IDENTIFICATION AND INFERENCE FOR MARGINAL AVERAGE TREATMENT EFFECT ON THE TREATED WITH AN INSTRUMENTAL VARIABLE

Area of Science:

• Biostatistics
• Epidemiology
• Econometrics

Background:

• Observational studies often suffer from confounding bias due to non-randomized treatments.
• Instrumental variable (IV) designs offer a quasi-experimental approach to mitigate bias.
• Estimating treatment effects in the presence of unmeasured confounding remains a significant challenge.

Purpose of the Study:

• To present a novel framework for identifying and inferring the marginal average treatment effect amongst the treated (ETT) using instrumental variables.
• To address the critical issue of unmeasured confounding in observational data.
• To develop robust semiparametric inference methods for causal effect estimation.

Main Methods:

• Utilized an instrumental variable (IV) design, leveraging its association with treatment and indirect effect on outcomes.
• Proposed three semiparametric inference approaches: inverse probability weighting (IPW), outcome regression (OR), and doubly robust (DR) estimation.
• Derived a closed-form locally semiparametric efficient estimator for binary IV and outcome, and established the efficiency bound for general cases.

Main Results:

• The proposed framework enables the identification and inference of ETT under unmeasured confounding.
• Doubly robust estimation offers consistency if either IPW or OR methods are consistent.
• A locally efficient estimator was derived for a specific common scenario, with efficiency bounds established for broader applications.

Conclusions:

• The novel IV framework provides a robust method for causal inference in observational studies with unmeasured confounding.
• The developed semiparametric approaches, particularly DR estimation, enhance the reliability of treatment effect estimates.
• This research contributes advanced statistical tools for more accurate causal effect estimation in complex observational settings.