Residual Weighted Learning for Estimating Individualized Treatment Rules

Stabilized direct learning for efficient estimation of individualized treatment rules

In recent years, the field of precision medicine has seen many advancements. Significant focus has been placed on creating algorithms to estimate individualized treatment rules (ITRs), which map from patient covariates to the space of available treatments with the goal of maximizing patient outcome. Direct learning (D-Learning) is a recent one-step method which estimates the ITR by directly modeling the treatment-covariate interaction. However, when the variance of the outcome is heterogeneous with respect to treatment and covariates, D-Learning does not leverage this structure. Stabilized direct learning (SD-Learning), proposed in this paper, utilizes potential heteroscedasticity in the error term through a residual reweighting which models the residual variance via flexible machine learning algorithms such as XGBoost and random forests. We also develop an internal cross-validation scheme which determines the best residual model among competing models. SD-Learning improves the efficiency of D-Learning estimates in binary and multi-arm treatment scenarios. The method is simple to implement and an easy way to improve existing algorithms within the D-Learning family, including original D-Learning, Angle-based D-Learning (AD-Learning), and Robust D-learning (RD-Learning). We provide theoretical properties and justification of the optimality of SD-Learning. Head-to-head performance comparisons with D-Learning methods are provided through simulations, which demonstrate improvement in terms of average prediction error (APE), misclassification rate, and empirical value, along with a data analysis of an acquired immunodeficiency syndrome (AIDS) randomized clinical trial.

On "Reflections on the concept of optimality of single decision point treatment regimes"

This is a discussion of "Reflections on the concept of optimality of single decision point treatment regimes" by Trung Dung Tran, Ariel Alonso Abad, Geert Verbeke, Geert Molenberghs, and Iven Van Mechelen. The authors propose a thoughtful consideration of optimization targets and the implications of such targets for the resulting optimal treatment rule. However, we contest the assertation that targets of optimization have been overlooked and suggest additional considerations that researchers must contemplate as part of a complete framework for learning about optimal treatment regimes.

Estimation in optimal treatment regimes based on mean residual lifetimes with right-censored data

An optimal individualized treatment regime (ITR) is a decision rule in allocating the best treatment to each patient and, hence, maximizing overall benefits. In this paper, we propose a novel framework based on nonparametric inverse probability weighting (IPW) and augmented inverse probability weighting (AIPW) estimators of the value function when the data are subject to right censoring. In contrast to most existing approaches that are designed to maximize the expected survival time under a binary treatment framework, the proposed method targets maximizing the mean residual lifetime of patients. Specifically, the proposed IPW method searches the optimal ITR by maximizing an estimator for the overall population outcome directly, without specifying the regression model for the conditional mean residual lifetime, whereas the AIPW method integrates the model information of the mean residual lifetime to improve the robustness. Furthermore, to overcome the computational difficulty in a nonsmooth value estimator, smoothed IPW and AIPW estimators are constructed. In theory, we establish the asymptotic properties of the proposed method under suitable regularity conditions. The empirical performances of the proposed IPW and AIPW estimators are evaluated using simulation studies and are further illustrated with an application to the real-world data set from the Acquired Immunodeficiency Syndrome Clinical Trial Group Protocol 175 (ACTG175).

Estimating optimal individualized treatment rules with multistate processes

Multistate process data are common in studies of chronic diseases such as cancer. These data are ideal for precision medicine purposes as they can be leveraged to improve more refined health outcomes, compared to standard survival outcomes, as well as incorporate patient preferences regarding quantity versus quality of life. However, there are currently no methods for the estimation of optimal individualized treatment rules with such data. In this paper, we propose a nonparametric outcome weighted learning approach for this problem in randomized clinical trial settings. The theoretical properties of the proposed methods, including Fisher consistency and asymptotic normality of the estimated expected outcome under the estimated optimal individualized treatment rule, are rigorously established. A consistent closed-form variance estimator is provided and methodology for the calculation of simultaneous confidence intervals is proposed. Simulation studies show that the proposed methodology and inference procedures work well even with small-sample sizes and high rates of right censoring. The methodology is illustrated using data from a randomized clinical trial on the treatment of metastatic squamous-cell carcinoma of the head and neck.

