Inference for Optimal Linear Treatment Regimes in Personalized Decision-making

Yuwen Cheng, Shu Yang
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:718-735, 2024.

Abstract

Personalized decision-making, tailored to individual characteristics, is gaining significant attention. The optimal treatment regime aims to provide the best-expected outcome in the entire population, known as the value function. One approach to determine this optimal regime is by maximizing the Augmented Inverse Probability Weighting (AIPW) estimator of the value function. However, the derived treatment regime can be intricate and nonlinear, limiting their use. For clarity and interoperability, we emphasize linear regimes and determine the optimal linear regime by optimizing the AIPW estimator within set constraints. While the AIPW estimator offers a viable path to estimating the optimal regime, current methodologies predominantly focus on its asymptotic distribution, leaving a gap in studying the linear regime itself. However, there are many benefits to understanding the regime, as pinpointing significant covariates can enhance treatment effects and provide future clinical guidance. In this paper, we explore the asymptotic distribution of the estimated linear regime. Our results show that the parameter associated with the linear regime follows a cube-root convergence to a non-normal limiting distribution characterized by the maximizer of a centered Gaussian process with a quadratic drift. When making inferences for the estimated linear regimes with cube-root convergence in practical scenarios, the standard nonparametric bootstrap is invalid. As a solution, we facilitate the Cattaneo et al. (2020) bootstrap technique to provide a consistent distributional approximation for the estimated linear regimes, validated further through simulations and real-world data applications from the eICU Collaborative Research Database.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-cheng24b, title = {Inference for Optimal Linear Treatment Regimes in Personalized Decision-making}, author = {Cheng, Yuwen and Yang, Shu}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {718--735}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/cheng24b/cheng24b.pdf}, url = {https://proceedings.mlr.press/v244/cheng24b.html}, abstract = {Personalized decision-making, tailored to individual characteristics, is gaining significant attention. The optimal treatment regime aims to provide the best-expected outcome in the entire population, known as the value function. One approach to determine this optimal regime is by maximizing the Augmented Inverse Probability Weighting (AIPW) estimator of the value function. However, the derived treatment regime can be intricate and nonlinear, limiting their use. For clarity and interoperability, we emphasize linear regimes and determine the optimal linear regime by optimizing the AIPW estimator within set constraints. While the AIPW estimator offers a viable path to estimating the optimal regime, current methodologies predominantly focus on its asymptotic distribution, leaving a gap in studying the linear regime itself. However, there are many benefits to understanding the regime, as pinpointing significant covariates can enhance treatment effects and provide future clinical guidance. In this paper, we explore the asymptotic distribution of the estimated linear regime. Our results show that the parameter associated with the linear regime follows a cube-root convergence to a non-normal limiting distribution characterized by the maximizer of a centered Gaussian process with a quadratic drift. When making inferences for the estimated linear regimes with cube-root convergence in practical scenarios, the standard nonparametric bootstrap is invalid. As a solution, we facilitate the Cattaneo et al. (2020) bootstrap technique to provide a consistent distributional approximation for the estimated linear regimes, validated further through simulations and real-world data applications from the eICU Collaborative Research Database.} }
Endnote
%0 Conference Paper %T Inference for Optimal Linear Treatment Regimes in Personalized Decision-making %A Yuwen Cheng %A Shu Yang %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-cheng24b %I PMLR %P 718--735 %U https://proceedings.mlr.press/v244/cheng24b.html %V 244 %X Personalized decision-making, tailored to individual characteristics, is gaining significant attention. The optimal treatment regime aims to provide the best-expected outcome in the entire population, known as the value function. One approach to determine this optimal regime is by maximizing the Augmented Inverse Probability Weighting (AIPW) estimator of the value function. However, the derived treatment regime can be intricate and nonlinear, limiting their use. For clarity and interoperability, we emphasize linear regimes and determine the optimal linear regime by optimizing the AIPW estimator within set constraints. While the AIPW estimator offers a viable path to estimating the optimal regime, current methodologies predominantly focus on its asymptotic distribution, leaving a gap in studying the linear regime itself. However, there are many benefits to understanding the regime, as pinpointing significant covariates can enhance treatment effects and provide future clinical guidance. In this paper, we explore the asymptotic distribution of the estimated linear regime. Our results show that the parameter associated with the linear regime follows a cube-root convergence to a non-normal limiting distribution characterized by the maximizer of a centered Gaussian process with a quadratic drift. When making inferences for the estimated linear regimes with cube-root convergence in practical scenarios, the standard nonparametric bootstrap is invalid. As a solution, we facilitate the Cattaneo et al. (2020) bootstrap technique to provide a consistent distributional approximation for the estimated linear regimes, validated further through simulations and real-world data applications from the eICU Collaborative Research Database.
APA
Cheng, Y. & Yang, S.. (2024). Inference for Optimal Linear Treatment Regimes in Personalized Decision-making. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:718-735 Available from https://proceedings.mlr.press/v244/cheng24b.html.

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