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.

Receiver operating characteristic curves and confidence bands for support vector machines.

Many problems that appear in biomedical decision-making, such as diagnosing disease and predicting response to treatment, can be expressed as binary classification problems. The support vector machine (SVM) is a popular classification technique that is robust to model misspecification and effectively handles high-dimensional data. The relative costs of false positives and false negatives can vary across application domains. The receiving operating characteristic (ROC) curve provides a visual representation of the trade-off between these two types of errors. Because the SVM does not produce a predicted probability, an ROC curve cannot be constructed in the traditional way of thresholding a predicted probability. However, a sequence of weighted SVMs can be used to construct an ROC curve. Although ROC curves constructed using weighted SVMs have great potential for allowing ROC curves analyses that cannot be done by thresholding predicted probabilities, their theoretical properties have heretofore been underdeveloped. We propose a method for constructing confidence bands for the SVM ROC curve and provide the theoretical justification for the SVM ROC curve by showing that the risk function of the estimated decision rule is uniformly consistent across the weight parameter. We demonstrate the proposed confidence band method using simulation studies. We present a predictive model for treatment response in breast cancer as an illustrative example.

Estimating individualized treatment regimes from crossover designs.

The field of precision medicine aims to tailor treatment based on patient-specific factors in a reproducible way. To this end, estimating an optimal individualized treatment regime (ITR) that recommends treatment decisions based on patient characteristics to maximize the mean of a prespecified outcome is of particular interest. Several methods have been proposed for estimating an optimal ITR from clinical trial data in the parallel group setting where each subject is randomized to a single intervention. However, little work has been done in the area of estimating the optimal ITR from crossover study designs. Such designs naturally lend themselves to precision medicine since they allow for observing the response to multiple treatments for each patient. In this paper, we introduce a method for estimating the optimal ITR using data from a 2 × 2 crossover study with or without carryover effects. The proposed method is similar to policy search methods such as outcome weighted learning; however, we take advantage of the crossover design by using the difference in responses under each treatment as the observed reward. We establish Fisher and global consistency, present numerical experiments, and analyze data from a feeding trial to demonstrate the improved performance of the proposed method compared to standard methods for a parallel study design.

Estimating individualized treatment rules with risk constraint.

Individualized treatment rules (ITRs) recommend treatments based on patient-specific characteristics in order to maximize the expected clinical outcome. At the same time, the risks caused by various adverse events cannot be ignored. In this paper, we propose a method to estimate an optimal ITR that maximizes clinical benefit while having the overall risk controlled at a desired level. Our method works for a general setting of multi-category treatment. The proposed procedure employs two shifted ramp losses to approximate the 0-1 loss in the objective function and constraint, respectively, and transforms the estimation problem into a difference of convex functions (DC) programming problem. A relaxed DC algorithm is used to solve the nonconvex constrained optimization problem. Simulations and a real data example are used to demonstrate the finite sample performance of the proposed method.

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.

Multicategory Outcome Weighted Margin-based Learning for Estimating Individualized Treatment Rules.

Due to heterogeneity for many chronic diseases, precise personalized medicine, also known as precision medicine, has drawn increasing attentions in the scientific community. One main goal of precision medicine is to develop the most effective tailored therapy for each individual patient. To that end, one needs to incorporate individual characteristics to detect a proper individual treatment rule (ITR), by which suitable decisions on treatment assignments can be made to optimize patients' clinical outcome. For binary treatment settings, outcome weighted learning (OWL) and several of its variations have been proposed recently to estimate the ITR by optimizing the conditional expected outcome given patients' information. However, for multiple treatment scenarios, it remains unclear how to use OWL effectively. It can be shown that some direct extensions of OWL for multiple treatments, such as one-versus-one and one-versus-rest methods, can yield suboptimal performance. In this paper, we propose a new learning method, named Multicategory Outcome weighted Margin-based Learning (MOML), for estimating ITR with multiple treatments. Our proposed method is very general and covers OWL as a special case. We show Fisher consistency for the estimated ITR, and establish convergence rate properties. Variable selection using the sparse l 1 penalty is also considered. Analysis of simulated examples and a type 2 diabetes mellitus observational study are used to demonstrate competitive performance of the proposed method.

Multicategory individualized treatment regime using outcome weighted learning.