Covariate-adjusted value-guided subgroup identification via boosting

It is widely recognized that treatment effects could differ across subgroups of patients. Subgroup analysis, which assesses such heterogeneity, provides valuable information in developing personalized therapies. There has been extensive research developing novel statistical methods for subgroup identification. The recent contribution is a value-guided subgroup identification method that directly maximizes treatment benefit at the subgroup level for survival outcome, rather than relying on individual treatment effect estimation. In this paper, we first completed this framework by illustrating its application to continuous and binary outcomes. More importantly, we extended the original framework to account for the prognostic effects and named this new method Covariate-Adjusted Value-guided subgroup identification via boosting (CAVboost). The original method directly used the outcome to formulate the value function for subgroup identification. Since the outcome can further be decomposed as prognostic effects and treatment effects, specifying the prognostic effects as the covariates of a model for the outcome can single out the treatment effects and improve the power to detect them across subgroups. Our proposed CAVboost was based on this key idea. It used a covariate-adjusted treatment effect estimator, instead of the outcome itself, to formulate the value function for subgroup identification. CAVboost estimates the treatment effect by using covariates to account for the prognostic effects, which mimics the idea of using covariates in an ANCOVA estimator. We showed that CAVboost could effectively improve the subgroup identification capability for both continuous and binary outcomes.

Optimizing Treatment for Human Immunodeficiency Virus to Improve Clinical Outcomes Using Precision Medicine

In first-line antiretroviral therapy (ART) for human immunodeficiency virus (HIV) treatment, some subgroups of patients may respond better to an efavirenz-based regimen than an integrase strand transfer inhibitor (InSTI)-based regimen, or vice versa, due to patient characteristics modifying treatment effects. Using data based on nearly 16,000 patients from the North American AIDS Cohort Collaboration on Research and Design from 2009-2016, statistical methods for precision medicine were employed to estimate an optimal treatment rule that minimizes the 5-year risk of the composite outcome of acquired immune deficiency syndrome (AIDS)-defining illnesses, serious non-AIDS events, and all-cause mortality. The treatment rules considered were functions that recommend either an efavirenz- or InSTI-based regimen conditional on baseline patient characteristics such as demographic information, laboratory results, and health history. The estimated 5-year risk under the estimated optimal treatment rule was 10.0% (95% confidence interval (CI): 8.6, 11.3), corresponding to an absolute risk reduction of 2.3% (95% CI: 0.9, 3.8) when compared with recommending an efavirenz-based regimen for all patients and 2.6% (95% CI: 1.0, 4.2) when compared with recommending an InSTI-based regimen for all. Tailoring ART to individual patient characteristics may reduce 5-year risk of the composite outcome compared with assigning all patients the same drug regimen.

Longitudinal self-learning of individualized treatment rules in a nutrient supplementation trial with missing data

Longitudinal outcomes are prevalent in clinical studies, where the presence of missing data may make the statistical learning of individualized treatment rules (ITRs) a much more challenging task. We analyzed a longitudinal calcium supplementation trial in the ELEMENT Project and established a novel ITR to reduce the risk of adverse outcomes of lead exposure on child growth and development. Lead exposure, particularly in the form of in utero exposure, can seriously impair children's health, especially their cognitive and neurobehavioral development, which necessitates clinical interventions such as calcium supplementation intake during pregnancy. Using the longitudinal outcomes from a randomized clinical trial of calcium supplementation, we developed a new ITR for daily calcium intake during pregnancy to mitigate persistent lead exposure in children at age 3 years. To overcome the technical challenges posed by missing data, we illustrate a new learning approach, termed longitudinal self-learning (LS-learning), that utilizes longitudinal measurements of child's blood lead concentration in the derivation of ITR. Our LS-learning method relies on a temporally weighted self-learning paradigm to synergize serially correlated training data sources. The resulting ITR is the first of this kind in precision nutrition that will contribute to the reduction of expected blood lead concentration in children aged 0-3 years should this ITR be implemented to the entire study population of pregnant women.

Penalized robust learning for optimal treatment regimes with heterogeneous individualized treatment effects

The growing popularity of personalized medicine motivates people to explore individualized treatment regimes according to heterogeneous characteristics of the patients. For the large-scale data analysis, however, the data are collected at different times and different locations, i.e. subjects are usually from a heterogeneous population, which causes that the optimal treatment regimes also vary for patients across different subgroups. In this paper, we mainly focus on the estimation of optimal treatment regimes for subjects come from a heterogeneous population with high-dimensional data. We first remove the main effects of the covariates for each subgroup to eliminate non-ignorable residual confounding. Based on the centralized outcome, we propose a penalized robust learning that estimates the coefficient matrix of the interactions between covariates and treatment by penalizing pairwise differences of the coefficients of any two subgroups for the same covariate, which can automatically identify the latent complex structure of the coefficient matrix with heterogeneous and homogeneous columns. At the same time, the penalized robust learning can also select the important variables that truly contribute to the individualized treatment decisions with commonly used sparsity structure penalty. Extensive simulation studies show that our proposed method outperforms current popular methods, and it is further illustrated in the real analysis of the Tamoxifen breast cancer data.

