Overlap-Weight Estimators With Machine-Learned Plug-Ins and Overlap-Weight Targeted Maximum Likelihood Estimator

Area of Science:

• Statistics
• Causal Inference
• Econometrics

Background:

• Semiparametric efficiency in estimating average treatment effect (ATE) is achieved by plug-in estimators and targeted maximum likelihood estimators (TMLE).
• Instability arises from small or large propensity scores (PS) in these estimators, often addressed by data trimming or truncation.
• These traditional methods modify the target parameter, moving away from the ATE.

Purpose of the Study:

• To propose a novel smooth weighting method using quadratic propensity scores (PS) for more stable treatment effect estimation.
• To introduce the "overlap-weight (OW) treatment effect" as an alternative target parameter with advantages over the ATE.
• To compare the performance of OW estimators against trimmed estimators.

Main Methods:

• Development of a smooth, quadratic propensity score (PS) weighting approach.
• Comparison of estimators including trimmed efficient influence function, TMLE, and their overlap-weight (OW) versions.
• Utilizing simulation studies and empirical data analysis for performance evaluation.
• Investigating the impact of "cross-fitting" on variance estimation.

Main Results:

• Overlap-weight (OW) versions of estimators demonstrated superior performance compared to trimmed versions.
• OW estimators exhibited lower absolute bias and root mean squared error in simulations where ATE was constant.
• "Cross-fitting" techniques were found to enhance the asymptotic variance estimators.

Conclusions:

• The proposed overlap-weight (OW) approach offers a more stable and accurate method for estimating treatment effects compared to traditional trimming techniques.
• OW estimators provide a valuable alternative for causal inference, particularly when dealing with propensity score instability.
• Cross-fitting is a beneficial technique for improving the precision of variance estimation in these models.