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Ames TestWherly P. Hoffman a; Michael L. Garriott b

a Department of Global Statistical Sciences, Lilly Research Laboratories, Eli Lilly and Company, Greenfield,Indiana, U.S.A. b Department of Investigative Toxicology, Lilly Research Laboratories, Eli Lilly and Company,Greenfield, Indiana, U.S.A.

Online Publication Date: 23 April 2003

To cite this Section Hoffman, Wherly P. and Garriott, Michael L.(2003)'Ames Test',Encyclopedia of Biopharmaceutical Statistics,1:1,28— 35

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Ames Test

Wherly P. HoffmanMichael L. GarriottLilly Research Laboratories, Eli Lilly and Company, Greenfield, Indiana, U.S.A.

INTRODUCTION

Genetic toxicology tests are among the early studies

conducted to assess the safety profile of a compound. A

battery of tests, each assessing a different genetic end-

point, is typically performed to thoroughly evaluate a

given compound since no single test is capable of de-

tecting all mutagens. The tests are designed to determine

whether the compound can interact with DNA and lead

to the production of gene mutations or chromosomal

breakage. Some tests can also detect compounds that

interact with components of the mitotic spindle apparatus.

The detection of mutagens is important because they may

also be either teratogens or carcinogens. Of a battery of

short-term genetic assays, the Samonella typhimurium/

microsome test developed by Ames et al.[1,2] is the most

commonly used genotoxicity test. Two- and threefold

rules and various parametric and nonparametric methods

have been applied to the Ames test data. A general re-

view of these analysis methods is the primary purpose

of this article. The design, statistical analyses, and in-

terpretation of results of the Ames test will be discussed.

‘‘Background’’ includes information pertaining to the

relevance of the Ames test to the toxicology safety

profile. The ‘‘Design’’ section describes the basic design

of the test. The section ‘‘Analysis Methods for Ames Test

Data’’ provides a review of some analysis methods em-

ployed for the evaluation of the mutagenicity of a

compound. In the ‘‘Discussion’’ section, we discuss the

methods reviewed and some important issues in the

evaluation of mutagenicity based on Ames test results,

and in the last section we draw concluding remarks to

summarize this article.

BACKGROUND

In this section, a brief summary is presented of why the

Ames test was developed and how this assay is conducted.

The procedure for conducting the Ames test is described

without too much detail. This section is not intended to

provide enough information to conduct the assay; it is

intended to provide readers with a general understanding

of how the responses are obtained and thus leads naturally

into the following sections on the design and statistical

methods employed for analysis of the test data.

Why the Ames Test

When developing a compound for commercial purposes,

one has to establish its safety profile. Animal in vivo

and in vitro tests are designed to serve this purpose. In

general, the testing includes acute toxicity tests in rodents,

genetic toxicity tests, developmental toxicity tests,

general animal toxicity tests from 30 days up to 1 year

in duration, and lifetime carcinogenicity tests in rodents.

Of these general tests that are needed to demonstrate the

safety of a compound and to ensure its registration

worldwide, the most costly and time-consuming test is the

carcinogenesis bioassay in rodents. Assays for genotoxi-

city were developed initially in an attempt to predict in a

shorter time frame the eventual outcome of the bioassay.

The basic premise revolved around the somatic theory of

carcinogenesis, which suggested that mutational events

were causative factors in the development of cancers.

Additionally, there was evidence that mutagenic events

were associated with embryonic mortality, birth defects,

and genetic disease. Therefore, the use of genotoxicity

tests seemed to have broad application in the overall

safety assessment. Although bacterial mutation tests had

been used since the 1950s, they were not efficient in

the detection of compounds acting by various mutagenic

mechanisms. Efforts by Dr. Bruce Ames and his col-

leagues at the University of California, Berkeley, to

develop a more efficient bacterial screening system cul-

minated in 1971 with the test that now bears his name.

