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Evaluation of the Fisher information matrix in nonlinear mixed effects models using Monte Carlo Markov Chains

Tuesday 7th July 2015 - 11:30 to 12:00
INI Seminar Room 1
For the analysis of longitudinal data, and especially in the field of pharmacometrics, nonlinear mixed effect models (NLMEM) are used to estimate population parameters and the interindividual variability. To design these studies, optimal design based on the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trials simulations. Until recently, the FIM in NLMEM was mostly evaluated with first-order linearization (FO). We propose an approach to evaluate the exact FIM using Monte Carlo (MC) approximation and Markov Chains Monte Carlo (MCMC). Our approach is applicable to continuous as well as discrete data and was implemented in R using the probabilistic programming language STAN. This language enables to efficiently draw MCMC samples and to calculate the partial derivatives of the conditional log-likelihood directly from the model. The method requires several minutes for a FIM evaluation but yields an asymptotically exact FIM. Furthermore, computation time remains similar even for complex models with many parameters. We compare our approach to clinical trials simulation for various continuous and discrete examples.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons