Estimating Dynamic Treatment Regimes in Mobile Health Using V-learning

Machine Learning and Health Science Research: Tutorial

Machine learning (ML) has seen impressive growth in health science research due to its capacity for handling complex data to perform a range of tasks, including unsupervised learning, supervised learning, and reinforcement learning. To aid health science researchers in understanding the strengths and limitations of ML and to facilitate its integration into their studies, we present here a guideline for integrating ML into an analysis through a structured framework, covering steps from framing a research question to study design and analysis techniques for specialized data types.

ASSESSING TIME-VARYING CAUSAL EFFECT MODERATION IN THE PRESENCE OF CLUSTER-LEVEL TREATMENT EFFECT HETEROGENEITY AND INTERFERENCE

The micro-randomized trial (MRT) is a sequential randomized experimental design to empirically evaluate the effectiveness of mobile health (mHealth) intervention components that may be delivered at hundreds or thousands of decision points. MRTs have motivated a new class of causal estimands, termed "causal excursion effects", for which semiparametric inference can be conducted via a weighted, centered least squares criterion (Boruvka et al., 2018). Existing methods assume between-subject independence and non-interference. Deviations from these assumptions often occur. In this paper, causal excursion effects are revisited under potential cluster-level treatment effect heterogeneity and interference, where the treatment effect of interest may depend on cluster-level moderators. Utility of the proposed methods is shown by analyzing data from a multi-institution cohort of first year medical residents in the United States.

Relative sparsity for medical decision problems

Existing statistical methods can estimate a policy, or a mapping from covariates to decisions, which can then instruct decision makers (eg, whether to administer hypotension treatment based on covariates blood pressure and heart rate). There is great interest in using such data-driven policies in healthcare. However, it is often important to explain to the healthcare provider, and to the patient, how a new policy differs from the current standard of care. This end is facilitated if one can pinpoint the aspects of the policy (ie, the parameters for blood pressure and heart rate) that change when moving from the standard of care to the new, suggested policy. To this end, we adapt ideas from Trust Region Policy Optimization (TRPO). In our work, however, unlike in TRPO, the difference between the suggested policy and standard of care is required to be sparse, aiding with interpretability. This yields "relative sparsity," where, as a function of a tuning parameter,λ $$ \lambda $$ , we can approximately control the number of parameters in our suggested policy that differ from their counterparts in the standard of care (eg, heart rate only). We propose a criterion for selectingλ $$ \lambda $$ , perform simulations, and illustrate our method with a real, observational healthcare dataset, deriving a policy that is easy to explain in the context of the current standard of care. Our work promotes the adoption of data-driven decision aids, which have great potential to improve health outcomes.

Monte Carlo sensitivity analysis for unmeasured confounding in dynamic treatment regimes

Data-driven methods for personalizing treatment assignment have garnered much attention from clinicians and researchers. Dynamic treatment regimes formalize this through a sequence of decision rules that map individual patient characteristics to a recommended treatment. Observational studies are commonly used for estimating dynamic treatment regimes due to the potentially prohibitive costs of conducting sequential multiple assignment randomized trials. However, estimating a dynamic treatment regime from observational data can lead to bias in the estimated regime due to unmeasured confounding. Sensitivity analyses are useful for assessing how robust the conclusions of the study are to a potential unmeasured confounder. A Monte Carlo sensitivity analysis is a probabilistic approach that involves positing and sampling from distributions for the parameters governing the bias. We propose a method for performing a Monte Carlo sensitivity analysis of the bias due to unmeasured confounding in the estimation of dynamic treatment regimes. We demonstrate the performance of the proposed procedure with a simulation study and apply it to an observational study examining tailoring the use of antidepressant medication for reducing symptoms of depression using data from Kaiser Permanente Washington.

A novel approach to assess dynamic treatment regimes embedded in a SMART with an ordinal outcome

Sequential multiple assignment randomized trials (SMARTs) are used to construct data-driven optimal intervention strategies for subjects based on their intervention and covariate histories in different branches of health and behavioral sciences where a sequence of interventions is given to a participant. Sequential intervention strategies are often called dynamic treatment regimes (DTR). In the existing literature, the majority of the analysis methodologies for SMART data assume a continuous primary outcome. However, ordinal outcomes are also quite common in clinical practice. In this work, first, we introduce the notion of generalized odds ratio ( G O R $$ GOR $$ ) to compare two DTRs embedded in a SMART with an ordinal outcome and discuss some combinatorial properties of this measure. Next, we propose a likelihood-based approach to estimate G O R $$ GOR $$ from SMART data, and derive the asymptotic properties of its estimate. We discuss alternative ways to estimate G O R $$ GOR $$ using concordant-discordant pairs and two-sample U $$ U $$ -statistic. We derive the required sample size formula for designing SMARTs with ordinal outcomes based on G O R $$ GOR $$ . A simulation study shows the performance of the estimated G O R $$ GOR $$ in terms of the estimated power corresponding to the derived sample size. The methodology is applied to analyze data from the SMART+ study, conducted in the UK, to improve carbohydrate periodization behavior in athletes using a menu planner mobile application, Hexis Performance. A freely available Shiny web app using R is provided to make the proposed methodology accessible to other researchers and practitioners.

