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

2026-04-21

AI Summary

This study addresses the sensitivity of existing targeted maximum likelihood estimation (TMLE) methods to model misspecification and extreme propensity scores under violations of the positivity assumption. Through extensive simulations, the authors systematically evaluate various targeting strategies and truncation mechanisms, finding that loss-weighted targeting tends to introduce bias, whereas a fixed truncation rule of the form $c/(\sqrt{n}\log n)$ with $c=5$ or $6$ yields robust performance. To enhance tuning stability, they propose a Lepski-type adaptive truncation procedure equipped with a “braking” mechanism. Furthermore, they integrate a targeted bootstrap approach for variance estimation, demonstrating its reliability across multiple truncation levels.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

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.

Problem

• average treatment effect
• practical positivity violations
• targeted maximum likelihood estimation
• truncation
• observational data

Innovation

• Targeted Maximum Likelihood Estimation
• Practical Positivity Violation
• Adaptive Truncation
• Lepski-type Procedure
• Double Robustness