We consider estimation of an optimal individualized treatment rule from observational and randomized studies when a high-dimensional vector of baseline variables is available. Our optimality criterion is with respect to delaying expected time to occurrence of an event of interest (e.g., death or relapse of cancer). We leverage semiparametric efficiency theory to construct estimators with desirable properties such as double robustness. We propose two estimators of the optimal rule, which arise from considering two loss functions aimed at (i) directly estimating the conditional treatment effect (also know as the blip function), and (ii) recasting the problem as a weighted classification problem that uses the 0-1 loss function. Our estimated rules are super learning ensembles that minimize the cross-validated risk of a linear combination in a user-supplied library of candidate estimators. We prove oracle inequalities bounding the finite sample excess risk of the estimator. The bounds depend on the excess risk of the oracle selector and a doubly robust term related to estimation of the nuisance parameters. We discuss some important implications of these oracle inequalities such as the convergence rates of the value of our estimator to that of the oracle selector. We illustrate our methods in the analysis of a phase III randomized study testing the efficacy of a new therapy for the treatment of breast cancer.
In many important applications of precision medicine, the outcome of interest is time to an event (e.g., death, relapse of disease) and the primary goal is to identify the optimal individualized decision rule (IDR) to prolong survival time. Existing work in this area have been mostly focused on estimating the optimal IDR to maximize the We propose a new robust framework for estimating an optimal static or dynamic IDR with time-to-event outcomes based on an easy-to-interpret quantile criterion. The new method does not need to specify an outcome regression model and is robust for heavy-tailed di…
In many clinical trials, individuals in different subgroups have experience differential treatment effects. This leads to individualized differences in treatment benefit. In this article, we introduce the general concept of predictive directions, which are risk scores motivated by potential outcomes considerations. These techniques borrow heavily from sufficient dimension reduction (SDR) and causal inference methodology. Under some conditions, one can use existing methods from the SDR literature to estimate the directions assuming an idealized complete data structure, which subsequently yields…
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 (ITR), 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 Dire…
Precision medicine is a rapidly expanding area of health research wherein patient level information is used to inform treatment decisions. A statistical framework helps to formalize the individualization of treatment decisions that characterize personalized management plans. Numerous methods have been proposed to estimate individualized treatment rules that optimize expected patient outcomes, many of which have desirable properties such as robustness to model misspecification. However, while individual data are essential in this context, there may be concerns about data confidentiality, partic…
Columbia University（哥伦比亚大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
For mental disorders, patients' underlying mental states are non-observed latent constructs which have to be inferred from observed multi-domain measurements such as diagnostic symptoms and patient functioning scores. Additionally, substantial heterogeneity in the disease diagnosis between patients needs to be addressed for optimizing individualized treatment policy in order to achieve precision medicine. To address these challenges, we propose an integrated learning framework that can simultaneously learn patients' underlying mental states and recommend optimal treatments for each individual.…
Individualized treatment rules can lead to better health outcomes when patients have heterogeneous responses to treatment. Very few individualized treatment rule estimation methods are compatible with a multi-treatment observational study with right censored survival outcomes. In this paper we extend policy evaluation methods to the right censored data setting. Existing approaches either make restrictive assumptions about the structure of the data, or use inverse weighting methods that increase the variance of the estimator resulting in decreased performance. We propose a method which uses bal…
Current Targeted Maximum Likelihood Estimation (TMLE) methods used to analyze time-to-event data estimate the survival probability for each time point separately, which result in estimates that are not necessarily monotone. In this paper, we present an extension of TMLE for observational time-to-event data, the one-step Targeted Maximum Likelihood Estimator for the treatment-rule specific survival curve. We construct a one-dimensional universal least favorable submodel that targets the entire survival curve, and thereby requires minimal extra fitting with data to achieve its goal of solving th…
