TL-HDMR: a transfer learning framework for advancing equitable causal inference reveals metabolic signatures of stroke across multiple ancestries

Abstract

The limited genetic diversity in genome-wide association studies (GWAS) poses a significant challenge to the generalizability and equity of biomedical discoveries. Most causal inferences, particularly from high-dimensional phenomes (e.g. metabolomics), are primarily based on European populations, and their applicability to other ancestries remains uncertain. Traditional multivariable Mendelian randomization (MVMR) methods further struggle in high-dimensional and correlated settings due to collinearity and model instability. To bridge this gap, we present a two-step transfer learning framework for high-dimensional MR (TL-HDMR), designed to enhance causal exposure detection in understudied populations. Our approach leverages the Minimax Concave Penalty for asymptotically unbiased estimation amidst exposure correlations. Crucially, we introduce two novel pre-transfer procedures—HDMR.TSD for sourcing beneficial data and HDMR.PRESSO for filtering pleiotropic instruments—to ensure robust knowledge transfer. Extensive simulations demonstrated TL-HDMR’s superior performance in ROC curves and mean absolute error over alternative methods. When applied to identify causal metabolites for stroke across multi-ancestry cohorts (European, East Asian, South Asian, and African), TL-HDMR successfully pinpointed both shared and ethnic-specific causal biomarkers, showcasing its unique capability for equitable causal inference. This work provides a powerful statistical tool that not only addresses critical methodological challenges but also promotes inclusivity and fairness in human health research.

Introduction

Mendelian randomization (MR) has emerged as a powerful epidemiological tool for assessing putative causal relationships between modifiable exposures and health outcomes. By using genetic variants as instrumental variables (IVs), MR can mitigate confounding and reverse causation, key limitations of observational studies [1]. The advent of high-throughput technologies has enabled the large-scale measurement of numerous potential exposures—such as proteins, metabolites, and gene expression levels—ushering in the era of MR with omics exposures [1–3]. This approach holds immense promise for systematically identifying causal mediators in disease pathways and proposing novel therapeutic targets.

However, this promise is tempered by significant methodological challenges. The very nature of omics data introduces a high degree of correlation among exposures, creating a complex network of interrelated variables. This correlation significantly complicates the selection of valid instruments, as genetic variants are frequently associated with multiple correlated exposures—a situation that can result in fewer IVs than the number of high-dimensional exposures. Moreover, horizontal pleiotropy, wherein genetic variants influence the outcome through biological pathways other than the exposure of interest, further challenges the validity of causal inference. Traditional multivariable Mendelian randomization (MVMR) methods—such as multivariable inverse-variance weighted (MVIVW) [4], MVMR-lasso [5], genome-wide MR analysis under pervasive pleiotropy (GRAPPLE) [6], multivariable MR constrained maximum likelihood (MVMRcML) [7], spectral-regularized IVW (SRIVW) [8], and MR using bias-corrected estimating equations (MRBEE) [9]—are designed to handle multiple exposures. However, they often face challenges in high-dimensional, correlated exposure settings, where issues such as collinearity and unstable model fitting arise. To address these limitations, Zuber et al. developed MR-BMA [10], a Bayesian method scalable to high-throughput experimental dimensions that facilitates risk factor selection from a large set of candidates. Similarly, Cho et al. proposed MR-TRYX [11], which employs LASSO regression to identify traits with pleiotropic effects on the outcome, but the LASSO penalty introduces biased causal effect estimates, a well-known limitation of this approach. In this paper, we refer to this class of approaches as high-dimensional MR (HDMR) methods.

A separate yet equally critical challenge in MR is the pervasive Eurocentric bias in genome-wide association studies (GWAS). The majority of large-scale GWAS cohorts are of European ancestry [12], meaning that genetic instruments and exposure-outcome estimates are primarily derived from this population. In contrast, non-European populations—such as Asian and African groups—still have limited sample sizes and lower genome-wide coverage, resulting in reduced true discovery rates (TDR) and increased false discovery rates (FDR) in causal exposure selection and causal inference. This imbalance not only limits the generalizability of findings but also perpetuates health disparities. The generalizability of European findings to other ethnic populations is uncertain due to differences in linkage disequilibrium (LD) patterns, allele frequencies, and underlying genetic architectures [13]. Applying instruments and estimates from European populations to non-European populations without adjustment can yield erroneous conclusions, exacerbate health disparities and limit the global applicability of MR findings.

Thus, there is a pressing need to develop novel methodological frameworks capable of simultaneously addressing two major challenges: correlated high-dimensional exposures and cross-population generalization. Transfer learning [14] offers a promising solution by leveraging knowledge from a data-rich source domain (e.g. European populations with well-estimated genetic instruments for correlated exposures) to enhance model performance in a data-scarce target domain (e.g. non-European populations). Hou et al. introduced trans-ethnic Mendelian randomization (TEMR) [15], one of the first methods designed to improve causal estimation in underrepresented ancestries. However, TEMR is a univariable MR (UVMR) approach that relies on the assumption that Wald ratios for genetic variants across ancestries follow a multivariate normal distribution, and it enhances statistical power only when genetic correlations are non-zero. Yang et al. proposed MRBEE-TL [16], one of the first multi-ancestry multivariable MR (MVMR) methods, which integrates transfer learning with bias-corrected estimating equations to boost power in underpowered populations and evaluate cross-ancestry heterogeneity of risk factors. Despite these advances, there remains a lack of transfer learning MR methods specifically designed to handle pleiotropic and correlated high-dimensional exposures.

In this study, we introduce a two-step statistical transfer learning method for high-dimensional MR, termed TL-HDMR, designed to enhance the detection of causal exposures in target populations. To mitigate the influence of correlations among exposures, we incorporate the Minimax Concave Penalty (MCP), which facilitates asymptotically unbiased estimation of causal effects. Additionally, we propose two pre-transfer procedures—HDMR.TSD, an algorithm that identifies source datasets conducive to positive transfer, and HDMR.PRESSO, which filters out pleiotropic instruments—to further optimize the performance of TL-HDMR. We evaluate the performance of the proposed method through extensive simulations and demonstrate its practical utility by applying TL-HDMR to identify causal biomarkers for stroke and its four subtypes among 899 blood metabolites. The results underscore the capability of TL-HDMR to produce equitable and generalizable causal inferences across diverse ancestral backgrounds.

Results

Method overview

The TL-HDMR method transfers information from K auxiliary source populations to the target population, thereby enhancing both the accuracy of causal variable selection and the precision of causal effect estimation in the target population. It is based on GWAS summary data and is designed for HDMR settings—specifically, scenarios where the number (P) of exposures is close to or exceeds that of IVs (J), that is P≥ J, and the exposures are also correlated.

The observed GWAS summary data consist of marginal genetic association, including association and its covariance matrix , as well as association and its covariance matrix . Since a large number of SNPs have non-zero LD relationships, we first transform them into conditional associations (association: and its covariance matrix , association: and its covariance matrix ). We denote the conditional statistics in the target population by (, , ), the k-th source population by (, , ), k=1,2,…, K. is a P× 1 vector with the causal effects of exposures () on the outcome (Y).

