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

TL;DR

This paper addresses the challenge of estimating causal effects in bi-directional Mendelian randomization with invalid instruments, providing theoretical identification conditions and a new estimation method that outperforms existing approaches.

Contribution

The paper offers the first theoretical conditions for identifying bi-directional MR models and introduces a novel cluster fusion-like method for valid IV discovery and causal effect estimation.

Findings

Theoretical identification conditions for bi-directional MR.

A new method effectively estimates causal effects with invalid instruments.

Experimental results demonstrate the method's superior performance.

Abstract

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.