect of gene expression on disease risk, consistent with the linear structural model framework adopted in MT-TWMR. All analyses were conducted under these assumptions, and their plausibility was evaluated through sensitivity analyses (e.g., cross-tissue consistency filtering, colocalization, and simulation under horizontal pleiotropy).

Model framework construction

We constructed the MT-TWMR model to investigate the causal inference problem, where gene expression across multiple tissues serves as exposure factors and complex diseases as outcome. Within a multi-tissue framework, we assume a single molecular trait (e.g., gene expression) as the exposure and a complex disease as the outcome. We consider summary-level data from K tissues incorporated into the analysis. Within a single gene region, eQTL of that gene region are treated as candidate IV. Suppose that in gene region g, there are n eQTLs available as IVs. Let X_ik denote the marginal effect of the i-th IV in tissue k on the exposure factor, and let Y_i represent the association effect of the i-th IV in gene g on the disease outcome. Here, X_ik is derived from eQTL summary statistics across tissues in the GTEx database, while Y_i is obtained from GWAS summary statistics. Following Fig. 2, we further assume that within a single gene region, the true causal relationship between GWAS and eQTL effects is linear, as expressed by Eq. (1).

1

Fig. 2.

Framework of the MT-TWMR

where β_k represents the causal effect of gene g on the disease outcome in tissue k, and ε_i is the random error term. This error term accounts for pleiotropic effects that do not influence the disease outcome through the exposure factor and are independent of confounding factors.

Formulation and solution of the objective function

Considering the high dimensionality of eQTL data X, penalized regularization regression methods such as Lasso are widely applied for variable selection. Currently, various penalized regularization regression algorithms, including MR-Lasso [23] and MVMR-Lasso [24], have been successfully employed in MR analyses.

However, while the Lasso method performs well in high-dimensional variable selection, it overlooks inter-tissue correlations in MR studies involving multiple tissues, potentially leading to unstable causal effect estimates. To address this issue, this study improves and extends the Lasso method. To fully account for information regarding correlations between tissues, we introduce a new penalty term to the objective function in addition to the L1 regularization penalty. In this paper, we refer to this as the weighted tissue-difference network penalty. The objective function, as shown in Eq. 2, allows us to estimate the causal effects of gene g on complex diseases across different tissues by minimizing this function.

2

Here, β_i and β_j represent the causal effects of gene g in tissue i and tissue j, respectively, and W_ij denotes the weight reflecting the similarity information between tissue i and tissue j. In our framework, the tissue similarity matrix can be derived from prior knowledge or computed based on gene expression levels when individual-level gene expression data are available. In this study, for real data analysis, we construct a tissue similarity matrix based on Euclidean distance using the median gene-level TPM (Transcripts Per Million) values provided by the GTEx project, categorized by tissue, to reflect the similarity in gene expression between tissues and provide a basis for cross-tissue information sharing.

The hyperparameters λ₁ > 0 and λ₂ > 0, which control the strength of the penalty terms, are tuned in this study using a five-fold cross-validation method [25]. The five-fold cross-validation method involves randomly dividing the dataset into five non-overlapping subsets, iteratively using four subsets to train the model and the remaining subset to validate model performance. By comparing the average prediction error on the validation sets across different parameter combinations, the optimal combination of λ₁ and λ₂ is selected. When λ₂ = 0, the model reduces to the standard Lasso method.

