CoMM-S2: a collaborative mixed model using summary statistics in transcriptome-wide association studies

SR-TWAS: leveraging multiple reference panels to improve transcriptome-wide association study power by ensemble machine learning

Multiple reference panels of a given tissue or multiple tissues often exist, and multiple regression methods could be used for training gene expression imputation models for transcriptome-wide association studies (TWAS). To leverage expression imputation models (i.e., base models) trained with multiple reference panels, regression methods, and tissues, we develop a Stacked Regression based TWAS (SR-TWAS) tool which can obtain optimal linear combinations of base models for a given validation transcriptomic dataset. Both simulation and real studies show that SR-TWAS improves power, due to increased training sample sizes and borrowed strength across multiple regression methods and tissues. Leveraging base models across multiple reference panels, tissues, and regression methods, our real studies identify 6 independent significant risk genes for Alzheimer's disease (AD) dementia for supplementary motor area tissue and 9 independent significant risk genes for Parkinson's disease (PD) for substantia nigra tissue. Relevant biological interpretations are found for these significant risk genes.

An overview of detecting gene-trait associations by integrating GWAS summary statistics and eQTLs

Detecting genes that affect specific traits (such as human diseases and crop yields) is important for treating complex diseases and improving crop quality. A genome-wide association study (GWAS) provides new insights and directions for understanding complex traits by identifying important single nucleotide polymorphisms. Many GWAS summary statistics data related to various complex traits have been gathered recently. Studies have shown that GWAS risk loci and expression quantitative trait loci (eQTLs) often have a lot of overlaps, which makes gene expression gradually become an important intermediary to reveal the regulatory role of GWAS. In this review, we review three types of gene-trait association detection methods of integrating GWAS summary statistics and eQTLs data, namely colocalization methods, transcriptome-wide association study-oriented approaches, and Mendelian randomization-related methods. At the theoretical level, we discussed the differences, relationships, advantages, and disadvantages of various algorithms in the three kinds of gene-trait association detection methods. To further discuss the performance of various methods, we summarize the significant gene sets that influence high-density lipoprotein, low-density lipoprotein, total cholesterol, and triglyceride reported in 16 studies. We discuss the performance of various algorithms using the datasets of the four lipid traits. The advantages and limitations of various algorithms are analyzed based on experimental results, and we suggest directions for follow-up studies on detecting gene-trait associations.

Transcriptome-Wide Association Study Reveals Potentially Candidate Genes Responsible for Milk Production Traits in Buffalo

Identifying key causal genes is critical for unraveling the genetic basis of complex economic traits, yet it remains a formidable challenge. The advent of large-scale sequencing data and computational algorithms, such as transcriptome-wide association studies (TWASs), offers a promising avenue for identifying potential causal genes. In this study, we harnessed the power of TWAS to identify genes potentially responsible for milk production traits, including daily milk yield (MY), fat percentage (FP), and protein percentage (PP), within a cohort of 100 buffaloes. Our approach began by generating the genotype and expression profiles for these 100 buffaloes through whole-genome resequencing and RNA sequencing, respectively. Through comprehensive genome-wide association studies (GWAS), we pinpointed a total of seven and four single nucleotide polymorphisms (SNPs) significantly associated with MY and FP traits, respectively. By using TWAS, we identified 55, 71, and 101 genes as significant signals for MY, FP, and PP traits, respectively. To delve deeper, we conducted protein-protein interaction (PPI) analysis, revealing the categorization of these genes into distinct PPI networks. Interestingly, several TWAS-identified genes within the PPI network played a vital role in milk performance. These findings open new avenues for identifying potentially causal genes underlying important traits, thereby offering invaluable insights for genomics and breeding in buffalo populations.

Leveraging molecular quantitative trait loci to comprehend complex diseases/traits from the omics perspective

Comprehending the molecular basis of quantitative genetic variation is a principal goal for complex diseases or traits. Molecular quantitative trait loci (molQTLs) have made it possible to investigate the effects of genetic variants hiding behind large-scale omics data. A deeper understanding of molQTL is urgently required in light of the multi-dimensionalization of omics data to more fully elucidate the pertinent biological mechanisms. Herein, we reviewed molQTLs with the corresponding resource from the omics perspective and further discussed the integrative strategy of GWAS-molQTL to infer their causal effects. Subsequently, we described the opportunities and challenges encountered by molQTL. The case studies showed that molQTL is essential for complex diseases and traits, whether single- or multi-omics QTLs. Overall, we highlighted the functional significance of genetic variants to employ the discovery of molQTL in complex diseases and traits.