The workflow of TL-HDMR is shown in Fig. 1. Prior to applying transfer learning, two preparatory processes are required: the removal of invalid IVs and the selection of informative auxiliary datasets. For the first one, we propose the high-dimensional version of PRESSO method [17], called HDMR.PRESSO (Fig. 1a). The HDMR.PRESSO identifies outlier IVs by sequentially excluding each variant, refitting the HDMR model, and comparing the residual sum of squares (RSS) between observed and predicted effects against a simulated Gaussian null distribution. Empirical P-values are derived and Bonferroni-corrected by multiplying by the number of variants.

Figure 1.

Workflow of TL-HDMR method. (a) Causal diagram of HDMR. The number of exposures (P) is equal to or greater than the number of instrumental variables (IVs) (). Additionally, the exposures are correlated with each other. The HDMR.PRESSO method identifies and removes invalid IVs that exhibit either correlated or uncorrelated pleiotropy. The observed GWAS summary statistics represent the marginal associations between SNPs and the trait. The TL-HDMR method transforms these marginal associations into conditional associations using a specific formula. The conditional statistics include G-X associations and their covariance matrix , as well as G-Y associations and their covariance matrix . We use the superscript 0 to denote the target dataset and superscript k (k = 1, ..., K) to denote the auxiliary source datasets. (b) HDMR.TSD method for transferable source detection. For K candidate source datasets, HDMR.TSD employs a data-driven cross-validation strategy to select the set () of auxiliary datasets that are closest to the loss of the target dataset. (c) TL-HDMR method. TL-HDMR method includes two steps: transferring and debiasing steps. The figure on the right illustrates the estimation concept of TL-HDMR. The green point denotes the true causal effect in the target population, and the surrounding navy blue circle denotes its estimation error. The orange point denotes the obtained by the transferring step, and the surrounding orange circle denotes its estimation error. his the biased distance in the transferring step. is the estimation in the transferring step using both source and target datasets. The pink point denotes the estimation in the debiasing step. The green point denotes the naïve estimation using only target dataset.

The second process is selecting the informative auxiliary datasets. We leverage the transferable source detection algorithm (HDMR.TSD) [18], which is a data-driven strategy (Fig. 1b). The detection algorithm proceeds as follows: the target data is split into three folds, though other fold counts are allowed. For each source dataset, TL-HDMR is applied using every pair of target folds. The loss function of HDMR

is evaluated on the withheld fold and the average cross-validation loss is computed per source. is the MCP penalty. Meanwhile, HDMR is fitted on each pair of target folds and evaluated on the remaining fold to obtain a target-specific loss benchmark . Sources are selected for the transfer set if the difference falls below a predefined threshold.

After the above two preparatory processes, our TL-HDMR method can be applied. TL-HDMR consists of two main stages (Fig. 1c). Initially, a transferring step is performed, leveraging both informative auxiliary datasets and the target dataset to compute an initial estimator

Under typical conditions, however, this estimator converges in probability to a biased limit (the orange point in Fig. 1c). This bias is subsequently corrected in the second step through the following debiasing process using only the target data

where

is the causal effect estimator of TL-HDMR. TL-HDMR assumes that and , where s is the number of true causal exposures. This assumption means that the difference is -sparsity at most h, i.e. is a sparse high-dimensional vector whose -norm is no longer than h.

Simulation

We conducted a series of simulation studies to evaluate the performance of TL-HDMR. Performance metrics included the Receiver Operating Characteristic (ROC) curve, which reflects variable selection accuracy, and the mean absolute error (MAE), which measures the precision of causal effect estimation. The methods compared consist of traditional HDMR approaches, along with three penalties—LDA.Lasso, LDA.Elas, and LDA.MCP—implemented using only the target dataset, along with versions enhanced by our TL-HDMR method to incorporate information from auxiliary datasets. We also varied multiple parameters across the simulations, including the correlations among IVs, correlations among exposures, genetic correlations between source and target datasets, the number of IVs, and the number of source datasets.

As summarized in Fig. 2a, we compared the performance metrics of traditional HDMR and TL-HDMR after knowledge transfer under three penalty terms, under the condition of zero correlations among exposures and no genetic associations among source and target datasets. The results indicated a marked improvement in the ROC curve following transfer, demonstrating that TL-HDMR achieves more accurate identification of causal variables. Figure 3a presents the corresponding MAE for causal effect estimation. Prior to transfer, the MCP penalty yielded the lowest MAE. After integration of auxiliary data through TL-HDMR, all methods exhibited a pronounced reduction in MAE, reflecting enhanced estimation precision. Figure 2b depicts the scenario with non-zero correlations among exposures. Compared with Fig. 2a, as correlations among exposures increased, the ROC performance of traditional HDMR improved somewhat, while TL-HDMR consistently and significantly outperformed the traditional approach. As shown in Figs S1 and S2, elevated correlations among exposures—particularly at a level of 0.8—lead to more limited improvement in ROC performance with TL-HDMR. Nevertheless, TL-HDMR consistently achieves significantly smaller MAE, underscoring its unbiased and robust properties in causal effect estimation. Figure 2c illustrates the case involving non-zero genetic associations between source and target datasets. Here, stronger genetic correlations resulted in a pronounced decrease in ROC curves for traditional HDMR approaches, including MCP. In contrast, TL-HDMR consistently demonstrated strong performance and achieved a significant reduction in MAE under these conditions (Fig. 3c). As indicated in Figs S3 and S4, TL-HDMR maintains similarly strong performance when genetic associations between source and target datasets are below 0.5. However, at a genetic association level of 0.8, the improvement in ROC becomes more modest, although TL-HDMR continues to achieve a significantly smaller MAE.

Figure 2.

Receiver operating characteristic (ROC) curves of TL-HDMR simulation results. The simulation settings are defined as follows: the linkage disequilibrium (LD) between SNPs is ; the number of instrumental variables (IVs) in the target dataset is ; the number of high-dimensional exposures is P=100; and the number of auxiliary source datasets is K =3. The parameter denotes the correlation between any two exposures, and denotes the cross-ancestry genetic correlation of the exposures between datasets. The panels illustrate variable selection accuracy under three distinct scenarios: (a) independent exposures with zero genetic correlation (, ); (b) correlated exposures with zero genetic correlation (, ); and (c) independent exposures with non-zero cross-ancestry genetic correlation (, ). LDA.Lasso, LDA.Elas, and LDA.MCP denote traditional target-only high-dimensional Mendelian randomization (MR) methods employing three distinct penalty forms. TL-HDMR.Lasso, TL-HDMR.Elas, and TL-HDMR.MCP represent our proposed transfer learning methods, which incorporate both the source and target datasets to improve causal exposure detection.

Figure 3.

Mean absolute error (MAE) of TL-HDMR simulation results. The simulation settings are identical to those in Fig. 2: the LD between SNPs is ; the number of IVs in the target dataset is ; the number of exposures is P=100; and the number of source datasets is K =3. The parameter is the correlation between any two exposures, and is the cross-ancestry genetic correlation between datasets. The panels display the estimation precision (where lower MAE indicates less bias) under three scenarios: (a) , ; (b) , ; and (c) , . LDA.Lasso, LDA.Elas, and LDA.MCP denote the traditional high-dimensional MR methods using only the target dataset. TL-HDMR.Lasso, TL-HDMR.Elas, and TL-HDMR.MCP represent the corresponding transfer learning methods, which utilize both source and target datasets to significantly reduce estimation error.

