Statistical methods for the Ames Salmonella assay: a review

doi:10.1016/S1383-5742(98)00025-8

Mutation Research/Reviews in Mutation Research

Volume 436, Issue 1, January 1999, Pages 113-122

https://doi.org/10.1016/S1383-5742(98)00025-8 Get rights and content

Abstract

The Ames Salmonella assay remains the most widely used in vitro genotoxicity assay. Several statistical methods have been proposed for its analysis [B.H. Margolin, N. Kaplan, E. Zeiger, Statistical analysis of the Ames Salmonella/microsome test, Proc. Natl. Acad. Sci., 78 (1981) 3779–3783; L.E. Myers, N.H. Saxton, L.I. Southerland, T.J. Wolff, Regression analysis of Ames test data, Environ. Mol. Mutagen., 3 (1981) 575–586; A.G. Stead, V. Hasselblad, J.P. Creason, L. Claxton, Modelling the Ames test, Mutation Res., 85 (1981) 13–27; L. Bernstein, J. Kaldor, J. McCaan, M.C. Pike, An empirical approach to the statistical analysis of mutagenesis data from the Salmonella test, Mutation Res., 97 (1982) 267–281; N.E. Breslow, Extra-Poisson variation in log-linear models, Appl. Stat., 33 (1984) 38–44; J. Wahrendorf, G.A.T. Mahon, M. Schumacher, A nonparametric approach to the statistical analysis of mutagenicity data, Mutation Res., 147 (1985) 5–13; D.G. Simpson, B.H. Margolin, Recursive nonparametric testing for dose–response relationships subject to downturns at high doses, Biometrika, 73 (1986) 589–596; D.G. Simpson, B.H. Margolin, Nonparametric testing for dose–response curves subject to downturns: Asymptotic power considerations, Annals Stat., 18 (1990) 373–390.]. In this paper we review recent literature to see what statistical methods are in fact employed for the analysis of the Ames assay. We then note that these methods can be classified into a common category in the framework of Haynes and Eckardt's mutation induction kinetics model [R.H. Haynes, F. Eckardt, Mathematical analysis of mutation induction kinetics, in: F.J. de Serres, A. Hollaender (Eds.), Chemical Mutagens, Principles and Methods for Their Detection, Vol. 6, Plenum, New York, 1980, pp. 271–307]. The value in knowing this is that most methods of analysis considered here will likely exhibit common statistical behavior. These analyses are computationally intensive, e.g., [B.H. Margolin, N. Kaplan, E. Zeiger, Statistical analysis of the Ames Salmonella/microsome test, Proc. Nat. Acad. Sci., 78 (1981) 3779–3783], hence the ready availability of computer programs is essential if biologists are to use these methods. We briefly review two statistical software programs that are available in the public domain, and describe in detail a third program, Salm, [B.H. Margolin, N. Kaplan, E. Zeiger, Statistical analysis of the Ames Salmonella/microsome test, Proc. Nat. Acad. Sci., 78 (1981) 3779–3783; B.H. Margolin, B.S. Kim, K. Risko, The Ames Salmonella/microsome assay: Issues of inference and validation, J. Amer. Stat. Assoc., 84 (1989) 651–661]. The Salm program is obtainable through the file transfer protocol (ftp) or using a WWW browser. Finally, we discuss two statistical consequences of naively applying the two-fold rule, a method of analysis employed by a number of researchers.

Introduction

The Ames Salmonella assay has been the most widely used mutagenicity assay; it has been employed in over 3000 locations. The popularity of the assay within genetic toxicology, and some of the unusual features of the data, have drawn the attention of statisticians. For example, the plate count of the revertant colonies of the Ames assay has been shown to be overdispersed, i.e., with a variance greater than its mean. This differs from the common Poisson model, where the variance and mean are equal. A second feature of interest in Ames assay data is that the dose–response curve is often not monotonically increasing, but rather exhibits a down-turn at high doses.

Margolin et al. [1]initially suggested a biologically based mechanistic model, accounting for the two features of the data described above. Since then, several statistical methods have been introduced 2, 3, 4, 5, 6, 7, 8. Recently, several authors have reviewed statistical procedures for analyzing Ames assay data 9, 10, 11. However, since the most recent review [11], the following developments have been noted: (1) There has been a growing trend in the risk assessment community to use biologically based mechanistic models [12]. (2) Several computer software programs are now available in the public domain 13, 14, 15. (3) There has been an increasing awareness that some aspects of the two-fold rule method of analysis do not have a sound scientific foundation 16, 17, 18. (4) The quasi-likelihood approach, which generalizes the likelihood approach, could be employed for the estimation of model parameters 5, 19. The quasi-likelihood approach requires knowledge of only the mean and variance relationship instead of the complete specification of the distribution, which the likelihood requires.

Recent developments motivate this paper. We first review recent articles in two major toxicological journals to determine what statistical methods are currently employed for the analysis of Ames assay data. We then focus on the mutation induction kinetics model suggested by Haynes and Eckardt [20]. We see that this class of models incorporates mutagenicity and toxicity in terms of competing risks and includes most statistical models, parametric or semi-parametric, that have been suggested. We then discuss three computer software programs available in the public domain, including the Salm program 1, 17. Finally, we review two published reports on the lack of scientific justification for the two-fold rule.

Section snippets

Materials and methods

We surveyed two complete years (1995–1996) of Mutation Research and Environmental and Molecular Mutagenesis (EMM), to find the frequency distribution of statistical methods currently employed in the analysis of Ames assay data. Regarding Mutation Research, we restricted the review to Genetic Toxicology (MUTGEN), Mutation Research Letters (MUTLET) and Environmental Mutagenesis and Related Subjects (MUTENV). We also restricted the assay to the standard Ames assay, which used either the plate

Frequency distribution of statistical methods

In Table 1 we have the frequency distributions of statistical methods that were employed for the analysis of Ames assays in the 1995–1996 volumes of EMM and a selected series of Mutation Research.

Most users of the two (or three) fold rule combined it with a dose-related increase and/or reproducibility. However, none indicated how to determine the dose related increase. Four papers applied the two-fold rule and the slope of the linear portion sequentially. These four papers were classified into

Discussion

More than 40% of the recent publications on the Ames assay still employ the two-fold rule for analysis, although this rule has been shown to be less than ideal. Authors recognized in 30% of the publications that the slope of the dose–response curve is key to the determination of mutagenic potency. However, fewer than 10% of the papers reviewed described explicitly how to calculate the slope or how to determine the initial linear region by referring to a biologically based mechanistic model.

Acknowledgements

We thank Errol Zeiger at NIEHS for his help in many aspects of this research. We gratefully acknowledge two anonymous referees for their invaluable comments and suggestions. Byung Soo Kim's research was partially supported by the Korea Research Foundation through its 1995 Overseas Research Program for University Professors.

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