Model for multi-tissue TWAS fine-mapping of binary traits

We consider a genome-wide association study (GWAS) of a binary trait conducted on n individuals, where represents the n-vector of binary phenotypes. Our objective is to use transcriptome-wide association study (TWAS) fine-mapping to identify genes whose genetically regulated expression (GReX) is associated with the trait and to prioritize the tissues most relevant to these associations. Different from existing single-tissue TWAS fine-mapping methods [5–7,15], we leverage tissue-specific GReX constructed from multiple tissues and jointly model all gene-tissue pairs within a defined genomic region, while explicitly accounting for the binary nature of the outcome trait. To do so, we consider K different tissues and examine genomic regions one at a time. For each genomic region of focus, we assume there are M genes in total and denote as the number of genes with GReX constructed in tissue k (). These GReX values are assumed to have been pre-computed using standard transcriptome prediction frameworks such as PrediXcan [2]. Let denote the corresponding GReX matrix for these genes across n individuals in tissue k. We then define the overall GReX matrix as an n × p matrix for all p gene-tissue pairs in that region as the concatenation of the K tissue-specific GReX matrices: , where . We denote as an n × s genotype matrix for the same n individuals, capturing all the s SNPs within the region of focus. We further denote as an n × c covariate matrix for the same n individuals, covering covariates like age, sex, and principal components. To facilitate computation, we center and standardize each column of , , and to have a mean of zero and a standard deviation of one following [16].

To accommodate the binary nature of the trait, we consider the following probit model linking the GReX to the binary outcome:

Here is the binary trait for the i’th individual; is a p-vector of GReX for p gene-tissue pairs for the i’th individual (i.e., the i’th row of ); is a p-vector of corresponding effect sizes for the gene-tissue pairs; is an s-vector of genotypes for the i’th individual (i.e., the i’th row of ); is an s-vector of corresponding effect sizes for SNPs, also known as the horizontal pleiotropic effects, capturing the SNPs’ effects on the trait not mediated through gene expression; is a c-vector of covariates for the i’th individual (i.e., the i’th row of ); is a c-vector of corresponding effect sizes for covariates; is a scalar representing the intercept; and is the cumulative distribution function (CDF) of the standard normal distribution.

The model above can be equivalently re-parameterized using a liability threshold framework. Specifically, following [17], we introduce a latent variable for each individual , representing their underlying liability. This yields the following equivalent latent variable representation of Equation (1):

(2)

(3)

The above formulation explicitly distinguishes between the effects mediated by tissue-specific gene expression () and those arising from horizontal pleiotropy () and other covariates (). Among them, the horizontal pleiotropic effects from SNPs are captured by the effect size vector , which represents the aggregate direct effects of genetic variants on the phenotype that are not mediated by the predicted expression features in . While explicit inclusion of the genotype matrix accounts for the correlation structure among SNPs, we further model the potential correlation among elements of using a Bayesian ridge regression framework. Specifically, we place an independent and identically distributed (i.i.d.) Gaussian prior on the SNP‐effect vector across the s SNPs following [18]:

(4)

where we further assume that follows a conjugate and weakly informative inverse-gamma prior . By using a ridge penalty induced by the Gaussian prior, the model robustly handles the high multicollinearity inherent in genotype data, while ensuring that our variable selection mechanism (SuSiE) remains focused on the primary features of our interest, the gene-tissue pairs.

For the intercept , we assume a normal distribution: , where as a non-informative prior. For the effect sizes on covariates, we also assume a normal distribution: , where . Both of them follow the common practice in Bayesian approaches, which is equivalent to treating them as a fixed effect.

Decomposition of gene-tissue pair effects

Our goal is to identify the potential causal gene-tissue pair underlying the trait through inferring the tissue-specific posterior probability that the GReX of each gene is associated with the trait. A critical challenge in identifying causal signals is the high correlation among the predicted expression levels (GReX) of genes located in the same linkage disequilibrium (LD) region. Standard marginal association approaches often implicate large blocks of correlated genes, obscuring the true causal drivers. Our model resolves this ambiguity by assuming only a small subset of the p possible gene-tissue pairs displays non-zero effects. To capture this sparse structure, we adopt the Sum of Single Effects (SuSiE) prior [19] for the gene-tissue effect sizes in Equation (3), which is decomposed as a sum of L single-effect components:

(5)

Here we assume that there are at most L gene-tissue pairs in the region with non-zero effects (L is set to be 10 in the present study following [19]). Each term is a single‐effect component, where is a scalar effect‐size parameter following a normal prior , for . For the l’th single-effect component (), we use a p-vector of binary indicators to indicate which gene-tissue pair is responsible for the l’th component: the element in that corresponds to the l’th non-zero effects is 1 while all the other elements in are 0’s. We further assume a prior distribution , allowing each single effect to correspond to a specific column of . Here, the prior non-zero probability for each element of is determined by each element of the p-vector . The structure of will be introduced in the following section.

By modeling the total GReX as a sum of L distinct, sparse components, the framework forces correlated gene-tissue pairs to compete for inclusion in the model. Importantly, inference is performed directly on the design matrix using regularized updates, ensuring numerical stability even when predictors are highly collinear or rank-deficient. During the variational inference procedure (will be introduced in the following sections), the posterior probability assigned to any specific gene-tissue pair is calculated conditional on the effects of all other selected features. This conditional updating, together with the sparsity-inducing SuSiE prior, enables the model to effectively fine-map the signal by assigning high posterior probability only to those pairs that provide additional explanatory power beyond correlated alternatives. In cases of extreme collinearity (e.g., nearly identical predictors across tissues), the model appropriately distributes posterior inclusion probability across indistinguishable features rather than producing unstable estimates, while shrinking the effects of non-causal neighbors that are correlated due to LD toward zero.

