### Approximation of the Fisher information and design in nonlinear mixed effects models

**Mielke, T ***(Otto-von-Guericke)*

Friday 12 August 2011, 11:00-11:45

Seminar Room 1, Newton Institute

#### Abstract

The missing closed form representation of the probability density of the observations is one main problem in the analysis of Nonlinear Mixed Effects Models. Often local approximations based on linearizations of the model are used to approximately describe the properties of estimators. The Fisher Information is of special interest for designing experiments, as its inverse yields a lower bound of the variance of any unbiased estimator. Different linearization approaches for the model yield different approximations of the true underlying stochastical model and the Fisher Information (Mielke and Schwabe (2010)).
Target of the presentation are alternative motivations of Fisher-Information approximations, based on conditional moments. For an individual design, known inter-individual variance and intra-individual variance, the Fisher Information for estimating the population location parameter vector results in an expression depending on conditional moments, such that approximations of the expectation of the conditional variance and the variance of the conditional expectation yield approximations of the Fisher Information, which are less based on distribution assumptions.
Tierney et. al. (1986) described fully exponential Laplace approximations as an accurate method for approximating posterior moments and densities in Bayesian models. We present approximations of the Fisher Information, obtained by approximations of conditional moments with a similar heuristic and compare the impact of different Fisher Information approximations on the optimal design for estimating the population location parameters in pharmacokinetic studies.

#### Presentation

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