Individualized treatment regimes (ITRs) aim to recommend treatments based on patient-specific characteristics in order to maximize the expected clinical outcome. Outcome weighted learning approaches have been proposed for this optimization problem with primary focus on the binary treatment case. Many require assumptions of the outcome value or the randomization mechanism. In this paper, we propose a general framework for multicategory ITRs using generic surrogate risk. The proposed method accommodates the situations when the outcome takes negative value and/or when the propensity score is unknown. Theoretical results about Fisher consistency, excess risk, and risk consistency are established. In practice, we recommend using differentiable convex loss for computational optimization. We demonstrate the superiority of the proposed method under multinomial deviance risk to some existing methods by simulation and application on data from a clinical trial.

Bagging and deep learning in optimal individualized treatment rules.

An ENsemble Deep Learning Optimal Treatment (EndLot) approach is proposed for personalized medicine problems. The statistical framework of the proposed method is based on the outcome weighted learning (OWL) framework which transforms the optimal decision rule problem into a weighted classification problem. We further employ an ensemble of deep neural networks (DNNs) to learn the optimal decision rule. Utilizing the flexibility of DNNs and the stability of bootstrap aggregation, the proposed method achieves a considerable improvement over existing methods. An R package "ITRlearn" is developed to implement the proposed method. Numerical performance is demonstrated via simulation studies and a real data analysis of the Cancer Cell Line Encyclopedia data.

Estimating individualized treatment rules for ordinal treatments.

Precision medicine is an emerging scientific topic for disease treatment and prevention that takes into account individual patient characteristics. It is an important direction for clinical research, and many statistical methods have been proposed recently. One of the primary goals of precision medicine is to obtain an optimal individual treatment rule (ITR), which can help make decisions on treatment selection according to each patient's specific characteristics. Recently, outcome weighted learning (OWL) has been proposed to estimate such an optimal ITR in a binary treatment setting by maximizing the expected clinical outcome. However, for ordinal treatment settings, such as individualized dose finding, it is unclear how to use OWL. In this article, we propose a new technique for estimating ITR with ordinal treatments. In particular, we propose a data duplication technique with a piecewise convex loss function. We establish Fisher consistency for the resulting estimated ITR under certain conditions, and obtain the convergence and risk bound properties. Simulated examples and an application to a dataset from a type 2 diabetes mellitus observational study demonstrate the highly competitive performance of the proposed method compared to existing alternatives.

Augmented outcome-weighted learning for estimating optimal dynamic treatment regimens.

Dynamic treatment regimens (DTRs) are sequential treatment decisions tailored by patient's evolving features and intermediate outcomes at each treatment stage. Patient heterogeneity and the complexity and chronicity of many diseases call for learning optimal DTRs that can best tailor treatment according to each individual's time-varying characteristics (eg, intermediate response over time). In this paper, we propose a robust and efficient approach referred to as Augmented Outcome-weighted Learning (AOL) to identify optimal DTRs from sequential multiple assignment randomized trials. We improve previously proposed outcome-weighted learning to allow for negative weights. Furthermore, to reduce the variability of weights for numeric stability and improve estimation accuracy, in AOL, we propose a robust augmentation to the weights by making use of predicted pseudooutcomes from regression models for Q-functions. We show that AOL still yields Fisher-consistent DTRs even if the regression models are misspecified and that an appropriate choice of the augmentation guarantees smaller stochastic errors in value function estimation for AOL than the previous outcome-weighted learning. Finally, we establish the convergence rates for AOL. The comparative advantage of AOL over existing methods is demonstrated through extensive simulation studies and an application to a sequential multiple assignment randomized trial for major depressive disorder.

Estimating individualized optimal combination therapies through outcome weighted deep learning algorithms.

With the advancement in drug development, multiple treatments are available for a single disease. Patients can often benefit from taking multiple treatments simultaneously. For example, patients in Clinical Practice Research Datalink with chronic diseases such as type 2 diabetes can receive multiple treatments simultaneously. Therefore, it is important to estimate what combination therapy from which patients can benefit the most. However, to recommend the best treatment combination is not a single label but a multilabel classification problem. In this paper, we propose a novel outcome weighted deep learning algorithm to estimate individualized optimal combination therapy. The Fisher consistency of the proposed loss function under certain conditions is also provided. In addition, we extend our method to a family of loss functions, which allows adaptive changes based on treatment interactions. We demonstrate the performance of our methods through simulations and real data analysis.

LIBERTI: A SMART study in plastic surgery.