Hierarchical prior for variable selection

To infer causal probabilities at both the gene and gene-tissue pair levels, we first define as the j’th element of the p-vector as defined in the preceding section. Here, the j’th index corresponds to the specific pair of the k’th tissue and the m’th gene, thus for K tissues and M genes. The prior probability , represents the probability that the j’th gene-tissue pair is responsible for the l’th single-effect component. We define this prior in a hierarchical fashion. Specifically, following [20], we first denote the vector of prior probabilities for selecting each of the M unique genes as an M-vector . For the m’th unique gene , we then denote the corresponding vector of prior probabilities for selecting each tissue given that the gene has been selected as a K-vector . Afterwards, we assume a priori on as:

(6)

where is ensured to be 1 under this structure.

We further specify Dirichlet priors on the gene-level probability vector and on each of the tissue probability vectors : and , to represent an uninformative starting belief that all genes, and all tissues within a gene, are equally likely to be selected. This choice is statistically motivated for two primary reasons. First, the Dirichlet distribution’s support is the probability simplex, which is the valid domain for probability vectors that must sum to one. Second, and critically for computational feasibility, it is the conjugate prior for the categorical selection process. This property of conjugacy ensures that the posterior distributions of the probability vectors remain in the Dirichlet family, making their estimation tractable within our following variational Bayes inference, and allowing the model to learn data-driven, gene- and tissue-specific probabilities empirically.

Scalable variational inference

With the above model settings, our goal is to infer the posterior probability that each element of equals one. This is achieved through the posterior estimates of the nested vectors and , which together enable the identification of causal genes, and subsequently, the causal tissues underlying these genes. To ensure scalable inference, we developed a variational Bayes algorithm. Specifically, we denote as the set of hyperparameters defined in the preceding section, where , and as the latent vector containing all ’s defined in Equations (2) and (3). We then employ an empirical Bayes approach to obtain an estimate of (details in the S1 Text). With the estimated , we approximate the complex conditional posterior distribution using an approximate conditional posterior distribution of .

We first assume that the approximate conditional posterior distribution is in the form of the following factorization:

(7)

This equation specifies the structural decomposition of the approximate conditional posterior distribution , encapsulating the mean-field independence assumptions required to render the inference computationally tractable. Following the common practice in Bayesian approaches for the simplicity of the notations, we omitted the conditioning on in Equation (7) as well as in the following text. Observed data like , , and enter the model through the coordinate ascent variational inference (CAVI) updates, where the optimal parameter values for each factor are derived by maximizing the evidence lower bound (ELBO).

Here, Equation (7) contains eight components: , , , , , , , and . For the approximate posterior , we assume it follows a truncated normal distribution, whose parameters are updated based on the observed binary trait . For the approximate posterior , we assume it follows a normal distribution, given has a normal prior as well as the normal-normal conjugation. Similarly, for the approximate posterior and , we assume each of them follows a multivariate normal distribution, given its multivariate normal prior defined earlier. For the approximate posterior , we assume it also follows a normal distribution for . For the approximate posterior , we assume it is in the form of a multinomial distribution, with

(8)

where the p-vector represents the posterior probability that each gene-tissue pair represents the l’th non-zero effect, and the corresponding estimate is known as the posterior inclusion probability (PIP). For the approximate posteriors and , both are assumed to follow the Dirichlet distributions, and the posterior Dirichlet distribution over the M unique genes is used to obtain the gene-level PIP. With the specified form of the approximate posterior , we aim to minimize its Kullback-Leibler (KL) divergence with the actual posterior . Minimizing the KL divergence is equivalent to maximizing the evidence lower bound (ELBO), which can be achieved by an iterative Bayesian stepwise selection algorithm following the strategy of SuSiE [19]. The detailed inference steps for each parameter are provided in the S1 Text.

Calculation of posterior inclusion probability (PIP)

To obtain the association evidence of each gene-tissue pair, we calculate the posterior probability that the j’th gene-tissue pair has a non-zero effect, or , which equals to that the j’th gene-tissue pair is selected by at least one of the L single-effect components. Within our variational approximation, we assume the selections for each component are independent in the posterior. Thus, we first calculated the posterior probability that none of the L single-effect component selects the j’th gene-tissue pair:

(9)

and the PIP for the j’th gene-tissue pair can be calculated as:

(10)

To obtain the association evidence of each gene, we calculate the overall posterior probability that the gene is involved in the phenotype through at least one of its tissues, or . Within our variational approximation, the parameter vector represents the probabilities of selecting each gene, so we can naturally estimate the gene-level PIP using the posterior mean of the corresponding gene selection probability. Specifically, assuming the final approximate posterior distribution for is: , and , we have:

(11)

The PIP in our model serves as an important measure of evidence for the gene or gene-tissue pair associated with the outcome trait. We refer to our method and inference algorithm as the multi-tissue Fine-mApping of causal genes for BInary Outcomes (mFABIO). mFABIO is implemented as an R package, freely available at https://superggbond.github.io/mFABIO/.

Simulations

We conducted simulations to assess the performance of mFABIO and compare it with four single-tissue TWAS fine-mapping methods (FABIO, FOCUS, GIFT, cTWAS) and one multi-tissue method (TGFM). We used real genotype data from the UK Biobank, simulating both gene expression and a binary outcome trait. Specifically, we randomly sampled 50,000–250,000 individuals of European ancestry in UK Biobank to serve as the GWAS data and another 500–10,000 individuals of European ancestry (disjoint from GWAS samples) to serve as the eQTL mapping data. Our simulations focused on 426,593 SNPs on chromosome 1, which were partitioned into 133 independent LD blocks using LDetect [21], following the same procedure of [5–7,15]. From these, we randomly selected 50 LD blocks, each containing at least five genes. Within these selected blocks (containing 5–43 genes per block; mean = 16, median = 13), we extracted cis-SNPs located within 100 kb upstream of the transcription start site (TSS) and 100 kb downstream of the transcription end site (TES) of each gene, following [6,15]. We retained 789 genes that had at least 10 cis-SNPs, and these were used for the following simulations.

