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Abstract Spatial transcriptomic studies are becoming increasingly common and large, posing important statistical and computational challenges for many analytic tasks. Here, we present SPARK-X, a non-parametric method for rapid and effective detection of spatially expressed genes in large spatial transcriptomic studies. SPARK-X not only produces effective type I error control and high power but also brings orders of magnitude computational savings. We apply SPARK-X to analyze three large datasets, one of which is only analyzable by SPARK-X. In these data, SPARK-X identifies many spatially expressed genes including those that are spatially expressed within the same cell type, revealing new biological insights. 

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.