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• W97679805 abstract "This thesis addresses optimal experimental design for nonlinear and generalized linear models. Until recently, the majority of optimal design research has focused on linear models. This research has provided the foundation for the comparatively new area of design for nonlinear situations and this thesis begins with an introduction to such relevant methodology. The recent interest in these models has been promoted by their ever expanding applications which include clinical trials, biological models, agricultural experiments and reliability studies. Indeed, one chapter of this thesis is devoted to a novel application of optimal experimental design to a biological model used to describe bioelectrical impedance data. This application was complicated by non-normal residuals and parameters varying between individuals in a nonlinear setting. Further, many clinical trials and biological experiments yield normal and/or non-normal data. Such experiments generally involve administration a drug, monitoring the elimination of the drug and how the drug effects the body. This can yield many types of data typically assumed to arise from a nested multiple response model. Such models explain more than a single response and are such that one model is contained within another. Experiments which yield multiple responses are generally poorly designed. This thesis develops design methodology for nested multiple response models and considers numerous applications to clinical trials. Data from reliability studies, product assessment experiments, warranty determinations and clinical trials are often modelled via ‘time to event’ or survival models. Little design research in this area exists in the literature with the majority being based on computationally intensive simulation techniques. This thesis develops model-based design theory by considering models for censored and clustered data, and accelerated life tests. These important areas of survival analysis have received much attention from an estimation sense. In general, the ability to estimate the parameters of a system is dependent upon the experimental design used. Hence, design considerations should be an integral part of, not only survival analysis, but statistical analysis in general. A primary goal of most experiments is parameter estimation. How well parameters are to be estimated is given by the expected Fisher information matrix, the inverse of which is the variance-covariance matrix of parameters. Forming such an information matrix is a non-trivial exercise, particularly when some model parameters are considered to be random variables. Specifically, for nonlinear mixed effects models, generally no closed form solution for the likelihood exists. Consequently, such models are typically linearized so that approximate maximum likelihood estimates and the expected Fisher information matrix can be formed. Such a task can be both technically and computationally challenging even though the nonlinear model is linearized. There has been some exploration in the literature about how accurate this approximation is. This is investigated further in this thesis where different approximations regarding the Fisher information matrix are explored to ultimately determine how this both effects the optimal design found and the precision of the predicted standard errors. Other design considerations include the ability to discriminate between rival models and the desire to maximize the probability of particular outcomes. Such considerations have led to the derivation of new optimality criteria. P-optimality, a criterion for increasing the probability of a success, is proposed in this thesis. Such a criterion is useful in situations where a design may efficient for parameter estimation, but offers few successful outcomes. Combining the properties of P-optimality and parameter estimation increases the number of successful outcomes of an experiment while maintaining precise estimates of parameters. Such dual goals of experiments have led to the consideration of compound optimality criteria. Few techniques exist in the literature for combining optimality criteria, especially for nonlinear models. This thesis not only proposes new techniques for combining criteria, but also investigates the performance of designs found when implementing such techniques. Searching for optimal designs requires a continuous search across a design space generally of high dimension. A simulated annealing algorithm was employed for this purpose. Computation for this thesis was predominately performed in the MATLAB package and with some also in NONMEM; a modelling package for mixed effects models and MAPLE; a mathematical and analytical software package." @default.
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• W97679805 date "2008-02-01" @default.
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• W97679805 title "Optimal Experimental Design for Nonlinear and Generalized Linear Models" @default.
• W97679805 hasPublicationYear "2008" @default.
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