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1. Non-asymptotic properties of individualized treatment rules from sequentially rule-adaptive trials

   Gao, D.; Liu, Y.; Zeng, D. (January 2022, Journal of machine learning research)

   Learning optimal individualized treatment rules (ITRs) has become increasingly important in the modern era of precision medicine. Many statistical and machine learning methods for learning optimal ITRs have been developed in the literature. However, most existing methods are based on data collected from traditional randomized controlled trials and thus cannot take advantage of the accumulative evidence when patients enter the trials sequentially. It is also ethically important that future patients should have a high probability to be treated optimally based on the updated knowledge so far. In this work, we propose a new design called sequentially rule-adaptive trials to learn optimal ITRs based on the contextual bandit framework, in contrast to the response-adaptive design in traditional adaptive trials. In our design, each entering patient will be allocated with a high probability to the current best treatment for this patient, which is estimated using the past data based on some machine learning algorithm (for example, outcome weighted learning in our implementation). We explore the tradeoff between training and test values of the estimated ITR in single-stage problems by proving theoretically that for a higher probability of following the estimated ITR, the training value converges to the optimal value at a faster rate, while the test value converges at a slower rate. This problem is different from traditional decision problems in the sense that the training data are generated sequentially and are dependent. We also develop a tool that combines martingale with empirical process to tackle the problem that cannot be solved by previous techniques for i.i.d. data. We show by numerical examples that without much loss of the test value, our proposed algorithm can improve the training value significantly as compared to existing methods. Finally, we use a real data study to illustrate the performance of the proposed method. 

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2. A reluctant additive model framework for interpretable nonlinear individualized treatment rules

   https://doi.org/10.1214/23-AOAS1767  

   Maronge, Jacob M; Huling, Jared D; Chen, Guanhua (December 2023, The Annals of Applied Statistics)

   Individualized treatment rules (ITRs) for treatment recommendation is an important topic for precision medicine as not all beneficial treatments work well for all individuals. Interpretability is a desirable property of ITRs, as it helps practitioners make sense of treatment decisions, yet there is a need for ITRs to be flexible to effectively model complex biomedical data for treatment decision making. Many ITR approaches either focus on linear ITRs, which may perform poorly when true optimal ITRs are nonlinear, or blackbox nonlinear ITRs, which may be hard to interpret and can be overly complex. This dilemma indicates a tension between interpretability and accuracy of treatment decisions. Here we propose an additive model-based nonlinear ITR learning method that balances interpretability and flexibility of the ITR. Our approach aims to strike this balance by allowing both linear and nonlinear terms of the covariates in the final ITR. Our approach is parsimonious in that the nonlinear term is included in the final ITR only when it substantially improves the ITR performance. To prevent overfitting, we combine crossfitting and a specialized information criterion for model selection. Through extensive simulations we show that our methods are data-adaptive to the degree of nonlinearity and can favorably balance ITR interpretability and flexibility. We further demonstrate the robust performance of our methods with an application to a cancer drug sensitive study. 

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3. Advancement of Inferences for GeneticTreatment Effects under Semiparametric Models

   https://doi.org/10.25394/pgs.28851797  

   Cui, Yishan (June 2025, Purdue University Graduate School)

   Abstract: This dissertation presents three methodological advancements in semiparametric modeling and inference, with applications in longitudinal data analysis and individualized treatment rules (ITRs).First, we enhance the semiparametric profile estimator for analyzing longitudinal data, addressing the challenge of within-subject correlation. By incorporating a nonparametric operator-regularized approach for estimating the covariance function, we develop a refined estimator that significantly improves efficiency over traditional local kernel smoothing methods, which assume an independent correlation structure. We further introduce an Empirical Likelihood (EL)-based inference method and demonstrate, through simulations and an application to the Genetic Analysis Workshop 18 dataset, that our approach attains the semiparametric efficiency bound and outperforms existing methods.Second, we propose a rank-based inference procedure for ITRs under a semiparametric single-index varying coefficient model, where the nonparametric coefficient function is assumed to be monotone increasing. By leveraging maximum rank correlation, our method circumvents direct estimation of the nonparametric function, thereby mitigating potential biases. For hypothesis testing, we derive the asymptotic distribution of the proposed estimator using de-biasing techniques. Monte Carlo simulations and an application to the ACTG175 dataset confirm the effectiveness of our approach.Finally, we develop a jackknife empirical likelihood ratio test to enhance hypothesis testing in the semiparametric single-index varying coefficient model. Existing methods often rely on plug-in variance-covariance estimators that approximate indicator functions using a sigmoid transformation, which are computationally complex and difficult to implement. Our proposed test offers a much simpler computational approach while achieving the same effectiveness. Extensive simulations and real-data analysis using the ACTG175 dataset further demonstrate the efficiency and practicality of our method.Together, these contributions enhance the efficiency and reliability of semiparametric estimation and inference, particularly in the contexts of longitudinal data analysis and individualized treatment decision-making. 

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4. An effective framework for estimating individualized treatment rules

   https://doi.org/10.52202/079017-0270  

   Chen, Guanhua; Huling, Jared; Lee, Joowon (December 2024, Neural Information Processing Systems Foundation, Inc. (NeurIPS))

   Estimating individualized treatment rules (ITRs) is fundamental in causal inference, particularly for precision medicine applications. Traditional ITR estimation methods rely on inverse probability weighting (IPW) to address confounding factors and L1-penalization for simplicity and interpretability. However, IPW can introduce statistical bias without precise propensity score modeling, while L1-penalization makes the objective non-smooth, leading to computational bias and requiring subgradient methods. In this paper, we propose a unified ITR estimation framework formulated as a constrained, weighted, and smooth convex optimization problem. The optimal ITR can be robustly and effectively computed by projected gradient descent. Our comprehensive theoretical analysis reveals that weights that balance the spectrum of a `weighted design matrix' improve both the optimization and likelihood landscapes, yielding improved computational and statistical estimation guarantees. In particular, this is achieved by distributional covariate balancing weights, which are model-free alternatives to IPW. Extensive simulations and applications demonstrate that our framework achieves significant gains in both robustness and effectiveness for ITR learning against existing methods. 

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5. Estimation and optimization of composite outcomes

   Lucket, Daniel (May 2021, Journal of Machine Learning Research)

   There is tremendous interest in precision medicine as a means to improve patient out- comes by tailoring treatment to individual characteristics. An individualized treatment rule formalizes precision medicine as a map from patient information to a recommended treatment. A treatment rule is defined to be optimal if it maximizes the mean of a scalar outcome in a population of interest, e.g., symptom reduction. However, clinical and intervention scientists often seek to balance multiple and possibly competing outcomes, e.g., symptom reduction and the risk of an adverse event. One approach to precision medicine in this setting is to elicit a composite outcome which balances all competing outcomes; unfortunately, eliciting a composite outcome directly from patients is difficult without a high-quality instrument, and an expert-derived composite outcome may not account for heterogeneity in patient preferences. We propose a new paradigm for the study of precision medicine using observational data that relies solely on the assumption that clinicians are approximately (i.e., imperfectly) making decisions to maximize individual patient utility. Estimated composite outcomes are subsequently used to construct an estimator of an individualized treatment rule which maximizes the mean of patient-specific composite out- comes. The estimated composite outcomes and estimated optimal individualized treatment rule provide new insights into patient preference heterogeneity, clinician behavior, and the value of precision medicine in a given domain. We derive inference procedures for the pro- posed estimators under mild conditions and demonstrate their finite sample performance through a suite of simulation experiments and an illustrative application to data from a study of bipolar depression. 

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