We then simulated the genetic architecture of gene expression across multiple tissues in both the GWAS and eQTL mapping panels. Following [11], we simulated all 789 selected genes to be expressed in three tissues and designated 50% of these gene-tissue pairs as cis-genetically heritable. For each heritable pair, we randomly assigned five causal cis-SNPs: three shared across tissues and two specific to each tissue, and assumed each causal cis-SNP to explain a fixed proportion of gene expression variance. Following [15,22], we denoted the proportion of gene expression variance explained by genetic effects for each heritable gene-tissue pair as . While all expressed gene-tissue pairs were considered during fine-mapping, only these heritable pairs were assigned simulated causal effects on the final trait. In the eQTL mapping panel, we applied SuSiE to the corresponding real genotypes and simulated gene expression data to generate prediction models for each gene-tissue pair.

We simulated the binary trait in the GWAS panel using a logistic regression model based on the simulated gene expression data. The probability of the binary trait for the i’th individual was determined by a latent variable as:

(12)

The latent variable links the trait to the predicted gene expression and is defined as a weighted sum of causal gene effects across three tissues, following the structure from [23]:

(13)

where is an intercept that controls the case:control ratio as it equals to the expectation of log(case#/control#); , , are the contributing weights for each tissue, with ; is an -vector of simulated gene expression of the selected causal gene-tissue pairs for the i’th individual in the corresponding tissue. For each tissue, we randomly selected causal gene-tissue pairs from the heritable pairs, and denote the proportion of the phenotype’s variance explained by each causal gene-tissue pair as , following [15,22]. And is an -vector of genes’ causal effect sizes in the corresponding tissue, with each element set to be: , following [15,22]. Notably, we intentionally used a logistic regression model instead of a probit model to assess our method’s performance under model misspecifications.

In the simulations, we first examined the calibration of test statistics from different methods under the null simulation settings, where we set so that none of the gene-tissue pairs were associated with the trait. Besides the null simulations, we also examined the power of different methods on detecting the causal genes among tissues under the alternative simulation settings with non-zero . For both the null and alternative simulations, we started from a baseline simulation setting and then varied one parameter at a time on top of the baseline setting to examine the influence of different parameters. Specifically, for , we set it to be 5%, 7.5%, 10% (baseline setting), following the same settings of [11]. For the number of causal cis-SNPs for each heritable gene-tissue pair, we set it to be either 5 (baseline setting), or a random number between 3 and 7 (inclusive) following [11]. For , we varied its value to be either 0% (null setting), 0.2%, 0.4% (baseline setting), or 0.6% following [15,22]. For the number of causal genes per tissue (), we fixed it to be 10 following [15]. In terms of the contributing weights for each tissue, we considered three settings following [23]: (1) ; (2) (baseline setting); and (3) . For the binary trait, we examined different case:control ratios by varying the intercept , using 1:1 as the baseline setting () while exploring other ratios of 1:10 (), and 1:50 (). Furthermore, we extended the baseline setting to incorporate horizontal pleiotropy, allowing SNPs to affect the trait independently of the modeled gene expression. Following [24], we assumed a total phenotypic heritability of 0.1, and set the variance explained by GReX effects to 4% same as our baseline setting, distributed as 0.4% per pair across 10 causal gene-tissue pairs. Consequently, the remaining genetic variance (6%) was assigned to SNP horizontal pleiotropy. To model these effects, we included all SNPs within the LD region, consistent with the ridge regression assumptions outlined in Equations (2)-(4). We also evaluated how the sample sizes of the GWAS study panel and the eQTL reference panel affect the performance of the methods. Specifically, we varied the GWAS sample size from 50K (baseline) to 100K, 150K, 200K, and 250K, and the eQTL reference sample size from 500 (baseline) to 1K, 5K, and 10K, while keeping all other parameters fixed at their baseline values.

We performed 100 simulation replicates for each simulation setting. In each replicate, we applied all methods, except TGFM, to analyze one LD block at a time following their design. TGFM was applied to each chromosome, as its software is specifically designed to internally partition chromosome-level data into overlapping 3 Mb loci for analysis, and modifying it to analyze LD blocks defined differently is technically challenging. For multi-tissue methods (mFABIO and TGFM), we directly applied them on gene-tissue pairs, while for single-tissue methods (FABIO, FOCUS, GIFT, and cTWAS), we applied them in two ways: (1) applied them on each tissue with corresponding tissue-specific predicted gene expression levels following their original designs, then combined the results across tissues; (2) naturally extended their designs to analyze gene-tissue pairs jointly, by preparing the gene-tissue pair level input files of cis-predicted expression models, and then applied them on gene-tissue pairs. We refer to the resulting methods in (2) as FABIO-gt, FOCUS-gt, GIFT-gt, and cTWAS-gt, respectively. In either approach, we summarized the results across simulation replicates. In the analysis, we first examined the calibration of test statistics from different methods under the null simulation settings, by examining the number of false discoveries at an estimated false discovery rate (FDR) of 0.05. The calculation of the estimated FDR will be introduced in the following paragraph. We then evaluated the power of different methods at the FDR of 0.05 under the alternative simulation settings. Since we knew the ground truth in the simulations, we first compared the power of different methods under a true FDR threshold of 0.05. Specifically, to compute the true FDR in the simulations, we first divided 100 simulation replicates into five groups, with 20 replicates per group. In each group, we obtained the test statistics from each method for all gene-tissue pairs across the 20 replicates, either in the form of p-values or PIPs. For each method in turn, we sorted the test statistics from the most significant (i.e., the smallest p-value or the largest PIP) to the least significant (i.e., the largest p-value or the smallest PIP). For each ordered test statistic in the sorted list, we counted the number of false positives detected above the threshold defined by this specific test statistic. The number of false positives, divided by the total number of gene-tissue pairs called significant at that threshold, is the true FDR. We then determined threshold that corresponds to a true FDR of 0.05, based on which we further calculated power. Power is calculated as the number of true positives above the threshold in the sorted list divided by the total number of causal gene-tissue pairs. Afterwards, we obtained the average power across five groups to minimize stochasticity [6,15,22].

