One-step TMLE for weighted average treatment effects

TL;DR

This paper develops a one-step TMLE method for estimating weighted average treatment effects, ensuring efficiency and finite-time convergence under explicit regularity conditions.

Contribution

It provides a comprehensive analysis of the one-step TMLE for WATEs, establishing conditions for well-definedness, convergence, and asymptotic efficiency.

Findings

The targeting procedure is well-defined and reaches a solution in finite time.

The estimator is asymptotically efficient under regularity conditions.

Convergence and second-order remainder control are derived from explicit conditions.

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.