Figures S5 and S6 present simulation results under different numbers of IVs. We considered three scenarios with 100 exposures: one where the number of IVs (50) was substantially smaller than the number of exposures, another where the number of IVs (80) was slightly smaller, and a third where the number of IVs (120) was slightly larger. The simulations demonstrate that TL-HDMR achieves the greatest improvement in ROC performance when the number of IVs is very small (50). As the number of IVs increases, the performance of traditional HDMR improves; nevertheless, TL-HDMR continues to exhibit a statistically significant enhancement in ROC performance. Figures S7 and S8 present the ROC and MAE performance of various methods as the correlation among IVs increases. When the correlation grows, all methods exhibit a slight decline in ROC performance, particularly at a correlation level of 0.8. Nonetheless, TL-HDMR still outperforms traditional HDMR. At correlation levels below 0.5, the MAE of traditional HDMR increases significantly with stronger correlations, while TL-HDMR maintains favorable performance. When the correlation exceeds 0.5, the MAE of traditional HDMR rises markedly. Similarly, TL-HDMR based on lasso and elastic-net penalties also show substantial increases in MAE. In contrast, the MCP-based TL-HDMR retains consistently low MAE values, producing asymptotically unbiased estimates. These results demonstrate the robustness of the MCP penalty to correlations among IVs.

As shown in Fig. 4, we evaluated the performance of the TSD algorithm for selecting informative auxiliary datasets prior to applying TL-HDMR in the presence of non-informative auxiliary sources. We generated 10 candidate auxiliary datasets, half of which were informative. The parameter is set to 1.6. The simulation results demonstrate that when all candidate auxiliary datasets were used directly without selection, TL-HDMR did not yield significant improvement in ROC compared to traditional HDMR; in fact, it led to an increased MAE, indicating greater bias in causal effect estimation. In contrast, after incorporating the TSD algorithm for dataset screening, TL-HDMR not only exhibited significantly improved ROC performance but also achieved a substantially reduced MAE, resulting in asymptotically unbiased estimates. These findings underscore the effectiveness of the TSD algorithm in identifying informative auxiliary datasets. Figures S9 and S10 present the scenario with five candidate auxiliary datasets, three of which are informative. The results indicate that when TL-HDMR is applied using all candidate datasets without selection, both its ROC and MAE performance are even less favorable than those of traditional HDMR. However, after incorporating TSD selection, TL-HDMR shows significant improvement in both ROC and MAE. Although the MCP-based TL-HDMR does not achieve the highest ROC performance, it attains the smallest MAE, indicating superior precision in causal effect estimation.

Figure 4.

Performance evaluation of the transferable source detection (HDMR.TSD) algorithm in the presence of incompatible auxiliary data. The simulation settings are defined as follows: LD between SNPs is ; the number of IVs in the target dataset is ; and the number of high-dimensional exposures is P=100. Both the exposure correlation () and cross-ancestry genetic correlation () are set to 0. The pool of candidate source datasets is set to K=10, comprising five informative (true) source datasets with a minor causal difference (δ =0.05) and five spurious (incompatible) source datasets with a large causal difference (δ =0.2). (a) Receiver operating characteristic (ROC) curves. This panel illustrates the variable selection accuracy by plotting the true positive rate (TPR) against the false positive rate (FPR) across the different models. (b) Mean absolute error (MAE) boxplots. This panel displays the distribution of estimation errors for the causal effects, where lower MAE values represent higher estimation precision. Methods compared:  LDA.Lasso, LDA.Elas, and LDA.MCP denote the high-dimensional MR methods utilizing only the target dataset without transfer learning. TL-HDMR.Lasso, TL-HDMR.Elas, and TL-HDMR.MCP represent baseline transfer learning methods that indiscriminately incorporate all 10 candidate source datasets, leading to negative transfer bias. In contrast, TL-HDMR.Lasso + TSD, TL-HDMR.Elas + TSD, and TL-HDMR.MCP + TSD represent our optimized framework where the HDMR.TSD algorithm is actively applied to objectively screen out incompatible datasets prior to transfer, successfully restoring high ROC and low MAE.

Figure 5 illustrates the performance of the HDMR.PRESSO algorithm in the presence of invalid IVs. Simulation results indicate that when invalid instruments are present, traditional HDMR exhibits limited discriminatory power in the ROC curve. Although TL-HDMR still achieves a marginal improvement in ROC performance under these conditions, it leads to a substantial reduction in MAE for methods with Lasso and Elastic Net penalties—though no significant change is observed for MCP. After incorporating the PRESSO algorithm, TL-HDMR demonstrates markedly enhanced performance in both ROC and MAE.

Figure 5.

Performance evaluation of the TL-HDMR.PRESSO algorithm in the presence of invalid instrumental variables (horizontal pleiotropy). The simulation settings are defined as follows: the linkage disequilibrium (LD) between SNPs is ; the target dataset contains 200 candidate instrumental variables (IVs), but the proportion of invalid IVs is 20%; the number of high-dimensional exposures is P=100. Both the exposure correlation () and cross-ancestry genetic correlation () are set to 0.2. The number of auxiliary source datasets is K=3. (a) Receiver operating characteristic (ROC) curves. This panel illustrates the variable selection accuracy by plotting the true positive rate (TPR) against the false positive rate (FPR) across the different models. (b) Mean absolute error (MAE) boxplots. This panel displays the distribution of estimation errors for the causal effects, where lower MAE values represent higher estimation precision. Methods compared:  LDA.Lasso, LDA.Elas, and LDA.MCP denote traditional high-dimensional MR methods utilizing only the target dataset. TL-HDMR.Lasso, TL-HDMR.Elas, and TL-HDMR.MCP represent baseline transfer learning methods that incorporate source datasets but do not filter out invalid IVs, leaving them susceptible to severe pleiotropic bias. In contrast, TL-HDMR.Lasso + PRESSO, TL-HDMR.Elas + PRESSO, and TL-HDMR.MCP + PRESSO represent our complete optimized framework where the HDMR.PRESSO algorithm is rigorously applied to identify and remove invalid IVs prior to causal estimation, successfully rescuing estimation accuracy and precision.

We further evaluated TL-HDMR under the non-ideal conditions designed in our sensitivity simulations. First, under the extreme violation of the sparsity assumption (dense differences), TL-HDMR demonstrated virtually no negative impact (Figs S11 and S12). Driven by HDMR.TSD’s adaptive source rejection, the framework successfully prevented negative transfer, maintaining ROC and MAE performance highly comparable to ideal sparse conditions and consistently outperforming target-only baselines. Second, in the weak instrument scenarios (Figs S13–S14), extremely weak IVs () predictably flattened ROC curves and increased estimation bias across all methods. However, incorporating cross-ancestry information via TL-HDMR alongside pleiotropic filtering (HDMR.PRESSO) consistently salvaged statistical power. Our complete framework yielded the highest variable selection accuracy and lowest estimation bias across all weak IV settings compared to traditional HDMR baselines. Third, we evaluated robustness in expanded feature spaces with P = 500 and P = 1000 (Figs S15–S18). As dimensionality scaled, traditional target-only methods suffered severe collapse in both variable selection (depressed ROC) and estimation precision (inflated MAE). All transfer learning variants successfully rescued ROC by leveraging auxiliary data. However, at P = 1000, L1-based transfer models (TL-HDMR.Lasso/Elas) exhibited inflated MAE due to accumulating attenuation bias. Only TL-HDMR.MCP maintained near-zero MAE, confirming the MCP penalty’s oracle property is uniquely essential for unbiased causal estimation in ultra-high-dimensional data.

