The goal of this course is for students to gain good understanding of the Bayesian concepts involved in the design, analysis and reporting of clinical trials. Bayesian statistical paradigm use prior information or beliefs, along with the current data, to guide the search for parameter estimates. In the Bayesian paradigm probabilities are subjective beliefs. Prior information/beliefs are input as a distribution, and the data then helps refine that distribution. The choice of prior distributions, posterior updating, as well as dedicated computing techniques are introduced through simple examples. Bayesian approaches for design, monitoring, and analysis of randomized clinical trials are taught in this class. These approaches are contrasted with traditional (frequentist) approaches. The emphasis will be on concepts. Examples are case studies from the instructors’ work and from medical literature. R, OpenBUGS and SAS will be the main computing tools used.
Upon completing this course the students will
- Have a thorough understanding of the components of Bayesian paradigm.
- Carry out probability calculations involving posterior distributions from simple conjugate Bayesian problems – Beta-Bernoulli, Gamma-Poisson, Normal-Normal.
- Have a critical understanding of the similarities and differences between the Bayesian and traditional (frequentist) approach to design, analysis and interpretations of results of data arising from randomized clinical trials.
- Be familiar with mechanism of eliciting prior distributions.
- Be able to design, analyze and report a clinical trial using Bayesian methods.
Prerequisites:
- Familiarity with basic concepts of clinical trials
- Working knowledge of statistics
- Working knowledge of R
Author
Thomas Zhou
Author
Introduction
Lesson 1 of 5 within section Introduction.
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This Course in the Context of Clinical Trials
Lesson 2 of 5 within section Introduction.
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Lesson 3 of 5 within section Introduction.
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Lesson 4 of 5 within section Introduction.
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Accessibility and Technical Support
Lesson 5 of 5 within section Introduction.
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Bayesian Methods Overview
Fundamentals: Bayes’ Theorem
Lesson 1 of 3 within section Bayesian Methods Overview.
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Bayesian Clinical Trials in Action
Lesson 2 of 3 within section Bayesian Methods Overview.
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Use of Bayesian statistics in drug development: Advantages and challenges
Lesson 3 of 3 within section Bayesian Methods Overview.
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Bayesian Approach to Statistics – Discrete Case
Lesson 1 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Lesson 2 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Lesson 3 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Conditional Probabilities
Lesson 4 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Lesson 5 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Lesson 6 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Lesson 7 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Bayes Theorem for discrete random variables and discrete parameter space
Lesson 8 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Lesson 9 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Lesson 10 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Overview of Basic Discrete Distributions
Lesson 11 of 11 within section Bayesian Approach to Statistics – Discrete Case.
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Bayesian Approach to Statistics – Continuous Case
Lesson 1 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Lesson 2 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Lesson 3 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Normal Data with Descrete Prior
Lesson 4 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Lesson 5 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Probability as Area, cont.
Lesson 6 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Continuous Distribution as Limits of Descrete Distributions
Lesson 7 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Beta Family of Distributions
Lesson 8 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Beta Family as Conjugate Priors for Binomial Data (Likelihoods)
Lesson 9 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Non-Canonical Parameterization
Lesson 10 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Gamma Family as Conjugate Priors for Poisson Data (Likelihoods)
Lesson 11 of 11 within section Bayesian Approach to Statistics – Continuous Case.
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Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach
Lesson 1 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Lesson 2 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Lesson 3 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Ways of expressing treatment effect in clinical trials
Lesson 4 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Normal approximations for Likelihoods
Lesson 5 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Normal likelihood approximation with Binomial data (likelihoods)
Lesson 6 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Normal likelihood approximations with Survival data
Lesson 7 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Normal likelihood approximation with Poisson data (likelihoods)
Lesson 8 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Interval Estimation and Hypothesis Testing
Lesson 9 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Bayesian Approach – Credible Intervals
Lesson 10 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Lesson 11 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Types of Hypotheses in Clinical Trials
Lesson 12 of 12 within section Estimation and Hypothesis Testing in Clinical Trials – Bayesian Approach.
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Prior Elicitation
Lesson 1 of 9 within section Prior Elicitation.
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Lesson 2 of 9 within section Prior Elicitation.
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Lesson 3 of 9 within section Prior Elicitation.
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Lesson 4 of 9 within section Prior Elicitation.
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Lesson 5 of 9 within section Prior Elicitation.
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Summary of external evidence
Lesson 6 of 9 within section Prior Elicitation.
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Lesson 7 of 9 within section Prior Elicitation.
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Checking prior-data compatibility
Lesson 8 of 9 within section Prior Elicitation.
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Lesson 9 of 9 within section Prior Elicitation.
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Wrapping Up
Lesson 1 of 2 within section Wrapping Up.
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Attributions and References
Lesson 2 of 2 within section Wrapping Up.
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