XMAP: Cross-population fine-mapping by leveraging genetic diversity and accounting for confounding bias

Fine-mapping prioritizes risk variants identified by genome-wide association studies (GWASs), serving as a critical step to uncover biological mechanisms underlying complex traits. However, several major challenges still remain for existing fine-mapping methods. First, the strong linkage disequilibrium among variants can limit the statistical power and resolution of fine-mapping. Second, it is computationally expensive to simultaneously search for multiple causal variants. Third, the confounding bias hidden in GWAS summary statistics can produce spurious signals. To address these challenges, we develop a statistical method for cross-population fine-mapping (XMAP) by leveraging genetic diversity and accounting for confounding bias. By using cross-population GWAS summary statistics from global biobanks and genomic consortia, we show that XMAP can achieve greater statistical power, better control of false positive rate, and substantially higher computational efficiency for identifying multiple causal signals, compared to existing methods. Importantly, we show that the output of XMAP can be integrated with single-cell datasets, which greatly improves the interpretation of putative causal variants in their cellular context at single-cell resolution.

Leveraging trans-ethnic genetic risk scores to improve association power for complex traits in underrepresented populations

Trans-ethnic genome-wide association studies have revealed that many loci identified in European populations can be reproducible in non-European populations, indicating widespread trans-ethnic genetic similarity. However, how to leverage such shared information more efficiently in association analysis is less investigated for traits in underrepresented populations. We here propose a statistical framework, trans-ethnic genetic risk score informed gene-based association mixed model (GAMM), by hierarchically modeling single-nucleotide polymorphism effects in the target population as a function of effects of the same trait in well-studied populations. GAMM powerfully integrates genetic similarity across distinct ancestral groups to enhance power in understudied populations, as confirmed by extensive simulations. We illustrate the usefulness of GAMM via the application to 13 blood cell traits (i.e. basophil count, eosinophil count, hematocrit, hemoglobin concentration, lymphocyte count, mean corpuscular hemoglobin, mean corpuscular hemoglobin concentration, mean corpuscular volume, monocyte count, neutrophil count, platelet count, red blood cell count and total white blood cell count) in Africans of the UK Biobank (n = 3204) while utilizing genetic overlap shared in Europeans (n = 746 667) and East Asians (n = 162 255). We discovered multiple new associated genes, which had otherwise been missed by existing methods, and revealed that the trans-ethnic information indirectly contributed much to the phenotypic variance. Overall, GAMM represents a flexible and powerful statistical framework of association analysis for complex traits in underrepresented populations by integrating trans-ethnic genetic similarity across well-studied populations, and helps attenuate health inequities in current genetics research for people of minority populations.

OTTERS: a powerful TWAS framework leveraging summary-level reference data

Most existing TWAS tools require individual-level eQTL reference data and thus are not applicable to summary-level reference eQTL datasets. The development of TWAS methods that can harness summary-level reference data is valuable to enable TWAS in broader settings and enhance power due to increased reference sample size. Thus, we develop a TWAS framework called OTTERS (Omnibus Transcriptome Test using Expression Reference Summary data) that adapts multiple polygenic risk score (PRS) methods to estimate eQTL weights from summary-level eQTL reference data and conducts an omnibus TWAS. We show that OTTERS is a practical and powerful TWAS tool by both simulations and application studies.

Dissecting Complex Traits Using Omics Data: A Review on the Linear Mixed Models and Their Application in GWAS

Genome-wide association study (GWAS) is the most popular approach to dissecting complex traits in plants, humans, and animals. Numerous methods and tools have been proposed to discover the causal variants for GWAS data analysis. Among them, linear mixed models (LMMs) are widely used statistical methods for regulating confounding factors, including population structure, resulting in increased computational proficiency and statistical power in GWAS studies. Recently more attention has been paid to pleiotropy, multi-trait, gene-gene interaction, gene-environment interaction, and multi-locus methods with the growing availability of large-scale GWAS data and relevant phenotype samples. In this review, we have demonstrated all possible LMMs-based methods available in the literature for GWAS. We briefly discuss the different LMM methods, software packages, and available open-source applications in GWAS. Then, we include the advantages and weaknesses of the LMMs in GWAS. Finally, we discuss the future perspective and conclusion. The present review paper would be helpful to the researchers for selecting appropriate LMM models and methods quickly for GWAS data analysis and would benefit the scientific society.

