Resampling-based confidence intervals for model-free robust inference on optimal treatment regimes

Area of Science:

• Biostatistics
• Machine Learning
• Causal Inference

Background:

• Optimal treatment regimes (OTRs) are crucial for personalized medicine.
• Existing model-free OTR estimators often lack reliable statistical inference due to asymptotic issues or surrogate loss functions.
• There is a need for robust, model-free methods that support valid inference for OTRs.

Purpose of the Study:

• To develop a novel procedure for statistical inference on OTRs in a model-free setting.
• To address limitations of existing estimators regarding asymptotic distributions and consistent parameter estimation.
• To provide a method for reliable inference on both the OTR parameter and the optimal value function.

Main Methods:

• Propose a smoothed robust estimator that directly targets the Bayes decision rule parameter for OTR estimation.
• Establish asymptotic normality for the proposed smoothed robust estimator.
• Develop and validate a resampling procedure for asymptotically accurate inference.
• Introduce a new algorithm for efficient and stable computation of the estimator.

Main Results:

• The proposed smoothed robust estimator demonstrates asymptotic normality.
• The resampling procedure ensures asymptotically accurate inference for OTR parameters and value functions.
• The new algorithm significantly improves computational speed and stability.
• Numerical simulations confirm the satisfactory performance of the developed methods.

Conclusions:

• The new procedure provides a statistically valid and computationally efficient approach for model-free OTR inference.
• This method overcomes key limitations of previous model-free estimators, enhancing their practical utility.
• The findings support the application of this method in personalized treatment strategies and decision-making.