Bayesian causal graphical model for joint Mendelian randomization analysis of multiple exposures and outcomes

Current Mendelian randomization (MR) methods do not reflect complex relationships among multiple exposures and outcomes as is typical for real-life applications. We introduce MrDAG, a Bayesian causal graphical model for summary-level MR analysis to detect dependency relations within the exposures, the outcomes, and between them to improve causal effects estimation. MrDAG combines three causal inference strategies. It uses genetic variation as instrumental variables to account for unobserved confounders. It performs structure learning to detect and orientate the direction of the dependencies within the exposures and the outcomes. Finally, interventional calculus is employed to derive principled causal effect estimates. In MrDAG the directionality of the causal effects between the exposures and the outcomes is assumed known, i.e., the exposures can only be potential causes of the outcomes, and no reverse causation is allowed. In the simulation study, MrDAG outperforms recently proposed one-outcome-at-a-time and multi-response multi-variable Bayesian MR methods as well as causal graphical models under the constraint on edges' orientation from the exposures to the outcomes. MrDAG was motivated to unravel how lifestyle and behavioral exposures impact mental health. It highlights first, education and second, smoking as effective points of intervention given their important downstream effects on mental health. It also enables the identification of a novel path between smoking and the genetic liability to schizophrenia and cognition, demonstrating the complex pathways toward mental health. These insights would have been impossible to delineate without modeling the paths between multiple exposures and outcomes at once.