METRO: Multi-ancestry transcriptome-wide association studies for powerful gene-trait association detection

Integrative analysis of genome-wide association studies (GWASs) and gene expression studies in the form of a transcriptome-wide association study (TWAS) has the potential to better elucidate the molecular mechanisms underlying disease etiology. Here we present a method, METRO, that can leverage gene expression data collected from multiple genetic ancestries to enhance TWASs. METRO incorporates expression prediction models constructed in different genetic ancestries through a likelihood-based inference framework, producing calibrated p values with substantially improved TWAS power. We illustrate the benefits of METRO in both simulations and applications to seven complex traits and diseases obtained from four GWASs. These GWASs include two of primarily European ancestry (n = 188,577 and 339,226) and two of primarily African ancestry (n = 42,752 and 23,827). In the real data applications, we leverage gene expression data measured on 1,032 African Americans and 801 European Americans from the Genetic Epidemiology Network of Arteriopathy (GENOA) study to identify a substantially larger number of gene-trait associations as compared to existing TWAS approaches. The benefits of METRO are most prominent in applications to GWASs of African ancestry where the sample size is much smaller than GWASs of European ancestry and where a more powerful TWAS method is crucial. Among the identified associations are high-density lipoprotein-associated genes including PLTP and PPARG that are critical for maintaining lipid homeostasis and the type II diabetes-associated gene MAPT that supports microtubule-associated protein tau as a key component underlying impaired insulin secretion.

A two-sample robust Bayesian Mendelian Randomization method accounting for linkage disequilibrium and idiosyncratic pleiotropy with applications to the COVID-19 outcomes

Mendelian randomization (MR) is a statistical method exploiting genetic variants as instrumental variables to estimate the causal effect of modifiable risk factors on an outcome of interest. Despite wide uses of various popular two-sample MR methods based on genome-wide association study summary level data, however, those methods could suffer from potential power loss or/and biased inference when the chosen genetic variants are in linkage disequilibrium (LD), and also have relatively large direct effects on the outcome whose distribution might be heavy-tailed which is commonly referred to as the idiosyncratic pleiotropy phenomenon. To resolve those two issues, we propose a novel Robust Bayesian Mendelian Randomization (RBMR) model that uses the more robust multivariate generalized t $t$ -distribution to model such direct effects in a probabilistic model framework which can also incorporate the LD structure explicitly. The generalized t $t$ -distribution can be represented as a Gaussian scaled mixture so that our model parameters can be estimated by the expectation maximization (EM)-type algorithms. We compute the standard errors by calibrating the evidence lower bound using the likelihood ratio test. Through extensive simulation studies, we show that our RBMR has robust performance compared with other competing methods. We further apply our RBMR method to two benchmark data sets and find that RBMR has smaller bias and standard errors. Using our proposed RBMR method, we find that coronary artery disease is associated with increased risk of critically ill coronavirus disease 2019. We also develop a user-friendly R package RBMR (https://github.com/AnqiWang2021/RBMR) for public use.

Towards the Genetic Architecture of Complex Gene Expression Traits: Challenges and Prospects for eQTL Mapping in Humans

The discovery of expression quantitative trait loci (eQTLs) and their target genes (eGenes) has not only compensated for the limitations of genome-wide association studies for complex phenotypes but has also provided a basis for predicting gene expression. Efforts have been made to develop analytical methods in statistical genetics, a key discipline in eQTL analysis. In particular, mixed model– and deep learning–based analytical methods have been extremely beneficial in mapping eQTLs and predicting gene expression. Nevertheless, we still face many challenges associated with eQTL discovery. Here, we discuss two key aspects of these challenges: 1, the complexity of eTraits with various factors such as polygenicity and epistasis and 2, the voluminous work required for various types of eQTL profiles. The properties and prospects of statistical methods, including the mixed model method, Bayesian inference, the deep learning method, and the integration method, are presented as future directions for eQTL discovery. This review will help expedite the design and use of efficient methods for eQTL discovery and eTrait prediction.

