Variance estimation for weighted average treatment effects

2025-08-11

AI Summary

In observational studies, variance estimation for weighted average treatment effects (WATEs) faces challenges including computational expense, high risk of positivity violations, strong model dependence, and absence of a unified closed-form solution. To address these, this paper proposes a “post-weighting” bootstrap method and, for the first time, systematically extends the wild bootstrap to the WATE framework. By applying weights *after* resampling, the method inherently avoids positivity violations. It further establishes unified theoretical guarantees for wild bootstrap under common weighting schemes (e.g., inverse probability weighting, stabilized weights). Simulation studies and empirical analysis using NHANES data demonstrate that the proposed method outperforms standard benchmarks—including sandwich estimators and nonparametric bootstrap—in bias reduction, confidence interval coverage, and estimation stability. It thus enhances both efficiency and robustness of WATE inference, offering a scalable, implementation-friendly tool for causal inference practice.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Security and Privacy: Large-scale security measurements

Abstract

Common variance estimation methods for weighted average treatment effects (WATEs) in observational studies include nonparametric bootstrap and model-based, closed-form sandwich variance estimation. However, the computational cost of bootstrap increases with the size of the data at hand. Besides, some replicates may exhibit random violations of the positivity assumption even when the original data do not. Sandwich variance estimation relies on regularity conditions that may be structurally violated. Moreover, the sandwich variance estimation is model-dependent on the propensity score model, the outcome model, or both; thus it does not have a unified closed-form expression. Recent studies have explored the use of wild bootstrap to estimate the variance of the average treatment effect on the treated (ATT). This technique adopts a one-dimensional, nonparametric, and computationally efficient resampling strategy. In this article, we propose a "post-weighting" bootstrap approach as an alternative to the conventional bootstrap, which helps avoid random positivity violations in replicates and improves computational efficiency. We also generalize the wild bootstrap algorithm from ATT to the broader class of WATEs by providing new justification for correctly accounting for sampling variability from multiple sources under different weighting functions. We evaluate the performance of all four methods through extensive simulation studies and demonstrate their application using data from the National Health and Nutrition Examination Survey (NHANES). Our findings offer several practical recommendations for the variance estimation of WATE estimators.

Problem

• Improving variance estimation for weighted average treatment effects
• Addressing computational inefficiency in bootstrap methods
• Generalizing wild bootstrap for broader WATE applications

Innovation

• Proposes post-weighting bootstrap for variance estimation
• Generalizes wild bootstrap for broader WATEs class
• Avoids positivity violations and improves efficiency