The first term of the objective function is the least squares loss, measuring model fit. The second term, an L1 regularization penalty, addresses the pronounced tissue specificity and sparsity of genetic effects on disease [19] by selecting eQTLs with true causal effects while removing irrelevant SNPs, thus controlling complexity and preventing overfitting in small-sample or high-dimensional settings. Although our method encourages sparsity via L1 regularization, it does not impose sparsity arbitrarily. The penalty strength is tuned via cross-validation, allowing the data to determine the appropriate degree of sparsity. However, in the unlikely scenario where a gene truly affects disease in many tissues simultaneously, users may consider a sensitivity analysis with a reduced or zero L1 penalty. The third term is a weighted tissue-difference network penalty, which uses the tissue similarity matrix W to encourage consistency of regression coefficients among biologically similar tissues [18] without forcing them to be identical. This design enables cross-tissue information sharing, improves capture of shared causal effects, and enhances inference precision. The penalty strength adapts to the degree of tissue similarity, providing a flexible and biologically informed approach for multi-tissue data analysis.

A similarity matrix is a specialized matrix used to measure the similarity or correlation between elements (e.g., samples, features) in a dataset [26]. Common metrics include Euclidean distance, cosine similarity, Pearson correlation coefficient, and Jaccard similarity coefficient. In this study, we introduce the concept of a similarity matrix and utilize gene expression data across tissues to construct tissue similarity matrices for each gene, aiming to enhance the accuracy of causal gene prediction. When individual-level gene expression data or other sources of tissue similarity information are unavailable, it is possible to assume uniform similarity by assigning equal weights. The similarity matrix in our framework was used only as a penalty weighting structure, rather than directly determining the causal effect estimates, which further reduced the risk that gene-specific variability introduces instability into the model.

The optimization of this objective function can be performed using gradient descent [27] or quasi-Newton methods [28]. In this study, we adopt the L-BFGS-B (Limited-memory Broyden–Fletcher–Goldfarb–Shanno with Box constraints) method [29] with default parameters to solve the objective function. This is a quasi-Newton method suitable for large-scale optimization problems. The detailed algorithm procedure is provided in the supplementary materials.

Simulation studies and method comparison

We conducted extensive simulation studies to compare the performance of MT-TWMR with existing univariate and multivariable MR approaches under diverse scenarios. The simulation framework, including the generation of GWAS and multi-tissue eQTL summary statistics, followed the procedure of Yihao Lu, Ke Xu, et al. [21] and incorporated settings from related MR literature [18, 19, 24, 30, 31]. Competing methods included MVMR-IVW, MVMR-Egger, MVMR-Lasso, MVMR-Median, MVMR-Robust, MintMR, MR-Egger, IVW, and a multiple-tissue meta-analysis (metaIV-IVW). Details of the data generation process, mathematical formulations (Eqs. S1–S3), parameter settings, method adaptations to the TWMR framework, and evaluation metrics (precision, accuracy, RMSE) are provided in the Supplementary Materials. These supplementary sections also describe the experimental scenarios, including variations in the number of instrumental variables, pleiotropy levels, cross-tissue eQTL effect consistency, sample sizes, and tissue numbers. Full details are available in the Supplementary Materials.

Sources of real data

In the real data application, this study utilized GWAS summary statistics as the association statistics between IV and outcome variables, and multi-tissue eQTL summary statistics as the association statistics between IV and exposure variables. We selected primary hypertension and MDD as disease outcomes.

For primary hypertension, GWAS summary statistics were obtained from Zhou et al. [32] via the MRC-IEU OpenGWAS database (Study ID: ukb-b-12493). The analysis included n = 463,010 individuals of European ancestry (54,358 cases and 408,652 controls). For MDD, GWAS summary statistics were obtained from the Psychiatric Genomics Consortium (PGC) via the IEU OpenGWAS database (Study ID: ieu-a-805), corresponding to the meta-analysis by Wray et al. [33]. This dataset comprised n = 18,759 individuals (9240 cases and 9519 controls). Detailed sample characteristics, phenotype definitions, and cohort information are provided in the respective source publications [32, 33] and database entries. All GWAS summary data are publicly available and were accessed without requiring specific permissions, in accordance with the data access policies of the MRC-IEU and PGC consortia.