CoMM-S4: A Collaborative Mixed Model Using Summary-Level eQTL and GWAS Datasets in Transcriptome-Wide Association Studies

Motivation: Genome-wide association studies (GWAS) have achieved remarkable success in identifying SNP-trait associations in the last decade. However, it is challenging to identify the mechanisms that connect the genetic variants with complex traits as the majority of GWAS associations are in non-coding regions. Methods that integrate genomic and transcriptomic data allow us to investigate how genetic variants may affect a trait through their effect on gene expression. These include CoMM and CoMM-S², likelihood-ratio-based methods that integrate GWAS and eQTL studies to assess expression-trait association. However, their reliance on individual-level eQTL data render them inapplicable when only summary-level eQTL results, such as those from large-scale eQTL analyses, are available. Result: We develop an efficient probabilistic model, CoMM-S⁴, to explore the expression-trait association using summary-level eQTL and GWAS datasets. Compared with CoMM-S², which uses individual-level eQTL data, CoMM-S⁴ requires only summary-level eQTL data. To test expression-trait association, an efficient variational Bayesian EM algorithm and a likelihood ratio test were constructed. We applied CoMM-S⁴ to both simulated and real data. The simulation results demonstrate that CoMM-S⁴ can perform as well as CoMM-S² and S-PrediXcan, and analyses using GWAS summary statistics from Biobank Japan and eQTL summary statistics from eQTLGen and GTEx suggest novel susceptibility loci for cardiovascular diseases and osteoporosis. Availability and implementation: The developed R package is available at https://github.com/gordonliu810822/CoMM.

Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects

With the increasing availability of large-scale GWAS summary data on various complex traits and diseases, there have been tremendous interests in applications of Mendelian randomization (MR) to investigate causal relationships between pairs of traits using SNPs as instrumental variables (IVs) based on observational data. In spite of the potential significance of such applications, the validity of their causal conclusions critically depends on some strong modeling assumptions required by MR, which may be violated due to the widespread (horizontal) pleiotropy. Although many MR methods have been proposed recently to relax the assumptions by mainly dealing with uncorrelated pleiotropy, only a few can handle correlated pleiotropy, in which some SNPs/IVs may be associated with hidden confounders, such as some heritable factors shared by both traits. Here we propose a simple and effective approach based on constrained maximum likelihood and model averaging, called cML-MA, applicable to GWAS summary data. To deal with more challenging situations with many invalid IVs with only weak pleiotropic effects, we modify and improve it with data perturbation. Extensive simulations demonstrated that the proposed methods could control the type I error rate better while achieving higher power than other competitors. Applications to 48 risk factor-disease pairs based on large-scale GWAS summary data of 3 cardio-metabolic diseases (coronary artery disease, stroke, and type 2 diabetes), asthma, and 12 risk factors confirmed its superior performance.

Integrating brain imaging endophenotypes with GWAS for Alzheimer's disease

Background

Genome wide association studies (GWAS) have identified many genetic variants associated with increased risk of Alzheimer's disease (AD). These susceptibility loci may effect AD indirectly through a combination of physiological brain changes. Many of these neuropathologic features are detectable via magnetic resonance imaging (MRI).

Methods

In this study, we examine the effects of such brain imaging derived phenotypes (IDPs) with genetic etiology on AD, using and comparing the following methods: two-sample Mendelian randomization (2SMR), generalized summary statistics based Mendelian randomization (GSMR), transcriptome wide association studies (TWAS) and the adaptive sum of powered score (aSPU) test. These methods do not require individual-level genotypic and phenotypic data but instead can rely only on an external reference panel and GWAS summary statistics.

Results

Using publicly available GWAS datasets from the International Genomics of Alzheimer's Project (IGAP) and UK Biobank's (UKBB) brain imaging initiatives, we identify 35 IDPs possibly associated with AD, many of which have well established or biologically plausible links to the characteristic cognitive impairments of this neurodegenerative disease.

Conclusions

Our results highlight the increased power for detecting genetic associations achieved by multiple correlated SNP-based methods, i.e., aSPU, GSMR and TWAS, over MR methods based on independent SNPs (as instrumental variables).

Novel Variance-Component TWAS method for studying complex human diseases with applications to Alzheimer's dementia

