One-step TMLE for weighted average treatment effects

2026-03-31

AI Summary

This study addresses the efficient and robust estimation of weighted average treatment effects (WATEs), including the average treatment effect (ATE) and the average treatment effect on the treated (ATT). Building upon the targeted maximum likelihood estimation (TMLE) framework, we construct a one-step estimator along a universal least favorable submodel. By explicitly incorporating a weight function and imposing mild regularity conditions on initial estimators, our approach ensures that the targeting procedure is well-defined, converges in finitely many steps, and intrinsically controls second-order remainder terms—without requiring additional assumptions. Under standard regularity conditions, the proposed method achieves asymptotic efficiency for WATEs, offering both theoretical optimality and numerical stability.

Abstract

We consider Targeted Maximum Likelihood Estimation (TMLE) of weighted average treatment effects (WATEs), a class of causal estimands that reweight the covariate distribution using a specified function of the propensity score. This class includes the average treatment effect and average treatment effect on the treated, as well as various overlap-based targets. We provide a comprehensive analysis of the one-step TMLE along the universal least favorable path for such parameters. Under explicit regularity conditions on the weight function and initialization, we show that the targeting procedure is well-defined, reaches a solution of the estimating equation in finite time, and yields an asymptotically efficient estimator. In particular, convergence of the targeting dynamics and control of the second-order remainder are derived from these conditions rather than imposed as separate assumptions on the output of the algorithm.

Problem

• weighted average treatment effects
• causal inference
• propensity score
• Targeted Maximum Likelihood Estimation
• asymptotic efficiency

Innovation

• one-step TMLE
• weighted average treatment effects
• universal least favorable path
• asymptotic efficiency
• propensity score weighting