Change plane model averaging for subgroup identification

Central to personalized medicine and tailored therapies is discovering the subpopulations that account for treatment effect heterogeneity and are likely to benefit more from given interventions. In this article, we introduce a change plane model averaging method to identify subgroups characterized by linear combinations of predictive variables and multiple cut-offs. We first fit a sequence of statistical models, each incorporating the thresholding effect of one particular covariate. The estimation of submodels is accomplished through an iterative integration of a change point detection method and numerical optimization algorithms. A frequentist model averaging approach is then employed to linearly combine the submodels with optimal weights. Our approach can deal with high-dimensional settings involving enormous potential grouping variables by adopting the sparsity-inducing penalties. Simulation studies are conducted to investigate the prediction and subgrouping performance of the proposed method, with a comparison to various competing subgroup detection methods. Our method is applied to a dataset from a warfarin pharmacogenetics study, producing some new findings.

The Sequential Multiple Assignment Randomized Trial for Controlling Infectious Diseases: A Review of Recent Developments

Infectious diseases have posed severe threats to public health across the world. Effective prevention and control of infectious diseases in the long term requires adapting interventions based on epidemiological evidence. The sequential multiple assignment randomized trial (SMART) is a multistage randomized trial that can provide valid evidence of when and how to adapt interventions for controlling infectious diseases based on evolving epidemiological evidence. We review recent developments in SMARTs to bring wider attention to the potential benefits of employing SMARTs in constructing effective adaptive interventions for controlling infectious diseases and other threats to public health. We discuss 2 example SMARTs for infectious diseases and summarize recent developments in SMARTs from the varied aspects of design, analysis, cost, and ethics. Public health investigators are encouraged to familiarize themselves with the related materials we discuss and collaborate with experts in SMARTs to translate the methodological developments into preeminent public health research. (Am J Public Health. 2023;113(1):49-59. https://doi.org/10.2105/AJPH.2022.307135).

Learning Optimal Group-structured Individualized Treatment Rules with Many Treatments

Data driven individualized decision making problems have received a lot of attentions in recent years. In particular, decision makers aim to determine the optimal Individualized Treatment Rule (ITR) so that the expected specified outcome averaging over heterogeneous patient-specific characteristics is maximized. Many existing methods deal with binary or a moderate number of treatment arms and may not take potential treatment effect structure into account. However, the effectiveness of these methods may deteriorate when the number of treatment arms becomes large. In this article, we propose GRoup Outcome Weighted Learning (GROWL) to estimate the latent structure in the treatment space and the optimal group-structured ITRs through a single optimization. In particular, for estimating group-structured ITRs, we utilize the Reinforced Angle based Multicategory Support Vector Machines (RAMSVM) to learn group-based decision rules under the weighted angle based multi-class classification framework. Fisher consistency, the excess risk bound, and the convergence rate of the value function are established to provide a theoretical guarantee for GROWL. Extensive empirical results in simulation studies and real data analysis demonstrate that GROWL enjoys better performance than several other existing methods.

Batch policy learning in average reward Markov decision processes

We consider the batch (off-line) policy learning problem in the infinite horizon Markov Decision Process. Motivated by mobile health applications, we focus on learning a policy that maximizes the long-term average reward. We propose a doubly robust estimator for the average reward and show that it achieves semiparametric efficiency. Further we develop an optimization algorithm to compute the optimal policy in a parameterized stochastic policy class. The performance of the estimated policy is measured by the difference between the optimal average reward in the policy class and the average reward of the estimated policy and we establish a finite-sample regret guarantee. The performance of the method is illustrated by simulation studies and an analysis of a mobile health study promoting physical activity.

Transfer learning of individualized treatment rules from experimental to real-world data

Individualized treatment effect lies at the heart of precision medicine. Interpretable individualized treatment rules (ITRs) are desirable for clinicians or policymakers due to their intuitive appeal and transparency. The gold-standard approach to estimating the ITRs is randomized experiments, where subjects are randomized to different treatment groups and the confounding bias is minimized to the extent possible. However, experimental studies are limited in external validity because of their selection restrictions, and therefore the underlying study population is not representative of the target real-world population. Conventional learning methods of optimal interpretable ITRs for a target population based only on experimental data are biased. On the other hand, real-world data (RWD) are becoming popular and provide a representative sample of the target population. To learn the generalizable optimal interpretable ITRs, we propose an integrative transfer learning method based on weighting schemes to calibrate the covariate distribution of the experiment to that of the RWD. Theoretically, we establish the risk consistency for the proposed ITR estimator. Empirically, we evaluate the finite-sample performance of the transfer learner through simulations and apply it to a real data application of a job training program.

Contrast weighted learning for robust optimal treatment rule estimation

Personalized medicine aims to tailor medical decisions based on patient-specific characteristics. Advances in data capturing techniques such as electronic health records dramatically increase the availability of comprehensive patient profiles, promoting the rapid development of optimal treatment rule (OTR) estimation methods. An archetypal OTR estimation approach is the outcome weighted learning, where OTR is determined under a weighted classification framework with clinical outcomes as the weights. Although outcome weighted learning has been extensively studied and extended, existing methods are susceptible to irregularities of outcome distributions such as outliers and heavy tails. Methods that involve modeling of the outcome are also sensitive to model misspecification. We propose a contrast weighted learning (CWL) framework that exploits the flexibility and robustness of contrast functions to enable robust OTR estimation for a wide range of clinical outcomes. The novel value function in CWL only depends on the pairwise contrast of clinical outcomes between patients irrespective of their distributional features and supports. The Fisher consistency and convergence rate of the estimated decision rule via CWL are established. We illustrate the superiority of the proposed method under finite samples using comprehensive simulation studies with ill-distributed continuous outcomes and ordinal outcomes. We apply the CWL method to two datasets from clinical trials on idiopathic pulmonary fibrosis and COVID-19 to demonstrate its real-world application.

Deep reinforcement learning for personalized treatment recommendation

In precision medicine, the ultimate goal is to recommend the most effective treatment to an individual patient based on patient-specific molecular and clinical profiles, possibly high-dimensional. To advance cancer treatment, large-scale screenings of cancer cell lines against chemical compounds have been performed to help better understand the relationship between genomic features and drug response; existing machine learning approaches use exclusively supervised learning, including penalized regression and recommender systems. However, it would be more efficient to apply reinforcement learning to sequentially learn as data accrue, including selecting the most promising therapy for a patient given individual molecular and clinical features and then collecting and learning from the corresponding data. In this article, we propose a novel personalized ranking system called Proximal Policy Optimization Ranking (PPORank), which ranks the drugs based on their predicted effects per cell line (or patient) in the framework of deep reinforcement learning (DRL). Modeled as a Markov decision process, the proposed method learns to recommend the most suitable drugs sequentially and continuously over time. As a proof-of-concept, we conduct experiments on two large-scale cancer cell line data sets in addition to simulated data. The results demonstrate that the proposed DRL-based PPORank outperforms the state-of-the-art competitors based on supervised learning. Taken together, we conclude that novel methods in the framework of DRL have great potential for precision medicine and should be further studied.

The optimal dynamic treatment rule superlearner: considerations, performance, and application to criminal justice interventions

The optimal dynamic treatment rule (ODTR) framework offers an approach for understanding which kinds of patients respond best to specific treatments - in other words, treatment effect heterogeneity. Recently, there has been a proliferation of methods for estimating the ODTR. One such method is an extension of the SuperLearner algorithm - an ensemble method to optimally combine candidate algorithms extensively used in prediction problems - to ODTRs. Following the ``causal roadmap," we causally and statistically define the ODTR and provide an introduction to estimating it using the ODTR SuperLearner. Additionally, we highlight practical choices when implementing the algorithm, including choice of candidate algorithms, metalearners to combine the candidates, and risk functions to select the best combination of algorithms. Using simulations, we illustrate how estimating the ODTR using this SuperLearner approach can uncover treatment effect heterogeneity more effectively than traditional approaches based on fitting a parametric regression of the outcome on the treatment, covariates and treatment-covariate interactions. We investigate the implications of choices in implementing an ODTR SuperLearner at various sample sizes. Our results show the advantages of: (1) including a combination of both flexible machine learning algorithms and simple parametric estimators in the library of candidate algorithms; (2) using an ensemble metalearner to combine candidates rather than selecting only the best-performing candidate; (3) using the mean outcome under the rule as a risk function. Finally, we apply the ODTR SuperLearner to the ``Interventions" study, an ongoing randomized controlled trial, to identify which justice-involved adults with mental illness benefit most from cognitive behavioral therapy to reduce criminal re-offending.

