Background: Advanced methods for causal inference, such as targeted maximum likelihood estimation (TMLE), require certain conditions for statistical inference. However, in situations where there is not differentiability due to data sparsity or near-positivity violations, the Donsker class condition is violated. In such situations, TMLE variance can suffer from inflation of the type I error and poor coverage, leading to conservative confidence intervals. Cross-validation of the TMLE algorithm (CVTMLE) has been suggested to improve on performance compared to TMLE in settings of positivity or Donsker class violations. We aim to investigate the performance of CVTMLE compared to TMLE in various settings. Methods: We utilised the data-generating mechanism as described in Leger et al. (2022) to run a Monte Carlo experiment under different Donsker class violations. Then, we evaluated the respective statistical performances of TMLE and CVTMLE with different super learner libraries, with and without regression tree methods. Results: We found that CVTMLE vastly improves confidence interval coverage without adversely affecting bias, particularly in settings with small sample sizes and near-positivity violations. Furthermore, incorporating regression trees using standard TMLE with ensemble super learner-based initial estimates increases bias and variance leading to invalid statistical inference. Conclusions: It has been shown that when using CVTMLE the Donsker class condition is no longer necessary to obtain valid statistical inference when using regression trees and under either data sparsity or near-positivity violations. We show through simulations that CVTMLE is much less sensitive to the choice of the super learner library and thereby provides better estimation and inference in cases where the super learner library uses more flexible candidates and is prone to overfitting.

翻译：背景：因果推断的先进方法，如目标最大似然估计（TMLE），需要满足特定条件才能进行统计推断。然而，在数据稀疏性或近似正性违例导致不可微的情况下，Donsker类条件会被违反。在此类情况下，TMLE方差可能遭受I类错误膨胀和覆盖率不足的问题，导致置信区间过于保守。已有研究表明，在正性条件或Donsker类违例的场景中，采用交叉验证的TMLE算法（CVTMLE）相比TMLE能提升性能。本研究旨在探究不同场景下CVTMLE与TMLE的性能差异。方法：我们采用Leger等人（2022）描述的数据生成机制，在不同程度的Donsker类违例条件下进行蒙特卡洛实验。随后，我们评估了TMLE与CVTMLE在使用不同超级学习器库（包含及不包含回归树方法）时的统计性能。结果：研究发现CVTMLE能显著提升置信区间覆盖率，且不会对偏差产生负面影响，这一优势在小样本量和近似正性违例的场景中尤为明显。此外，在使用基于集成超级学习器的初始估计时，标准TMLE结合回归树方法会增加偏差和方差，从而导致无效的统计推断。结论：研究表明，当使用回归树方法且在数据稀疏性或近似正性违例条件下，采用CVTMLE时不再需要满足Donsker类条件即可获得有效的统计推断。我们通过模拟实验证明，CVTMLE对超级学习器库的选择敏感度显著降低，因此在超级学习器库采用更灵活的候选模型且容易过拟合的情况下，能提供更优的估计和推断结果。