Performance of Cross-Validated Targeted Maximum Likelihood Estimation.

Area of Science:

• Causal inference
• Statistical methodology
• Machine learning in statistics

Background:

• Targeted maximum likelihood estimation (TMLE) relies on Donsker class conditions for valid inference.
• Violations of these conditions, due to data sparsity or near-positivity issues, inflate bias and lead to anti-conservative variance.
• Cross-validation of TMLE (CVTMLE) offers a robust alternative in such challenging settings.

Purpose of the Study:

• To investigate the performance of CVTMLE compared to standard TMLE.
• To evaluate their effectiveness under various Donsker class violations.
• To assess the impact of super learner libraries and regression trees on estimation and inference.

Main Methods:

• A Monte Carlo experiment was conducted using a data-generating mechanism with varying Donsker class violations.
• The statistical performance of TMLE and CVTMLE was evaluated.
• Different super learner libraries, with and without regression tree methods, were employed.

Main Results:

• CVTMLE significantly enhances confidence interval coverage without increasing bias, particularly in small sample sizes and near-positivity violation scenarios.
• Standard TMLE with ensemble super learner and regression trees increased bias and reduced variance, compromising statistical inference.
• CVTMLE demonstrated reduced sensitivity to super learner library choice, improving estimation and inference.

Conclusions:

• CVTMLE provides superior statistical estimation and inference compared to standard TMLE when Donsker class conditions are violated.
• The method is particularly beneficial in settings prone to overfitting with flexible super learner candidates.
• CVTMLE offers a more reliable approach for causal inference in challenging data conditions.