For the selection of exposure variables, the GTEx database (V10) offers eQTL data across 54 tissues [9]. We chose the tissues with the largest sample sizes from eleven representative organs for processing and analysis, including: (1) Brain: frontal cortex (BA9); (2) Heart: left ventricle; (3) Lung tissue; (4) Liver tissue; (5) Kidney: kidney cortex; (6) Muscle: skeletal muscle; (7) Digestive System: esophagus mucosa; (8) Skin: sun-Exposed skin (lower leg); (9) Thyroid; (10) Whole blood; 11. Subcutaneous adipose tissue. Additionally, we obtained summary statistics for blood tissue from the eQTLGen Consortium [34]. Sample size information is presented in Supply Table 2. Add a note acknowledging that tissue selection was guided by both statistical and biological considerations, and that future studies may benefit from including additional tissues as sample sizes increase.

Table 2.

Number of IVs and causal genes by tissue in the primary hypertension study

Samples	Summary IV	Causal genes
Adipose-Subcutaneous	41,473	17(30%)
Brain-Frontal Cortex (BA9)	19,507	4(7%)
Heart-Left Ventricle	36,833	3(5%)
Lung	18,896	8(14%)
Liver	3015	0
Kidney-Cortex	10,240	1(2%)
Muscle-Skeletal	32,708	6(11%)
Esophagus-Mucosa	35,113	12(21%)
Sun Exposed (Lower leg)	49,442	8(14%)
Thyroid	49,272	7(12%)
Whole Blood	32,858	1(2%)

Given that both the cis-eQTL exposure data (from GTEx v10) and the outcome GWAS summary statistics (for MDD and primary hypertension) were derived from individuals of predominantly European ancestry, we assume that the genetic variant–exposure associations are consistent across the two samples, minimizing potential bias from population stratification. Furthermore, the GTEx cohort—comprising post-mortem tissue donors with modest sample sizes (maximum < 1,000 per tissue)—and the large-scale GWAS cohorts (UK Biobank and PGC; total N > 480,000) were recruited under fundamentally different protocols and from non-overlapping populations. We therefore consider sample overlap to be negligible, satisfying the independence assumption required for valid two-sample Mendelian randomization.

STROBE-MR statement

This study was conducted and reported in accordance with the Strengthening the Reporting of Observational Studies in Epidemiology using Mendelian Randomization (STROBE-MR) guidelines.

Results

Simulations to evaluate the performance of MT-TWMR and competing MR methods

We evaluated MT-TWMR against univariate and multivariable MR methods (MVMR-IVW, MVMR-Egger, MVMR-Lasso, MVMR-Median, MVMR-Robust, MintMR, MR-Egger, IVW, metaIV-IVW) across four simulation settings: (i) varying the proportion of phenotypic variance explained by uncorrelated horizontal pleiotropy (UHP) [35], (ii) varying the number of IVs, (iii) varying the number of tissues, and (iv) varying cross-study effect consistency between eQTL and GWAS.

Across all scenarios, MT-TWMR consistently achieved the highest or near-highest power, the lowest RMSE, and effective type I error control, particularly when IV numbers were small or effect consistency was low. With increasing UHP effects, all methods showed reduced power, but only MT-TWMR, MintMR, and MVMR-Robust maintained type I error rates within acceptable bounds. Increasing IV numbers or tissue counts generally improved all methods, but MT-TWMR maintained superiority under low-IV or low-tissue conditions and avoided the type I error inflation observed in some competitors. Lower effect consistency markedly reduced power for all methods, highlighting the importance of selecting eQTLs with consistent effects across tissues.

Detailed simulation settings, parameter values, and additional results (including univariate MR performance) are provided in the Supplementary Materials.

