Based on the condition of alcohol dependant patients (S1), the physician may prescribe a medication or behavioral therapy (X1).

Treatment individualization and adaptation over time are crucial for managing chronic diseases.

Individualized treatment regimes (ITRs) aim to improve clinical outcomes by assigning treatment based on patient-specific characteristics. However, existing methods often struggle with high-dimensional covariates, limiting accuracy, interpretability, and real-world applicability. We propose a novel sufficient dimension reduction approach that directly targets the contrast between potential outcomes and identifies a low-dimensional subspace of the covariates capturing treatment effect heterogeneity. This reduced representation enables more accurate estimation of optimal ITRs through outcome-weighted learning. To accommodate observational data, our method incorporates kernel-based covariate balancing, allowing treatment assignment to depend on the full covariate set and avoiding the restrictive assumption that the subspace sufficient for modeling heterogeneous treatment effects is also sufficient for confounding adjustment. We show that the proposed method achieves universal consistency, i.e., its risk converges to the Bayes risk, under mild regularity conditions. We demonstrate its finite sample performance through simulations and an analysis of intensive care unit sepsis patient data to determine who should receive transthoracic echocardiography.

The formal definition of sensitive variables will be given in Section 3.

The formal definition of sensitive variables will be given in Section 3.

Dynamic treatment regimes are sequential decision rules that adapt treatment according to individual time-varying characteristics and outcomes to achieve optimal effects, with applications in precision medicine, personalized recommendations, and dynamic marketing. Estimating optimal dynamic treatment regimes via sequential randomized trials might face costly and ethical hurdles, often necessitating the use of historical observational data. In this work, we utilize proximal causal inference framework for learning optimal dynamic treatment regimes when the unconfoundedness assumption fails. Our contributions are four-fold: (i) we propose three nonparametric identification methods for optimal dynamic treatment regimes; (ii) we establish the semiparametric efficiency bound for the value function of a given regime; (iii) we propose a (K+1)-robust method for learning optimal dynamic treatment regimes, where K is the number of stages; (iv) as a by-product for marginal structural models, we establish identification and estimation of counterfactual means under a static regime. Numerical experiments validate the efficiency and multiple robustness of our proposed methods.

The ICH E9(R1) guideline presents a framework for clinical trials to align planning, design, conduct, analysis, and interpretation (ICH, 2020). The three key steps in the framework are: estimand, estimator, and sensitivity analysis (Mallinckrodt et al., 2020). ICH E9(R1) highlights the importance of dealing with intercurrent events (ICEs), which are defined as: "Events occurring after treatment initiation that affect either the interpretation or the existence of the measurements associated with the clinical question of interest. It is necessary to address intercurrent events when describing the clinical question of interest in order to precisely define the treatment effect that is to be estimated." ICH E9(R1) proposes five strategies for dealing with ICEs in clinical trials with quantitative outcomes and categorical outcomes: treatment policy strategy, hypothetical strategy, composite variable strategy, while-on-treatment strategy, and principal stratum strategy.