Transcriptome-wide association studies (TWAS) have been widely used to integrate transcriptomic and genetic data to study complex human diseases. Within a test dataset lacking transcriptomic data, traditional two-stage TWAS methods first impute gene expression by creating a weighted sum that aggregates SNPs with their corresponding cis-eQTL effects on reference transcriptome. Traditional TWAS methods then employ a linear regression model to assess the association between imputed gene expression and test phenotype, thereby assuming the effect of a cis-eQTL SNP on test phenotype is a linear function of the eQTL's estimated effect on reference transcriptome. To increase TWAS robustness to this assumption, we propose a novel Variance-Component TWAS procedure (VC-TWAS) that assumes the effects of cis-eQTL SNPs on phenotype are random (with variance proportional to corresponding reference cis-eQTL effects) rather than fixed. VC-TWAS is applicable to both continuous and dichotomous phenotypes, as well as individual-level and summary-level GWAS data. Using simulated data, we show VC-TWAS is more powerful than traditional TWAS methods based on a two-stage Burden test, especially when eQTL genetic effects on test phenotype are no longer a linear function of their eQTL genetic effects on reference transcriptome. We further applied VC-TWAS to both individual-level (N = ~3.4K) and summary-level (N = ~54K) GWAS data to study Alzheimer's dementia (AD). With the individual-level data, we detected 13 significant risk genes including 6 known GWAS risk genes such as TOMM40 that were missed by traditional TWAS methods. With the summary-level data, we detected 57 significant risk genes considering only cis-SNPs and 71 significant genes considering both cis- and trans- SNPs, which also validated our findings with the individual-level GWAS data. Our VC-TWAS method is implemented in the TIGAR tool for public use.

Using Collaborative Mixed Models to Account for Imputation Uncertainty in Transcriptome-Wide Association Studies

Transcriptome-wide association studies (TWASs) integrate expression quantitative trait loci (eQTLs) studies with genome-wide association studies (GWASs) to prioritize candidate target genes for complex traits. TWASs have become increasingly popular. They have been used to analyze many complex traits with expression profiles from different tissues, successfully enhancing the discovery of genetic risk loci for complex traits. Though conceptually straightforward, some steps are required to perform the TWAS properly. Here we provide a step-by-step guide to integrate eQTL data with both GWAS individual-level data and GWAS summary statistics from complex traits.

Aggregating multiple expression prediction models improves the power of transcriptome-wide association studies

Transcriptome-wide association study (TWAS) is an important integrative method for identifying genes that are causally associated with phenotypes. A key step of TWAS involves the construction of expression prediction models for every gene in turn using its cis-SNPs as predictors. Different TWAS methods rely on different models for gene expression prediction, and each such model makes a distinct modeling assumption that is often suitable for a particular genetic architecture underlying expression. However, the genetic architectures underlying gene expression vary across genes throughout the transcriptome. Consequently, different TWAS methods may be beneficial in detecting genes with distinct genetic architectures. Here, we develop a new method, HMAT, which aggregates TWAS association evidence obtained across multiple gene expression prediction models by leveraging the harmonic mean P-value combination strategy. Because each expression prediction model is suited to capture a particular genetic architecture, aggregating TWAS associations across prediction models as in HMAT improves accurate expression prediction and enables subsequent powerful TWAS analysis across the transcriptome. A key feature of HMAT is its ability to accommodate the correlations among different TWAS test statistics and produce calibrated P-values after aggregation. Through numerical simulations, we illustrated the advantage of HMAT over commonly used TWAS methods as well as ad hoc P-value combination rules such as Fisher's method. We also applied HMAT to analyze summary statistics of nine common diseases. In the real data applications, HMAT was on average 30.6% more powerful compared to the next best method, detecting many new disease-associated genes that were otherwise not identified by existing TWAS approaches. In conclusion, HMAT represents a flexible and powerful TWAS method that enjoys robust performance across a range of genetic architectures underlying gene expression.

A tissue-specific collaborative mixed model for jointly analyzing multiple tissues in transcriptome-wide association studies

Transcriptome-wide association studies (TWASs) integrate expression quantitative trait loci (eQTLs) studies with genome-wide association studies (GWASs) to prioritize candidate target genes for complex traits. Several statistical methods have been recently proposed to improve the performance of TWASs in gene prioritization by integrating the expression regulatory information imputed from multiple tissues, and made significant achievements in improving the ability to detect gene-trait associations. Unfortunately, most existing multi-tissue methods focus on prioritization of candidate genes, and cannot directly infer the specific functional effects of candidate genes across different tissues. Here, we propose a tissue-specific collaborative mixed model (TisCoMM) for TWASs, leveraging the co-regulation of genetic variations across different tissues explicitly via a unified probabilistic model. TisCoMM not only performs hypothesis testing to prioritize gene-trait associations, but also detects the tissue-specific role of candidate target genes in complex traits. To make full use of widely available GWASs summary statistics, we extend TisCoMM to use summary-level data, namely, TisCoMM-S2. Using extensive simulation studies, we show that type I error is controlled at the nominal level, the statistical power of identifying associated genes is greatly improved, and the false-positive rate (FPR) for non-causal tissues is well controlled at decent levels. We further illustrate the benefits of our methods in applications to summary-level GWASs data of 33 complex traits. Notably, apart from better identifying potential trait-associated genes, we can elucidate the tissue-specific role of candidate target genes. The follow-up pathway analysis from tissue-specific genes for asthma shows that the immune system plays an essential function for asthma development in both thyroid and lung tissues.

