Investigating Targeting Strategies and Truncation in TMLE for the Average Treatment Effect under Practical Positivity Violations

TL;DR

This paper evaluates how targeting strategies and truncation levels influence TMLE performance in estimating average treatment effects under positivity violations, proposing adaptive truncation methods for improved stability.

Contribution

It introduces a Lepski-type adaptive truncation procedure with a brake mechanism and compares variance estimators to enhance TMLE robustness under practical positivity issues.

Findings

Loss-weighted targeting induces bias compared to clever-covariate scaling.

Insufficient truncation causes inflated variance and instability.

Fixed truncation rules like c/(sqrt(n) log n) offer robust defaults.

Abstract

Estimating average treatment effects from observational data is challenging under practical violations of the positivity assumption. Targeted Maximum Likelihood Estimators (TMLEs) are widely used because of their double robustness and efficiency, but they can remain sensitive to such violations. We conduct extensive simulation studies to examine how targeting strategies and truncation levels affect TMLE performance under varying degrees of outcome regression misspecification and practical positivity stress. We show that loss-weighted targeting can induce substantial systematic bias relative to clever-covariate-scaled targeting, while insufficient truncation for clever-covariate-scaled targeting leads to inflated variance and unstable estimation. We further find that fixed truncation rules of the form c/(sqrt(n) log n), especially with c = 5 or c = 6, provide robust practical defaults in many settings, although the optimal choice varies with sample size. Motivated by the limitations of standard Lepski selection, we propose a Lepski-type adaptive truncation procedure with a brake mechanism that improves stability in data-adaptive tuning. We also compare variance estimators and find that targeted bootstrap variance estimation provides a stable alternative across truncation levels.