We will provide a guided hands-on experience in the use of Stan (http://mc-stan.org/), rstan (http://mc-stan.org/interfaces/rstan.html), rstanarm (http://mc-stan.org/users/interfaces/rstanarm.html) and Torsten (https://github.com/metrumresearchgroup/example-models) for Bayesian analysis of categorical, count and time-to-event data. Stan is a flexible open-source software tool for Bayesian data analysis using Hamiltonian Monte Carlo (HMC) simulation—a type of MCMC simulation. Torsten is a Stan extension containing a library of functions to simplify implementation of PKPD models. This workshop builds on the foundations presented in our previous introductory Stan workshops (https://www.metrumrg.com/course/brief-introduction-bayesian-modeling-using-stan/). The hands-on examples will focus on implementation of Stan models for each of the basic data types covered in the workshop, i.e., binary, ordinal, count and time-to-event data. We will also present examples that illustrate how those component models may be extended and combined for joint analysis of multiple data types. Those examples include latent variable models such as IRT models as well as joint modeling of continuous and time-to-event data.

October 7, 2017 8:00am-5:00pm (ACoP9 satellite workshop)

Course Instructor: Bill Gillespie

Topic Outline of Workshop:

Start: 8:00am

• Some general theory/background:
  • Modeling from a probabilistic point of view: the likelihood function
  • Maximum likelihood for continuous data
  • Extending ML to odd-type data
  • Bayesian modeling of odd-type data
• Brief review of the use of Stan and rstan
  • User-defined functions
  • Modeling workflow using rstan
• Modeling binary data
  • Logistic regression models
  • Bernoulli model for individual binary data
  • Binomial model for summary data
  • Mixed effects modeling of longitudinal binary data

Break: 10:15-10:30am

• Modeling ordered categorical (ordinal) data
  • Cumulative logit models
• Modeling count data
  • The Poisson model
  • Variations on the Poisson model to deal with over-dispersion or zero inflation

Lunch: 12:00-1:00pm

• Modeling time-to-event data for a single event per individual
  • Principles and methods of survival analysis for modeling censored data
• Torsten: Library of PKPD functions for Stan
  • Built-in models: 1 and 2 compartment models with 1st order absorption
  • Numerical solution of user-specified ODEs
• Models with time-varying hazard

Break: 3:00-3:15pm

• Modeling repeated time-to-event data
• Markov models for joint modeling of event times and their magnitudes
• Item response theory (IRT) and related models for joint modeling of multiple outcomes
• Joint modeling of continuous and time-to-event data

Adjourn: 5:00pm

Materials Provided by Sponsor: Course slides, data and code for all examples, online access for one week to a cloud-based compute server on which the software used in the course is installed

Requirements for Attendees: Knowledge and experience in population PKPD modeling and the use of R and Stan. The workshop assumes a knowledge of Stan comparable to the content of our previous introductory workshops (http://metrumrg.com/events/2016/10/23/bayesianpkpd.html). For those who do not yet have the required knowledge of Stan we offer a recorded online version of an introductory workshop (http://metrumrg.com/course/brief-introduction-bayesian-modeling-using-stan/).

Participants should bring a laptop on which the Google Chrome browser has been installed and that may access the internet via Wi-Fi.