Finding the Optimal Number of Splits and Repetitions in Double Cross-Fitting Targeted Maximum Likelihood Estimators

Area of Science:

• * Causal inference and statistical learning.
• * Application of machine learning in biostatistics and epidemiology.

Background:

• * Flexible machine learning algorithms in double robust methods (e.g., Targeted Maximum Likelihood Estimator - TMLE) can lead to undercoverage.
• * The Double Cross-Fitting (DCF) procedure allows diverse machine learning estimators but lacks clear guidelines on data splits and repetitions.

Purpose of the Study:

• * To investigate the impact of varying data splits and repetitions in DCF on TMLE estimators.
• * To compare statistical properties of DCF configurations using different split numbers and generalizations.
• * To assess the practical implications of DCF split variations in a real-world health study.

Main Methods:

• * Statistical simulations comparing DCF configurations with varying splits (e.g., 3, 5) and repetitions.
• * Evaluation of two DCF generalizations: equal splits and full data use for nuisance estimation.
• * Application of DCF TMLE to National Health and Nutrition Examination Survey (NHANES) data to study obesity and diabetes risk.

Main Results:

• * Five splits in DCF demonstrated satisfactory bias, variance, and coverage in simulations.
• * DCF TMLE risk difference estimates were consistent across splits in the NHANES analysis, but standard errors increased with more splits in one generalization.
• * Increasing repetitions beyond 25 did not yield performance improvements.

Conclusions:

• * Judicious selection of splits (3-5 recommended) and repetitions is crucial for DCF TMLE methods.
• * Using full data for nuisance estimation in DCF provides more consistent variance estimation.
• * Cautious management of splits in DCF is advised for accurate causal inference with machine learning.