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

arXiv 1401.5755 ↗First posted 22 Jan 2014stat.MEcited by 22

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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.

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

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Citing papers per year: 2021: 2; 2022: 8; 2023: 3; 2024: 5; 2025: 1; 2026: 3.

22 papers.

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  1. 2021Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decompositioncited by 19
  2. 2022Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Surveycited by 19
  3. 2022Instrumental Variables in Causal Inference and Machine Learning: A Surveycited by 10
  4. 2022Identifiability of Sparse Causal Effects using Instrumental Variablescited by 9
  5. 2022Discovering Ancestral Instrumental Variables for Causal Inference from Observational Datacited by 7
  6. 2022Ancestral Instrument Method for Causal Inference without Complete Knowledgecited by 6
  7. 2022Causal Inference with Conditional Instruments using Deep Generative Modelscited by 6
  8. 2024Disentangled Representation Learning for Causal Inference with Instrumentscited by 6
  9. 2025Ice Cream Doesn't Cause Drowning: Benchmarking LLMs Against Statistical Pitfalls in Causal Inferencecited by 6
  10. 2023Sequential Underspecified Instrument Selection for Cause-Effect Estimationcited by 4
  11. 2022On the instrumental variable estimation with many weak and invalid instrumentscited by 2
  12. 2023Causal Discovery with Generalized Linear Models through Peeling Algorithmscited by 2
10 more
  1. 2024Automating the Selection of Proxy Variables of Unmeasured Confounderscited by 2
  2. 2024Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Datacited by 2
  3. 2023Personalized Pricing with Invalid Instrumental Variables: Identification, Estimation, and Policy Learningcited by 1
  4. 2026Robust Weighted Triangulation of Causal Effects Under Model Uncertaintycited by 1
  5. 2021Agglomerative Hierarchical Clustering for Selecting Valid Instrumental Variablescited by 0
  6. 2022A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariatescited by 0
  7. 2024Bounding Causal Effects with Leaky Instrumentscited by 0
  8. 2024Identification and Estimation of the Bi-Directional MR with Some Invalid Instrumentscited by 0
  9. 2026Towards causal effect estimation with learned instrument representationscited by 0
  10. 2026Proximal Balancing for Causal Effect Estimation under Unmeasured Confoundingcited by 0