Propensity score specification for optimal estimation of average treatment effect with binary response

Area of Science:

• Statistics
• Observational Data Analysis
• Causal Inference

Background:

• Propensity score methods are crucial for reducing confounding bias in observational studies.
• Accurate estimation of average treatment effect (ATE) relies on precise propensity score specification.
• Previous simulations suggested optimal ATE estimation uses true confounders, but lacked theoretical basis.

Purpose of the Study:

• To provide a theoretical proof for the optimal specification of propensity scores using true confounders.
• To introduce a novel method for variable selection and propensity score estimation using elastic net regression.
• To compare the proposed method with existing techniques for ATE estimation.

Main Methods:

• Theoretical derivation of propensity score optimality.
• Elastic net regression for variable selection and propensity score estimation.
• Extensive simulation studies comparing proposed method with outcome-adaptive lasso and covariate balancing propensity score.
• Application to a real-world dataset of pre-cardiac surgery patients.

Main Results:

• Theoretical proof confirms that propensity scores should be functions of true confounders and predictors only for optimal ATE.
• The proposed elastic net regression method demonstrated effectiveness in simulations.
• Comparative analysis identified specific conditions where each method (proposed, outcome-adaptive lasso, covariate balancing propensity score) performed best.
• The method was successfully applied to analyze the impact of coagulation indicators on mortality in cardiac surgery patients.

Conclusions:

• The theoretical framework supports precise propensity score construction for unbiased ATE estimation.
• The elastic net regression approach offers a robust method for variable selection and propensity score estimation.
• This research provides valuable insights for researchers analyzing observational data and aiming for accurate causal effect inference.