We further evaluated the framework’s adaptability under zero cross-ancestry genetic correlation and domain-specific omics challenges (Figs S19–S24). Despite complete divergence in population-specific instrument-exposure associations, TL-HDMR achieved asymptotically unbiased estimation by transferring downstream causal effects rather than shared genetic architectures. Furthermore, we validated its broad omics utility: in transcriptomics-like settings (high noise, weak instruments), the transfer learning architecture successfully salvaged statistical power by effectively amplifying weak genetic signals; conversely, in proteomics-like settings (extreme multicollinearity, sparse strong effects), TL-HDMR.MCP uniquely isolated true causal proteins, utilizing the MCP’s oracle property to avoid over-shrinking. These results confirm that our framework is ancestry-agnostic and systematically equipped to resolve the distinct statistical bottlenecks of multi-omics data.

Finally, we assessed estimation bias and coverage probability (CP) (Figs S25–S28). For true causal signals, traditional methods suffered from severe attenuation bias and under-coverage (CP). In contrast, TL-HDMR.MCP leveraged auxiliary data to achieve near-zero bias, successfully maintaining median CP closely at the 95% nominal level. For noise variables, all methods maintained zero median bias and CP, strictly controlling false positives. However, whereas Lasso-based methods artificially inflated CP to a rigid 1.0 via absolute zero-shrinkage, TL-HDMR.MCP exhibited a broader, yet statistically valid, CP distribution. This reflects a recognized theoretical trade-off of the non-convex MCP: slightly increased resampling variability near the zero boundary is exchanged for the unique ability to completely eliminate attenuation bias in active pathways.

Application

We utilized GWAS summary data from four distinct ancestry groups (European (EUR), African (AFR), East Asian (EA) and South Asian (SA)) to investigate the causal relationships between 899 metabolites and stroke as well as its four subtypes (cardioembolic stroke, ischemic stroke, large artery stroke, and small vessel stroke), and separately analyzed ancestry-specific and stroke subtype-specific metabolic biomarkers. Finally, we performed functional enrichment analysis on the identified causal biomarkers. The details of workflow are shown in Fig. S29.

Ancestry-specific metabolic biomarkers for stroke and its subtypes

Figure 6 presents the results of causal metabolic biomarker identification for stroke across diverse ancestral groups. Figure 6a compares the number of causal metabolic biomarkers identified by our proposed transfer learning-based MR method (TL-HDMR) against the conventional non-transfer approach within each of the four ancestries. The results reveal a substantial increase in detected causal biomarkers after applying transfer learning, particularly when the target dataset has an extremely small sample size, such as the AFR cohort (sample size <100). Furthermore, even with target datasets of relatively larger sample sizes, like EUR, the TL-HDMR method demonstrated enhanced biomarker identification capabilities when employing the asymptotically unbiased penalty term MCP. However, when using the Elastic Net penalty, although the conventional method identified a greater absolute number of biomarkers, TL-HDMR provided a crucial correction by reducing the proportion of false discoveries, even though the overall count of causal biomarkers decreased. Figure 6b illustrates our findings on the distribution of causal biomarkers. We identified 93 metabolites serving as common causal factors across all four ethnic groups. Additionally, we found 17 metabolic markers specifically associated with stroke etiology in the EA population, 34 unique to the AFR population, 37 specific to the EUR population, and 25 metabolites uniquely associated with stroke etiology in the SA population.

Figure 6.

Ancestry-specific and shared causal metabolic biomarkers for stroke. (a) Identification of causal metabolites across four ancestries. A barcode-style plot displaying the individual causal metabolites selected by six different statistical methods across African (AFR), East Asian (EA), European (EUR), and South Asian (SA) populations. Each vertical stroke represents a distinct causal metabolite. The integers on the far right denote the total count of causal metabolites identified by each respective method. TL-HDMR.Lasso, TL-HDMR.Elas, and TL-HDMR.MCP represent our proposed transfer learning methods utilizing auxiliary source datasets, whereas LDA.Lasso, LDA.Elas, and LDA.MCP denote traditional target-only high-dimensional Mendelian randomization methods. (b) Cross-ancestry overlap of causal metabolites. A four-way Venn diagram illustrating the distribution of the causal metabolites identified by the optimal TL-HDMR.MCP method. The diagram distinguishes between the intersection sets (shared causal metabolites across multiple populations) and disjoint sets (ancestry-specific causal metabolites). The central core highlights 93 universally shared biomarkers (accounting for 31.1% of the total unique discoveries), while the outer non-overlapping regions detail population-specific biomarkers (e.g. 34 unique to AFR, 17 to EA, 37 to EUR, and 25 to SA). (c) Pathway enrichment for shared and ancestry-specific causal metabolites. A detailed mapping connecting specific causal metabolites (left) to their significantly enriched biological pathways (right) determined via Over-Representation Analysis (ORA). The results are stratified into two main categories: universally shared pathways (“Share” driven by the 93 cross-ancestry metabolites) and population-specific pathways uniquely driven by the distinct causal metabolites of the EA, AFR, SA, and EUR populations.

To focus on the most robust core findings, the exhaustive lists of specific metabolites driving each enriched pathway have been detailed in the Supplementary Materials (Supplementary Data 10). Our analysis identified several core metabolic pathways significantly enriched across all four ethnic groups, indicating a universal role in stroke pathogenesis (Fig. 6c). These include Glutamate Metabolism, Arginine and Proline Metabolism, and Sphingolipid Metabolism. Glutamate metabolism is critical due to stroke-induced glutamate release leading to excitotoxicity, while sphingolipid metabolism is essential for endothelial barrier function and is linked to blood–brain barrier impairment. The urea cycle and arginine metabolism also play shared roles, highlighting their importance in vasodilation and endothelial function.

Striking ethnic-specific metabolic signatures were also observed, reflecting divergent biological mechanisms underlying stroke etiology. In East Asian populations, unique disruption in Tryptophan Metabolism implicates excitotoxicity and neuroinflammation. Conversely, African populations exhibited extensive dysregulation across TCA cycle, glutathione, and broader amino acid pathways, indicative of profound systemic oxidative stress potentially linked to distinct comorbidity profiles. In South Asian populations, altered branched-chain amino acid (BCAA) catabolism—alongside disrupted glycolysis and insulin signaling—suggests a prominent pathogenic link between insulin resistance and stroke risk [19, 20]. Finally, European populations presented a distinct BCAA metabolism profile, complemented by unique enrichments in tyrosine and polyunsaturated fatty acid (PUFA) metabolism, highlighting the recognized roles of these specific pathways in inflammation resolution and cardiovascular integrity [21, 22].

Through our multi-ancestral analysis, we identified both conserved and ancestry-specific metabolic pathways causally associated with cardioembolic stroke (Figs S30–S32). Key shared mechanisms underlying its pathogenesis encompass platelet activation, glutamate-mediated excitotoxicity, and post-ischemic injury driven by global energy dysregulation and oxidative stress [23, 24]. Furthermore, ancestry-stratified investigations illuminated distinct, population-specific etiologies: African populations exhibited dysregulated phospholipid catabolism indicative of pronounced inflammatory activation [25]; East Asian cohorts displayed impaired Krebs cycle and amino acid metabolism reflecting cerebral energy deficits; European populations were characterized by ceramide-mediated insulin resistance, a known driver of atrial fibrillation susceptibility [26]; and South Asian populations demonstrated disrupted carnitine metabolism, linking compromised fatty acid oxidation to arrhythmogenesis [27].

