Quasi Instrumental Variable Methods for Stable Hidden Confounding and Binary Outcome

2025-08-22

AI Summary

Conventional instrumental variable (IV) methods for binary outcomes often fail to satisfy the exclusion restriction and independence assumptions. Method: Under the stable confounding and stable treatment effect assumptions, we introduce the novel concept of a “quasi-instrumental variable” (QIV)—a weaker construct requiring only predictive power for the outcome, not full IV validity. Leveraging a structural equilibrium dynamic generative model, we establish a nonparametric identification framework for both marginal and conditional average treatment effects (ATEs/CATEs). We further propose a generalized odds-product reparameterization and develop maximum likelihood and triple-robust semiparametric efficient estimators. Results: Simulation studies and empirical analysis using UK Biobank data demonstrate that the method achieves strong robustness and high estimation accuracy even in small samples and near-boundary settings, substantially broadening the applicability and reliability of causal inference for binary outcomes in observational studies.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Instrumental variable (IV) methods are central to causal inference from observational data, particularly when a randomized experiment is not feasible. However, of the three conventional core IV identification conditions, only one, IV relevance, is empirically verifiable; often one or both of the other conditions, exclusion restriction and IV independence from unmeasured confounders, are unmet in real-world applications. These challenges are compounded when the outcome is binary, a setting for which robust IV methods remain underdeveloped. A fundamental contribution of this paper is the development of a general identification strategy justified under a structural equilibrium dynamic generative model of so-called stable confounding and a quasi instrumental variable (QIV), i.e. a variable that is only assumed to be predictive of the outcome. Such a model implies (a) stability of confounding on the multiplicative scale, and (b) stability of the additive average treatment effect among the treated (ATT), across levels of that QIV. The former is all that is necessary to ensure a valid test of the causal null hypothesis; together those two conditions establish nonparametric identification and estimation of the conditional and marginal ATT. To address the statistical challenges posed by the need for boundedness in binary outcomes, we introduce a generalized odds product re-parametrization of the observed data distribution, and we develop both a principled maximum likelihood estimator and a triply robust semiparametric locally efficient estimator, which we evaluate through simulations and an empirical application to the UK Biobank.

Problem

• Developing quasi-IV methods for binary outcomes with hidden confounding
• Addressing unmet exclusion and independence conditions in IV analysis
• Ensuring valid causal null tests and ATT estimation stability

Innovation

• Quasi Instrumental Variable for stable confounding
• Generalized odds product re-parametrization for binary outcomes
• Triply robust semiparametric locally efficient estimator