Scientific Publications by FDA Staff

Environmetrics 1996 Sep;7(5):503-12

Analysis of Quantal Response Data from Mixture Experiments

Chen JJ, Li LA, Jackson CD

This 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 and Becker (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.