Semiparametric Efficient G-estimation with Invalid Instrumental Variables

TL;DR

This paper introduces a new class of semiparametric g-estimators for causal effect estimation using multiple instruments, which remain consistent even when some instruments are invalid, supported by efficiency theory, simulations, and real data.

Contribution

It proposes a novel semiparametric g-estimator that tolerates invalid instruments without knowing their identities, enhancing causal inference robustness.

Findings

Estimator remains consistent with up to γ invalid instruments

Simulation studies show superior performance over existing methods

Application to UK Biobank data demonstrates practical utility

Abstract

The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple instruments are routinely used, leading to concerns about bias due to possible violation of the instrumental variable assumptions. To address this concern, we introduce a new class of g-estimators that are guaranteed to remain consistent and asymptotically normal for the causal effect of interest provided that a set of at least $\gamma$ out of $K$ candidate instruments are valid, for $\gamma\leq K$ set by the analyst ex ante, without necessarily knowing the identities of the valid and invalid instruments. We provide formal semiparametric efficiency theory supporting our results. Both simulation studies and applications to the UK Biobank data demonstrate the superior empirical performance of our estimators compared to competing methods.