On two-stage estimation of structural instrumental variable models.

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Two-stage least squares (2SLS) is common for structural equation models with unmeasured confounders.
• Standard 2SLS assumes complete observation of outcomes and exposures.
• Censored event times in outcomes and exposures present challenges for standard methods.

Purpose of the Study:

• To propose novel two-stage minimum distance estimators for structural equation models with incompletely observed outcomes and exposures.
• To address situations involving censored event times for both outcomes and exposures.
• To develop an optimal minimum distance estimator that may outperform standard 2SLS.

Main Methods:

• Proposed a general class of two-stage minimum distance estimators.
• Separately fitted linear models for outcome and exposure.
• Utilized a minimum distance criterion based on the reduced-form outcome model.
• Identified an optimal minimum distance estimator.

Main Results:

• The proposed estimators handle incompletely observed outcomes and exposures, including censored data.
• An optimal minimum distance estimator was identified, potentially superior to standard 2SLS.
• Simulation studies confirmed good performance with realistic sample sizes.

Conclusions:

• The developed two-stage minimum distance estimators are effective for analyzing complex observational data with censoring.
• These methods offer practical utility, as demonstrated in a colon cancer treatment effectiveness study.
• The approach provides a robust alternative for causal inference when outcomes and exposures are not fully observed.