| Summary: | This thesis is concerned primarily with the practical implementation of Bayesian methodology within the context of the pharmaceutical industry. The implementation includes the development, where appropriate, of analytic approximations to the posterior distributions of interest and graphical methods for mapping prior assumptions to posterior inference. Two critical areas within pharmaceutical research, critical in the sense of the controversy which they have aroused, have been investigated. First, Bayesian methods for the analysis of two-treatment crossover designs which fell in to disfavour in the late 1970's and early 1980's because of the US Food and Drug Administration's published view that the two-treatment two-period design was not the design of first choice if unequivocal evidence of a treatment effect was required were developed. Each type of design considered and for which methods are developed are illustrated with examples from clinical trials which have already been reported in the medical literature. Second, a Bayesian method is developed whose purpose is to classify test compounds into one of several toxicity classes on the basis of an LD50 estimate. The method is generalised to deal with a non-standard LD50 problem related to the prediction of results from a future LD50 experiment. Both of these applications arose out of a practical consultancy session within the context of a statistics group in the chemical/pharmaceutical industry. As part of the methods required for carrying out these analyses the zeros and weights associated with some non-standard orthogonal polynomial are developed as a result of which a new asymptotic expansion of the Behrens-Fisher density is developed. Further applications of the polynomials orthogonal to t-kernels are developed including problems associated with prediction in clinical trials. A FORTRAN program which has been implemented at a laboratory level within the pharmaceutical toxicology department at CIBA-GEIGY in Switzerland is provided SAS programs for a variety of the analyses developed for the two-treatment crossover designs are provided as are SAS programs for determining the zeros and weights of a number of different classes of orthogonal polynomials.
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