Data analysis: identifying major depressive disorder and primary hypertension risk associated genes via MT-TWMR

In the first real data application, we applied MT-TWMR to investigate risk genes for MDD across different tissues and to identify the tissues most relevant to this disease. MDD is a complex mental health disorder with profound global impact, its etiology involving the interplay of genetic susceptibility and multi-system physiological changes [36]. Although previous studies have elucidated some of the neurobiological foundations of MDD [37], the molecular regulatory mechanisms spanning multiple tissues remain largely unexplored. We obtained summary statistics for blood tissue from the eQTLGen Consortium (N = 31,684) and for muscle tissue (N = 818), lung tissue (N = 604), and brain tissue (N = 269) from version 10 of the GTEx project. For the selection of IV, we chose significant cis-eSNPs (p ≤ 0.005) with nonzero effects and consistent directions in at least two tissues. There “nonzero effects” refers to eQTLs with estimated effects that are not exactly zero (which is automatically true for all continuous estimates), and that the actual selection relies on statistical significance and direction consistency. This approach reduces the chances of selecting invalid IVs and enhances the consistency of the effect from IVs to exposure effects across GWAS and reference eQTL samples. To address linkage disequilibrium (LD), we set the r² threshold at 0.01. After processing, the total number of available IVs for each tissue is shown in Table 1. These were combined to yield 16,760 unique genes. We restricted our analysis to genes with at least two IVs overall, ultimately screening 1,242 genes for inclusion in the analysis.

Table 1.

Number of available IVs and causal genes by tissue in the MMD study

Samples	Summary IV	Causal genes
Brain-Frontal Cortex (BA9)	19,507	18(65%)
Lung	32,708	14(50%)
Muscle-Skeletal	35,113	4(14%)
Whole Blood	32,858	3(11%)

We applied the processed data as input for the MT-TWMR method. The results identified 28 genes with causal effects out of the 1,242 genes included in the analysis. As shown in Table 1, the frontal cortex of the brain dominated the identification of causal genes for MDD, with 18 causal genes (accounting for 65% of the total), which is highly consistent with the neurobiological basis of MDD as a psychiatric disorder. Additionally, 14 causal genes (50%) were identified in lung tissue, suggesting that lung tissue may play a significant role in the pathophysiology of MDD.

In the second real data application, we applied the proposed MT-TWMR method to investigate risk genes for primary hypertension across different tissues. As a typical systemic disease, primary hypertension has a complex etiology potentially involving genetic factors, infections, immune dysregulation, and other multifaceted factors, and it may lead to dysfunction in multiple organ systems [38]. Given its complex pathogenesis, multi-tissue MR analysis is an ideal approach for studying such diseases. In this study, we utilized summary statistics from GWAS on primary hypertension as input for IV-outcome associations, and summary statistics from multi-tissue eQTL studies as input for the IV-exposure associations. For the eQTL data, we obtained summary statistics from version 10 of the GTEx project for the following tissues. Brain: frontal cortex (BA9), Heart: left ventricle, Lung tissue, Liver tissue, Kidney: kidney cortex, Muscle: skeletal muscle, Digestive System: esophagus mucosa, Skin: sun-Exposed skin (lower leg), Thyroid, Subcutaneous adipose tissue and Whole Blood. Detailed data information is provided in the Methods section. For IV selection and LD pruning, we applied the same criteria as described earlier. After processing, the number of IVs included in the analysis for each tissue is summarized in Table 2. We restricted the analysis to genes with at least two IVs overall, ultimately screening 4854 genes for inclusion in the analysis.

We applied the processed data as input to both the MT-TWMR method and the univariate IVW method for analysis. The results showed that the MT-TWMR identified 57 causal genes, whereas IVW identified 275 causal genes. This finding is consistent with our simulation study results, further confirming that IVW exhibits weaker control over type I error rates when dealing with multi-tissue settings with a limited number of IVs. Moreover, compared to MVMR approaches, univariable methods are more prone to including pleiotropic variants, potentially leading to less robust conclusions. As shown in Table 2, adipose tissue exhibited the strongest association with primary hypertension, which is highly consistent with existing research findings. Notably, the absence of detected causal genes in kidney cortex was unexpected, as the kidney is traditionally considered to play a critical role in blood pressure regulation. This phenomenon may be related to the quality and insufficient sample size of eQTL studies from kidney cortex. Furthermore, in addition to subcutaneous adipose tissue and kidney, multiple other tissues, including esophagus mucosa, lung tissue, skeletal muscle, and thyroid, also showed signals of causal genes. This suggests that the pathogenesis of primary hypertension may involve a complex regulatory network across multiple systems and tissues, rather than being limited to the traditional cardio-renal axis. These finding provides a new perspective for deepening our understanding of the mechanisms underlying primary hypertension and underscores the importance of multi-tissue joint analysis in the study of complex diseases.

