Bayesian Inference with Stan for Pharmacometrics: 3 Day Course

The class will be taught by the two members of the Stan development team: Daniel Lee, and Michael Betancourt. We use an interactive training format with frequent hands-on exercises to reinforce new concepts. Participants should expect to fit many models in Stan and are encouraged to bring their own research problems for discussion and review. We have some flexibility with the content on Days 2 and 3 and will solicit feedback during Day 1 as to what topics to focus on during the rest of the course.

Prerequisites

People should be familiar with basic Probability and Statistics including common distributions and GLMs and with basic programming in a high-level language, preferably R. We do not expect you to have familiarity with Bayesian Inference or Stan although some knowledge of the former may be helpful.

Day 1

Introduction to Bayesian statistics

• Likelihood / sampling distributions
• Priors, Posteriors via Bayes's rule
• Posterior expectations and quantiles
• Events as expectations of indicator functions

Introduction to Stan

• Basic data types
• Variable declarations
• Constrained parameters and transforms to unconstrained
• Program blocks and execution
• Derived quantities
• Built-in functions and operators
• Statements: sampling, assignment, loops, conditionals, blocks
• How to use Stan within R with RStan

Hands-on examples

Day 2

ODE and PK/PD Modeling

• Parameters and data to ODEs
• Non-stiff ODE solver
• Stiff ODE solver
• Control parameters and tolerances
• Coupled ODE systems for sensitivities
• Elimination half-lifes

Inference with Markov chain Monte Carlo

• Monte Carlo methods and plug-in inference
• Markov chain Monte Carlo
• Convergence diagnostics, R-hat, effective sample size
• Effective sample size vs. number of iterations
• Plug-in posterior expectations and quantiles
• Event probability calculations

Hands-on examples

Day 3

Additional Topics in PK/PD Modeling

• Bolus and infusion dosing
• Lag time and absorption models
• Linear versus Michaelis/Menten elimination
• Hierarchical models for patient-level effects
• Transit compartment models and time lags
• Multi-compartment models and varying time scales
• Joint PK/PD modeling: Bayes vs. "cut"
• Meta-analysis
• Formulating informative priors
• Clinical trial simulations and power calculations

Stan programming techniques

• Reproducible research practices
• Probabilistic programming principles
• Generated quantities for inference
• Data simulation and model checking
• Posterior predictive checks
• Cross-validation and predictive calibration
• Variable transforms for sampling efficiency
• Multiple indexing and range slicing
• Marginalizing discrete parameters
• Handling missing data
• Ragged and sparse data structures
• Identifiability and problematic posteriors
• Weakly informative priors

Hands-on examples