Syllabus

Course content

Bayesian analysis is a statistical approach that is becoming increasingly popular in medical research. Notably, Bayesian methods have become commonly used in adaptive designs for Phase I/II trials, in meta-analyses, and also in transcriptomics analysis. This course provides a comprehensive introduction to the Bayesian paradigm and toolbox, with an emphasis on biostatistics applications, in order to familiarize students with such methods and their practical applications.

Thanks to its rich modeling possibilities the Bayesian framework is appealing, especially when the number of observations is scarce. It can adaptively incorporate information as it becomes available, an important feature for early phase clinical trials. Thus, adaptive Bayesian designs for Phase I/II trials reduce the chances of unnecessarily exposing participants to inappropriate doses and have better decision-making properties compared to the standard rule-based dose-escalation designs. Besides, the use of a Bayesian approach is also very appealing in meta-analyses because of: i) the often relatively small number of studies available, ii) its flexibility, iii) and its better handling of heterogeneity from aggregated results, especially in network meta-analyses. Thanks to modern computing tools, practical Bayesian analysis has become relatively straightforward, which is contributing to its increasing popularity. JAGS is a flexible software interfaced with R, that allows to easily specify a Bayesian model and that automatically perform inference for posterior parameters distributions as well as graphic outputs to monitor the quality of the analysis.

The aim of the course is to provide insights into Bayesian statistics in the context of medical studies. We will cover the following topics:

1. Bayesian modeling (prior, posterior, likelihood, Bayes theorem);
   
2. Bayesian estimation (Credibility intervals, Maximum a posteriori, Bayes factor);
3. Bayesian meta-analyses;
4. Practical Bayesian Analysis with R and JAGS softwares;
5. Critical reading of medical publications. All concepts will be illustrated with real-life examples from the medical literrature.

All concepts will be illustrated with real-life examples from the medical literature.

Course objectives

A student who has met the objectives of the course will be able to:

• Familiarize oneself with the Bayesian framework:
  1. understand and assess a Bayesian modeling strategy, and discuss its underlying assumptions
  2. rigorously describe expert knowledge by a quantitative prior distribution
• Study and perform Bayesian analyses in biomedical applications:
  1. understand, discuss and reproduce a Bayesian (re-)estimation of a Relative Risk
  2. perform a Bayesian regression using , applied to meta-analysis
  3. put into perspective the results from a Bayesian analysis described in a scientific article

Targeted audience

To be able to follow this course, participants need both:

• some knowledge in statistics (most notably some familiarity with usual probability distributions, probability density functions, confidence intervals and Maximum Likelihood Estimation), and
• a practical knowledge of R programming (especially functional programming, for loops and “if” statements, vector allocation, linear regression).

Advanced mathematical training is not required as we will explain the methods on an elementary mathematical level, but some familiarity with function integration could be helpful.

⚠️ The audience for this class is often diverse. Students with different backgrounds and different expertises will get different experiences of this class, and some parts can feel hard, frustrating or even not very relevant. But everyone should find interesting ideas, concept and tools to learn all along the class. For some, the important focus will be medical applications, for other it will be the practical programming, or the new philosophical framework, or the statistical tools.

Technical tools

During the practicals on their laptop, the students will learn how to technically apply the Bayesian tools on real data, and should be able to perform a Bayesian regression by the end of the course. Note that several statistical software can be used for Bayesian analysis, however solutions will be provided for the statistical softwares and JAGS only (alternatives such as WinBUGS or STAN will not be covered).

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