BACKGROUND/AIMS: Laser treatment of burns scars is considered by some providers to be standard of care. However, there is little evidence-based research as to the true benefit. A number of factors hinder evaluation of the benefit of laser treatment. These include significant heterogeneity in patient response and possible delayed effects from the laser treatment. Moreover, laser treatments are often provided sequentially using different types of equipment and settings, so there are effectively a large number of overall treatment options that need to be compared. We propose a trial capable of coping with these issues and that also attempts to take advantage of the heterogeneous response in order to estimate optimal treatment plans personalized to each individual patient. It will be the first large-scale randomized trial to compare the effectiveness of laser treatments for burns scars and, to our knowledge, the very first example of the utility of a Sequential Multiple Assignment Randomized Trial in plastic surgery. METHODS: We propose using a Sequential Multiple Assignment Randomized Trial design to investigate the effect of various permutations of laser treatment on hypertrophic burn scars. We will compare and test hypotheses regarding laser treatment effects at a general population level. Simultaneously, we hope to use the data generated to discover possible beneficial personalized treatment plans, tailored to individual patient characteristics. RESULTS: We show that the proposed trial has good power to detect laser treatment effect at the overall population level, despite comparing a large number of treatment combinations. The trial will simultaneously provide high-quality data appropriate for estimating precision-medicine treatment rules. We detail population-level comparisons of interest and corresponding sample size calculations. We provide simulations to suggest the power of the trial to detect laser effect and also the possible benefits of personalization of laser treatment to individual characteristics. CONCLUSION: We propose, to our knowledge, the first use of a Sequential Multiple Assignment Randomized Trial in surgery. The trial is rigorously designed so that it is reasonably straightforward to implement and powered to answer general overall questions of interest. The trial is also designed to provide data that are suitable for the estimation of beneficial precision-medicine treatment rules that depend both on individual patient characteristics and on-going real-time patient response to treatment.

Discussion of combining biomarkers to optimize patient treatment recommendations.

Kang, Janes and Huang propose an interesting boosting method to combine biomarkers for treatment selection. The method requires modeling the treatment effects using markers. We discuss an alternative method, outcome weighted learning. This method sidesteps the need for modeling the outcomes, and thus can be more robust to model misspecification.

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.

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.

Decision making and uncertainty quantification for individualized treatments using Bayesian Additive Regression Trees.

Individualized treatment rules can improve health outcomes by recognizing that patients may respond differently to treatment and assigning therapy with the most desirable predicted outcome for each individual. Flexible and efficient prediction models are desired as a basis for such individualized treatment rules to handle potentially complex interactions between patient factors and treatment. Modern Bayesian semiparametric and nonparametric regression models provide an attractive avenue in this regard as these allow natural posterior uncertainty quantification of patient specific treatment decisions as well as the population wide value of the prediction-based individualized treatment rule. In addition, via the use of such models, inference is also available for the value of the optimal individualized treatment rules. We propose such an approach and implement it using Bayesian Additive Regression Trees as this model has been shown to perform well in fitting nonparametric regression functions to continuous and binary responses, even with many covariates. It is also computationally efficient for use in practice. With Bayesian Additive Regression Trees, we investigate a treatment strategy which utilizes individualized predictions of patient outcomes from Bayesian Additive Regression Trees models. Posterior distributions of patient outcomes under each treatment are used to assign the treatment that maximizes the expected posterior utility. We also describe how to approximate such a treatment policy with a clinically interpretable individualized treatment rule, and quantify its expected outcome. The proposed method performs very well in extensive simulation studies in comparison with several existing methods. We illustrate the usage of the proposed method to identify an individualized choice of conditioning regimen for patients undergoing hematopoietic cell transplantation and quantify the value of this method of choice in relation to the optimal individualized treatment rule as well as non-individualized treatment strategies.

Tree based weighted learning for estimating individualized treatment rules with censored data.

Estimating individualized treatment rules is a central task for personalized medicine. [23] and [22] proposed outcome weighted learning to estimate individualized treatment rules directly through maximizing the expected outcome without modeling the response directly. In this paper, we extend the outcome weighted learning to right censored survival data without requiring either inverse probability of censoring weighting or semiparametric modeling of the censoring and failure times as done in [26]. To accomplish this, we take advantage of the tree based approach proposed in [28] to nonparametrically impute the survival time in two different ways. The first approach replaces the reward of each individual by the expected survival time, while in the second approach only the censored observations are imputed by their conditional expected failure times. We establish consistency and convergence rates for both estimators. In simulation studies, our estimators demonstrate improved performance compared to existing methods. We also illustrate the proposed method on a phase III clinical trial of non-small cell lung cancer.