arXiv subjects

Susan A. Murphy

Publications and source records attributed to Susan A. Murphy.

At least 37 records · Page 2Linked to original sources

arXiv2023

Assessing the Impact of Context Inference Error and Partial Observability on RL Methods for Just-In-Time Adaptive Interventions

Just-in-Time Adaptive Interventions (JITAIs) are a class of personalized health interventions developed within the behavioral science community. JITAIs aim to provide the right type and amount of support by iteratively selecting a sequence of intervention options from a pre-defined set of components in response to each individual's time varying state. In this work, we explore the application of reinforcement learning methods to the problem of learning intervention option selection policies. We study the effect of context inference error and partial observability on the ability to learn effective policies. Our results show that the propagation of uncertainty from context inferences is critical to improving intervention efficacy as context uncertainty increases, while policy gradient algorithms can provide remarkable robustness to partially observed behavioral state information.

cs.LG↗

arXiv2023

Statistical Inference After Adaptive Sampling for Longitudinal Data

Online reinforcement learning and other adaptive sampling algorithms are increasingly used in digital intervention experiments to optimize treatment delivery for users over time. In this work, we focus on longitudinal user data collected by a large class of adaptive sampling algorithms that are designed to optimize treatment decisions online using accruing data from multiple users. Combining or "pooling" data across users allows adaptive sampling algorithms to potentially learn faster. However, by pooling, these algorithms induce dependence between the sampled user data trajectories; we show that this can cause standard variance estimators for i.i.d. data to underestimate the true variance of common estimators on this data type. We develop novel methods to perform a variety of statistical analyses on such adaptively sampled data via Z-estimation. Specifically, we introduce the \textit{adaptive} sandwich variance estimator, a corrected sandwich estimator that leads to consistent variance estimates under adaptive sampling. Additionally, to prove our results we develop novel theoretical tools for empirical processes on non-i.i.d., adaptively sampled longitudinal data which may be of independent interest. This work is motivated by our efforts in designing experiments in which online reinforcement learning algorithms optimize treatment decisions, yet statistical inference is essential for conducting analyses after experiments conclude.

cs.LG↗

arXiv2022

Reward Design For An Online Reinforcement Learning Algorithm Supporting Oral Self-Care

Dental disease is one of the most common chronic diseases despite being largely preventable. However, professional advice on optimal oral hygiene practices is often forgotten or abandoned by patients. Therefore patients may benefit from timely and personalized encouragement to engage in oral self-care behaviors. In this paper, we develop an online reinforcement learning (RL) algorithm for use in optimizing the delivery of mobile-based prompts to encourage oral hygiene behaviors. One of the main challenges in developing such an algorithm is ensuring that the algorithm considers the impact of the current action on the effectiveness of future actions (i.e., delayed effects), especially when the algorithm has been made simple in order to run stably and autonomously in a constrained, real-world setting (i.e., highly noisy, sparse data). We address this challenge by designing a quality reward which maximizes the desired health outcome (i.e., high-quality brushing) while minimizing user burden. We also highlight a procedure for optimizing the hyperparameters of the reward by building a simulation environment test bed and evaluating candidates using the test bed. The RL algorithm discussed in this paper will be deployed in Oralytics, an oral self-care app that provides behavioral strategies to boost patient engagement in oral hygiene practices.

cs.AI↗

arXiv2022

Designing Reinforcement Learning Algorithms for Digital Interventions: Pre-implementation Guidelines

Online reinforcement learning (RL) algorithms are increasingly used to personalize digital interventions in the fields of mobile health and online education. Common challenges in designing and testing an RL algorithm in these settings include ensuring the RL algorithm can learn and run stably under real-time constraints, and accounting for the complexity of the environment, e.g., a lack of accurate mechanistic models for the user dynamics. To guide how one can tackle these challenges, we extend the PCS (Predictability, Computability, Stability) framework, a data science framework that incorporates best practices from machine learning and statistics in supervised learning (Yu and Kumbier, 2020), to the design of RL algorithms for the digital interventions setting. Further, we provide guidelines on how to design simulation environments, a crucial tool for evaluating RL candidate algorithms using the PCS framework. We illustrate the use of the PCS framework for designing an RL algorithm for Oralytics, a mobile health study aiming to improve users' tooth-brushing behaviors through the personalized delivery of intervention messages. Oralytics will go into the field in late 2022.

cs.LG↗

arXiv2022

An Actor-Critic Contextual Bandit Algorithm for Personalized Mobile Health Interventions

