Variance Estimation for Weighted Average Treatment Effects

Area of Science:

• Statistics
• Observational Studies
• Causal Inference

Background:

• Estimating variance for weighted average treatment effects (WATEs) in observational studies commonly uses nonparametric bootstrap or sandwich variance estimation.
• Both methods have limitations: bootstrap's computational cost and potential positivity violations in replicates, and sandwich estimation's reliance on regularity conditions and model dependence.

Purpose of the Study:

• To propose and evaluate new variance estimation methods for WATEs.
• To address computational inefficiency and positivity violations in existing bootstrap methods.
• To generalize wild bootstrap for average treatment effect on the treated (ATT) to WATEs.

Main Methods:

• Proposed a "post-weighting" bootstrap approach to enhance conventional bootstrap.
• Generalized the wild bootstrap algorithm from ATT to WATEs.
• Evaluated four methods (including conventional bootstrap, sandwich, post-weighting bootstrap, and generalized wild bootstrap) via simulations and a real-world dataset (NHANES).

Main Results:

• The proposed post-weighting bootstrap avoids random positivity violations and improves computational efficiency.
• The generalized wild bootstrap effectively extends to WATEs, accounting for multiple sources of sampling variability.
• Simulation studies and NHANES data application demonstrated the performance of the evaluated methods.

Conclusions:

• The post-weighting bootstrap and generalized wild bootstrap offer practical and efficient alternatives for WATE variance estimation.
• Findings provide recommendations for choosing appropriate variance estimation techniques in observational research.
• The study highlights the importance of robust variance estimation for reliable causal inference.