Statistical analysis of joint toxicity in biological growth experiments

The authors formulate a model for the analysis of designed biological growth experiments where a mixture of toxicants is applied to biological target organisms. The purpose of such experiments is to assess the toxicity of the mixture in comparison with the toxicity observed when the toxicants are applied individually to the organisms. The analysis is based on a random differential equation describing the growth of the organisms. This model yields a natural measure of interaction between toxicants and the hypothesis of independent action from a mixture of toxicants can be tested. The proposed model is applied on data from an experiment where inhibition of the growth of the bacteria Pseudomonas fluorescens caused by different mixtures of pentachlorophenol and aniline was studied.