Increasing technological sophistication and widespread use of smartphones and wearable devices provide opportunities for innovative and highly personalized health interventions. A Just-In-Time Adaptive Intervention (JITAI) uses real-time data collection and communication capabilities of modern mobile devices to deliver interventions in real-time that are adapted to the in-the-moment needs of the user. The lack of methodological guidance in constructing data-based JITAIs remains a hurdle in advancing JITAI research despite the increasing popularity of JITAIs among clinical scientists. In this article, we make a first attempt to bridge this methodological gap by formulating the task of tailoring interventions in real-time as a contextual bandit problem. Interpretability requirements in the domain of mobile health lead us to formulate the problem differently from existing formulations intended for web applications such as ad or news article placement. Under the assumption of linear reward function, we choose the reward function (the "critic") parameterization separately from a lower dimensional parameterization of stochastic policies (the "actor"). We provide an online actor-critic algorithm that guides the construction and refinement of a JITAI. Asymptotic properties of the actor-critic algorithm are developed and backed up by numerical experiments. Additional numerical experiments are conducted to test the robustness of the algorithm when idealized assumptions used in the analysis of contextual bandit algorithm are breached.

stat.ML↗

arXiv2022

Estimating causal effects with optimization-based methods: A review and empirical comparison

In the absence of randomized controlled and natural experiments, it is necessary to balance the distributions of (observable) covariates of the treated and control groups in order to obtain an unbiased estimate of a causal effect of interest; otherwise, a different effect size may be estimated, and incorrect recommendations may be given. To achieve this balance, there exist a wide variety of methods. In particular, several methods based on optimization models have been recently proposed in the causal inference literature. While these optimization-based methods empirically showed an improvement over a limited number of other causal inference methods in their relative ability to balance the distributions of covariates and to estimate causal effects, they have not been thoroughly compared to each other and to other noteworthy causal inference methods. In addition, we believe that there exist several unaddressed opportunities that operational researchers could contribute with their advanced knowledge of optimization, for the benefits of the applied researchers that use causal inference tools. In this review paper, we present an overview of the causal inference literature and describe in more detail the optimization-based causal inference methods, provide a comparative analysis of the prevailing optimization-based methods, and discuss opportunities for new methods.

stat.ME↗

arXiv2021

The Micro-Randomized Trial for Developing Digital Interventions: Experimental Design and Data Analysis Considerations

Just-in-time adaptive interventions (JITAIs) are time-varying adaptive interventions that use frequent opportunities for the intervention to be adapted--weekly, daily, or even many times a day. The micro-randomized trial (MRT) has emerged for use in informing the construction of JITAIs. MRTs can be used to address research questions about whether and under what circumstances JITAI components are effective, with the ultimate objective of developing effective and efficient JITAI. The purpose of this article is to clarify why, when, and how to use MRTs; to highlight elements that must be considered when designing and implementing an MRT; and to review primary and secondary analyses methods for MRTs. We briefly review key elements of JITAIs and discuss a variety of considerations that go into planning and designing an MRT. We provide a definition of causal excursion effects suitable for use in primary and secondary analyses of MRT data to inform JITAI development. We review the weighted and centered least-squares (WCLS) estimator which provides consistent causal excursion effect estimators from MRT data. We describe how the WCLS estimator along with associated test statistics can be obtained using standard statistical software such as R (R Core Team, 2019). Throughout we illustrate the MRT design and analyses using the HeartSteps MRT, for developing a JITAI to increase physical activity among sedentary individuals. We supplement the HeartSteps MRT with two other MRTs, SARA and BariFit, each of which highlights different research questions that can be addressed using the MRT and experimental design considerations that might arise.

stat.AP↗

arXiv2021

Statistical Inference with M-Estimators on Adaptively Collected Data

Bandit algorithms are increasingly used in real-world sequential decision-making problems. Associated with this is an increased desire to be able to use the resulting datasets to answer scientific questions like: Did one type of ad lead to more purchases? In which contexts is a mobile health intervention effective? However, classical statistical approaches fail to provide valid confidence intervals when used with data collected with bandit algorithms. Alternative methods have recently been developed for simple models (e.g., comparison of means). Yet there is a lack of general methods for conducting statistical inference using more complex models on data collected with (contextual) bandit algorithms; for example, current methods cannot be used for valid inference on parameters in a logistic regression model for a binary reward. In this work, we develop theory justifying the use of M-estimators -- which includes estimators based on empirical risk minimization as well as maximum likelihood -- on data collected with adaptive algorithms, including (contextual) bandit algorithms. Specifically, we show that M-estimators, modified with particular adaptive weights, can be used to construct asymptotically valid confidence regions for a variety of inferential targets.