We also compared the methods at gene level. For multi-tissue methods mFABIO and TGFM that output gene-level PIPs, we directly used the same way to calculate the power at a true FDR of 0.05, based on the gene-level PIPs. For single-tissue methods FABIO, FOCUS, and cTWAS that only output PIPs at gene-tissue pair level, we first estimated the gene-level PIP by calculating the probability that the gene is causal in at least one tissue with the assumption of independence: . Then we calculate the power at a true FDR of 0.05, based on the estimated gene-level PIPs. For single-tissue method GIFT that only outputs p-values at gene-tissue pair level, we first estimated the gene-level p-values using Fisher’s method [25] to combine the p-values with the assumption of independence. Then we calculated the power at a true FDR of 0.05, based on the estimated gene-level p-values.

Because we can only compute the true FDR in the simulations but not in the real data, we also compared the power of different methods under an estimated FDR threshold of 0.05. We estimated FDR using different approaches: the Benjamini-Hochberg approach [26] to estimate FDR using p-values from the frequentist method (GIFT), and the local FDR approach [27] to estimate FDR using PIPs from the Bayesian methods (mFABIO, TGFM, FABIO, FOCUS, and cTWAS). Specifically for the local FDR approach, we first calculated the local FDR for all the gene-tissue pairs, which is effectively 1-PIP [6,15]. We then sorted gene-tissue pairs based on these local FDRs from small to large. For each gene-tissue pair in turn, we estimated FDR for that pair by aggregating the local FDRs from the first pair up to that pair in the sorted list. Afterwards, we identified the cutoff value of PIP/local FDR that corresponds to a targeted FDR threshold of 0.05. This is the significant threshold we use that corresponds to an estimated FDR of 0.05. We also compared the methods at gene level, by first estimating the gene-level PIPs or p-values as illustrated previously, and then we calculated the power at an estimated FDR of 0.05.

Real datasets

Real data application

We performed fine-mapping on six binary disease traits through integrating the GTEx cis-predicted expression models on different meta-tissues with the UKBB genotype data. The examined disease traits include asthma, breast cancer, gout, hypertension, prostate cancer, and rheumatoid arthritis. These disease traits were selected following [15,29] and have a wide range of prevalence (0.02 to 0.38). For the two sex-related traits (breast cancer and prostate cancer), we limited our analysis to female individuals (for breast cancer) or male individuals (for prostate cancer). For a given trait in UKBB, we kept all individuals of European ancestry with self-reported case status of that trait in the GWAS data. Same as the simulations, SuSiE-based cis-predicted expression models were used for all the comparing methods (mFABIO, TGFM, FABIO, FOCUS, GIFT, and cTWAS). For the multi-tissue methods mFABIO and TGFM, we directly used the cis-predicted expression models from all 38 meta-tissues. In contrast, for the single-tissue methods (FABIO, FOCUS, GIFT, and cTWAS), we naturally extended their designs to analyze gene-tissue pairs jointly, a strategy that showed superior performance in simulations over single-tissue analyses. Same as the simulations, we prepared the gene-tissue pair level input files of cis-predicted expression models, and then applied them on gene-tissue pairs. The genotype input data was then prepared based on each method’s design. For mFABIO and FABIO, which are built for binary outcomes, we used individual-level GWAS genotypes. For the other four methods (TGFM, FOCUS, GIFT, and cTWAS), which require summary statistics, we generated these by performing a logistic regression on the GWAS data using PLINK 2.0 [30], adjusting for the top 10 genotype PCs and sex. We then paired either the individual-level GWAS or the GWAS summary statistics with the variant weights from cis-predicted expression models as input, and analyzed 1,433 independent LD blocks [21] across all 22 autosomal chromosomes one at a time, except for TGFM. We applied TGFM to 2,682 overlapping 3 Mb loci spanning the entire genome following its own design. We also performed marginal TWAS analysis for each tissue-disease pair using FUSION [1] with the same GWAS summary statistics and the variant weights. For a fair comparison across methods, we used an estimated FDR threshold of 0.05 for all methods to declare significance, as described in detail in the simulations.

To assess the robustness of mFABIO when eQTL reference panels originated from independent cohorts, we used the same UK Biobank hypertension dataset and replaced the GTEx whole blood eQTL panel (n = 320) with a pseudobulk PBMC eQTL panel (n = 113; SNP weights available at https://doi.org/10.7910/DVN/8UL8XB), while keeping all other tissue models from GTEx unchanged. To ensure comparability, the PBMC panel was restricted to European-ancestry samples and harmonized to the same genomic reference build and variant set used in GTEx. Gene expression normalization procedures were matched to those used in GTEx, and allele alignment and variant harmonization were performed by the panel’s publisher to ensure consistency with the GTEx reference models. This resulted in 628 genes modeled in both panels, comprising 538,801 SNPs.

To validate our findings, we further evaluated whether significant gene-tissue pairs (estimated FDR < 0.05) were enriched in tissues with known disease relevance. We established this relevance by querying PubMed for publications over the last 10 years for each disease-tissue combination. The three GTEx tissue categories with the highest publication counts for each disease were designated potentially “disease-relevant”. This literature review yielded the following classifications:

• • asthma: lung, skin (GTEx tissues: Skin_Sun_Exposed_Lower_leg and Skin_Not_Sun_Exposed_Suprapubic), and blood (GTEx tissue: Whole_Blood)
• • breast cancer: breast mammary tissue, blood (GTEx tissue: Whole_Blood), and liver
• • gout: blood (GTEx tissue: Whole_Blood), liver, and skin (GTEx tissues: Skin_Sun_Exposed_Lower_leg and Skin_Not_Sun_Exposed_Suprapubic)
• • hypertension: blood (GTEx tissue: Whole_Blood), heart (GTEx tissues: Heart_Atrial_Appendage and Heart_Left_Ventricle), and artery (GTEx tissues: Artery_Aorta, Artery_Coronary, and Artery_Tibial)
• • prostate cancer: prostate, blood (GTEx tissue: Whole_Blood), and liver
• • rheumatoid arthritis: blood (GTEx tissue: Whole_Blood), fibroblast (GTEx tissue: Cells_Cultured_fibroblasts), and spleen

Based on this classification, we generated the absolute counts and calculated the proportion of each method’s significant gene-tissue pairs that fell within the relevant tissues for a given disease.