On Robustness of Individualized Decision Rules

With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize the expected outcome for each individual. Motivated by complex individualized decision making procedures and the popular conditional value at risk (CVaR) measure, we propose a new robust criterion to estimate optimal IDRs in order to control the average lower tail of the individuals' outcomes. In addition to improving the individualized expected outcome, our proposed criterion takes risks into consideration, and thus the resulting IDRs can prevent adverse events. The optimal IDR under our criterion can be interpreted as the decision rule that maximizes the "worst-case" scenario of the individualized outcome when the underlying distribution is perturbed within a constrained set. An efficient non-convex optimization algorithm is proposed with convergence guarantees. We investigate theoretical properties for our estimated optimal IDRs under the proposed criterion such as consistency and finite sample error bounds. Simulation studies and a real data application are used to further demonstrate the robust performance of our methods. Several extensions of the proposed method are also discussed.

Estimating the optimal individualized treatment rule from a cost-effectiveness perspective

Optimal individualized treatment rules (ITRs) provide customized treatment recommendations based on subject characteristics to maximize clinical benefit in accordance with the objectives in precision medicine. As a result, there is growing interest in developing statistical tools for estimating optimal ITRs in evidence-based research. In health economic perspectives, policy makers consider the tradeoff between health gains and incremental costs of interventions to set priorities and allocate resources. However, most work on ITRs has focused on maximizing the effectiveness of treatment without considering costs. In this paper, we jointly consider the impact of effectiveness and cost on treatment decisions and define ITRs under a composite-outcome setting, so that we identify the most cost-effective ITR that accounts for individual-level heterogeneity through direct optimization. In particular, we propose a decision-tree-based statistical learning algorithm that uses a net-monetary-benefit-based reward to provide nonparametric estimations of the optimal ITR. We provide several approaches to estimating the reward underlying the ITR as a function of subject characteristics. We present the strengths and weaknesses of each approach and provide practical guidelines by comparing their performance in simulation studies. We illustrate the top-performing approach from our simulations by evaluating the projected 15-year personalized cost-effectiveness of the intensive blood pressure control of the Systolic Blood Pressure Intervention Trial (SPRINT) study.

Ranking tailoring variables for constructing individualized treatment rules: an application to schizophrenia

As with many chronic conditions, matching patients with schizophrenia to the best treatment options is difficult. Selecting antipsychotic medication is especially challenging because many of the medications can have burdensome side effects. Adjusting or tailoring medications based on patients' characteristics could improve symptoms. However, it is often not known which patient characteristics are most helpful for informing treatment selection. In this paper, we address the challenge of identifying and ranking important variables for tailoring treatment decisions. We consider a value-search approach implemented through dynamic marginal structural models to estimate an optimal individualized treatment rule. We apply our methodology to the Clinical Antipsychotics Trial of Intervention and Effectiveness (CATIE) study for schizophrenia, to evaluate if some tailoring variables have greater potential than others for selecting treatments for patients with schizophrenia (Stroup et al., 2003).

Learning dynamic treatment strategies for coronary heart diseases by artificial intelligence: real-world data-driven study

BACKGROUND

Coronary heart disease (CHD) has become the leading cause of death and one of the most serious epidemic diseases worldwide. CHD is characterized by urgency, danger and severity, and dynamic treatment strategies for CHD patients are needed. We aimed to build and validate an AI model for dynamic treatment recommendations for CHD patients with the goal of improving patient outcomes and learning best practices from clinicians to help clinical decision support for treating CHD patients.

METHODS

We formed the treatment strategy as a sequential decision problem, and applied an AI supervised reinforcement learning-long short-term memory (SRL-LSTM) framework that combined supervised learning (SL) and reinforcement learning (RL) with an LSTM network to track patients' states to learn a recommendation model that took a patient's diagnosis and evolving health status as input and provided a treatment recommendation in the form of whether to take specific drugs. The experiments were conducted by leveraging a real-world intensive care unit (ICU) database with 13,762 admitted patients diagnosed with CHD. We compared the performance of the applied SRL-LSTM model and several state-of-the-art SL and RL models in reducing the estimated in-hospital mortality and the Jaccard similarity with clinicians' decisions. We used a random forest algorithm to calculate the feature importance of both the clinician policy and the AI policy to illustrate the interpretability of the AI model.

RESULTS

Our experimental study demonstrated that the AI model could help reduce the estimated in-hospital mortality through its RL function and learn the best practice from clinicians through its SL function. The similarity between the clinician policy and the AI policy regarding the surviving patients was high, while for the expired patients, it was much lower. The dynamic treatment strategies made by the AI model were clinically interpretable and relied on sensible clinical features extracted according to monitoring indexes and risk factors for CHD patients.

