Over a decade of genome-wide association studies have led to the finding that significant genetic associations tend to be spread across the genome for complex traits, leading to the recent proposal of an ''omnigenic'' model where almost all genes contribute to every complex trait. Such an omnigenic phenomenon complicates Mendelian Randomization studies, where natural genetic variations are used as instruments to infer the causal effect of heritable risk factors. We reexamine the assumptions of existing Mendelian Randomization methods and show how they need to be revised to allow for pervasive pleiotropy and heterogeneous effect sizes. We propose a comprehensive framework GRAPPLE(Genome-wide mR Analysis under Pervasive PLEiotropy) to analyze the causal effect of a target risk factor with heterogeneous genetic instruments and identify possible pleiotropic patterns from data. By using summary statistics from genome-wide association studies, GRAPPLE can efficiently use both strong and weak genetic instruments, detect the existence of multiple pleiotropic pathways, adjust for confounding risk factors, and determine the causal direction. With GRAPPLE, we analyze the effect of blood lipids, body mass index, and systolic blood pressure on 25 disease outcomes, gaining new information on their causal relationships and the potential pleiotropic pathways. ### Competing Interest Statement The authors have declared no competing interest.
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