### 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. The robust or sandwich variance estimator.