Dynamic treatment regimes (DTR) are a statistical paradigm in precision medicine which aim to optimize patient outcomes by individualizing treatments. At its simplest, a DTR may require only a single decision to be made; this special case is called an individualized treatment rule (ITR) and is often used to maximize short-term rewards. Generalized dynamic weighted ordinary least squares (G-dWOLS), a DTR estimation method that offers theoretical advantages such as double robustness of parameter estimators in the decision rules, has been recently extended to now accommodate categorical treatment…
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 must balance multiple and possibly competing outcomes, e.g., symptom reduction and the risk of an adverse event. One approach to precision…
University of North Carolina（北卡罗来纳大学）；University of Southern California（南加利福尼亚大学）；University of Texas at Austin（得克萨斯大学奥斯汀分校）
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 pre-specified 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 crossove…
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；University of Minnesota（明尼苏达大学）
Medical treatments tailored to a patient's baseline characteristics hold the potential of improving patient outcomes while reducing negative side effects. Learning individualized treatment rules (ITRs) often requires aggregation of multiple datasets(sites); however, current ITR methodology does not take between-site heterogeneity into account, which can hurt model generalizability when deploying back to each site. To address this problem, we develop a method for individual-level meta-analysis of ITRs, which jointly learns site-specific ITRs while borrowing information about feature sign-cohere…
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 p…
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 article, we propose a nonparametric outcome weighted learning approach for this problem in randomized clinical trial settings. The theoretical prope…
Multicategory Matched Learning for Estimating Optimal Individualized Treatment Rules in Observational Studies with Application to a Hepatocellular Carcinoma Study
Evaluating Surrogates in Individualized Treatment Rules
School of Statistics, Renmin University of China（中国人民大学统计学院）；School of Economics and Management, Tsinghua University（清华大学经济管理学院）；Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学应用统计科学中心及统计学院）
The sequential treatment decisions made by physicians to treat chronic diseases are formalized in the statistical literature as dynamic treatment regimes. To date, methods for dynamic treatment regimes have been developed under the assumption that observation times, i.e., treatment and outcome monitoring times, are determined by study investigators. That assumption is often not satisfied in electronic health records data in which the outcome, the observation times, and the treatment mechanism are associated with patients' characteristics. The treatment and observation processes can lead to spu…
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；North Carolina State University（北卡罗来纳州立大学）
The complexity of human cancer often results in significant heterogeneity in response to treatment. Precision medicine offers 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 opti…
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…
Randomized trials typically estimate average relative treatment effects, but decisions on the benefit of a treatment are possibly better informed by more individualized predictions of the absolute treatment effect. In case of a binary outcome, these predictions of absolute individualized treatment effect require knowledge of the individual's risk without treatment and incorporation of a possibly differential treatment effect (i.e. varying with patient characteristics). In this paper we lay out the causal structure of individualized treatment effect in terms of potential outcomes and describe t…
The George Washington University（乔治华盛顿大学）；University of Southern California（南加利福尼亚大学）；University of North Carolina（北卡罗来纳大学）
Recent exploration of optimal individualized decision rules (IDRs) for patients in precision medicine has attracted a lot of attention due to the heterogeneous responses of patients to different treatments. In the existing literature of precision medicine, an optimal IDR is defined as a decision function mapping from the patients' covariate space into the treatment space that maximizes the expected outcome of each individual. Motivated by the concept of Optimized Certainty Equivalent (OCE) introduced originally in \cite{ben1986expected} that includes the popular conditional-value-of risk (CVaR…
Maximin Learning of Individualized Treatment Effect on Multi-Domain Outcomes
Department of Biostatistics, Columbia Mailman School of Public Health（哥伦比亚大学梅尔曼公共卫生学院生物统计系）；Department of Biostatistics, Peking University Health Science Center（北京大学医学部生物统计系）；Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）
This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression approach. The primary motivation is to estimate an optimal individualized dose rule in an observational study. To model possibly nonlinear interaction effects between patients' covariates and a continuous treatment variable, we employ a two-dimensional penalized spline regression on an index-treatment domain, where the index is defined as a linear projection of the covariates. The method is illustrated using two a…
We study the problem of learning individualized dose intervals using observational data. There are very few previous works for policy learning with continuous treatment, and all of them focused on recommending an optimal dose rather than an optimal dose interval. In this paper, we propose a new method to estimate such an optimal dose interval, named probability dose interval (PDI). The potential outcomes for doses in the PDI are guaranteed better than a pre-specified threshold with a given probability (e.g., 50%). The associated nonconvex optimization problem can be efficiently solved by the D…