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.

The Future of Causal Inference

The past several decades have seen exponential growth in causal inference approaches and their applications. In this commentary, we provide our top-10 list of emerging and exciting areas of research in causal inference. These include methods for high-dimensional data and precision medicine, causal machine learning, causal discovery, and others. These methods are not meant to be an exhaustive list; instead, we hope that this list will serve as a springboard for stimulating the development of new research.

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.

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.

Estimating time-varying causal excursion effect in mobile health with binary outcomes

Advances in wearables and digital technology now make it possible to deliver behavioral mobile health interventions to individuals in their everyday life. The micro-randomized trial is increasingly used to provide data to inform the construction of these interventions. In a micro-randomized trial, each individual is repeatedly randomized among multiple intervention options, often hundreds or even thousands of times, over the course of the trial. This work is motivated by multiple micro-randomized trials that have been conducted or are currently in the field, in which the primary outcome is a longitudinal binary outcome. The primary aim of such micro-randomized trials is to examine whether a particular time-varying intervention has an effect on the longitudinal binary outcome, often marginally over all but a small subset of the individual's data. We propose the definition of causal excursion effect that can be used in such primary aim analysis for micro-randomized trials with binary outcomes. Under rather restrictive assumptions one can, based on existing literature, derive a semiparametric, locally efficient estimator of the causal effect. Starting from this estimator, we develop an estimator that can be used as the basis of a primary aim analysis under more plausible assumptions. Simulation studies are conducted to compare the estimators. We illustrate the developed methods using data from the micro-randomized trial, BariFit. In BariFit, the goal is to support weight maintenance for individuals who received bariatric surgery.

Beyond Two Cultures: Cultural Infrastructure for Data-driven Decision Support

In the twenty years since Dr. Leo Breiman's incendiary paper Statistical Modeling: The Two Cultures was first published, algorithmic modeling techniques have gone from controversial to commonplace in the statistical community. While the widespread adoption of these methods as part of the contemporary statistician's toolkit is a testament to Dr. Breiman's vision, the number of high-profile failures of algorithmic models suggests that Dr. Breiman's final remark that "the emphasis needs to be on the problem and the data" has been less widely heeded. In the spirit of Dr. Breiman, we detail an emerging research community in statistics - data-driven decision support. We assert that to realize the full potential of decision support, broadly and in the context of precision health, will require a culture of social awareness and accountability, in addition to ongoing attention towards complex technical challenges.

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.

Off-Policy Estimation of Long-Term Average Outcomes with Applications to Mobile Health

Due to the recent advancements in wearables and sensing technology, health scientists are increasingly developing mobile health (mHealth) interventions. In mHealth interventions, mobile devices are used to deliver treatment to individuals as they go about their daily lives. These treatments are generally designed to impact a near time, proximal outcome such as stress or physical activity. The mHealth intervention policies, often called just-in-time adaptive interventions, are decision rules that map a individual's current state (e.g., individual's past behaviors as well as current observations of time, location, social activity, stress and urges to smoke) to a particular treatment at each of many time points. The vast majority of current mHealth interventions deploy expert-derived policies. In this paper, we provide an approach for conducting inference about the performance of one or more such policies using historical data collected under a possibly different policy. Our measure of performance is the average of proximal outcomes over a long time period should the particular mHealth policy be followed. We provide an estimator as well as confidence intervals. This work is motivated by HeartSteps, an mHealth physical activity intervention.

Personalized Policy Learning using Longitudinal Mobile Health Data

Personalized policy represents a paradigm shift from one-decision-rule-for-all users to an individualized decision rule for each user. Developing personalized policy in mobile health applications imposes challenges. First, for lack of adherence, data from each user are limited. Second, unmeasured contextual factors can potentially impact on decision making. Aiming to optimize immediate rewards, we propose using a generalized linear mixed modeling framework where population features and individual features are modeled as fixed and random effects, respectively, and synthesized to form the personalized policy. The group lasso type penalty is imposed to avoid overfitting of individual deviations from the population model. We examine the conditions under which the proposed method work in the presence of time-varying endogenous covariates, and provide conditional optimality and marginal consistency results of the expected immediate outcome under the estimated policies. We apply our method to develop personalized push ("prompt") schedules in 294 app users, with the goal to maximize the prompt response rate given past app usage and other contextual factors. The proposed method compares favorably to existing estimation methods including using the R function "glmer" in a simulation study.

A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity

There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach to learning optimal treatment regimes under endogeneity. Specifically, we establish identification of both value function E [ Y D ( L ) ] for a given regime D and optimal regimes arg max D E [ Y D ( L ) ] with the aid of a binary instrumental variable, when no unmeasured confounding fails to hold. We also construct novel multiply robust classification-based estimators. Furthermore, we propose to identify and estimate optimal treatment regimes among those who would comply to the assigned treatment under a monotonicity assumption. In this latter case, we establish the somewhat surprising result that complier optimal regimes can be consistently estimated without directly collecting compliance information and therefore without the complier average treatment effect itself being identified. Our approach is illustrated via extensive simulation studies and a data application on the effect of child rearing on labor participation.