Subsequently, we performed colocalization analysis on the above genes to identify colocalization signals. Among them, ENPEP (PH4 = 0.686), ASS1P13 (PH4 = 0.99), KCNK15 (PH4 = 0.979), LYZ (PH4 = 0.987), and NAGLU (PH4 = 0.693) exhibited strong evidence of colocalization. However, KCNK15 and NAGLU were not identified by the univariate method. KCNK15 (potassium channel subfamily K member 15) belongs to the two-pore domain potassium channel family, and similar family members (e.g., KCNK1, KCNK2, KCNK3) have been shown to be associated with pulmonary arterial hypertension [39, 40]. NAGLU (α-N-acetylglucosaminidase gene) encodes an enzyme involved in lysosomal degradation. Its downregulation may lead to abnormal lysosomal accumulation, exacerbating vascular endothelial injury and atherosclerosis progression, making it a potential biomarker for cardiovascular diseases [41]. Additionally, we also performed Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses on the identified causal genes to uncover the primary biological processes and signaling pathways these genes are involved in [42]. The enriched pathways are illustrated in Fig. 3. The analysis revealed that these genes are significantly enriched in several biological processes and pathways related to the pathogenesis of primary hypertension, including: amide metabolic processes [43], carbohydrate and lipid metabolic processes [44], positive regulation of adaptive immune responses based on somatic recombination of immunoglobulin superfamily domain-based immune receptors [45], regulation of G protein-coupled receptor signaling pathways [46], negative regulation of inflammatory responses [47–49], CRISPR-based primary cilium development-related genes [50], and neutrophil degranulation [51, 52]. These findings provide a new perspective for deepening our understanding of the molecular mechanisms of primary hypertension and lay a theoretical foundation for future development of targeted therapeutic strategies for specific pathways in hypertension.

Fig. 3.

GO\KEGG enrichment analysis

Discussion

We propose MT-TWMR, a multi-tissue TWMR method that uses eQTLs as IVs to jointly analyze multiple tissues within each gene region. By combining L1 regularization for feature selection and a weighted tissue-difference network penalty leveraging tissue similarity [18], MT-TWMR enables cross-tissue information sharing, reduces confounding from correlated eQTLs, and improves causal inference precision. Simulations show it controls type I error and maintains high power with limited IVs and sparse effects.

Applied to MDD and primary hypertension, MT-TWMR revealed tissue-specific risk genes consistent with known pathophysiology: 65% of MDD genes in the frontal cortex [38], and 30% of hypertension genes in subcutaneous adipose tissue [53–56]. Gene annotation highlighted biologically plausible candidates such as ENPEP [57, 58], ASS1P13 [59, 60], KCNK15 [39, 40], LYZ [61], and NAGLU [41], with colocalization supporting their relevance. Enrichment analyses implicated pathways in vascular regulation, primary cilia function [62, 63], glycolipid metabolism [44], immune responses [45], GPCR signaling [46], and inflammation [47–49], underscoring the complexity of hypertension pathogenesis. Detailed interpretations, extended gene functional annotations, and additional biological discussions are provided in the Supplementary Discussion.

