SUMMARYThis paper presents a logistic regression procedure for the analysis of mixture data. The design of the mixture experiment is based on the simplex-lattice designs where the components represent the proportions of a mixture. i.e. each component is expressed as a fraction of the mixture with the sum equal to one. The Scheffe (1958) and Cox (1971) polynomial andBecker (1968) non-polynomial forms are used to model relationships between the expected response and individual components of the mixture. In a three components mixture it was shown that if one component is completely linear with the remaining two components, then the proper representation of such a system is the Becker non-polynomial model. An experimental data set designed to study the interrelating effects of calories from dietary fat, carbohydrate and fibre on tumour incidence is used to illustrate the analysis and the additive effect of the fibre component. Each mixture (diet) of fat. carbohydrate and fibre was administered to provide the same total caloric consumption.
A biologically-based dose-response model for predicting developmental malformation effects from exposure to a toxic substance during pregnancy is developed. The biological basis of this model arises from the expectation of exponential growth in rodents during gestation, and the exponential growth rate assumed to be reduced by dose raised to a power when a toxic substance is administered during gestation. The prenatal foetal weight is used as a biomarker to link the incidence of cleft palate to the dose level. A dose-response growth model for prenatal foetal weight as a function of both time and dose is established. This dose-response function is then combined with a dose-response function between the incidence of cleft palate and the prenatal foetal weight to form a dose-response function between the cleft palate and dose. Two experiments, a dexamethasone (DEX) exposure in rats and a 2,4,5-trichlorophenoxyacetic (2,4,5-T) acid exposure in mice, were conducted for purpose of checking the models empirically and for demonstration of modelling process. The proposed dose-response growth model for prenatal foetal weight fits adequately to both experimental data, but the model from prenatal foetal weight and incidence of cleft palate combined seems inadequate to describe the relationship between the dose and incidence of cleft palate fully.
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