Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments
This work addresses a challenging issue in causal inference for observational data in genetics, offering a novel approach but is incremental as it builds on existing MR methods.
The paper tackles the problem of estimating causal effects in bi-directional Mendelian randomization with invalid instruments and unmeasured confounding, by providing identification conditions and developing a cluster fusion-like method that shows effectiveness in experiments.
We consider the challenging problem of estimating causal effects from purely observational data in the bi-directional Mendelian randomization (MR), where some invalid instruments, as well as unmeasured confounding, usually exist. To address this problem, most existing methods attempt to find proper valid instrumental variables (IVs) for the target causal effect by expert knowledge or by assuming that the causal model is a one-directional MR model. As such, in this paper, we first theoretically investigate the identification of the bi-directional MR from observational data. In particular, we provide necessary and sufficient conditions under which valid IV sets are correctly identified such that the bi-directional MR model is identifiable, including the causal directions of a pair of phenotypes (i.e., the treatment and outcome). Moreover, based on the identification theory, we develop a cluster fusion-like method to discover valid IV sets and estimate the causal effects of interest. We theoretically demonstrate the correctness of the proposed algorithm. Experimental results show the effectiveness of our method for estimating causal effects in bi-directional MR.