Method overview

mFABIO is described in the Materials and Methods section, with technical details provided in the S1 Text and a method schematic shown in Fig 1.

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Fig 1. Schematic overview of mFABIO for multi-tissue TWAS fine-mapping of binary outcomes.

Similar to other existing single-tissue and multi-tissue methods, mFABIO is a two-step TWAS fine-mapping approach that requires the predicted genetically regulated expression (GReX) in the study cohort as input. Shown under the “Input Data” section, mFABIO analyzes one genomic region at a time. For each genomic region containing s SNPs and M genes, mFABIO begins with individual-level genotypes of s SNPs within the region of interest. It also takes as input the SNP prediction weights for each of the M genes, which can be obtained from eQTL mapping cohorts across different tissues using standard methods such as SuSiE. Because each tissue may include a different subset of the M genes, the gene notations in this figure are tissue-specific. The term denotes the weight of the -th SNP for the -th gene in the K-th tissue. These genotypes and SNP weights are then combined to generate predicted GReX for the p gene-tissue pairs in the study cohort. Additionally, mFABIO requires the genotypes of all s SNPs used in the GReX modeling to account for potential horizontal pleiotropic effects. Shown under the “mFABIO” section, mFABIO explicitly models the binary nature of the outcome trait through a latent variable z with a sum of L single-effects prior on the gene-tissue pair effect sizes . It also simultaneously models all gene-tissue pairs on a region of interest to account for the GReX correlation, through the input of individual-level GReX matrix. We apply variational inference to estimate the approximate posterior distribution of the single-effect selection vector , and use the posterior inclusion probability (PIP) as the evidence for the gene-tissue pair associated with the binary outcome trait (“Multi-tissue TWAS Fine-mapping” section). * Icons in this figure were generated using ChatGPT (OpenAI).

https://doi.org/10.1371/journal.pgen.1012157.g001

Briefly, mFABIO is a multi-tissue TWAS fine-mapping method designed to identify gene-tissue pairs whose GReX is associated with a binary trait of interest. Different from existing TWAS fine-mapping approaches, mFABIO explicitly models the binary nature of the outcome trait through a probit model and jointly analyzes genes within a given region across multiple tissues. This joint modeling accounts for GReX correlations among genes and tissues to enhance the power and precision of TWAS fine-mapping. We adapt the variational inference within an iterative Bayesian stepwise selection algorithm of SuSiE, making mFABIO scalable to large biobank scale datasets.

mFABIO controls false signals in null simulations

We first assessed the false positive rates of all methods across eight null simulation settings (, and other parameters were varied one at a time on top of the baseline setting) using an estimated FDR threshold of 0.05. All methods demonstrated well-controlled false positives, identifying fewer than 0.50 false signals on average per replicate at both the gene-tissue pair (S1a Fig) and gene levels (S1b Fig). The multi-tissue methods, mFABIO and TGFM, were particularly stringent, showing no false positives under most settings. The only exceptions were an average of 0.20 false-positive gene-tissue pairs and 0.10 false-positive genes when the case:control ratio was 1:50 for both mFABIO and TGFM, and an average of 0.10 false-positive gene-tissue pairs and 0.10 false-positive genes when there were 3 causal tissues for TGFM; all well below the expected one (0.05 × 20 replicates per simulation group) false signal. The single-tissue methods also exhibited low error rates. On average, their false positive identifications ranged from 0.10 to 0.23 at the gene-tissue pair level and from 0.08 to 0.18 at the gene level across all null scenarios.

mFABIO produces calibrated PIPs and improves power for fine-mapping causal signals in alternative simulations

We then evaluated how calibrated the PIPs/p-values are from different methods in terms of controlling the false discovery rate (FDR) at an estimated FDR threshold of 0.05 in our alternative simulations. Under the baseline setting at the gene-tissue pair level, the actual FDR for multi-tissue methods was well-calibrated to this threshold, with mFABIO and TGFM both at 0.04. In contrast, the actual FDR for all single-tissue methods (FABIO-gt, FABIO, FOCUS-gt, FOCUS, GIFT-gt, GIFT, cTWAS-gt, and cTWAS) was inflated, ranging from 0.13 to 0.16 (S2a Fig). Similar results were observed under different case:control ratios (S2a Fig) and numbers of causal tissue(s) (S2b Fig), as well as other simulation settings (S2c–S2f Fig): across all settings, the actual FDR that corresponds to the estimated FDR of 0.05 was on average 0.04 for both mFABIO and TGFM, while ranged from 0.12 to 0.15 for single-tissue methods. The superiority of the multi-tissue approach was also evident at the gene level, where the average true FDR under an estimated FDR threshold of 0.05 was 0.04 for mFABIO and TGFM, versus 0.11 to 0.14 for single-tissue methods (S3a-S3f Fig).

Next, we evaluated the power of different methods in detecting causal gene-tissue pairs and genes under alternative settings. To ensure a fair comparison that accounts for the previously observed FDR inflation, we first computed the power based on a true FDR threshold of 0.05. We found that mFABIO is more powerful than other methods under all alternative simulation settings. For example, in the baseline setting at a true FDR of 0.05, mFABIO substantially outperformed the other approaches. For identifying causal gene-tissue pairs, mFABIO achieved a power of 34.5%, compared to 27.5% for TGFM and a range of 15.0%-19.0% for the single-tissue methods (Fig 2a). This trend held for identifying causal genes, where mFABIO’s power was 36.3%, versus 28.9% for TGFM and 15.8%-19.5% for the single-tissue methods (Fig 2b).

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Fig 2. Power of different methods under the true FDR threshold of 0.05 across different case:control ratios.

