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

arXiv: https://arxiv.org/abs/2407.07933 · HTML: https://mlsanity.com/paper/2407.07933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 48 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 7 of 7)

- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization](https://mlsanity.com/paper/1401.5755/) (2014)
- [Valid Causal Inference with (Some) Invalid Instruments](https://mlsanity.com/paper/2006.11386/) (2020)
- [Discovering Ancestral Instrumental Variables for Causal Inference from Observational Data](https://mlsanity.com/paper/2206.01931/) (2022)
- [Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables](https://mlsanity.com/paper/1612.03451/) (2016)
- [Semi-Instrumental Variables: A Test for Instrument Admissibility](https://mlsanity.com/paper/1301.2261/) (2013)
- [A Focusing Framework for Testing Bi-Directional Causal Effects with GWAS Summary Data](https://mlsanity.com/paper/2203.06887/) (2022)

## Abstract (arXiv)

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.