On regression adjustment for the propensity score.

Area of Science:

• Epidemiology
• Biostatistics
• Observational Research Methods

Background:

• Propensity scores are crucial for adjusting high-dimensional confounders in observational studies.
• Methods like stratification, matching, and inverse weighting by propensity scores reduce extrapolation risks compared to outcome regression alone.
• Standard regression adjustment with propensity scores offers an alternative, but its benefits require further examination.

Purpose of the Study:

• To investigate the properties of standard regression adjustment using propensity scores.
• To demonstrate the robustness of this method against outcome model misspecification.
• To propose efficient estimators for standardized effects with causal interpretation.

Main Methods:

• Analysis of standard tests for null hypothesis of no exposure effect using robust variance estimators.
• Development of efficient estimators for standardized effects.
• Evaluation of robustness against outcome model misspecification under correct propensity score model specification.

Main Results:

• Standardized effects and null hypothesis tests from regression adjusted by propensity scores are robust to outcome model misspecification if the propensity score model is correct.
• The proposed estimators for standardized effects maintain causal interpretability even with a misspecified propensity score model, provided the outcome regression model is correctly specified.
• This method avoids the diagnostic challenges of extrapolation inherent in purely outcome regression models.

Conclusions:

• Standard regression adjustment using propensity scores provides a reliable method for causal inference in observational studies.
• The approach offers protection against extrapolation errors, a common issue in outcome regression models.
• Efficient estimators enhance the utility and interpretability of results, even under certain model misspecifications.