Bayesian Adaptive Clinical Trial Designs
Bayesian approach is intuitive, logical, coherent, elegant, and adaptive in nature. It is uniquely suitable for the design and analysis of clinical trials. This short course is designed to provide an overview of Bayesian adaptive clinical trials. The main application areas include adaptive dose finding, adaptive toxicity and efficacy evaluation, designs for simply and complex endpoints, posterior probability and predictive probability for interim monitoring of study endpoints, outcome-adaptive randomization, adaptive biomarker identification and validation, master protocols, umbrella, basket and platform trials, hierarchical models for information borrowing, etc. Bayesian adaptive designs allow flexibility in clinical trial conduct, increase study efficiency, enhance clinical trial ethics by treating more patients with more effective treatments, increase the overall success rate for drug development and can still preserve frequentist operating characteristics by controlling type I and type II error rates. Lessons learned from real trial examples and practical considerations for conducting adaptive designs and will be given. Easy-to-use Shiny applications and downloadable standalone programs will be introduced to facilitate the study design, conduct, and analysis of Bayesian adaptive methods. (https://trialdesign.org)
Advanced Topics in Variable Selection and Model Averaging
In this course we will cover a wide range of topics related to variable selection and model averaging within the Bayesian paradigm. We will begin with the standard linear regression model where we will discuss issues relating to prior choice, implementation, and theory. Practical issues such as the sensitivity to the prior distribution will be illustrated through examples. We will then move to more complex regression models, showing how the same ideas can be applied with little additional effort. We will first move to additive models that drop the linearity assumption for each covariate. We will illustrate these ideas using flexible parametric specifications, and then we will move towards fully nonparametric Gaussian process priors as a means to flexible regression modeling, and how these can also easily accommodate variable selection through spike-and-slab prior distributions. Next, the additivity assumption will be dropped and we will move to Bayesian models that allow for interactions among each covariate within the regression model. In particular, we will focus on tree-based models and how they can be coupled with sparsity-inducing priors to simultaneously allow for highly flexible modeling and variable selection. All of these ideas will be presented with the goal that attendees will be able to apply these methods after taking the course. For this reason, all derivations of conditional distributions for Gibbs samplers will be provided along with R codes and data sets that are used throughout the course.
Course instructor short bio
Joseph Antonelli is an assistant professor of statistics at the University of Florida. He primarily works on high-dimensional models and causal inference with applications to both environmental science and criminology.
Antonio Linero is an Assistant Professor in the Department of Statistics and Data Sciences at the University of Texas at Austin. His research interests focus primarily on developing flexible Bayesian models which allow principled uncertainty quantification in causal inference and in settings with missing data.
Bayesian Modeling of Brain Imaging Data
Statistical methods play a crucial role in understanding and analyzing brain-imaging data. Bayesian approaches, in particular, have shown great promise in applications, as they allow a flexible modeling of the spatial and temporal correlations in the data. In this short course, we will focus especially on the analysis of functional MRI data, although we will provide some review of Bayesian methods for some other common data types (e.g., EEG, PET/MRI, DTI). We will divide methods according to the objective of the analysis. In particular, we will discuss spatio-temporal models for fMRI data that detect task-related activation patterns. We will also address the very important problem of estimating brain connectivity and touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We also briefly discuss the emerging field of imaging genetics.
Applied Bayesian Nonparametric Mixture Modeling
Bayesian methods are central to the application of modern statistical modeling in a wide variety of fields. Bayesian nonparametric and semiparametric methods expand considerably the flexibility of Bayesian models. This course will provide an introduction to Bayesian nonparametric methods, with emphasis on modeling approaches built from nonparametric mixtures and with a focus on applications. The course will start by motivating Bayesian nonparametric modeling and providing an overview of nonparametric prior models for spaces of random functions. The main focus will be on models based on the Dirichlet process, a nonparametric prior for random distributions. Particular emphasis will be placed on Dirichlet process mixtures, which provide a flexible framework for nonparametric modeling. We will discuss methodological details for Dirichlet process mixture models, computational techniques for posterior inference, practically relevant extensions to modeling for collections of dependent distributions, and applications. Examples will be drawn from fields such as density estimation, nonparametric regression, hierarchical generalized linear models, survival analysis, and inference for point processes.
The course targets graduate students and researchers interested in an introduction to the area of Bayesian nonparametrics. Required background includes training (at least) to the MS level, including substantial exposure to parametric Bayesian hierarchical modeling and computing.
Course instructor short bio
Athanasios Kottas obtained a Ph.D. in Statistics from the University of Connecticut in 2000. From 2000 to 2002, he was Visiting Assistant Professor in the Institute of Statistics and Decision Sciences at Duke University, and, since 2002, he has been at the University of California, Santa Cruz. He is currently Professor in the Department of Statistics at UCSC. His research interests include Bayesian nonparametrics, mixture models, nonparametric regression, point process modeling, and analysis, with applications in biometrics, ecology and the environmental sciences. He is currently serving as Editor for Bayesian Analysis, and Past Chair of the ISBA Program Council. He has published 55 journal papers and book chapters, and has been PI or Co-PI on 10 NSF grants, 2 NASA grants, and 1 NOAA grant. He has co-advised one NSF Bioinformatics postdoctoral fellow, supervised 12 Ph.D. dissertations, and is currently advising/co-advising six Ph.D. students.