Sensitivity Analysis of G-estimators to Invalid Instrumental Variables

TL;DR

This paper introduces a new sensitivity analysis method for G-estimators in causal models, addressing violations of instrumental variable assumptions, applicable to both linear and non-linear models, with theoretical justification and practical illustrations.

Contribution

It proposes a novel sensitivity analysis framework using a single parameter for violations of IV assumptions, extending to non-linear models, with theoretical and empirical validation.

Findings

The method effectively quantifies the impact of assumption violations.

Simulation studies demonstrate the robustness of the approach.

Application to real data shows practical utility and provides guidelines.

Abstract

Instrumental variables regression is a tool that is commonly used in the analysis of observational data. The instrumental variables are used to make causal inference about the effect of a certain exposure in the presence of unmeasured confounders. A valid instrumental variable is a variable that is associated with the exposure, affects the outcome only through the exposure (exclusion criterion), and is not confounded with the outcome (exogeneity). These assumptions are generally untestable and rely on subject-matter knowledge. Therefore, a sensitivity analysis is desirable to assess the impact of assumptions violation on the estimated parameters. In this paper, we propose and demonstrate a new method of sensitivity analysis for G-estimators in causal linear and non-linear models. We introduce two novel aspects of sensitivity analysis in instrumental variables studies. The first is a single sensitivity parameter that captures violations of exclusion and exogeneity assumptions. The second is an application of the method to non-linear models. The introduced framework is theoretically justified and is illustrated via a simulation study. Finally, we illustrate the method by application to real-world data and provide practitioners with guidelines on conducting sensitivity analysis.