Similarly, for large artery stroke, our analysis delineated both conserved and divergent metabolic pathways (Figs S33–S35). Common mechanisms involve serotonin-mediated platelet activation, excitotoxicity, and post-ischemic energy and oxidative imbalance [28, 29]. Population-specific profiles further highlighted distinct metabolic etiologies: African cohorts exhibited phospholipid-driven inflammatory alterations; East Asian populations demonstrated Krebs cycle disruptions; European cohorts were characterized by ceramide-induced insulin resistance; and South Asian populations displayed impaired carnitine metabolism affecting cardiac function [30–32]. Collectively, these findings underscore universal thrombogenic and ischemic mechanisms alongside ancestry-dependent metabolic susceptibilities that contribute to ethnic disparities in large artery stroke risk.

For small vessel stroke, our multi-ancestry approach implicates both shared and distinct metabolic pathways (Figs S36–S38). Commonly disrupted pathways include nitric oxide and methionine metabolism, essential for endothelial and vascular integrity [33]. Ancestry-stratified profiles further delineated distinct population-specific vulnerabilities: African cohorts exhibited altered fatty acid and energy metabolism; East Asian populations demonstrated urea cycle and glutamate dysregulation; European cohorts were characterized by impaired sulfur and NAD+ metabolism; and South Asian populations displayed anomalies in homocysteine and cysteine pathways linked to profound oxidative stress and vascular dysfunction [34, 35].

Finally, in ischemic stroke, multi-ancestry analysis reveals conserved and group-specific metabolic influences (Figs S39–S41). Shared elements encompass dysregulated sphingolipid metabolism, arachidonic acid signaling, and NMDA-related neurotransmission and apoptosis pathways [36, 37]. Ancestry-stratified findings show altered amino acid and carnitine metabolism in African ancestry; disrupted bile acid metabolism and cytochrome P450 activity in East Asian ancestry; imbalances in alpha-linolenic acid and trans-sulfuration in European ancestry; and dysregulated linoleic acid metabolism and PPAR signaling in South Asian ancestry [38–41].

Stroke subtype-specific metabolic biomarkers for different ancestries

Figure 7 summarizes the shared and distinct causal metabolomic biomarkers across stroke subtypes in the EA ancestry. Figure 7a highlights the superior performance of TL-HDMR over conventional methods in identifying causal metabolites. Figure 7b shows the distribution of shared and subtype-specific biomarkers: 11 metabolites were common to all subtypes, while stroke, cardioembolic stroke, ischemic stroke, large artery stroke, and small vessel stroke had 15, 43, 27, 36, and 37 unique metabolites, respectively.

Figure 7.

Stroke subtype-specific and shared causal metabolic biomarkers in the East Asian (EA) population. (a) Identification of causal metabolites across stroke subtypes. A barcode-style plot displaying the individual causal metabolites identified by six different statistical methods for general stroke and its four subtypes (cardioembolic, ischemic, large artery, and small vessel stroke) within the EA population. Each vertical stroke represents a distinct causal metabolite. The integers on the far right denote the total count of causal metabolites identified by each respective method. TL-HDMR.Lasso, TL-HDMR.Elas, and TL-HDMR.MCP represent our proposed transfer learning methods utilizing auxiliary source datasets, whereas LDA.Lasso, LDA.Elas, and LDA.MCP denote traditional target-only high-dimensional Mendelian randomization methods without transfer learning. (b) Cross-subtype overlap of causal metabolites. A five-way Venn diagram illustrating the distribution of causal metabolites identified by the optimal TL-HDMR.MCP method across the five stroke phenotypes. The diagram distinguishes between the intersection sets (shared causal metabolites across all or multiple subtypes) and disjoint sets (subtype-specific causal metabolites). For instance, 11 metabolites (2.51%) are universally shared across all five phenotypes, while varying counts are uniquely associated with specific subtypes (e.g. 43 unique to cardioembolic stroke, 36 to large artery stroke, 27 to ischemic stroke, and 37 to small vessel stroke). (c) Pathway enrichment for shared and subtype-specific causal metabolites. A detailed mapping connecting specific causal metabolites (left) to their significantly enriched biological pathways (right) determined via over-representation analysis (ORA). The results are stratified into universally shared pathways (“Share,” driven by the common core metabolites) and subtype-specific biological pathways uniquely driven by the distinct causal metabolites of cardioembolic, ischemic, large artery, small vessel, and general stroke.

We further identified both common and subtype-specific metabolic pathways associated with stroke in the EA population (Fig. 7c; detailed metabolite mappings are provided in Supplementary Data 11). Shared pathways across all subtypes included dysregulated bile acid and glutathione metabolism suggesting impaired detoxification and oxidative stress response [42, 43]. Additionally, homocysteine and methionine metabolism abnormalities indicate broader disruptions in methylation cycles and amino acid homeostasis that may influence cerebrovascular integrity [44].

Subtype-specific pathway alterations were also evident. Large artery stroke involved perturbations in amino acid metabolism, implicating neurotransmitter imbalance and energetic deficits [45]. Cardioembolic stroke was characterized by platelet degranulation and HDL metabolism, underscoring roles of thrombogenesis and dyslipidemia [46, 47]. Ischemic stroke exhibited dysregulation of branched-chain amino acid catabolism, suggesting compromised energy substrate utilization [48]. Small vessel stroke featured disruptions in betaine and choline metabolism, pointing to aberrant methylation and lipid handling in microvascular dysfunction [49]. Lastly, general stroke phenotypes revealed impaired glutamate metabolism and glutathione recycling, indicating widespread deficits in neurotransmission and antioxidant defense.

Our analysis identifies distinct metabolic profiles underlying stroke and its subtypes in the African ancestry population (Figs S42–S43). Pan-subtype mechanisms prominently featured dysregulated serotonin and platelet pathways driving thrombotic predisposition, alongside altered sphingolipid and cholesterol metabolism indicative of broad vascular lipid defects [50]. Subtype-specific etiologies further highlighted distinct risks: glutamate and methionine shifts in cardioembolic stroke; BCAA dysregulation in overall ischemic stroke; fatty acid and ceramide-mediated inflammation in large artery stroke; and glycolytic and phosphatidylcholine impairments in small vessel stroke [51, 52].

Our analysis reveals shared and subtype-specific metabolic alterations underlying stroke in the South Asian population (Figs S44–S45). Common across all subtypes were impaired glutathione and glutamate metabolism, indicating disrupted antioxidant defense and neurotransmission, alongside dysregulated TCA cycle and glycolysis, reflecting energy failure [53, 54]. Subtype-stratified analyses further revealed distinct etiological drivers: platelet degranulation in cardioembolic stroke; BCAA catabolism defects in overall ischemic stroke; methionine and sphingolipid disruptions in large artery stroke; and homocysteine-related oxidative stress in small vessel stroke [35, 44].

