An application of optimal experimental design theory and extended least squares parameter estimation methods to a stochastic one compartment model Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/12579v656

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  • The two major objectives of this thesis are: (1) demonstrating and applying optimal design theory by developing an optimal sampling-time strategy for parameter estimation in stochastic one compartment models, and (2) examining in depth the extended least squares (ELS) method of estimating population pharmacokinetic parameters. The nonlinear weighted least squares parameter estimation method and deterministic pharmacokinetic models have been employed for the development of optimal experimental designs in almost all prior research. The present study extends the existing literature by using the ELS estimation method to develop the local D-, A-, and C-optimal experimental designs for the stochastic one compartment model. Also, comparisons of the efficiency of the ELS estimators from local optimal designs with those from the uniform and conventional pharmacokinetic designs, have been made. Several practical difficulties encountered in calculating any closed form representation of the bias of the ELS estimators for a stochastic model are explored. Box's measure of bias is used as a rough estimate of the predicted bias in nonlinear weighted least squares and the ELS estimates for a typical one compartment open model. The reasons for not using the Quenouille jackknife technique as an estimation procedure are also explained. The traditional approach of the analytical and computational methods of constructing various criteria of optimal designs are discussed. Due to the inability to extend the general equivalence theorems to complex systems, the problem of finding a local optimal design is solved by a modified flexible polyhedron search method, a type of Nelder-Mead simplex method. The sampling properties of estimators from four estimation methods and the usual nonlinear least squares method are compared via computer simulation. Evidence has been summarized suggesting that just about any estimation method-design combination can practically give reliable estimators for the mean values of the parameters. However, special detailed procedures (discussed in the text) are necessary to simultaneously estimate all the parameters including the variance components.
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