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Background Adaptive clinical trials have been increasingly commonly employed to select a potential target population for one trial without conducting trials separately. Such enrichment designs typically consist of two or three stages, where the first stage serves as a screening process for selecting a specific subpopulation. Methods We propose a Bayesian design for randomized clinical trials with a binary outcome that focuses on restricting the inclusion to a subset of patients who are likely to benefit the most from the treatment during trial accrual. Several Bayesian measures of efficacy and treatment-by-subset interactions were used to dictate the enrichment, either based on Gail and Simon’s or Millen’s criteria. A simulation study was used to assess the performance of our design. The method is exemplified in a real randomized clinical trial conducted in patients with respiratory failure that failed to show any benefit of high flow oxygen supply compared with standard oxygen. Results The use of the enrichment rules allowed the detection of the existence of a treatment-by-subset interaction more rapidly compared with Gail and Simon’s criteria, with decreasing proportions of enrollment in the whole sample, and the proportions of enrichment lower, in the presence of interaction based on Millen’s criteria. In the real dataset, this may have allowed the detection of the potential interest of high flow oxygen in patients with a SOFA neurological score ≥ 1. Conclusion Enrichment designs that handle the uncertainty in treatment efficacy by focusing on the target population offer a promising balance for trial efficiency and ease of interpretation.

Immunotherapy is an innovative treatment approach that stimulates a patient's immune system to fight cancer. It demonstrates characteristics distinct from conventional chemotherapy and stands to revolutionize cancer treatment. We propose a Bayesian phase I/II dose-finding design that incorporates the unique features of immunotherapy by simultaneously considering three outcomes: immune response, toxicity, and efficacy. The objective is to identify the biologically optimal dose, defined as the dose with the highest desirability in the risk-benefit tradeoff. An Emax model is utilized to describe the marginal distribution of the immune response. Conditional on the immune response, we jointly model toxicity and efficacy using a latent variable approach. Using the accumulating data, we adaptively randomize patients to experimental doses based on the continuously updated model estimates. A simulation study shows that our proposed design has good operating characteristics in terms of selecting the target dose and allocating patients to the target dose. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

This paper constructs an efficient, budget-balanced, Bayesian incentive-compatible mechanism for a general dynamic environment with quasilinear payoffs in which agents observe private information and decisions are made over countably many periods. First, under the assumption of \"private values\" (other agents' private information does not directly affect an agent's payoffs), we construct an efficient, ex post incentive-compatible mechanism, which is not budget-balanced. Second, under the assumption of \"independent types\" (the distribution of each agent's private information is not directly affected by other agents' private information), we show how the budget can be balanced without compromising agents' incentives. Finally, we show that the mechanism can be made self-enforcing when agents are sufficiently patient and the induced stochastic process over types is an ergodic finite Markov chain.

In phase I trials, effectively treating patients and minimizing the chance of exposing them to subtherapeutic and overly toxic doses are clinicians' top priority. Motived by this practical consideration, we propose Bayesian optimal interval (BOIN) designs to find the maximum tolerated dose and to minimize the probability of inappropriate dose assignments for patients. We show, both theoretically and numerically, that the BOIN design not only has superior finite and large sample properties but also can be easily implemented in a simple way similar to the traditional '3+3' design. Compared with the well-known continual reassessment method, the BOIN design yields comparable average performance to select the maximum tolerated dose but has a substantially lower risk of assigning patients to subtherapeutic and overly toxic doses. We apply the BOIN design to two cancer clinical trials.

Optimal design procedures provide a framework to leverage the learning generated by ecological models to flexibly and efficiently deploy future monitoring efforts. At the same time, Bayesian hierarchical models have become widespread in ecology and offer a rich set of tools for ecological learning and inference. However, coupling these methods with an optimal design framework can become computationally intractable. Recursive Bayesian computation offers a way to substantially reduce this computational burden, making optimal design accessible for modern Bayesian ecological models. We demonstrate the application of so-called prior-proposal recursive Bayes to optimal design using a simulated data binary regression and the real-world example of monitoring and modeling sea otters in Glacier Bay, Alaska. These examples highlight the computational gains offered by recursive Bayesian methods and the tighter fusion of monitoring and science that those computational gains enable.

Rothschild and Stiglitz (1970) represent random variables as convex functions (integrals of the cumulative distribution function). Combining this representation with Blackwell's Theorem (1953), we characterize distributions of posterior means that can be induced by a signal. This characterization provides a novel way to analyze a class of Bayesian persuasion problems.