cs.LG↗

arXiv2021

Comparison and Unification of Three Regularization Methods in Batch Reinforcement Learning

In batch reinforcement learning, there can be poorly explored state-action pairs resulting in poorly learned, inaccurate models and poorly performing associated policies. Various regularization methods can mitigate the problem of learning overly-complex models in Markov decision processes (MDPs), however they operate in technically and intuitively distinct ways and lack a common form in which to compare them. This paper unifies three regularization methods in a common framework -- a weighted average transition matrix. Considering regularization methods in this common form illuminates how the MDP structure and the state-action pair distribution of the batch data set influence the relative performance of regularization methods. We confirm intuitions generated from the common framework by empirical evaluation across a range of MDPs and data collection policies.

cs.LG↗

arXiv2021

Inference for Batched Bandits

As bandit algorithms are increasingly utilized in scientific studies and industrial applications, there is an associated increasing need for reliable inference methods based on the resulting adaptively-collected data. In this work, we develop methods for inference on data collected in batches using a bandit algorithm. We first prove that the ordinary least squares estimator (OLS), which is asymptotically normal on independently sampled data, is not asymptotically normal on data collected using standard bandit algorithms when there is no unique optimal arm. This asymptotic non-normality result implies that the naive assumption that the OLS estimator is approximately normal can lead to Type-1 error inflation and confidence intervals with below-nominal coverage probabilities. Second, we introduce the Batched OLS estimator (BOLS) that we prove is (1) asymptotically normal on data collected from both multi-arm and contextual bandits and (2) robust to non-stationarity in the baseline reward.

cs.LG↗

arXiv2020

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 (MRT) is increasingly used to provide data to inform the construction of these interventions. In an MRT, 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 MRTs 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 MRTs 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 MRTs with binary outcomes. Under rather restrictive assumptions one can, based on existing literature, derive a semiparametric, locally efficient estimator of the causal effect. We, starting from this estimator, 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 MRT, BariFit. In BariFit, the goal is to support weight maintenance for individuals who received bariatric surgery.

stat.ME↗

arXiv2020

Sample Size Calculations for Micro-randomized Trials in mHealth

The use and development of mobile interventions are experiencing rapid growth. In "just-in-time" mobile interventions, treatments are provided via a mobile device and they are intended to help an individual make healthy decisions "in the moment," and thus have a proximal, near future impact. Currently the development of mobile interventions is proceeding at a much faster pace than that of associated data science methods. A first step toward developing data-based methods is to provide an experimental design for testing the proximal effects of these just-in-time treatments. In this paper, we propose a "micro-randomized" trial design for this purpose. In a micro-randomized trial, treatments are sequentially randomized throughout the conduct of the study, with the result that each participant may be randomized at the 100s or 1000s of occasions at which a treatment might be provided. Further, we develop a test statistic for assessing the proximal effect of a treatment as well as an associated sample size calculator. We conduct simulation evaluations of the sample size calculator in various settings. Rules of thumb that might be used in designing a micro-randomized trial are discussed. This work is motivated by our collaboration on the HeartSteps mobile application designed to increase physical activity.

stat.ME↗

arXiv2020

The Micro-Randomized Trial for Developing Digital Interventions: Experimental Design Considerations

Just-in-time adaptive interventions (JITAIs) are time-varying adaptive interventions that use frequent opportunities for the intervention to be adapted such as weekly, daily, or even many times a day. This high intensity of adaptation is facilitated by the ability of digital technology to continuously collect information about an individual's current context and deliver treatments adapted to this information. The micro-randomized trial (MRT) has emerged for use in informing the construction of JITAIs. MRTs operate in, and take advantage of, the rapidly time-varying digital intervention environment. MRTs can be used to address research questions about whether and under what circumstances particular components of a JITAI are effective, with the ultimate objective of developing effective and efficient components. The purpose of this article is to clarify why, when, and how to use MRTs; to highlight elements that must be considered when designing and implementing an MRT; and to discuss the possibilities this emerging optimization trial design offers for future research in the behavioral sciences, education, and other fields. We briefly review key elements of JITAIs, and then describe three case studies of MRTs, each of which highlights research questions that can be addressed using the MRT and experimental design considerations that might arise. We also discuss a variety of considerations that go into planning and designing an MRT, using the case studies as examples.

cs.HC↗

arXiv2020

The Micro-Randomized Trial for Developing Digital Interventions: Data Analysis Methods