CONCLUSIONS

We proposed a pipeline for constructing an AI model to learn dynamic treatment strategies for CHD patients that could improve patient outcomes and mimic the best practices of clinicians. And a lot of further studies and efforts are needed to make it practical.

Individualized treatment rules under stochastic treatment cost constraints

Estimation and evaluation of individualized treatment rules have been studied extensively, but real-world treatment resource constraints have received limited attention in existing methods. We investigate a setting in which treatment is intervened upon based on covariates to optimize the mean counterfactual outcome under treatment cost constraints when the treatment cost is random. In a particularly interesting special case, an instrumental variable corresponding to encouragement to treatment is intervened upon with constraints on the proportion receiving treatment. For such settings, we first develop a method to estimate optimal individualized treatment rules. We further construct an asymptotically efficient plug-in estimator of the corresponding average treatment effect relative to a given reference rule.

Non-asymptotic Properties of Individualized Treatment Rules from Sequentially Rule-Adaptive Trials

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.

Risk controlled decision trees and random forests for precision Medicine

Statistical methods generating individualized treatment rules (ITRs) often focus on maximizing expected benefit, but these rules may expose patients to excess risk. For instance, aggressive treatment of type 2 diabetes (T2D) with insulin therapies may result in an ITR which controls blood glucose levels but increases rates of hypoglycemia, diminishing the appeal of the ITR. This work proposes two methods to identify risk-controlled ITRs (rcITR), a class of ITR which maximizes a benefit while controlling risk at a prespecified threshold. A novel penalized recursive partitioning algorithm is developed which optimizes an unconstrained, penalized value function. The final rule is a risk-controlled decision tree (rcDT) that is easily interpretable. A natural extension of the rcDT model, risk controlled random forests (rcRF), is also proposed. Simulation studies demonstrate the robustness of rcRF modeling. Three variable importance measures are proposed to further guide clinical decision-making. Both rcDT and rcRF procedures can be applied to data from randomized controlled trials or observational studies. An extensive simulation study interrogates the performance of the proposed methods. A data analysis of the DURABLE diabetes trial in which two therapeutics were compared is additionally presented. An R package implements the proposed methods ( https://github.com/kdoub5ha/rcITR).

The impact of pregnancy on antihypertensive drug metabolism and pharmacokinetics: current status and future directions

INTRODUCTION

Hypertensive disorders of pregnancy (HDP) are rising in prevalence, and increase risk of adverse maternal and fetal outcomes. Physiologic changes occur during pregnancy that alter drug pharmacokinetics. However, antihypertensive drugs lack pregnancy-specific dosing recommendations due to critical knowledge gaps surrounding the extent of gestational changes in antihypertensive drug pharmacokinetics and underlying mechanisms.

AREAS COVERED

This review (1) summarizes currently recommended medications and dosing strategies for non-emergent HDP treatment, (2) reviews and synthesizes existing literature identified via a comprehensive Pubmed search evaluating gestational changes in the maternal pharmacokinetics of commonly prescribed HDP drugs (notably labetalol and nifedipine), and (3) offers insight into the metabolism and clearance mechanisms underlying altered HDP drug pharmacokinetics during pregnancy. Remaining knowledge gaps and future research directions are summarized.

EXPERT OPINION

A series of small pharmacokinetic studies illustrate higher oral clearance of labetalol and nifedipine during pregnancy. Pharmacokinetic modeling and preclinical studies suggest these effects are likely due to pregnancy-associated increases in hepatic UGT1A1- and CYP3A4-mediated first-pass metabolism and lower bioavailability. Accordingly, higher and/or more frequent doses may be needed to lower blood pressure during pregnancy. Future research is needed to address various evidence gaps and inform the development of more precise antihypertensive drug dosing strategies.

A parsimonious personalized dose-finding model via dimension reduction

Learning an individualized dose rule in personalized medicine is a challenging statistical problem. Existing methods often suffer from the curse of dimensionality, especially when the decision function is estimated nonparametrically. To tackle this problem, we propose a dimension reduction framework that effectively reduces the estimation to a lower-dimensional subspace of the covariates. We exploit that the individualized dose rule can be defined in a subspace spanned by a few linear combinations of the covariates, leading to a more parsimonious model. Also, our framework does not require the inverse probability of the propensity score under observational studies due to a direct maximization of the value function. This distinguishes us from the outcome weighted learning framework, which also solves decision rules directly. Under the same framework, we further propose a pseudo-direct learning approach focuses more on estimating the dimensionality-reduced subspace of the treatment outcome. Parameters in both approaches can be estimated efficiently using an orthogonality constrained optimization algorithm on the Stiefel manifold. Under mild regularity assumptions, the asymptotic normality results of the proposed estimators can are established, respectively. We also derive the consistency and convergence rate for the value function under the estimated optimal dose rule. We evaluate the performance of the proposed approaches through extensive simulation studies and a warfarin pharmacogenetic dataset.

