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

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.