A family of statistical models for analysis of Ames Salmonella/microsome test data is constructed that considers mutation and toxicity as competing risks and allows hyper-Poisson variability. These models have a parameter than can be employed as a mutagenic index because it approximates the slope at zero dose of a dose-response curve adjusted for toxicity. A second parameter quantifies plate-to-plate variability and lends itself to the study of factors affecting internal test reproducibility. The detection of aberrant plate counts is also addressed. This methodology is illustrated with data from a Salmonella test.