Compared with existing MVMR methods, MT-TWMR is tailored for TWMR with limited IVs, yet applicable when multiple exposures are available. By incorporating multiple tissues, it mitigates pleiotropy and confounding from shared eQTLs. In extreme cases where the number of IVs is smaller than the number of tissues, we advise against overinterpretation and suggest that such genes be flagged as having insufficient IVs for reliable multi-tissue inference. Limitations include assumptions of linear homogeneous effects, residual identifiability issues under weak or correlated instrumental variables, reliance on MR assumptions and summary statistic quality. We also acknowledge that differences in eQTL discovery power across tissues remain an inherent limitation when integrating datasets with heterogeneous sample sizes. Moreover, the current framework does not provide p-values or confidence intervals for the estimated effects, precluding formal multiple-testing corrections. Experimental validation remains necessary to confirm the causal genes identified.

Conclusions

We introduce a Multi-Tissue Transcriptome-Wide Mendelian Randomization (MT-TWMR) method that integrates multi-tissue eQTL data to identify tissue-specific causal risk genes. MT-TWMR selects eQTLs with significant and directionally consistent effects across multiple tissues as instrumental variables and constructs a sparse regression model to estimate the causal effects of gene expression on disease in each tissue. The model incorporates both an L1 regularization term and a tissue-difference penalty based on a tissue similarity network, enabling the preservation of tissue-specific signals while facilitating information sharing across related tissues. Through extensive simulations and real-data applications involving major depressive disorder and primary hypertension, MT-TWMR demonstrates superior performance in causal gene identification, accurate tissue localization, and model robustness compared to existing multivariable Mendelian Randomization methods. Implemented via an efficient optimization algorithm, MT-TWMR offers a powerful tool for constructing tissue-specific disease gene maps.

Supplementary Information

Below is the link to the electronic supplementary material.

Abbreviations

eQTL

Expression quantitative trait loci

GTEx

Genotype-tissue expression

GWAS

Genome-wide association studies

IV

Instrumental variable

Lasso

Least absolute shrinkage and selection operator

MDD

Major depressive disorder

MR

Mendelian randomization

MT-TWMR

Multi-tissue transcriptome-wide mendelian randomization

RCT

Randomized controlled trial

RMSE

root mean square error

TWMR

Transcriptome-wide mendelian randomization

UHP

Uncorrelated horizontal pleiotropy

Author contributions

T.-T.L. and S.-Y.W. conceived the design of the study. S.-Y.W. developed the methodology, conducted the numerical studies, analyzed the real data, and drafted the manuscript. M.-N.X. conducted the numerical studies, and drafted the manuscript.S.-Y.W., M. -N.X., Y.-X.T., K. -X.W., J.-B.W. and Y.C. collected and analyzed the data.S.-Y.W., M. -N.X., Y.-X.T., K. -X.W., and J.-B.W. drew the figures. F.-R.Y. and T.-T.L. revised the manuscript and provided comments to refine the manuscript All authors read and approved the final manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (82273735, 82404380, 82473737, 82304252), the Key Laboratory of Scientific and Engineering Computing (Ministry of Education), and the Shanghai Frontiers Science Center of Modern Analysis.

Data availability

All summary statistics used in this study are publicly available. The GWAS summary statistics for primary hypertension are available through the MRC-IEU OpenGWAS database under accession identifier ukb-b-12493 (https://opengwas.io/datasets/ukb-b-12493). The GWAS summary statistics for major depressive disorder are available through the IEU OpenGWAS database under accession identifier ieu-a-805 (https://opengwas.io/datasets/ieu-a-805). The GTEx study data (v10) are available through dbGaP under accession number phs000424.v10. p2. Summary statistics of eQTLs are available at the adult GTEx Portal (https://gtexportal.org/home/downloads/adult-gtex/qtl). The eQTLGen data released by eQTLGen Consortium are available at https://www.eqtlgen.org. Code for simulation and real data analysis for the mintMR paper is available at https://github.com/sywstat/mt_twmr.

Declarations

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.