Leveraging functional annotation to identify genes associated with complex diseases

To increase statistical power to identify genes associated with complex traits, a number of transcriptome-wide association study (TWAS) methods have been proposed using gene expression as a mediating trait linking genetic variations and diseases. These methods first predict expression levels based on inferred expression quantitative trait loci (eQTLs) and then identify expression-mediated genetic effects on diseases by associating phenotypes with predicted expression levels. The success of these methods critically depends on the identification of eQTLs, which may not be functional in the corresponding tissue, due to linkage disequilibrium (LD) and the correlation of gene expression between tissues. Here, we introduce a new method called T-GEN (Transcriptome-mediated identification of disease-associated Genes with Epigenetic aNnotation) to identify disease-associated genes leveraging epigenetic information. Through prioritizing SNPs with tissue-specific epigenetic annotation, T-GEN can better identify SNPs that are both statistically predictive and biologically functional. We found that a significantly higher percentage (an increase of 18.7% to 47.2%) of eQTLs identified by T-GEN are inferred to be functional by ChromHMM and more are deleterious based on their Combined Annotation Dependent Depletion (CADD) scores. Applying T-GEN to 207 complex traits, we were able to identify more trait-associated genes (ranging from 7.7% to 102%) than those from existing methods. Among the identified genes associated with these traits, T-GEN can better identify genes with high (>0.99) pLI scores compared to other methods. When T-GEN was applied to late-onset Alzheimer's disease, we identified 96 genes located at 15 loci, including two novel loci not implicated in previous GWAS. We further replicated 50 genes in an independent GWAS, including one of the two novel loci.

A Review of Integrative Imputation for Multi-Omics Datasets

Multi-omics studies, which explore the interactions between multiple types of biological factors, have significant advantages over single-omics analysis for their ability to provide a more holistic view of biological processes, uncover the causal and functional mechanisms for complex diseases, and facilitate new discoveries in precision medicine. However, omics datasets often contain missing values, and in multi-omics study designs it is common for individuals to be represented for some omics layers but not all. Since most statistical analyses cannot be applied directly to the incomplete datasets, imputation is typically performed to infer the missing values. Integrative imputation techniques which make use of the correlations and shared information among multi-omics datasets are expected to outperform approaches that rely on single-omics information alone, resulting in more accurate results for the subsequent downstream analyses. In this review, we provide an overview of the currently available imputation methods for handling missing values in bioinformatics data with an emphasis on multi-omics imputation. In addition, we also provide a perspective on how deep learning methods might be developed for the integrative imputation of multi-omics datasets.

MR-LDP: a two-sample Mendelian randomization for GWAS summary statistics accounting for linkage disequilibrium and horizontal pleiotropy

The proliferation of genome-wide association studies (GWAS) has prompted the use of two-sample Mendelian randomization (MR) with genetic variants as instrumental variables (IVs) for drawing reliable causal relationships between health risk factors and disease outcomes. However, the unique features of GWAS demand that MR methods account for both linkage disequilibrium (LD) and ubiquitously existing horizontal pleiotropy among complex traits, which is the phenomenon wherein a variant affects the outcome through mechanisms other than exclusively through the exposure. Therefore, statistical methods that fail to consider LD and horizontal pleiotropy can lead to biased estimates and false-positive causal relationships. To overcome these limitations, we proposed a probabilistic model for MR analysis in identifying the causal effects between risk factors and disease outcomes using GWAS summary statistics in the presence of LD and to properly account for horizontal pleiotropy among genetic variants (MR-LDP) and develop a computationally efficient algorithm to make the causal inference. We then conducted comprehensive simulation studies to demonstrate the advantages of MR-LDP over the existing methods. Moreover, we used two real exposure-outcome pairs to validate the results from MR-LDP compared with alternative methods, showing that our method is more efficient in using all-instrumental variants in LD. By further applying MR-LDP to lipid traits and body mass index (BMI) as risk factors for complex diseases, we identified multiple pairs of significant causal relationships, including a protective effect of high-density lipoprotein cholesterol on peripheral vascular disease and a positive causal effect of BMI on hemorrhoids.