Although there is much excitement surrounding the use of mobile and wearable technology for the purposes of delivering interventions as people go through their day-to-day lives, data analysis methods for constructing and optimizing digital interventions lag behind. Here, we elucidate data analysis methods for primary and secondary analyses of micro-randomized trials (MRTs), an experimental design to optimize digital just-in-time adaptive interventions. We provide a definition of causal "excursion" effects suitable for use in digital intervention development. We introduce the weighted and centered least-squares (WCLS) estimator which provides consistent causal excursion effect estimators for digital interventions from MRT data. We describe how the WCLS estimator along with associated test statistics can be obtained using standard statistical software such as SAS or R. Throughout we use HeartSteps, an MRT designed to increase physical activity among sedentary individuals, to illustrate potential primary and secondary analyses.

stat.AP↗

arXiv2019

Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study

Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying linear mixed models is problematic because potential moderators of the treatment effect are frequently endogenous---that is, may depend on prior treatment. We discuss model interpretation and biases that arise in the absence of additional assumptions when endogenous covariates are included in a linear mixed model. In particular, when there are endogenous covariates, the coefficients no longer have the customary marginal interpretation. However, these coefficients still have a conditional-on-the-random-effect interpretation. We provide an additional assumption that, if true, allows scientists to use standard software to fit linear mixed model with endogenous covariates, and person-specific predictions of effects can be provided. As an illustration, we assess the effect of activity suggestion in the HeartSteps MRT and analyze the between-person treatment effect heterogeneity.

stat.ME↗

arXiv2018

Practical Considerations for Data Collection and Management in Mobile Health Micro-randomized Trials

There is a growing interest in leveraging the prevalence of mobile technology to improve health by delivering momentary, contextualized interventions to individuals' smartphones. A just-in-time adaptive intervention (JITAI) adjusts to an individual's changing state and/or context to provide the right treatment, at the right time, in the right place. Micro-randomized trials (MRTs) allow for the collection of data which aid in the construction of an optimized JITAI by sequentially randomizing participants to different treatment options at each of many decision points throughout the study. Often, this data is collected passively using a mobile phone. To assess the causal effect of treatment on a near-term outcome, care must be taken when designing the data collection system to ensure it is of appropriately high quality. Here, we make several recommendations for collecting and managing data from an MRT. We provide advice on selecting which features to collect and when, choosing between "agents" to implement randomization, identifying sources of missing data, and overcoming other novel challenges. The recommendations are informed by our experience with HeartSteps, an MRT designed to test the effects of an intervention aimed at increasing physical activity in sedentary adults. We also provide a checklist which can be used in designing a data collection system so that scientists can focus more on their questions of interest, and less on cleaning data.

stat.OT↗

arXiv2017

The stratified micro-randomized trial design: sample size considerations for testing nested causal effects of time-varying treatments

Technological advancements in the field of mobile devices and wearable sensors have helped overcome obstacles in the delivery of care, making it possible to deliver behavioral treatments anytime and anywhere. Increasingly the delivery of these treatments is triggered by predictions of risk or engagement which may have been impacted by prior treatments. Furthermore the treatments are often designed to have an impact on individuals over a span of time during which subsequent treatments may be provided. Here we discuss our work on the design of a mobile health smoking cessation experimental study in which two challenges arose. First the randomizations to treatment should occur at times of stress and second the outcome of interest accrues over a period that may include subsequent treatment. To address these challenges we develop the "stratified micro-randomized trial," in which each individual is randomized among treatments at times determined by predictions constructed from outcomes to prior treatment and with randomization probabilities depending on these outcomes. We define both conditional and marginal proximal treatment effects. Depending on the scientific goal these effects may be defined over a period of time during which subsequent treatments may be provided. We develop a primary analysis method and associated sample size formulae for testing these effects.

stat.AP↗

arXiv2016

Assessing Time-Varying Causal Effect Moderation in Mobile Health

In mobile health interventions aimed at behavior change and maintenance, treatments are provided in real time to manage current or impending high risk situations or promote healthy behaviors in near real time. Currently there is great scientific interest in developing data analysis approaches to guide the development of mobile interventions. In particular data from mobile health studies might be used to examine effect moderators-i.e., individual characteristics, time-varying context or past treatment response that moderate the effect of current treatment on a subsequent response. This paper introduces a formal definition for moderated effects in terms of potential outcomes, a definition that is particularly suited to mobile interventions, where treatment occasions are numerous, individuals are not always available for treatment, and potential moderators might be influenced by past treatment. Methods for estimating moderated effects are developed and compared. The proposed approach is illustrated using BASICS-Mobile, a smartphone-based intervention designed to curb heavy drinking and smoking among college students.

stat.ME↗