(a) Results at gene-tissue pair level. (b) Results at gene level.

https://doi.org/10.1371/journal.pgen.1012157.g002

We carefully examined the influence of different simulation parameters on the power of different methods. In terms of case:control ratio, we found that the power decreased for all methods as the case:control ratio became more imbalanced. However, the relative performance ranking remained consistent, with the two multi-tissue methods outperforming the single-tissue methods and mFABIO ranking as the most powerful in all conditions. For instance, at the gene-tissue pair level, as the ratio decreased from 1:1–1:10 and 1:50, mFABIO’s power went from 34.5% to 29.0% and 24.5%. Following the same trend, TGFM’s power decreased from 27.5% to 23.0% and 19.5%, while the power for single-tissue methods dropped from a range of 15.0%-19.0% down to 11.0%-13.0% (Fig 2a). A similar trend was observed at the gene level (Fig 2b). Next, we investigated how the number of causal tissues affects the power, and we found that the power of all methods decreased as the number of causal tissues increased from one to three. This was an expected result of our simulation design, as the total effect size across causal gene-tissue pairs was fixed, and scenarios with more causal tissues had a smaller effect size for each pair. Despite this overall power reduction, the performance ranking of different methods remained consistent. At the gene-tissue pair level, mFABIO was the most powerful, with its power decreasing from 41.0% (with one causal tissue) to 29.3% (with three). For comparison, TGFM’s power dropped from 35.0% to 24.3%, while the power range for single-tissue methods fell from 23.0%-28.0% to 14.3%-17.7% under the same conditions (Fig 3a). A similar trend was also observed at the gene level (Fig 3b).

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Fig 3. Power of different methods under the true FDR threshold of 0.05 across different numbers of causal tissue(s).

(a) Results at gene-tissue pair level. (b) Results at gene level.

https://doi.org/10.1371/journal.pgen.1012157.g003

In terms of SNP effects on gene expression (), we observed that the performance of all methods improved with increasing , and their performance ranking remained stable, with mFABIO consistently outperforming TGFM and both multi-tissue methods surpassing the single-tissue methods, at both gene-tissue pair level (S4a Fig) and gene level (S4b Fig). Specifically, for the most challenging setting (), mFABIO still achieved a power of 19.0% at the gene-tissue pair level and 19.5% at the gene level. This was considerably higher than TGFM (15.0% and 15.4%, respectively) and the single-tissue methods (which ranged from 7.5%-10.5% and 7.7%-10.8%, respectively). Additionally, we had a simulation setting fixing at 10% and randomizing the number of causal cis-SNPs, which yielded power trends similar to the baseline setting at both gene-tissue pair level (S4a Fig) and gene level (S4b Fig). Next, we investigated how power was affected by the gene’s effects on the outcome trait (). We found that the power of all methods grew as increased, with mFABIO consistently remaining the most powerful method. At gene-tissue pair level, as was raised from 0.2% to 0.4% and 0.6%, mFABIO’s power rose from 25.5% to 34.5% and 46.5%, respectively. Under the same conditions, TGFM’s power increased from 20.5% to 27.5% and 37.5%. The power range for single-tissue methods also improved, increasing from 11.0%-14.0% to 15.0%-19.0% and finally to 21.0%-26.0% (S5a Fig). A similar trend was also observed at the gene level (S5b Fig). When horizontal pleiotropy was introduced to the baseline setting, the power of each method decreased slightly due to confounding from the pleiotropic effects. However, mFABIO still outperformed other methods at both the gene-tissue pair level (S5a Fig) and the gene level (S5b Fig).

Finally, we evaluated how statistical power changes with increasing GWAS or eQTL panel sample sizes. At the gene-tissue pair level, when the GWAS sample size increased from 50K to 100K, 150K, 200K, and 250K, the power of mFABIO increased from 34.5% to 45.5%, 49.0%, 55.0%, and 59.0%, respectively. Under the same settings, TGFM’s power increased from 27.5% to 37.5%, 41.0%, 45.0%, and 52.5%. The power of single-tissue methods also improved, rising from 15.0%-19.0% at baseline to 27.0%-31.0% when the GWAS sample size reached 250K (S6a Fig). A similar trend was observed at the gene level (S6b Fig). Increasing the eQTL reference panel size also led to improved power. At the gene-tissue pair level, when the eQTL sample size increased from 500 to 1K, 5K, and 10K, the power of mFABIO increased from 34.5% to 40.5%, 57.5%, and 66.5%, respectively, and remained higher than that of all other methods (S7a Fig). The same ranking was observed at the gene level (S7b Fig). Overall, statistical power increased with larger GWAS and eQTL panel sizes, with mFABIO consistently achieving the highest power across scenarios.

The power comparisons described above were based on a true FDR threshold of 0.05, a metric that can only be calculated in simulations. To better mimic a real-data scenario, we also compared power using an estimated FDR threshold of 0.05. We acknowledge this comparison is inherently biased: as shown above, this threshold is well-calibrated for multi-tissue methods but leads to significant FDR inflation for single-tissue methods (S2 and S3 Figs), potentially boosting their apparent power. Despite this unfair advantage, the single-tissue methods did not outperform mFABIO. At the gene-tissue pair level, mFABIO retained the highest power, achieving 34.5% in the baseline setting and averaging 40.0% across all 18 alternative simulations. In comparison, TGFM’s power was 28.5% (baseline) and 33.3% (average), while the single-tissue methods’ power had a range of 22.0%-26.0% (baseline) and 24.0%-27.0% (average). Though the power of single-tissue methods appeared more comparable under this threshold, it came at the cost of excessive false discoveries. The conclusion holds regardless of the case:control ratio (S8a Fig), the number of causal tissue(s) (S8b Fig), the SNP effect on gene expression (S8c Fig), the number of causal cis-SNPs (S8c Fig), and the gene’s effects on the outcome trait (S8d Fig), as well as at the gene level (S9a–S9d Fig). The same conclusion also holds when varying the sample sizes of the GWAS and eQTL panels at both the gene-tissue pair level (S8e and S8f Fig) and the gene level (S9e and S9f Fig). For the single-tissue methods, we also observed that a joint analysis of all gene-tissue pairs by naturally extending their designs was marginally more powerful, than applying them on each tissue and combining the results across tissues. The joint analysis yielded higher average power at both the gene-tissue pair level (24.8%-27.0% vs. 24.0%-24.4%) and the gene level (25.5%-27.5% vs. 24.4%-25.0%). Therefore, we exclusively used this more powerful joint analysis strategy for all single-tissue methods in our subsequent real-data applications.