Our multi-ancestry analysis reveals conserved and subtype-specific metabolic pathways linked to stroke in the European population (Figs S46–S47). Shared mechanisms include disrupted glutathione and glutamate metabolism, indicating impaired antioxidant capacity and neurotransmission, alongside homocysteine and amino acid metabolic imbalances linked to vascular risk. Recurrent cAMP signaling suggests a conserved role in ischemic response [55, 56]. Subtype-stratified analyses further revealed distinct etiological drivers: hemostasis and lipid regulation in cardioembolic stroke; BCAA dysregulation in overall ischemic stroke; altered PUFA metabolism in large artery stroke; and TMAO and carnitine disruptions in small vessel stroke [57, 58].

Discussion

In this paper, we introduce TL-HDMR, a two-step transfer learning framework designed to address two major challenges in cross-population causal inference: high-dimensional exposure spaces and limited sample sizes in non-European cohorts. By leveraging genetic information from well-powered source populations, TL-HDMR significantly improves the accuracy and generalizability of causal estimates in underpowered target populations. The method integrates a penalized regression approach using the MCP to handle correlated exposures and introduces two novel pre-transfer procedures—HDMR.TSD and HDMR.PRESSO—to select transferable source datasets and filter out invalid instruments. Through comprehensive simulations and real-data analyses of blood metabolites in relation to stroke, we demonstrate that TL-HDMR outperforms existing high-dimensional MR methods in both ROC performance and robustness, providing a powerful tool for equitable causal discovery across diverse ancestries.

While TL-HDMR builds upon the transfer-learning architecture of standard high-dimensional linear models (e.g. Trans-Lasso), it introduces fundamental adaptations to address the unique complexities of MR. Traditional algorithms require individual-level data and assume a single-stage regression with perfectly measured predictors. To overcome these limitations, TL-HDMR utilizes linkage disequilibrium matrices to transform marginal GWAS summary statistics into conditional statistics, enabling robust summary-level integration. Furthermore, to account for the heteroskedasticity and correlation inherent in genetic estimates, we employ a weighted least squares inverse-weighting approach and decouple the estimation into a two-stage architecture that sequentially models instrument-exposure and instrument-outcome associations. Finally, to mitigate the risks of horizontal pleiotropy and negative knowledge transfer in cross-ancestry MR, we fortified the framework with HDMR.PRESSO to filter invalid instruments and HDMR.TSD to adaptively select compatible source datasets. Collectively, these modifications elevate conventional transfer learning into a tailored causal inference tool.

The proposed TL-HDMR framework offers a highly adaptable and theoretically grounded approach for enhancing causal inference in high-dimensional settings, particularly when generalizing findings across diverse populations. While initially developed and validated in the context of genomic and metabolomic data, the method is by no means limited to omics-based exposures. Its flexible architecture allows for the inclusion of a wide range of exposure types, including clinical variables, imaging-derived features, environmental factors, and behavioral indicators. This significantly broadens its applicability beyond molecular epidemiology to fields such as social science, environmental health, and public policy, where high-dimensional causal inference is increasingly needed but remains challenging due to collinearity and weak instruments.

Notably, the method supports knowledge transfer not only across different ethnic groups but also between subpopulations within the same broader ancestry. Genetic heterogeneity, environmental exposures, and social determinants can drive divergence in causal mechanisms even among groups that share continental ancestry. TL-HDMR enables the use of auxiliary data from any well-characterized source population—whether from a different geographic region, a different cohort within the same ethnicity, or a population with distinct environmental profiles—to strengthen causal estimation in an underpowered target population. This capability is critical for advancing health equity and precision medicine, as it allows more nuanced and representative causal inference across increasingly stratified populations.

A core assumption enabling robust transfer learning is the sparsity of causal effect heterogeneity between source and target populations. More precisely, we assume that the difference in causal effects, denoted as δ^k, is sparse in the l₁-norm, with , where h is bounded above by . This sparsity condition implies that only a limited subset of exposures exhibits divergent effects across populations. When satisfied, it ensures that the auxiliary data can provide meaningful information gain without introducing substantial bias, thereby facilitating asymptotically unbiased estimation and reducing variance in the target population. This assumption is biologically plausible and supported by empirical evidence across multiple domains. For instance, in pharmaceutical research, drug-target pathways often remain consistent across ancestries, while only specific metabolic enzymes (e.g. CYP450 family) show clinically relevant effect modifications. Similarly, in studies of cardiovascular traits, core biological mechanisms such as lipid metabolism and blood pressure regulation are largely conserved across populations, with heterogeneity confined to a limited number of context-specific genetic or environmental modifiers. In complex trait genetics, most causal variants exhibit consistent effects across ancestries, with heterogeneous effects typically restricted to a small number of loci influenced by local adaptation or gene–environment interactions. Such patterns of limited heterogeneity justify the sparsity assumption in practice and enhance the robustness of transfer learning applications. Even when the strict sparsity assumption is partially violated, the two-step architecture of TL-HDMR provides empirical robustness in the settings examined. The massive variance reduction provided by auxiliary datasets outweighs the minor introduced bias, while the subsequent target-only debiasing step effectively filters out dense structural noises, ensuring consistent etiological network reconstruction.

Despite these robust theoretical properties, our approach remains susceptible to weak instrument bias, particularly in trans-ancestry GWAS where the target populations typically suffer from extremely small sample sizes. Our sensitivity analyses demonstrated that extreme weak IV environments inevitably lead to residual attenuation bias and constrained discovery power. It is crucial to acknowledge the limitations of our current methodological safeguards in mitigating this specific bias. First, while the MCP penalty achieves asymptotic unbiasedness in ideal settings, extreme weak IVs exhibit a fundamentally low signal-to-noise ratio. In such environments, regularization may inadvertently over-shrink true but weak causal signals, failing to fully correct the attenuation bias. Second, while HDMR.PRESSO effectively filters heterogeneous structural noise (i.e. horizontal pleiotropy) by evaluating outlier residuals, weak instruments systematically dilute the global effect size rather than manifesting as distinct outliers, rendering PRESSO ineffective at identifying pure weak IV bias. Future methodological iterations of the TL-HDMR framework could directly tackle this challenge in underpowered target cohorts by integrating Bayesian prior weighting or pleiotropy-robust variance corrections to further stabilize the estimates.

In summary, TL-HDMR provides a scalable, robust, and inclusive framework for causal discovery in complex datasets spanning diverse populations and exposure types. It represents a meaningful step toward more equitable and generalizable scientific insights.

Materials and methods

Model and notation

The TL-HDMR method transfers information from auxiliary source populations to the target population, thereby enhancing both the accuracy of causal variable selection and the precision of causal effect estimation in the target population. It is based on GWAS summary data and is designed for HDMR settings—specifically, scenarios where the number of exposures is close to or exceeds that of IVs, that is, and the exposures are also correlated. The workflow of TL-HDMR is shown in Fig. 1.

In MR, assume P exposures () and one outcome Y, and the J valid IVs (), which may be correlated with each other, must satisfy the following three assumptions:

A1. is associated with at least one of P exposures;

A2. is not associated with the confounder between P exposures and the outcome;

A3. affects the outcome only through exposures.

The MR model based on the individual data is:

(1)

Where is a N× P matrix with exposures’ individual-level data, is a N× J matrix with genotype data, is a J× P matrix with conditional (joint) genetic association of exposures, is a N× 1 vector with confounding’s individual-data, is a 1× P vector with the effects of confounding on the exposures, is a P× 1 vector with the causal effects of exposures on the outcome, is the effect of confounding on the outcome, and are error terms with normal distribution.

