Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments

• DOI: 10.48550/arxiv.2407.07933
• Publication Date: 2024-07-10
• Authors: Feng Xie; Zhen Yao; Lin Xie; Yan Zeng; Zhi Geng
• Keywords: Identification

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