Application to analyzing binary traits in UKBB

We performed multi-tissue TWAS fine-mapping analysis on six binary disease traits through integrating the GTEx cis-predicted expression models of 38 meta-tissues and the GWAS of UK Biobank (details in Materials and Methods). Specifically, we focused on 13,700 genes and 119,270 unique gene-tissue pairs and examined their associations with each of the six binary traits. The six binary traits include asthma (AS), breast cancer (BRCA), gout (GO), hypertension (HT), prostate cancer (PRCA), and rheumatoid arthritis (RA).

While we did not include age, sex, and principal components as covariates in our main analysis, we assess robustness of such approach by applying mFABIO to the same UK Biobank asthma dataset with and without sex and the top 10 genotype principal components as covariates. The results showed minimal differences between the two sets of analysis: 57 vs. 58 identified genes and 41 vs. 41 identified gene-tissue pairs. For other GWAS summary-statistics-based methods, these covariates had already been adjusted during the generation of GWAS summary statistics, as described in the Materials and Methods.

We first evaluated the results at gene-level among these traits. We identified 1,427 (1,355 unique) GWAS risk genes that contain at least one genome-wide significant SNP (p < 5 × 10⁻⁸) across the six disease traits. We performed the TWAS marginal analysis using FUSION for each pair of meta-tissue and disease trait, and considered those genes that are significant in at least one pair of meta-tissue and trait as TWAS risk genes. We identified a total of 479 (470 unique) TWAS risk genes across the six traits. Overlapping the results from the two analyses leads to a total of 1,766 (1,661 unique) risk genes that contain at least one genome-wide significant SNP or shows marginal TWAS significance (Table 1). We consider these risk genes more likely to be the potentially “true” causal genes compared to the rest.

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Table 1. Gene-level results of multi-tissue TWAS fine-mapping in UK Biobank.

https://doi.org/10.1371/journal.pgen.1012157.t001

Same as what we did in the simulations, we estimated FDR using the test statistics generated by different methods and declared significant gene associations based on an estimated FDR threshold of 0.05 for all methods. mFABIO identified an average of 42 causal genes per disease, with 60.9% of those genes supported by GWAS or TWAS evidence (Table 1). As a comparison, the other multi-tissue method TGFM, identified an average of 29 causal genes per disease, with 52.2% of those genes supported by GWAS or TWAS evidence. Among the four single-tissue methods - FABIO, FOCUS, GIFT, and cTWAS - the average numbers of identified causal genes were 88, 110, 86, and 87, respectively, with corresponding proportions of GWAS/TWAS-supported genes at 25.2%, 17.6%, 23.9%, and 19.0% (Table 1). Although mFABIO and TGFM identified fewer causal gene candidates at an FDR of 0.05 compared to single-tissue methods, the proportions of GWAS/TWAS-supported genes were substantially higher. When considering the total number of GWAS/TWAS-supported genes identified across the six disease traits, mFABIO identified at least 14.9% more than any of the other methods (Table 1). Overall, mFABIO not only outperformed other methods in identifying a greater number of GWAS/TWAS-supported gene candidates, but also achieved the smallest candidate gene set with the highest proportion of supported genes compared to those single-tissue methods, both of which highlighted its superior performance at gene-level.

We then evaluated the identified gene-tissue pairs across different methods. In total, we identified 11,613 (11,076 unique) GWAS risk gene-tissue pairs, where the gene of each pair contains at least one genome-wide significant SNP (p < 5 × 10 ⁻ ⁸) associated with the corresponding trait. Additionally, we identified 2,152 (2,116 unique) TWAS risk gene-tissue pairs that showed significance in our marginal TWAS analysis for each meta-tissue and disease trait pair. Combining these two sets resulted in 13,148 (12,466 unique) risk gene-tissue pairs that either contain a genome-wide significant SNP or show marginal TWAS significance (Table 2). We consider these risk gene-tissue pairs to be more likely representative of the “true” associations with the corresponding disease traits.

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Table 2. Gene-tissue pair-level results of multi-tissue TWAS fine-mapping in UK Biobank.

https://doi.org/10.1371/journal.pgen.1012157.t002

At the gene-tissue pair-level, mFABIO identified an average of 65 causal gene-tissue pairs per disease, with 77.2% of those pairs supported by GWAS or TWAS evidence (Table 2). TGFM identified an average of 38 causal pairs per disease, with 66.7% of those pairs supported by GWAS or TWAS evidence. Among the four single-tissue methods - FABIO, FOCUS, GIFT, and cTWAS - the average numbers of identified causal pairs were 145, 167, 132, and 137, respectively, with corresponding proportions of GWAS/TWAS-supported pairs at 30.1%, 24.9%, 30.3%, and 29.3% (Table 2). Similar to our observations at gene-level, mFABIO and TGFM identified fewer causal gene-tissue pairs at an FDR of 0.05 compared to single-tissue methods, however, the proportions of GWAS/TWAS-supported pairs were substantially higher. Again, if we consider the total number of GWAS/TWAS-supported pairs identified across the six disease traits, mFABIO identified at least 14.8% more than any of the other methods (Table 2). Therefore, mFABIO had superior performance at the gene-tissue pair-level as well.

