Quasi Instrumental Variable Methods for Stable Hidden Confounding and Binary Outcome

TL;DR

This paper develops a new causal inference method using quasi instrumental variables under stable confounding, enabling identification and estimation of treatment effects with binary outcomes even when traditional IV assumptions are not fully met.

Contribution

It introduces a general identification strategy based on a structural equilibrium model and quasi IV, addressing challenges in binary outcomes and partial IV assumptions.

Findings

Proposes a generalized odds product re-parametrization for binary outcomes.

Develops maximum likelihood and triply robust estimators.

Validates methods through simulations and UK Biobank application.

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.