The importance of chemically induced mutation for human health is discussed briefly, and the biological basis for the primary in vitro assay for mutagenicity, the AmesSalmonella/microsome assay, is reviewed. A previous analysis for Ames test data, based on two mathematical models of the competing risks of mutation and toxicity, is shown to have inflated false-positive rates. A reason for this is the existence of local singularities in the Fisher information matrix. A new likelihood ratio test incorporating a pretest of a nuisance parameter is proposed, and its size is validated with replicated experimental data through an analysis based on a finite-mixture-of-binomials model.