Workshop I: Bayesian Modeling and Population Heterogeneity

Instructor:   Dr. Tanzy M. T. Love, University of Rochester

Abstract:    Bayes theorem is a foundation for inference that relies on updating probability distributions instead of large sample asymptotics. It is often advantageous for small sample problems and those with complex dependency structures. This course will cover an introduction to Bayesian modeling and computation. 

As an example of models well suited to Bayesian estimation, clustering models will be introduced that are model-based instead of distance-based. These mixtures of distributions have many parameters which are interpreted to describe population heterogeneity. These models can be estimated by maximum likelihood with the EM algorithm, or full posterior inference can be obtained with Bayesian methods driven by Markov chain Monte Carlo (MCMC) algorithms.

By the end of the course, students will be familiar with the framework for Bayesian inference and how it differs from frequentist inference.   Students will be able to derive posterior distributions in closed form for parameters when using conjugate priors.  Students will have examples of MCMC code written in the R and BUGS languages for a variety of models to perform parameter estimation and inference. Students will have examples of fitting mixtures of normal distributions to describe heterogeneous populations. They will have techniques for choosing an appropriate number of clusters and whether to use variance restrictions in estimation. Students will see a non-Gaussian example of a mixture model for modeling counts of genetic changes in a virus population.

Major topics:

• Introduction to Bayesian statistics including Bayes theorem, the likelihood principle, comparison to the frequentist approach

• Bayesian inference for single parameter models with conjugate priors

• Introduction to Markov Chain Monte Carlo, including Gibbs sampling and the Metropolis-Hastings algorithm, with examples in R/BUGS code for building MCMC samplers 

• Bayesian inference for multiple parameter models with conjugate, semi-conjugate, and non-informative priors

• Models of mixtures of distributions, the Gaussian Mixture Model

• The Shifted Poisson Mixture Model for HIV genetic diversity

Workshop II:   Bayesian Approaches for Improved Clinical Trial Designs in Drug and Medical Device Development

Instructor:   Dr. Bradley P. Carlin, PhaseV Trials, Inc.

Abstract:  Thanks to the sudden emergence of Markov chain Monte Carlo (MCMC) computational methods in the 1990s, Bayesian methods now have a more than 25-year history of utility in statistical and biostatistical design and analysis. However, their uptake in regulatory science has been much slower due to the high premium this field places on bias prevention and Type I error control and its historical reliance on p-values and other traditional frequentist statistical tools. Fortunately, recent actions by regulators in the United States and elsewhere have indicated a new willingness to consider more innovative statistical methods, especially in settings (such as rare and pediatric diseases) where traditional methods are ill-suited or demonstrably inadequate.

In this half-day short course, we will begin with an overview of the Bayesian adaptive approach to clinical trial design and analysis, as well as recent supportive efforts by regulatory agencies in the United States (FDA) and Europe (EMA).  We will then discuss a variety of areas in which Bayesian methods offer a better (and perhaps the only) path to regulatory approval.

Major topics:

• Methods for borrowing strength from historical controls and other auxiliary data, including power priors, commensurate priors, robust mixture priors, and more recent techniques that build on these ideas
• Prior elicitation methods, including meta-analytic predictive (MAP) priors
• Approaches that incorporate patients’ own natural history data, a generalization of crossover designs in which each patient “acts as their own control.”  
• Platform/umbrella/seamless multiphase studies
• Master protocols/basket trials for evaluating efficacy and safety of therapy in multiple diseases that share a common molecular alteration
• Causal inference tools to incorporate real-world data (RWD)/real-world evidence (RWE), including propensity score matching

Throughout the course, the presentation will be illustrated with real-data examples to illustrate the methods.  Ample time will be reserved for questions from the floor.