Precision Medicine Approach to Develop and Internally Validate Optimal Exercise and Weight-Loss Treatments for Overweight and Obese Adults With Knee Osteoarthritis: Data From a Single-Center Randomized Trial

OBJECTIVE

To apply a precision medicine approach to determine the optimal treatment regime for participants in an exercise (E), dietary weight loss (D), and D + E trial for knee osteoarthritis that would maximize their expected outcomes.

METHODS

Using data from 343 participants of the Intensive Diet and Exercise for Arthritis (IDEA) trial, we applied 24 machine-learning models to develop individualized treatment rules on 7 outcomes: Short Form 36 physical component score, weight loss, Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) pain/function/stiffness scores, compressive force, and interleukin-6 level. The optimal model was selected based on jackknife value function estimates that indicate improvement in the outcomes if future participants follow the estimated decision rule compared to the optimal single, fixed treatment model.

RESULTS

Multiple outcome random forest was the optimal model for the WOMAC outcomes. For the other outcomes, list-based models were optimal. For example, the estimated optimal decision rule for weight loss indicated assigning the D + E intervention to participants with baseline weight not exceeding 109.35 kg and waist circumference above 90.25 cm, and assigning D to all other participants except those with a history of a heart attack. If applied to future participants, the optimal rule for weight loss is estimated to increase average weight loss to 11.2 kg at 18 months, contrasted with 9.8 kg if all participants received D + E (P = 0.01).

CONCLUSION

The precision medicine models supported the overall findings from IDEA that the D + E intervention was optimal for most participants, but there was evidence that a subgroup of participants would likely benefit more from diet alone for 2 outcomes.

Multithreshold change plane model: Estimation theory and applications in subgroup identification

We propose a multithreshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of observed covariates and thus multiple thresholds produce change planes in the covariate space. We contribute a novel two-stage estimation approach to determine the number of subgroups, the location of thresholds, and all other regression parameters. In the first stage we adopt a group selection principle to consistently identify the number of subgroups, while in the second stage change point locations and model parameter estimates are refined by a penalized induced smoothing technique. Our procedure allows sparse solutions for relatively moderate- or high-dimensional covariates. We further establish the asymptotic properties of our proposed estimators under appropriate technical conditions. We evaluate the performance of the proposed methods by simulation studies and provide illustrations using two medical data examples. Our proposal for subgroup identification may lead to an immediate application in personalized medicine.

Discussion of Kallus (2020) and Mo et al (2020)

We discuss the results on improving the generalizability of individualized treatment rule following the work in Kallus [1] and Mo et al. [5]. We note that the advocated weights in Kallus [1] are connected to the efficient score of the contrast function. We further propose a likelihood-ratio-based method (LR-ITR) to accommodate covariate shifts, and compare it to the CTE-DR-ITR method proposed in Mo et al. [5]. We provide the upper-bound on the risk function of the target population when both the covariate shift and the contrast function shift are present. Numerical studies show that LR-ITR can outperform CTE-DR-ITR when there is only covariate shift.

Estimation and Optimization of Composite Outcomes

There is tremendous interest in precision medicine as a means to improve patient outcomes 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 outcomes. 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 proposed 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.

A nonparametric method for value function guided subgroup identification via gradient tree boosting for censored survival data

In randomized clinical trials with survival outcome, there has been an increasing interest in subgroup identification based on baseline genomic, proteomic markers, or clinical characteristics. Some of the existing methods identify subgroups that benefit substantially from the experimental treatment by directly modeling outcomes or treatment effect. When the goal is to find an optimal treatment for a given patient rather than finding the right patient for a given treatment, methods under the individualized treatment regime framework estimate an individualized treatment rule that would lead to the best expected clinical outcome as measured by a value function. Connecting the concept of value function to subgroup identification, we propose a nonparametric method that searches for subgroup membership scores by maximizing a value function that directly reflects the subgroup-treatment interaction effect based on restricted mean survival time. A gradient tree boosting algorithm is proposed to search for the individual subgroup membership scores. We conduct simulation studies to evaluate the performance of the proposed method and an application to an AIDS clinical trial is performed for illustration.

