Course Agenda

DAY 1 (9h00-18h00):


  • What is a population? An individual?
  • Random variable, distribution of a random variable, parameters
  • Gaussian distribution: unidimensional vs. multidimensional Gaussian, mixture of Gaussians
  • What is a model? A statistical model?


  • Definition of an estimator
  • Maximum likelihood estimator
  • Confidence vs. prediction intervals
  • Hypotheses testing (definition of hypotheses, risk, decision rule)

DAY 2 (9h00-18h00):

Linear statistical model

  • Definitions (linear vs. nonlinear models, fixed effects, random effects and mixed effects models)
  • Underlying assumptions (independence, normality, homoscedasticity)
  • Estimation (least squares) and hypothesis testing
  • Model diagnostics (residuals, normality graphs and tests)
  • Application to covariate models in pharmacokinetics

Nonlinear models

  • Definitions
  • Underlying assumptions
  • Estimation methods (criteria and their optimisation: handling NONMEM warnings and error messages)
  • Diagnostics
  • Exercises: application to classical (individual) pharmacokinetic analysis using NONMEM

DAY3 (9h00-18h00):

Nonlinear mixed effects models (hierarchical population models)

  • Definitions and sources of variability
  • Underlying assumptions
  • Likelihood & estimation methods: everything you always wanted to know about two-stage, FO, FOCE, FOCE-I, SAEM… methods but were afraid to ask
  • What are empirical Bayes estimates (EBEs)? How to handle eta- or epsilon-shrinkage?
  • Monte-Carlo simulations
  • Exercises in population pharmacokinetics using NONMEM

DAY4 (9h00-18h00):

Nonlinear mixed effects models (ctd’)

  • Standard diagnostics (IPRED, PRED, WRES, IWRES)
  • Model building strategy, model selection criteria (AIC, BIC), Likelihood Ratio Test, Wald Test
  • Model validation (internal vs. external, cross-validation, visual predictive checks, NPDE)
  • Modeling covariate effects: a clear view on covariate selection
  • Exercises in population pharmacokinetics using NONMEM

DAY5 (9h00-17h00):

Nonlinear mixed effects models (ctd’)

  • Modeling inter-occasion variability
  • Exercises in population pharmacokinetics using NONMEM

DAY6 (9h00-12h00):

  • FINAL EXAM: data analysis on a case study