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Proper Inference for Value Function in High-Dimensional Q-Learning for Dynamic Treatment Regimes.

Wensheng Zhu1, Donglin Zeng2, Rui Song3

  • 1Key Laboratory for Applied Statistics of MOE,School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China (wszhu@nenu.edu.cn).

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|January 14, 2020
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Summary
This summary is machine-generated.

This study introduces high-dimensional Q-learning (HQ-learning) for optimal dynamic treatment regimes. The method effectively handles non-respondents and high-dimensional data for accurate statistical inference.

Keywords:
Hard thresholdQ-learningValue function inferenceVariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Dynamic treatment regimes tailor medical decisions over time based on patient responses and history.
  • Statistical inference for optimal dynamic treatment regimes faces challenges, particularly with non-respondents and high-dimensional data.

Purpose of the Study:

  • To develop a robust statistical inference method for optimal dynamic treatment regimes.
  • To address challenges posed by non-respondents and high-dimensional tailoring variables.
  • To simultaneously estimate optimal regimes and identify key predictive variables.

Main Methods:

  • Proposes high-dimensional Q-learning (HQ-learning) for parameter and value function estimation.
  • Incorporates hard thresholding to mitigate the impact of non-respondents.
  • Establishes asymptotic properties of estimators, adjusting for thresholding bias.

Main Results:

  • HQ-learning effectively estimates optimal dynamic treatment regimes and selects important variables.
  • The method demonstrates satisfactory performance in simulation studies and real data analysis.
  • Accurate inference for the value function of optimal dynamic treatment regimes is achieved.

Conclusions:

  • HQ-learning provides a powerful tool for statistical inference in complex dynamic treatment regimes.
  • The approach successfully handles non-respondents and high-dimensional data.
  • This method enhances the reliability of identifying optimal treatment strategies.