Statistical characterization of negative control data in the Ames Salmonella/microsome test.

A statistical characterization of negative control data in the Ames Salmonella/microsome reverse mutation test was performed using data obtained at Takeda Analytical Research Laboratories during January 1989 to April 1990. The lot-to-lot variability of bacterial stock cultures and day-to-day variability of experiments were small for Salmonella typhimurium strains TA1535 and TA1537 and Escherichia coli WP2uvrA, but they were larger for S. typhimurium TA100. The number of revertant colonies for all test strains studied here followed Poisson distributions within the same day. The two-fold rule that is an empirical method to evaluate the Ames Salmonella/microsome test results has been widely used in Japan. This two-fold rule was evaluated statistically. The comparison-wise type I error rate was less than 0.05 for TA98, TA100, TA1535, TA1537, and WP2uvrA. Moreover, this rule is particularly conservative for TA100, for which the type I error rate was nearly 0.


Introduction
The Ames Salmonella/microsome test (Escherichia coli WP2uvrA is also included in the present study) is commonly used to evaluate the mutagenicity of chemicals and potential drugs, and many statistical procedures for analyzing the test results have been proposed. These procedures were reviewed, and a recommended method was selected by the United Kingdom Environmental Mutagen Society (1). In Japan, however, the empirical two-fold rule is widely used. In the Guidelines for Toxicity Studies ofDrugs (2), the evaluation oftest results is described as follows: "The test substance is considered to be positive for mutagenic activity when the number of revertant colonies per plate with the test substance is more than twice that per negative control plate and, in addition, when a dose-related increase in mutation count is observed." The aims of the present study were to a) evaluate the lot-tolot variability ofbacterial stock cultures, day-to-day variability of experiments, and also plate-to-plate variability in the Ames Salmonella/microsome test; b) determine whether the distribution of frequencies ofrevertant colonies follows Poisson distributions; and c) evaluate the two-fold rule statistically.

Data Used for Analysis
The test strains considered in the present study were Salmonella typhimurium TA1535 and TA100 and Escherichia coli WP2uvrA for base substitution and S. typhimurium TA1537 and TA98 for frameshift mutation. Escherichia coli WP2uvrA was obtained from T. Matsusima ofthe University of Tokyo, and all other strains were obtained from B. N. Ames of the University of California, Berkeley. Small portions of stock cultures containing 8 % dimethyl sulfoxide (DMSO) were stored in polypropylene tubes at less than -80oC. These were used as the seed for culture ofthe test strain at an interval ofabout 6 months. For the exogenous metabolic activation system (S9 mix), the postmitochondrial fraction of sodium phenobarbital and (-naphthoflavone pretreated rat liver homogenate supplemented with cofactors was used. Bacteria, solvent (distilled water or DMSO) and S9 mix (or phosphate buffer for nonmetabolic activation) were mixed and preincubated at 37 0C for 20 min. Revertant colonies on agar plates were counted using an electronic colony counter after 48 hr of incubation at 37'C.
Two different kinds of negative control data were used for analysis. One was the historical control data obtained from the duplicate, negative control plates in the course of routine work during January 1989 to April 1990 at lhdeda Analytical Research Laboratories. The other was data obtained from 50 replicate solvent negative control plates within the same day.

Methods for Analysis
To examine sources ofvariability in the negative control data, differences among the lots ofbacterial stock cultures, among the days when experiments were performed, and also among the plates within the same day were studied using the SAS System (3,4). The UNIVARIATE, GLM, NESTED, and VARCOMP procedures were used. Analysis of variance (ANOVA) for the historical control data was performed based on the following nested model (Eq. 1). Models a, b, and c were applied to the historical control data including three lots ofeach test strain obtained during a period of 70-84 days. Model d was applied to 50 replicate plates to assess the intra-day distribution.
The type I error of the empirical two-fold rule was evaluated by the following procedures. Equation 6 is the experimentwise error rate under the complete null hypothesis, which is the probability that at least one mean colony count of duplicate plates among k-i treated groups is equal to or greater than twice that in the concurrent negative control.

Results
The number ofplates, the mean of revertant colonies per plate, and the variance for each test strain for historical data (inter-day) and 50 replicate plate data (intra-day) are summarized in Table  1. The mean colony counts were liable to large variation among strains; for example, TA1535 showed less than 10 colonies per plate on the average, but TA100 showed more than 100. The intra-(4) and inter-day variances for all strains were more or less comparable to their mean, except for the inter-day variances of TA100, which showed overdispersion, i.e., the variances were about five times greater than the mean. To examine the contribution ofeach source ofvariability, lot, day, and plate, ANOVA was performed for the historical control data ( Table 2). WP2uvr were found to be much less than the plate-to-plate variation.
The Poisson assumption was evaluated for each test strain using models a, b, and c for historical data and using model d for 50 replicate plates. Results are summarized in Table 3. ment data showed a larger type I error rate than the two-group experiment data. Table 5 shows values of type I error based on empirical distribution ofthe 50 replicate plates. The values oftype I error TA100 and TA98, were much less than 5 %. These results infor strain TA1535 were the highest among the five strains dicate that although the two-fold rule has no theoretical basis, the studied but were still less than or nearly equal to 5 %. The values values oftype I error are smaller than 5 %, the commonly used of type I error for other strains, especially TA100 and TA98, statistical significance level.  are almost always below 5 %, and using duplicate plates is suf-Abbreviatons: DW, distilled water; DMSO, dimethyl sulfoxide. ficient to reduce the type I error rate. The application ofthe twofold rule to the data obtained with strain TA100 might be too carefully to eliminate sources of variability as completely as conservative.
possible, the data from the Ames Salmonella/microsome test In conclusion, we believe that ifan experiment is carried out follow Poisson distributions. A sophisticated and complicated statistical model is therefore not necessarily required to evaluate the test results. The two-fold rule is acceptable from the viewpoint oftype I error rate, but could be too conservative; this rule might be improved by incorporating a method for evaluating the dose-response relationship.