Asymptotic Inference for Multi-Stage Stationary Treatment Policy with Variable Selection

Area of Science:

• Biostatistics
• Machine Learning
• Causal Inference

Background:

• Dynamic treatment regimes tailor decisions to individual patient features over time.
• Multi-stage stationary policies use consistent decision functions across stages based on evolving biomarkers.
• Existing research often overlooks policy inference, particularly with high-dimensional data.

Purpose of the Study:

• To develop a method for constructing and performing valid inference on multi-stage stationary treatment policies.
• To address challenges posed by high-dimensional features in dynamic treatment regimes.
• To enhance the efficiency and accuracy of policy estimation.

Main Methods:

• Obtained multi-stage stationary treatment policies by minimizing an augmented inverse probability weighted estimator.
• Applied an L1 penalty for feature selection in policy parameters.
• Constructed one-step improvements for policy parameter estimators to ensure valid inference.

Main Results:

• The proposed method yields a sparse policy with a near-optimal value function.
• The improved estimators demonstrate asymptotic normality, even with high-dimensional and slowly converging nuisance parameters.
• Numerical studies confirm the method's effectiveness in estimating policies and conducting valid inference.

Conclusions:

• The developed approach effectively estimates sparse dynamic treatment policies in high-dimensional settings.
• The method provides a robust framework for valid statistical inference on treatment policies.
• This work advances personalized medicine by enabling more accurate and efficient treatment decisions.