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Summary A treatment regime is a sequence of decision rules, one per decision point, that maps accumulated patient information to a recommended intervention. An optimal treatment regime maximises expected cumulative utility if applied to select interventions in a population of interest. As a treatment regime seeks to improve the quality of healthcare by individualising treatment, it can be viewed as an approach to formalising precision medicine. Increased interest and investment in precision medicine has led to a surge of methodological research focusing on estimation and evaluation of optimal treatment regimes from observational and/or randomised studies. These methods are becoming commonplace in biomedical research, although guidance about how to choose among existing methods in practice has been somewhat limited. The purpose of this review is to describe some of the most commonly used methods for estimation of an optimal treatment regime, and to compare these estimators in a series of simulation experiments and applications to real data. The results of these simulations along with the theoretical/methodological properties of these estimators are used to form recommendations for applied researchers. 

Abstract Osteoarthritis (OA) is a chronic condition often associated with pain, affecting approximately fourteen percent of the population, and increasing in prevalence. A globally aging population have made treating OA-associated pain as well as maintaining mobility and activity a public health priority. OA affects all mammals, and the use of spontaneous animal models is one promising approach for improving translational pain research and the development of effective treatment strategies. Accelerometers are a common tool for collecting high-frequency activity data on animals to study the effects of treatment on pain related activity patterns. There has recently been increasing interest in their use to understand treatment effects in human pain conditions. However, activity patterns vary widely across subjects; furthermore, the effects of treatment may manifest in higher or lower activity counts or in subtler ways like changes in the frequency of certain types of activities. We use a zero inflated Poisson hidden semi-Markov model to characterize activity patterns and subsequently derive estimators of the treatment effect in terms of changes in activity levels or frequency of activity type. We demonstrate the application of our model, and its advance over traditional analysis methods, using data from a naturally occurring feline OA-associated pain model. 

Summary Malaria is an infectious disease affecting a large population across the world, and interventions need to be efficiently applied to reduce the burden of malaria. We develop a framework to help policy-makers decide how to allocate limited resources in realtime for malaria control. We formalize a policy for the resource allocation as a sequence of decisions, one per intervention decision, that map up-to-date disease related information to a resource allocation. An optimal policy must control the spread of the disease while being interpretable and viewed as equitable to stakeholders. We construct an interpretable class of resource allocation policies that can accommodate allocation of resources residing in a continuous domain and combine a hierarchical Bayesian spatiotemporal model for disease transmission with a policy-search algorithm to estimate an optimal policy for resource allocation within the pre-specified class. The estimated optimal policy under the proposed framework improves the cumulative long-term outcome compared with naive approaches in both simulation experiments and application to malaria interventions in the Democratic Republic of the Congo. 

Most linear experimental design problems assume homogeneous variance, while the presence of heteroskedastic noise is present in many realistic settings. Let a learner have access to a finite set of measurement vectors that can be probed to receive noisy linear responses. We propose, analyze and empirically evaluate a novel design for uniformly bounding estimation error of the variance parameters. We demonstrate this method on two adaptive experimental design problems under heteroskedastic noise, fixed confidence transductive best-arm identification and level-set identification and prove the first instance-dependent lower bounds in these settings. Lastly, we construct near-optimal algorithms and demonstrate the large improvements in sample complexity gained from accounting for heteroskedastic variance in these designs empirically. 

The sequential multiple assignment randomized trial (SMART) is the gold standard trial design to generate data for the evaluation of multistage treatment regimes. As with conventional (single‐stage) randomized clinical trials, interim monitoring allows early stopping; however, there are few methods for principled interim analysis in SMARTs. Because SMARTs involve multiple stages of treatment, a key challenge is that not all enrolled participants will have progressed through all treatment stages at the time of an interim analysis. Wu et al. (2021) propose basing interim analyses on an estimator for the mean outcome under a given regime that uses data only from participants who have completed all treatment stages. We propose an estimator for the mean outcome under a given regime that gains efficiency by using partial information from enrolled participants regardless of their progression through treatment stages. Using the asymptotic distribution of this estimator, we derive associated Pocock and O'Brien‐Fleming testing procedures for early stopping. In simulation experiments, the estimator controls type I error and achieves nominal power while reducing expected sample size relative to the method of Wu et al. (2021). We present an illustrative application of the proposed estimator based on a recent SMART evaluating behavioral pain interventions for breast cancer patients. 

There is tremendous interest in precision medicine as a means to improve patient out- comes 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 out- comes. 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 pro- posed 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.