GWAS summary statistics (marginal genetic associations) including association and its covariance matrix , as well as association and its covariance matrix . is a J× J covariance matrix, R is the J× J LD matrix of correlated IVs and its element is the LD between two SNPs and , is a J× 1 vector with standard error of association. Similarly, the covariance matrix of is . We can express the conditional genetic associations using marginal genetic associations [59]:

association: and its covariance matrix ,

association: and its covariance matrix .

The relationship between and . Under the assumption of NO Measurement Error (NOME) [60], LD-Aware (LDA) IVW [61] regresses the on by weighting the inverse of covariance matrix :

Therefore, the causal effect () of exposures on the outcome can be estimated by the Weighted Least Squares (WLS), minimizing the following objective function:

HDMR: high-dimensional multivariable MR

The traditional WLS methods are not applicable in the high-dimensional exposures setting. This is firstly due to the existence of many correlated exposures, which WLS cannot handle, and secondly due to the curse of dimensionality, especially when the number of exposures is extremely large (P≈ J or P>J). Penalized regression methods accomplish this by minimizing the objective function that is composed of a loss function plus a penalty function:

(2)

where is a function of the coefficients indexed by a parameter λ that controls the tradeoff between the loss function and penalty, and that also may be shaped by one or more tuning parameters (γ). MR-TRYX [11] uses the Lasso penalty

to assess the effects of the candidate traits on the outcome. Generally, Lasso penalty is a special case of the Elastic-net penalty

When γ =1, the Elastic-net penalty reduces to the Lasso penalty. However, both the Lasso and Elastic-net penalty obtain the biased estimation for causal effects of exposures on the outcome. Here, we use the MCP penalty [62].

which achieves asymptotically unbiased estimation of causal effects. Unlike Lasso, which introduces shrinkage bias, non-convex penalties like SCAD and MCP yield asymptotically unbiased estimates. In high-dimensional settings with severely correlated instruments, MCP is theoretically and practically superior to SCAD. Its minimax concavity shrinks unassociated coefficients to zero at a faster rate, preventing the over-penalization of true causal signals that share variance. Consequently, MCP ensures greater feature selection stability and computational efficiency in extremely collinear environments.

TL-HDMR: transfer learning for HDMR

Denote the conditional genetic associations in the target dataset as , , , and the conditional genetic statistics in the auxiliary datasets are , , , k=1,2,…, K. Assuming that the IVs selected in different datasets are different and the numbers of IVs are , the total number of IVs in the auxiliary datasets is . The model in the target dataset is

The model in the k-th auxiliary dataset is

We propose TL-HDMR, an algorithm designed to enhance the accuracy of causal estimands in the target population by transferring information from auxiliary source populations. TL-HDMR builds upon the core idea of the Oracle Trans-Lasso algorithm proposed by Li et al. [63] The algorithm comprises two steps. The first step is the transferring step, in which an initial estimator is computed using all the informative auxiliary and target datasets. However, its probabilistic limit is generally biased away from , since under typical conditions. This bias is then corrected in the second step using the target data.

The causal effects between the target and auxiliary populations may be either identical or different. When the causal effects are identical, we can directly use the auxiliary populations and leverage the aforementioned TL-HDMR algorithm for transfer to achieve higher accuracy. However, when the causal effects differ, it becomes necessary to filter the auxiliary population to exclude incompatible subsets [63]. The difference of causal effects between target and the k-th auxiliary dataset is, TL-HDMR assumes that if and , where s is the number of true causal exposures, then the k-th auxiliary dataset is transferable. This assumption means that the difference is -sparsity at most h, i.e. is a sparse high-dimensional vector whose -norm is no longer than h. However, in practical applications, the true value of s is unknown. Following we provide the HDMR.TSD method to select the informative auxiliary dataset.

HDMR.TSD: transferable source detection

Here we present a transferable source detection algorithm termed HDMR.TSD using data-driven strategy [18], to achieve the optimal accuracy. The procedure of this detection algorithm is outlined as follows. First, the target data are divided into three folds—denoted as —though other numbers of folds are also permitted. Next, the TL-HDMR algorithm is applied to each source dataset in combination with every pair of target data folds. For a given loss function, its value is computed on the held-out fold of the target data, and the average cross-validation loss is obtained for each source. As a benchmark, HDMR is fitted on each pair of target folds, and the corresponding loss is evaluated on the remaining fold; the average cross-validation loss is regarded as the target-specific loss. Finally, the difference between and is computed and compared against a predefined threshold. Sources whose difference falls below this threshold are selected and included in the transfer set . This threshold is defined by the parameter , which can be chosen using the AIC criteria:

where RSS is calculated by , and .

HDMR.PRESSO: detection of invalid instruments

The assumption A2 and A3 are easily violated in the applications. We integrate the HDMR into the framework of MR-PRESSO [17] to remove the invalid IVs. Algorithm 3 outlines the HDMR.PRESSO procedure. The HDMR.PRESSO algorithm detects outlier IVs by first refitting the HDMR model after sequentially removing each variant j to obtain causal estimates . For each variant, the RSS is computed between the observed effect size and the model-predicted effect size . This observed RSS is then compared against a simulated null distribution—generated under the assumption of no outliers—by repeatedly drawing effect sizes from multivariable Gaussian distributions around . An empirical P-value is derived by evaluating the position of the observed RSS within the null distribution of expected RSS values, and a Bonferroni correction is applied by multiplying the P-value by the number of variants J.

Simulation setting

Data generation process for k-th datasets (k=0,1,…, K) is:

1. Generate the true conditional effects of G-X by standard normal distribution for p=1,2,…, P.

2. Generate the LD matrix using autoregressive model with .

3. Set the proportion of genetic variability in exposure, , and rescale the effect according to , .

4. Generate the observed exposure GWAS estimates (marginal effects) , where is the Cholesky decomposition of the LD matrix .

5. Set the true causal effects in the target dataset, the proportion of non-zero elements is 10% and their effects are 0.05; the causal effects in the auxiliary datasets are generated by .

6. Generate the conditional effects of G-Y by .

7. Generate the observed outcome GWAS estimates (marginal effects) .

To ensure practical relevance, parameter values were selected to reflect realistic epidemiological scenarios. We set K =3, and the number of exposures P=100 to mimic high-throughput omics networks. To reflect the real-world Eurocentric bias where target cohorts are typically underpowered, target sample sizes ( =500, =5000) were deliberately generated to be smaller than the auxiliary sources (, ). The LD between SNPs was set to =0.2, 0.5 and 0.8, representing typical genomic block structures, with the number of IVs =50, 80 or 120 and To capture varying degrees of biological co-regulation among exposures, conditional effects were generated using a multivariable normal distribution with maximum correlations () of 0.2, 0.5 or 0.8. Genetic correlations between datasets were similarly parameterized to reflect shared genetic architectures across populations.

To evaluate HDMR.TSD under cross-ancestry heterogeneity, we simulated K =10 candidate sources: five informative ( =0.05) and five spurious ( =0.2), emulating varying degrees of evolutionary divergence. For HDMR.PRESSO, we generated 200 IVs including 20% invalid IVs to emulate the pervasive horizontal pleiotropy characteristic of complex traits. Finally, two sensitivity scenarios assessed robustness under non-ideal conditions. First, mimicking an extreme violation of the sparsity assumption, 50% of exposures exhibited dense but small causal divergences (). Second, to evaluate weak instrument bias commonly seen in modest GWAS yields, we systematically tested extreme to mild weak IV settings (=0.01 and 0.03).

