A targeted maximum likelihood estimator of a causal effect on a bounded continuous outcome

Area of Science:

• Statistics
• Causal Inference
• Econometrics

Background:

• Targeted maximum likelihood estimation (TMLE) is a powerful statistical method for parameter estimation in semi-parametric models.
• A key challenge in TMLE is ensuring that parametric fluctuations remain within the bounds of the observed data model, particularly in sparse data situations.
• Violations can lead to poor estimator performance and inflated variance, especially when dealing with heavily weighted observations.

Purpose of the Study:

• To develop a novel fluctuation approach for TMLE that guarantees fluctuated density estimators stay within the data model's bounds.
• To enhance the robustness of TMLE in sparse data settings and when dealing with influential observations.
• To apply this method to estimate the causal effect of a binary treatment on a bounded continuous outcome.

Main Methods:

• The study proposes a new fluctuation strategy for TMLE that inherently respects known bounds of the data generating distribution.
• This approach is demonstrated in the context of estimating causal effects with binary treatments and bounded continuous outcomes.
• An alternative TMLE method is presented to dampen the influence of heavily weighted observations, offering an improvement over simple weight truncation.

Main Results:

• The proposed TMLE approach inherently respects known bounds, leading to more robust estimation in sparse data compared to naive fluctuation models.
• Simulation studies show the new method is comparable or superior to linear scale fluctuations, particularly in sparse data scenarios.
• The method effectively dampens the effect of heavily weighted observations, reducing variance inflation and potential bias.

Conclusions:

• The developed fluctuation approach ensures TMLE estimators remain within the semi-parametric model's bounds, enhancing robustness.
• This method provides a more stable and reliable way to estimate causal effects, especially in challenging data conditions like sparsity.
• The TMLE approach offers a superior alternative to traditional methods for handling influential observations and ensuring model validity.