Underweight and obesity are associated with adverse health outcomes throughout the life course. We estimated the individual and combined prevalence of underweight or thinness and obesity, and their changes, from 1990 to 2022 for adults and school-aged children and adolescents in 200 countries and territories. We used data from 3663 population-based studies with 222 million participants that measured height and weight in representative samples of the general population. We used a Bayesian hierarchical model to estimate trends in the prevalence of different BMI categories, separately for adults (age ≥20 years) and school-aged children and adolescents (age 5–19 years), from 1990 to 2022 for 200 countries and territories. For adults, we report the individual and combined prevalence of underweight (BMI <18·5 kg/m2) and obesity (BMI ≥30 kg/m2). For school-aged children and adolescents, we report thinness (BMI <2 SD below the median of the WHO growth reference) and obesity (BMI >2 SD above the median). From 1990 to 2022, the combined prevalence of underweight and obesity in adults decreased in 11 countries (6%) for women and 17 (9%) for men with a posterior probability of at least 0·80 that the observed changes were true decreases. The combined prevalence increased in 162 countries (81%) for women and 140 countries (70%) for men with a posterior probability of at least 0·80. In 2022, the combined prevalence of underweight and obesity was highest in island nations in the Caribbean and Polynesia and Micronesia, and countries in the Middle East and north Africa. Obesity prevalence was higher than underweight with posterior probability of at least 0·80 in 177 countries (89%) for women and 145 (73%) for men in 2022, whereas the converse was true in 16 countries (8%) for women, and 39 (20%) for men. From 1990 to 2022, the combined prevalence of thinness and obesity decreased among girls in five countries (3%) and among boys in 15 countries (8%) with a posterior probability of at least 0·80, and increased among girls in 140 countries (70%) and boys in 137 countries (69%) with a posterior probability of at least 0·80. The countries with highest combined prevalence of thinness and obesity in school-aged children and adolescents in 2022 were in Polynesia and Micronesia and the Caribbean for both sexes, and Chile and Qatar for boys. Combined prevalence was also high in some countries in south Asia, such as India and Pakistan, where thinness remained prevalent despite having declined. In 2022, obesity in school-aged children and adolescents was more prevalent than thinness with a posterior probability of at least 0·80 among girls in 133 countries (67%) and boys in 125 countries (63%), whereas the converse was true in 35 countries (18%) and 42 countries (21%), respectively. In almost all countries for both adults and school-aged children and adolescents, the increases in double burden were driven by increases in obesity, and decreases in double burden by declining underweight or thinness. The combined burden of underweight and obesity has increased in most countries, driven by an increase in obesity, while underweight and thinness remain prevalent in south Asia and parts of Africa. A healthy nutrition transition that enhances access to nutritious foods is needed to address the remaining burden of underweight while curbing and reversing the increase in obesity. UK Medical Research Council, UK Research and Innovation (Research England), UK Research and Innovation (Innovate UK), and European Union.

A large-sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by an identifiable finitedimensional reduced-form parameter vector. It is used to analyze the differences between Bayesian credible sets and frequentist confidence sets. We define a plug-in estimator of the identified set and show that asymptotically Bayesian highest-posteriordensity sets exclude parts of the estimated identified set, whereas it is well known that frequentist confidence sets extend beyond the boundaries of the estimated identified set. We recommend reporting estimates of the identified set and information about the conditional prior along with Bayesian credible sets. A numerical illustration for a two-player entry game is provided.

Deep convolutional neural networks (DCNNs) have demonstrated promising performance in classifying breast lesions in 2D ultrasound (US) images. Exiting approaches typically use pre-trained models based on architectures designed for natural images with transfer learning. Fewer attempts have been made to design customized architectures specifically for this purpose. This paper presents a comprehensive evaluation on transfer learning based solutions and automatically designed networks, analyzing the accuracy and robustness of different recognition models in three folds. First, we develop six different DCNN models (BNet, GNet, SqNet, DsNet, RsNet, IncReNet) based on transfer learning. Second, we adapt the Bayesian optimization method to optimize a CNN network (BONet) for classifying breast lesions. A retrospective dataset of 3034 US images collected from various hospitals is then used for evaluation. Extensive tests show that the BONet outperforms other models, exhibiting higher accuracy (83.33%), lower generalization gap (1.85%), shorter training time (66 min), and less model complexity (approximately 0.5 million weight parameters). We also compare the diagnostic performance of all models against that by three experienced radiologists. Finally, we explore the use of saliency maps to explain the classification decisions made by different models. Our investigation shows that saliency maps can assist in comprehending the classification decisions. Graphical Abstract

Understanding the preferences of potential users of digital health products is beneficial for digital health policy and planning. Stated preference methods could help elicit individuals’ preferences in the absence of observational data. A discrete choice experiment (DCE) is a commonly used stated preference method—a quantitative methodology that argues that individuals make trade-offs when engaging in a decision by choosing an alternative of a product or a service that offers the greatest utility, or benefit. This methodology is widely used in health economics in situations in which revealed preferences are difficult to collect but is much less used in the field of digital health. This paper outlines the stages involved in developing a DCE. As a case study, it uses the application of a DCE to reveal preferences in targeting the uptake of smoking cessation apps. It describes the establishment of attributes, the construction of choice tasks of 2 or more alternatives, and the development of the experimental design. This tutorial offers a guide for researchers with no prior knowledge of this research technique.