Abstract
Mendelian randomization (MR) is a powerful method that uses genetic variants as instrumental variables to infer the causal effect of a modifiable exposure on an outcome. We study inference for bi-directional causal relationships and causal directions with possibly pleiotropic genetic variants. We show that assumptions for common MR methods are often impossible or too stringent given the potential bi-directional relationships. We propose a new focusing framework for testing bi-directional causal effects and it can be coupled with many state-of-the-art MR methods. We provide theoretical guarantees for our proposal and demonstrate its performance using several simulated and real datasets.