Inference of causal metabolite networks in the presence of invalid instrumental variables with GWAS summary data

We propose structural equation models (SEMs) as a general framework to infer causal networks for metabolites and other complex traits. Traditionally SEMs are used only for individual-level data under the assumption that all instrumental variables (IVs) are valid. To overcome these limitations, we propose both one- and two-sample approaches for causal network inference based on SEMs that can: (1) perform causal analysis and discover causal relationships among multiple traits; (2) account for the possible presence of some invalid IVs; (3) allow for data analysis using only genome-wide association studies (GWAS) summary statistics when individual-level data are not available; (4) consider the possibility of bidirectional relationships between traits. Our method employs a simple stepwise selection to identify invalid IVs, thus avoiding false positives while possibly increasing true discoveries based on two-stage least squares (2SLS). We use both real GWAS data and simulated data to demonstrate the superior performance of our method over the standard 2SLS/SEMs. For real data analysis, our proposed approach is applied to a human blood metabolite GWAS summary data set to uncover putative causal relationships among the metabolites; we also identify some metabolites (putative) causal to Alzheimer's disease (AD), which, along with the inferred causal metabolite network, suggest some possible pathways of metabolites involved in AD.