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Genetic and environmental covariances between pairs of complex traits are important quantitative measurements that characterize their shared genetic and environmental architectures. Accurate estimation of genetic and environmental covariances in genome-wide association studies (GWASs) can help us identify common genetic and environmental factors associated with both traits and facilitate the investigation of their causal relationship. Genetic and environmental covariances are often modeled through multivariate linear mixed models. Existing algorithms for covariance estimation include the traditional restricted maximum likelihood (REML) method and the recent method of moments (MoM). Compared to REML, MoM approaches are computationally efficient and require only GWAS summary statistics. However, MoM approaches can be statistically inefficient, often yielding inaccurate covariance estimates. In addition, existing MoM approaches have so far focused on estimating genetic covariance and have largely ignored environmental covariance estimation. Here we introduce a new computational method, GECKO, for estimating both genetic and environmental covariances, that improves the estimation accuracy of MoM while keeping computation in check. GECKO is based on composite likelihood, relies on only summary statistics for scalable computation, provides accurate genetic and environmental covariance estimates across a range of scenarios, and can accommodate SNP annotation stratified covariance estimation. We illustrate the benefits of GECKO through simulations and applications on analyzing 22 traits from five large-scale GWASs. In the real data applications, GECKO identified 50 significant genetic covariances among analyzed trait pairs, resulting in a twofold power gain compared to the previous MoM method LDSC. In addition, GECKO identified 20 significant environmental covariances. The ability of GECKO to estimate environmental covariance in addition to genetic covariance helps us reveal strong positive correlation between the genetic and environmental covariance estimates across trait pairs, suggesting that common pathways may underlie the shared genetic and environmental architectures between traits. 

Abstract 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. 

Abstract Integrating results from genome-wide association studies (GWASs) and gene expression studies through transcriptome-wide association study (TWAS) has the potential to shed light on the causal molecular mechanisms underlying disease etiology. Here, we present a probabilistic Mendelian randomization (MR) method, PMR-Egger, for TWAS applications. PMR-Egger relies on a MR likelihood framework that unifies many existing TWAS and MR methods, accommodates multiple correlated instruments, tests the causal effect of gene on trait in the presence of horizontal pleiotropy, and is scalable to hundreds of thousands of individuals. In simulations, PMR-Egger provides calibrated type I error control for causal effect testing in the presence of horizontal pleiotropic effects, is reasonably robust under various types of model misspecifications, is more powerful than existing TWAS/MR approaches, and can directly test for horizontal pleiotropy. We illustrate the benefits of PMR-Egger in applications to 39 diseases and complex traits obtained from three GWASs including the UK Biobank.