We further evaluated whether significant gene-tissue pairs (estimated FDR < 0.05) were enriched in the likely disease-relevant tissues based on PubMed literature (details in Materials and Methods). We first compared the absolute number of significant pairs found within these tissues. By this metric, mFABIO identified the most relevant pairs for all diseases except hypertension (Fig 4a). The exception for hypertension is likely due to that, single-tissue methods are confounded by a much larger total number of discoveries, which may include a high rate of false positives as shown in Table 2. To account for this, we calculated the proportion of a method’s significant pairs located in relevant tissues as a more robust metric. This analysis showed that mFABIO achieved the highest proportion of relevant discoveries for every disease (Fig 4b), with an overall average of 29.7%. This average was higher than that of TGFM (27.2%) and substantially higher than the range for single-tissue methods (12.5%–15.5%). These results demonstrate mFABIO’s superior ability to prioritize biologically relevant gene-tissue associations in real-data applications.

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Fig 4. Comparison of significant gene-tissue pairs located in relevant tissues.

(a) Absolute number of significant gene-tissue pairs located in relevant tissues determined by PubMed literature for each method across diseases. (b) Proportion of a method’s significant gene-tissue pairs located in relevant tissues determined by PubMed literature across diseases.

https://doi.org/10.1371/journal.pgen.1012157.g004

We list a few gene-tissue examples that are uniquely identified by mFABIO. The first example is D2HGDH (D-2-hydroxyglutarate dehydrogenase) in lung tissue associated with asthma (gene-tissue PIP = 1, marginal TWAS p-value = 2.9410^-6). D2HGDH has been associated with asthma in a previous GWAS [31] through its cis-SNP rs34290285, which is consistent with our GWAS results on asthma that highlighted the same marker within the gene locus (Fig 5a). And the previous lung eQTL analysis of the top SNPs revealed that the G allele of rs34290285 is associated with reduced expression of D2HGDH mRNA in the lung [31]. This downregulation leads to the accumulation of the metabolite D-2-hydroxyglutarate (D-2HG). Critically, in murine models, accumulating D-2HG was shown to potently suppress key hallmarks of allergic asthma, including airway hyperreactivity, Th2 cell responses, and IgE-mediated inflammation [32]. This provides a direct mechanistic pathway connecting lower D2HGDH expression in the lung to a protective effect against asthma.

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Fig 5. LocusZoom plots of selected gene candidates uniquely identified by mFABIO.

(a) Plot of the corresponding locus with the GWAS p-value of the top cis-SNP rs34290285 in D2HGDH for asthma. (b) Plot of the corresponding locus with the GWAS p-value of the top cis-SNP rs13020413 in CYBRD1 for breast cancer. (c) Plot of the corresponding locus with the GWAS p-value of the top cis-SNP rs1571878 in CCR6 for rheumatoid arthritis. All these LocusZoom plots were generated using [39].

https://doi.org/10.1371/journal.pgen.1012157.g005

The second example is CYBRD1 (cytochrome b reductase 1) in breast mammary tissue associated with breast cancer (gene-tissue PIP = 1). Notably, while the top cis-SNP in its coding region (rs13020413) did not reach genome-wide significance in previous studies and our GWAS (Fig 5b), CYBRD1 was flagged as a significant gene in our TWAS pairing the breast mammary tissue with breast cancer (marginal TWAS p-value = 8.9010^-6). This finding is biologically relevant, as CYBRD1 (also known as DCYTB) plays a crucial role in iron metabolism [33], a process linked to tumor-infiltrating lymphocytes (TILs) and regulated by hypoxia-inducible factor (HIF) in malignant breast cells [34]. Furthermore, CYBRD1 serves as a prognostic marker for breast cancer, as its increased expression is associated with a favorable prognosis and is implicated in regulating cancer cell proliferation and apoptosis [35]. The successful identification of CYBRD1 demonstrates that mFABIO can nominate credible, tissue-specific candidate genes that lack strong statistical support from traditional GWAS.

The third example is CCR6 (C-C chemokine receptor type 6) in spleen associated with rheumatoid arthritis (gene-tissue PIP = 0.98). While the top cis-SNP for CCR6 in our GWAS (rs1571878) was not genome-wide significant (Fig 5c), it has been previously associated with rheumatoid arthritis (RA) in another GWAS study [36]. Also, CCR6 is a significant gene candidate in our TWAS pairing spleen with RA (marginal TWAS p-value = 3.9210^-6). The involvement of the spleen in RA is well-established, as spleen is a major hub for immune activity, and its enlargement is a characteristic of Felty’s syndrome, a known complication of severe RA [37]. This connection is further strengthened by mechanistic evidence from animal models. One study found that in mice with collagen-induced arthritis, regulatory T-cells (Tregs) in the spleen significantly increased their expression of CCR6 compared to the healthy control [38]. This suggests that during arthritic inflammation, splenic Tregs upregulate CCR6, a key receptor that mediates the migration of immune cells to inflammatory sites.

Benchmark of runtime and memory usage

Although mFABIO employs a relatively complex Bayesian inference procedure with a probit link designed for binary outcomes, we observed competitive computational efficiency compared with other methods. In simulations, at the largest simulated GWAS sample size (N = 250,000), mFABIO required approximately 2.66 hours and 8 GB of memory to sequentially fine-map all 50 LD loci in a single simulation replicate. In comparison, summary-statistics-based methods required 1.95-3.78 hours in total, including approximately 1.7 hours to compute GWAS summary statistics and 0.25-2.08 hours for the fine-mapping step. Memory usage for these methods was about 8 GB for GWAS summary statistics computation and 3–6 GB for the subsequent fine-mapping stage.

In real data analysis using 337,198 individuals from the UK Biobank, and utilizing 8 CPU threads, mFABIO required an average of 9.77 hours to sequentially fine-map all LD loci on a single chromosome (with an average of 1,430 cis-SNPs per LD locus, and 65 LD loci per chromosome). By comparison, methods relying on GWAS summary statistics required an average of 7.21 hours per chromosome to generate the necessary GWAS summary statistics, followed by 1.02 hours for fine-mapping with TGFM and 0.90-5.84 hours for single-tissue methods. Regarding memory usage, the peak memory requirement for mFABIO was approximately 10 GB. In contrast, other methods required approximately 16 GB of peak memory during the GWAS summary statistics precomputation step, in addition to 4–8 GB of memory for the subsequent fine-mapping stage.