mlsanityData to 7 Oct 2026

Partial Identification of Causal Effects Using Proxy Variables

arXiv 2304.04374 ↗First posted 10 Apr 2023stat.ME math.ST stat.MLcited by 7

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Abstract (arXiv)

Proximal causal inference is a framework for evaluating the causal effects in the presence of unmeasured confounding. For point identification, it leverages a pair of proxy variables to identify a bridge function that matches the dependence of potential outcomes or treatment variables on the hidden factors to corresponding functions of observed proxies. Unique identification requires that proxies are sufficiently relevant for hidden factors, a requirement that has previously been formalized as a completeness condition. However, completeness is not empirically testable, and although a bridge function may be well-defined in a given setting, lack of completeness, sometimes manifested by availability of a single type of proxy, may severely limit prospects for identification of a bridge function and thus a causal effect; therefore, potentially restricting the application of the framework. In this paper, we propose partial identification methods that do not require completeness and obviate the need for identification of a bridge function. We establish that proxies can be leveraged to obtain bounds on the causal effect even if available information does not suffice to identify either a bridge function or a corresponding causal effect of interest. Our bounds are non-smooth functionals of the underlying distribution. For inference, we employ LogSumExp approximations that yield smooth lower and upper bounds, and we derive the efficient influence functions of the resulting bound functionals which enable analytic variance estimation, while bootstrap confidence intervals remain available for regular plug-in implementations. We further establish analogous results in related settings where identification hinges upon hidden mediators for which proxies are available, however such proxies are not sufficiently rich for point identification of a bridge function or a corresponding causal effect of interest.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 19 of its 35 references that are in the map. First posted on arXiv 10 Apr 2023.

Builds on

19 of 35 references.

References · 19

  1. 2021Convex optimizationcited by 2,479
  2. 2013Direct and Indirect Effectscited by 276
  3. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 138
  4. 2020An Introduction to Proximal Causal Learningcited by 91
  5. 2020Semiparametric proximal causal inferencecited by 58
  6. 2018A confounding bridge approach for double negative control inference on causal effectscited by 36
  7. 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
  8. 2021Proximal Causal Inference for Complex Longitudinal Studiescited by 16
  9. 2020A Selective Review of Negative Control Methods in Epidemiologycited by 15
  10. 2023Minimax Instrumental Variable Regression and L2 Convergence Guarantees without Identification or Closednesscited by 13
  11. 2021The Proximal ID Algorithmcited by 11
  12. 2021Proximal mediation analysiscited by 10
7 more
  1. 2023Covariate-assisted bounds on causal effects with instrumental variablescited by 10
  2. 2019A Universal Approximation Result for Difference of log-sum-exp Neural Networkscited by 9
  3. 2021Causal Inference with Hidden Mediatorscited by 6
  4. 2022Double Negative Control Inference in Test-Negative Design Studies of Vaccine Effectivenesscited by 5
  5. 2023Single Proxy Controlcited by 4
  6. 2021Identification and Estimation of Causal Peer Effects Using Double Negative Controls for Unmeasured Network Confoundingcited by 3
  7. 2023Proximal Causal Inference without Uniqueness Assumptionscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 1; 2026: 3.

7 papers.

  1. 2023Causal Reinforcement Learning: A Surveycited by 22
  2. 2023Causal Discovery via Conditional Independence Testing with Proxy Variablescited by 3
  3. 2024Predictive Performance Comparison of Decision Policies Under Confoundingcited by 2
  4. 2026Information-Theoretic Causal Bounds under Unmeasured Confoundingcited by 2
  5. 2025Detecting clinician implicit biases in diagnoses using proximal causal inferencecited by 1
  6. 2026Computational Identifiabilitycited by 1
  7. 2026Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxiescited by 0