Workshop Topics

 

This workshop begins with the fundamental question "why use statistics?" and, in a step by step fashion, it introduces the ideas and statistical concepts that underpin pharmacometric modelling and simulation today. The following list gives an idea of the breadth of the workshop;

  • Probability and statistical inference.
  • Laws of probability and Bayes theorem.
  • Univariate probability distributions – Expected value and variance.
  • Multivariate probability distributions – joint, marginal and conditional distributions. The covariance matrix. Independence and conditional independence.
  • Modelling, estimation, estimators, sampling distributions, bias, efficiency, standard error and mean squared error.
  • Point and interval estimators. Confidence intervals.
  • Hypothesis testing, null and alternative hypotheses. P-value, Type I and type II errors and power.
  • Likelihood inference, maximum likelihood estimator (MLE), likelihood ratio. BQL and censored data.
  • Invariance of the likelihood ratio and the MLE.
  • The score function, hessian, Fisher information, quadratic approximation and standard error.
  • Wald confidence intervals and hypothesis tests.
  • Likelihood ratio tests.
  • Profile likelihood, nested models.
  • Model selection, Akaike and Bayesian Information Criteria (AIC & BIC).
  • Maximising the likelihood, Newton’s method.
  • Mixed effects models, the hierarchical and marginal likelihoods.
  • Estimation of the fixed effects, conditional independence, prior and posterior distributions.
  • Approximating the integrals, First order (FO & FOCE) and Laplace approximations, numerical quadrature.
  • The Expectation Maximisation (EM) algorithm.
  • MU-modelling,Iterative Two Stage (ITS).
  • Monte Carlo EM (MCEM), Importance sampling, Direct sampling, SAEM, Markov Chain Monte Carlo
  • Estimating the random effects, empirical bayes estimates (EBE) and shrinkage.
  • Minimal sufficiency, asymptotic properties of the MLE, efficiency, the Cramer-Rao Lower Bound (CRLB), normality.
  • Robustness of the MLE, the Kullback-Liebler distance. Quasi likelihood and the robust or sandwich variance estimator.