Individualized treatment rules aim to identify if, when, which, and to whom treatment should be applied. A globally aging population, rising healthcare costs, and increased access to patient-level data have created an urgent need for high-quality estimators of individualized treatment rules that can be applied to observational data. A recent and promising line of research for estimating individualized treatment rules recasts the problem of estimating an optimal treatment rule as a weighted classification problem. We consider a class of estimators for optimal treatment rules that are analogous …
It is common to compare individualized treatment rules based on the value function, which is the expected potential outcome under the treatment rule. Although the value function is not point-identified when there is unmeasured confounding, it still defines a partial order among the treatment rules under Rosenbaum's sensitivity analysis model. We first consider how to compare two treatment rules with unmeasured confounding in the single-decision setting and then use this pairwise test to rank multiple treatment rules. We consider how to, among many treatment rules, select the best rules and sel…
Conventional survival analysis approaches estimate risk scores or individualized time-to-event distributions conditioned on covariates. In practice, there is often great population-level phenotypic heterogeneity, resulting from (unknown) subpopulations with diverse risk profiles or survival distributions. As a result, there is an unmet need in survival analysis for identifying subpopulations with distinct risk profiles, while jointly accounting for accurate individualized time-to-event predictions. An approach that addresses this need is likely to improve characterization of individual outcome…
Balanced representation learning methods have been applied successfully to counterfactual inference from observational data. However, approaches that account for survival outcomes are relatively limited. Survival data are frequently encountered across diverse medical applications, i.e., drug development, risk profiling, and clinical trials, and such data are also relevant in fields like manufacturing (e.g., for equipment monitoring). When the outcome of interest is a time-to-event, special precautions for handling censored events need to be taken, as ignoring censored outcomes may lead to bias…
We propose a new modeling and estimation approach to select the optimal treatment regime from different options through constructing a robust estimating equation. The method is protected against misspecification of the propensity score model, the outcome regression model for the non-treated group, or the potential non-monotonic treatment difference model. Our method also allows residual errors to depend on covariates. A single index structure is incorporated to facilitate the nonparametric estimation of the treatment difference. We then identify the optimal treatment through maximizing the val…
With the increasing adoption of electronic health records, there is an increasing interest in developing individualized treatment rules, which recommend treatments according to patients' characteristics, from large observational data. However, there is a lack of valid inference procedures for such rules developed from this type of data in the presence of high-dimensional covariates. In this work, we develop a penalized doubly robust method to estimate the optimal individualized treatment rule from high-dimensional data. We propose a split-and-pooled de-correlated score to construct hypothesis …
University of California Irvine（加州大学欧文分校）；London School of Economics and Political Science（伦敦政治经济学院）；North Carolina State University（北卡罗来纳州立大学）
An individualized decision rule (IDR) is a decision function that assigns each individual a given treatment based on his/her observed characteristics. Most of the existing works in the literature consider settings with binary or finitely many treatment options. In this paper, we focus on the continuous treatment setting and propose a jump interval-learning to develop an individualized interval-valued decision rule (I2DR) that maximizes the expected outcome. Unlike IDRs that recommend a single treatment, the proposed I2DR yields an interval of treatment options for each individual, making it mo…
Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment rule (ITR) that maximizes the expected outcome. Existing methods typically require initial estimation of some nuisance models. The double robustness property that can protect from misspecification of either the treatment-free effect or the propensity score has been widely advocated. However, when model misspecification exists, a doubly robust estima…
Covariate Balancing Value Estimation for Optimal Individualized Treatment Rules
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；School of Mathematics and Statistics, Beijing Technology and Business University（北京工商大学数学与统计学院）
Individualized Dynamic Mediation Analysis Using Latent Factor Models
University of Pennsylvania（宾夕法尼亚大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；The University of Texas at San Antonio（圣安东尼奥德克萨斯大学）；Fudan University（复旦大学）；University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）
