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.

翻译：从观测数据估计平均处理效应在实际违背正性假设时面临挑战。靶向最大似然估计量（TMLEs）因其双重稳健性和高效性被广泛使用，但对此类违背仍可能保持敏感。我们通过大量模拟研究，探讨在不同程度的结果回归误设定和实际正性压力下，靶向策略与截断水平对TMLE性能的影响。研究表明，与基于巧妙协变量缩放的靶向相比，损失加权靶向可能引发显著系统性偏差，而巧妙协变量缩放靶向的截断不足会导致方差膨胀和估计不稳定。进一步发现，形式为c/(sqrt(n) log n)的固定截断规则（尤其是c=5或c=6）在多种情境下可作为稳健的实践默认值，尽管最优选择随样本量变化。受标准莱普斯基选择局限性的启发，我们提出一种含制动机制的莱普斯基型自适应截断程序，可提升数据自适应调优的稳定性。我们还比较了方差估计量，发现靶向自举方差估计在不同截断水平下提供了稳定的替代方案。