Inference for optimal dynamic treatment regimes using an adaptive m-out-of-n bootstrap scheme. A dynamic treatment regime consists of a set of decision rules that dictate how to individualize treatment to patients based on available treatment and covariate history. A common method for estimating an optimal dynamic treatment regime from data is Q-learning which involves nonsmooth operations of the data. This nonsmoothness causes standard asymptotic approaches for inference like the bootstrap or Taylor series arguments to breakdown if applied without correction. Here, we consider the m-out-of-n bootstrap for constructing confidence intervals for the parameters indexing the optimal dynamic regime. We propose an adaptive choice of m and show that it produces asymptotically correct confidence sets under fixed alternatives. Furthermore, the proposed method has the advantage of being conceptually and computationally much simple than competing methods possessing this same theoretical property. We provide an extensive simulation study to compare the proposed method with currently available inference procedures. The results suggest that the proposed method delivers nominal coverage while being less conservative than alternatives. The proposed methods are implemented in the qLearn R-package and have been made available on the Comprehensive R-Archive Network (http://cran.r-project.org/). Analysis of the Sequenced Treatment Alternatives to Relieve Depression (STAR * D) study is used as an illustrative example.

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  1. Ertefaie, Ashkan; McKay, James R.; Oslin, David; Strawderman, Robert L.: Robust Q-learning (2021)
  2. Qian, Min; Chakraborty, Bibhas; Maiti, Raju; Cheung, Ying Kuen: A sequential significance test for treatment by covariate interactions (2021)
  3. Hong, Han; Li, Jessie: The numerical bootstrap (2020)
  4. Simoneau, Gabrielle; Moodie, Erica E. M.; Wallace, Michael P.; Platt, Robert W.: Optimal dynamic treatment regimes with survival endpoints: introducing \textttDWSurvin the \textttRpackage \textttDTRreg (2020)
  5. Zhu, Wensheng; Zeng, Donglin; Song, Rui: Proper inference for value function in high-dimensional Q-learning for dynamic treatment regimes (2019)
  6. Kidwell, Kelley M.; Seewald, Nicholas J.; Tran, Qui; Kasari, Connie; Almirall, Daniel: Design and analysis considerations for comparing dynamic treatment regimens with binary outcomes from sequential multiple assignment randomized trials (2018)
  7. Laber, Eric B.; Staicu, Ana-Maria: Functional feature construction for individualized treatment regimes (2018)
  8. Murray, Thomas A.; Yuan, Ying; Thall, Peter F.: A Bayesian machine learning approach for optimizing dynamic treatment regimes (2018)
  9. Michael Wallace; Erica Moodie; David Stephens: Dynamic Treatment Regimen Estimation via Regression-Based Techniques: Introducing R Package DTRreg (2017) not zbMATH
  10. Tao, Yebin; Wang, Lu: Adaptive contrast weighted learning for multi-stage multi-treatment decision-making (2017)
  11. Chakraborty, Bibhas; Ghosh, Palash; Moodie, Erica E. M.; Rush, A. John: Estimating optimal shared-parameter dynamic regimens with application to a multistage depression clinical trial (2016)
  12. Cheung, Ying Kuen; Chakraborty, Bibhas; Davidson, Karina W.: Sequential multiple assignment randomized trial (SMART) with adaptive randomization for quality improvement in depression treatment program (2015)
  13. Wallace, Michael P.; Moodie, Erica E. M.: Doubly-robust dynamic treatment regimen estimation via weighted least squares (2015)
  14. Xu, Yaoyao; Yu, Menggang; Zhao, Ying-Qi; Li, Quefeng; Wang, Sijian; Shao, Jun: Regularized outcome weighted subgroup identification for differential treatment effects (2015)
  15. Laber, Eric B.; Lizotte, Daniel J.; Qian, Min; Pelham, William E.; Murphy, Susan A.: Dynamic treatment regimes: technical challenges and applications (2014)
  16. Chakraborty, Bibhas; Laber, Eric B.; Zhao, Yingqi: Inference for optimal dynamic treatment regimes using an adaptive (m)-out-of-(n) bootstrap scheme (2013)
  17. Chakraborty, Bibhas; Moodie, Erica E. M.: Statistical methods for dynamic treatment regimes. Reinforcement learning, causal inference, and personalized medicine (2013)
  18. Zhang, Baqun; Tsiatis, Anastasios A.; Laber, Eric B.; Davidian, Marie: Robust estimation of optimal dynamic treatment regimes for sequential treatment decisions (2013)
  19. Moodie, Erica E. M.; Chakraborty, Bibhas; Kramer, Michael S.: Q-learning for estimating optimal dynamic treatment rules from observational data (2012)
  20. Wang, Weiwei; Scharfstein, Daniel; Wang, Chenguang; Daniels, Michael; Needham, Dale; Brower, Roy: Estimating the causal effect of low tidal volume ventilation on survival in patients with acute lung injury (2011)