# Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization

arXiv: https://arxiv.org/abs/1401.5755 · HTML: https://mlsanity.com/paper/1401.5755/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2014.

## Built on by (most cited first, 22 of 22)

- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Instrumental Variables in Causal Inference and Machine Learning: A Survey](https://mlsanity.com/paper/2212.05778/) (2022)
- [Identifiability of Sparse Causal Effects using Instrumental Variables](https://mlsanity.com/paper/2203.09380/) (2022)
- [Discovering Ancestral Instrumental Variables for Causal Inference from Observational Data](https://mlsanity.com/paper/2206.01931/) (2022)
- [Ancestral Instrument Method for Causal Inference without Complete Knowledge](https://mlsanity.com/paper/2201.03810/) (2022)
- [Causal Inference with Conditional Instruments using Deep Generative Models](https://mlsanity.com/paper/2211.16246/) (2022)
- [Disentangled Representation Learning for Causal Inference with Instruments](https://mlsanity.com/paper/2412.04641/) (2024)
- [Ice Cream Doesn't Cause Drowning: Benchmarking LLMs Against Statistical Pitfalls in Causal Inference](https://mlsanity.com/paper/2505.13770/) (2025)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [On the instrumental variable estimation with many weak and invalid instruments](https://mlsanity.com/paper/2207.03035/) (2022)
- [Causal Discovery with Generalized Linear Models through Peeling Algorithms](https://mlsanity.com/paper/2310.16698/) (2023)
- [Automating the Selection of Proxy Variables of Unmeasured Confounders](https://mlsanity.com/paper/2405.16130/) (2024)
- [Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data](https://mlsanity.com/paper/2406.06452/) (2024)
- [Personalized Pricing with Invalid Instrumental Variables: Identification, Estimation, and Policy Learning](https://mlsanity.com/paper/2302.12670/) (2023)
- [Robust Weighted Triangulation of Causal Effects Under Model Uncertainty](https://mlsanity.com/paper/2603.01119/) (2026)
- [Agglomerative Hierarchical Clustering for Selecting Valid Instrumental Variables](https://mlsanity.com/paper/2101.05774/) (2021)
- [A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates](https://mlsanity.com/paper/2205.00171/) (2022)
- [Bounding Causal Effects with Leaky Instruments](https://mlsanity.com/paper/2404.04446/) (2024)
- [Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments](https://mlsanity.com/paper/2407.07933/) (2024)
- [Towards causal effect estimation with learned instrument representations](https://mlsanity.com/paper/2602.10370/) (2026)
- [Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding](https://mlsanity.com/paper/2609.40051/) (2026)

## Abstract (arXiv)

Instrumental variables have been widely used for estimating the causal effect between exposure and outcome. Conventional estimation methods require complete knowledge about all the instruments' validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments' validity is equivalent to complete knowledge about the involved genes' functions. In this paper, we propose a method for estimation of causal effects when this complete knowledge is absent. It is shown that causal effects are identified and can be estimated as long as less than 50% of instruments are invalid, without knowing which of the instruments are invalid. We also introduce conditions for identification when the 50% threshold is violated. A fast penalized ℓ1 estimation method, called sisVIVE, is introduced for estimating the causal effect without knowing which instruments are valid, with theoretical guarantees on its performance. The proposed method is demonstrated on simulated data and a real Mendelian randomization study concerning the effect of body mass index on health-related quality of life index. An R package sisVIVE is available online.