Modeling the Ames test

Despite the value and widespread use of the Ames test, little attention has been focused on standardizing quantitative methods of analyzing these data. In this paper, a realistic and statistically tractable model is developed for the evaluation of Ames-type data. The model assumes revertant colony formation at any dose follows a Poisson process, while the mean number of revertants per plate is a nonlinear function of up to 4 parameters. An exponential decay term can be included in the model to adjust for toxicity. The resultant system of nonlinear equations is solved using a modified Gauss-Newton iterative scheme to obtain maximum likelihood estimates of the model parameters. Significance of the key parameters is tested by fitting reduced models and using likelihood ratio tests. The model's performance is demonstrated on data from organic extracts of various environmental contaminants. Among the advantages of the proposed model are (1) no data is discarded in the parameter estimation process, (2) no arbitrary constants need to be added to zero counts or doses, and (3) no mathematical transformation of the data is required.