Robust and optimal experimental designs for non-linear models in chemical kinetics

Abstract

This thesis considers the problem of selecting robust and optimal experimental designs for accurately estimating the unknown mean parameters of non-linear models in chemical kinetics. The design selection criteria used are local, Bayesian and maximin D-optimality. The thesis focuses on an example provided by GlaxoSmithKline which concerns a chemical reaction where the temperature at which runs of the reaction are conducted and the times at which observations can be made during the reaction are to be varied. Optimal designs for non-linear models are usually dependent on the unknown values of the model parameters. This problem may be overcome by finding designs whose performance is robust to a range of values for each model parameter.

Optimal designs are investigated for situations when observations are independent and when correlation exists between observations made on the same run of the process; different forms and strengths of correlation between observations are considered. Designs robust to the correlation and mean parameters are found and assessed via both theoretical measures and a large simulation study which compares the designs found to alternatives currently used in practice.

Designs for the situation when the error variables have non-constant variance are obtained by use of a model formed via a power transformation on the response and its expected value. Designs robust to the value of the transformation parameter as well as the correlation and mean parameters are found and assessed.

Analytic results are established for obtaining locally D-optimal designs when the model is assumed to have independent observations and the response and expected response have been transformed to remove heteroscedasticity. Where analytic results are not available, numerical methods are used to obtain optimal designs.

The differing costs of a run of a reaction and of making an observation on a run are incorporated into design selection. A criterion which includes the cost of the time taken to run a reaction in an experiment is formulated and used to find designs.

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Identifiers

ORCID for Stefanie Biedermann: orcid.org/0000-0001-8900-8268

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