We evaluated the performance of the method using the ROC curve, the MAE, estimation bias, and CP. The ROC curve was constructed via cross-validation over a range of lambda values from e⁻¹⁵ to e⁵. The ROC metric reflects the accuracy of variable selection across different methods, while MAE measures the precision of causal effect estimation. Furthermore, estimation bias was utilized to assess the accuracy and unbiasedness of the identified causal effects, and CP was utilized to evaluate the reliability of the constructed confidence intervals. The detailed sparsity-aware bias-corrected bootstrap procedure for calculating CP is described in Supplementary Note S1. The entire simulation was repeated 200 times independently to ensure robustness. The compared methods include: (a) Traditional HDMR approaches—specifically, Equation (2)—with three penalty terms named LDA.Lasso, LDA.Elas and LDA.MCP, implemented using only the target dataset; (b) The same three penalized HDMR models as in (a), enhanced with our TL-HDMR method to incorporate both the target and auxiliary datasets; (c) An adaptation for cases where some auxiliary datasets are unavailable, using the HDMR.TSD algorithm to select suitable auxiliary datasets before applying TL-HDMR; (d) A strategy for handling invalid IVs, where HDMR.PRESSO is first used to remove invalid IVs, followed by TL-HDMR estimation.

Application

Metabolites can reveal key pathological pathways and serve as potential biomarkers for early detection or subtype stratification. Identifying causal metabolites—such as lipids or inflammatory mediators—could inform targeted prevention strategies and support the development of personalized interventions. Therefore, we apply TL-HDMR for investigating causal relationships between 899 metabolites and stroke as well as its subtypes. We use GWAS summary statistics from four ancestries: African (AFR), East Asian (EA), South Asian (SA) and European (EUR). GWAS summary statistics for metabolites were extracted from Chen et al. [64], who conducted transethnic and ancestry-specific GWASs from four populations (>8000 European, >100 East/South Asian, >60 African). GWAS summary statistics for stroke and its four subtypes were extracted from Mishra et al. [65] with >1 200 000 European, >200 000 East Asian, >8000 South Asian and >20 000 African. The details are shown in Supplementary Data 1 and 2.

Figure S29 outlines the procedure for IV selection and statistical analysis. For each metabolite, we selected SNPs with a GWAS P-value below 5 × 10⁻⁸ as IVs. If no SNP reached this threshold, the most significant SNP was chosen. We then took the union of all candidate IVs and retained only those present across all databases, including 899 metabolite- and five stroke (and its subtypes)-related GWAS summary datasets. This process yielded 552 metabolites (Supplementary Data 3) with IVs available in every database. Further population-specific filtering resulted in 523 IVs in South Asians, 538 in Africans, 536 in East Asians, and 411 in Europeans, noting that some SNPs served as IVs for multiple metabolites (Supplementary Data 4-7). Since TL-HDMR allows for non-zero LD between SNPs, no LD clumping was performed. We subsequently extracted GWAS summary statistics for these SNPs corresponding to each metabolite and stroke outcome. LD reference panels for four ancestries were derived from 1000 Genomes Project Phase 3, and were used to transform the marginal genetic associations into conditional associations. Each ethnic group was alternately treated as the target dataset, with the remaining three serving as candidate auxiliary datasets.

We first applied conventional HDMR using the target dataset alone. We then integrated target and auxiliary datasets by: (i) removing invalid IVs using HDMR.PRESSO, (ii) selecting informative auxiliary datasets with HDMR.TSD, and (iii) performing causal variable selection and causal effect estimation via TL-HDMR. λ is chosen by 10-fold cross validation from the range from e⁻¹⁰ to e⁻². The parameter is set to 1.6. For the pathway enrichment analysis of metabolites, we performed Over-Representation Analysis (ORA) using the MetaboAnalyst tool. The pathways were sourced from the RaMP-DB library, which includes 3694 metabolite and lipid pathways from RaMP-DB (integrating KEGG via HMDB, Reactome, and WikiPathways). All results are shown in Supplementary Data 8 and 9.

To clarify the analytical pipeline for biological interpretation, we emphasize that the TL-HDMR framework operates strictly at the individual metabolite level and does not algorithmically prioritize specific pathways. The pathway enrichment results presented in our study were derived through a structured post-hoc analysis. First, for each stroke outcome, we iteratively applied TL-HDMR—treating one ancestry as the target and the others as auxiliary sources—to robustly identify causal metabolites within that specific population. Second, we cross-referenced the selected causal metabolites across all ancestries to systematically isolate shared causal intersections from ancestry-unique biomarkers. Finally, ORA was conducted on these categorized metabolite sets independently. A parallel comparative pipeline was applied across different stroke subtypes to delineate subtype-specific metabolic pathways. Through this hierarchical workflow, any enriched shared pathways are strictly driven by cross-ancestry consistent metabolites rescued by the transfer learning framework, while population- or subtype-specific pathways are driven entirely by distinct biomarkers preserved by the HDMR.TSD algorithm.

Key Points

• A novel statistical framework for genetic causality. TL-HDMR is built on a rigorous two-step transfer learning architecture combined with the Minimax Concave Penalty, providing a statistically robust solution to the challenges of high-dimensionality and correlation in exposure data.

• Promotion of Health Equity. The method is designed to improve the generalizability and fairness of causal inference in genomics, directly addressing the bias in current genetic databases by enabling reliable inference in non-European populations.

• Broad utility across omics domains. While applied here to metabolomics and stroke, the statistical framework of TL-HDMR is generalizable to proteomics, transcriptomics, and other high-dimensional phenotypes, making it a scalable tool for cross-omics causal discovery in diverse populations.

Acknowledgement and Funding

This work for LH was supported by the National Natural Science Foundation of Shandong province (Grant No. ZR2026QC1185). This work for HC was supported by the National Natural Science Foundation of China (Grants No. 82404378 and No. T2341018), Young Scholars Program of Shandong University, Young Talent of Lifting Engineering for Science and Technology in Shandong, China. This work for FX was supported by the National Natural Science Foundation of China (Grant No. 82330108).

Author contributions

FX and HC contributed to conceptualization. LH and HC performed methodology and software (including theoretical derivation and simulation), with XZ providing validation. HC and XZ contributed to data curation for the application. The original draft of the manuscript was written by LH and HC with input from all authors, and writing – review & editing was carried out by LH, HC, and FX. All authors have read and approved the final manuscript.

Data availability

The GWAS summary statistics for 899 metabolites and five stroke-related traits are publicly available through GWAS Catalog. All dataset accession IDs are comprehensively listed in Supplementary Data 1-2.

Competing interest

The authors declare no competing interests.

Code availability

The R package TL.HDMR is available in the GitHub repository at https://github.com/hhoulei/TLHDMR. All code for simulation is available in the GitHub repository at https://github.com/hhoulei/TLHDMR_Simul. All the analyses in our article were implemented in R software (version 4.5.1). The R packages used in our analysis include MASS, ncvreg, mrcovreg, glmnet, foreach, doParallel, doMC and ggplot2.