Bias testing, bias correction, and confounder selection using an instrumental variable model.

Area of Science:

• Statistics
• Econometrics
• Epidemiology

Background:

• Instrumental variable (IV) analysis is used to estimate causal effects, but can be biased by unmeasured confounders or weak instrument correlation.
• Existing methods for comparing IV and OLS estimator bias often rely on unproven proxy assumptions for unmeasured confounders.

Purpose of the Study:

• To develop a formal testing framework for comparing the bias of IV and OLS estimators.
• To create a criterion for selecting informative covariates for bias comparison and regression adjustment.
• To propose a bias-correction method for using invalid IVs to improve OLS or IV estimators.

Main Methods:

• Developed a novel testing framework to formally compare bias between IV and OLS estimators.
• Proposed a criterion for selecting measured covariates to aid in bias comparison and regression adjustment.
• Introduced a bias-correction technique applicable even with invalid instrumental variables.

Main Results:

• The proposed testing framework and bias-correction method were evaluated through numerical studies.
• The methods demonstrated good performance with realistic sample sizes, suggesting practical utility.
• The criterion for covariate selection aids in identifying relevant variables for bias mitigation.

Conclusions:

• The developed framework provides a formal approach to assess IV estimator bias relative to OLS.
• The bias-correction method offers a way to improve causal effect estimates when standard IV assumptions are violated.
• These advancements enhance the reliability of causal inference in the presence of unobserved confounding.