Outcome weighted ψ-learning for individualized treatment rules

An individualized treatment rule is often employed to maximize a certain patient-specific clinical outcome based on his/her clinical or genomic characteristics as well as heterogeneous response to treatments. Although developing such a rule is conceptually important to personalized medicine, existing methods such as the partial least squares Qian and Murphy (2011) suffers from the difficulty of indirect maximization of a patient's clinical outcome, while the outcome weighted learning Y. Zhao, Zeng, Rush, and Kosorok (2012) is not robust against any perturbation of the outcome. In this article, we propose a weighted ψ-learning method to optimize an individualized treatment rule, which is robust against any data perturbation near the decision boundary by seeking the maximum separation. To solve nonconvex minimization, we employ a difference convex algorithm to relax the non-convex minimization iteratively based on a decomposition of the cost function into a difference of two convex functions. On this ground, we also introduce a variable selection method for further removing redundant variables for a higher performance. Finally, we illustrate the proposed method by simulations and a lung health study and demonstrate that it yields higher performances in terms of accuracy of prediction of individualized treatment.

High-Dimensional Precision Medicine From Patient-Derived Xenografts

The complexity of human cancer often results in significant heterogeneity in response to treatment. Precision medicine offers the potential to improve patient outcomes by leveraging this heterogeneity. Individualized treatment rules (ITRs) formalize precision medicine as maps from the patient covariate space into the space of allowable treatments. The optimal ITR is that which maximizes the mean of a clinical outcome in a population of interest. Patient-derived xenograft (PDX) studies permit the evaluation of multiple treatments within a single tumor, and thus are ideally suited for estimating optimal ITRs. PDX data are characterized by correlated outcomes, a high-dimensional feature space, and a large number of treatments. Here we explore machine learning methods for estimating optimal ITRs from PDX data. We analyze data from a large PDX study to identify biomarkers that are informative for developing personalized treatment recommendations in multiple cancers. We estimate optimal ITRs using regression-based (Q-learning) and direct-search methods (outcome weighted learning). Finally, we implement a superlearner approach to combine multiple estimated ITRs and show that the resulting ITR performs better than any of the input ITRs, mitigating uncertainty regarding user choice. Our results indicate that PDX data are a valuable resource for developing individualized treatment strategies in oncology. Supplementary materials for this article are available online.

Ascertaining properties of weighting in the estimation of optimal treatment regimes under monotone missingness

Dynamic treatment regimes operationalize precision medicine as a sequence of decision rules, one per stage of clinical intervention, that map up-to-date patient information to a recommended intervention. An optimal treatment regime maximizes the mean utility when applied to the population of interest. Methods for estimating an optimal treatment regime assume the data to be fully observed, which rarely occurs in practice. A common approach is to first use multiple imputation and then pool the estimators across imputed datasets. However, this approach requires estimating the joint distribution of patient trajectories, which can be high-dimensional, especially when there are multiple stages of intervention. We examine the application of inverse probability weighted estimating equations as an alternative to multiple imputation in the context of monotonic missingness. This approach applies to a broad class of estimators of an optimal treatment regime including both Q-learning and a generalization of outcome weighted learning. We establish consistency under mild regularity conditions and demonstrate its advantages in finite samples using a series of simulation experiments and an application to a schizophrenia study.

Learning Individualized Treatment Rules for Multiple-Domain Latent Outcomes

For many mental disorders, latent mental status from multiple-domain psychological or clinical symptoms may perform as a better characterization of the underlying disorder status than a simple summary score of the symptoms, and they may also serve as more reliable and representative features to differentiate treatment responses. Therefore, in order to address the complexity and heterogeneity of treatment responses for mental disorders, we provide a new paradigm for learning optimal individualized treatment rules (ITRs) by modeling patients' latent mental status. We first learn the multi-domain latent states at baseline from the observed symptoms under a restricted Boltzmann machine (RBM) model, through which patients' heterogeneous symptoms are represented using an economical number of latent variables and yet remains flexible. We then optimize a value function defined by the latent states after treatment by exploiting a transformation of the observed symptoms based on the RBM without modeling the relationship between the latent mental states before and after treatment. The optimal treatment rules are derived using a weighted large margin classifier. We derive the convergence rate of the proposed estimator under the latent models. Simulation studies are conducted to test the performance of the proposed method. Finally, we apply the developed method to real world studies and we demonstrate the utility and advantage of our method in tailoring treatments for patients with major depression, and identify patient subgroups informative for treatment recommendations.