Despite its utility, it was realized that bacteria are not

mammalian cells and that the organization of the genetic

material was different such that other short-term muta-

genicity tests would be required to ensure the detection

of the majority of rodent carcinogens.[3] Although over

200 mutagenicity tests have been developed, few have

been well validated, and current regulatory requirements

for product registration include only a battery consisting

Adapted from WP Hoffman. In: SC Chow and JP Liu, eds. Design and

Analysis of Animal Studies in Pharmaceutical Development. New York:

Marcel Dekker, 1998, pp. 357–372.

28 Encyclopedia of Biopharmaceutical Statistics

DOI: 10.1081/E-EBS 120007383

Copyright D 2003 by Marcel Dekker, Inc. All rights reserved.

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of two to four tests of the seven most thoroughly vali-

dated standard tests.[4–6] Of these required tests, the

Ames test is the most commonly used and for this rea-

son alone merits discussion.

The Ames Test

The Ames bacterial mutation test is an in vitro assay in

that it does not use live animals; instead, it uses bacterial

cells. Typically, the S. typhimurium bacterial tester strains

TA1535, TA1537, TA98, and TA100 and an Escherichia

coli tester strain WP2uvrA are used in the Ames test.

Although WP2uvrA was added to the bacterial test system

after the Ames test was developed, it is handled the same

as the four S. typhimurium strains in all aspects of the

conduct and analysis of the experiment. Therefore, in this

article, Ames test will refer to the assay of the four S.

typhimurium strains and the E. coli strain. For each strain

of the bacteria, a mixture of the proper amounts of three

ingredients is first prepared in a tube. See Fig. 1. The

three ingredients are: 1) from 10 to 100 million bacterial

cells from a particular strain, 2) a compound, which can

be a test article, negative control, or positive control,

and 3) minimal agar, which includes trace amounts

of histidine, tryptophan, and biotin. The mixture is

then poured into a plate containing a layer of solidified

minimal agar for the growth of revertant colonies. Some

compounds are not directly mutagenic in vivo but are

metabolized to a compound that is. Therefore, all in vitro

genotoxicity tests, including the Ames test, are conducted

so that cells are exposed to the test article both in the

presence and in the absence of an exogenous metabolic

activation system. This metabolic activation system con-

sists of a postmitochondrial supernatant (S9) of homo-

genized liver tissue from rats. This cell-free extract

contains a variety of drug-metabolizing enzymes. The S9

is supplemented with cofactors, salts, and a buffer system

collectively known as S9 mix.

Histidine and tryptophan are amino acids essential for

the growth of the tester strains of S. typhimurium and E.

coli, respectively. The Ames tester strains contain mu-

tations in the genes that allow normal bacteria (proto-

trophs) to manufacture their own histidine or tryptophan.

The tester strains are dependent upon the inclusion of the

amino acids into the minimal agar to support their

growth. These mutant bacteria are called auxotrophs. The

Ames test is often referred to as a ‘‘reverse’’ mutation

assay because what is measured is the reverse mutation

rate from histidine/tryptophan dependency (auxotrophy)

to histidine/tryptophan independence (prototrophy). Bac-

terial cells that have undergone the reverse mutational

event are called ‘‘revertants.’’ Trace amounts of histidine

and tryptophan are provided at the start of the experiment

to sustain the bacterial cells at the beginning and thus to

allow the possible expression of reverse mutation events

later. After a 48-hr incubation period, the revertant cells

will form visible colonies, which are counted. Because

reverse mutation may occur without treatment with a

mutagen, a negative control is always included in the

assay to account for the spontaneous reverse mutation

rate. If a compound is not a mutagen, then one would

not expect a large increase in the number of revertant

colonies compared to the number of spontaneous re-

vertant colonies in the negative control. Therefore, the

number of revertant colonies is the response evaluated to

determine the mutagenic effect of a test article. A sig-

nificant increase in revertant colonies on the compound-

treated plates is an indication of a positive response for

bacterial mutation.

DESIGN

The Ames test procedure is rather strictly defined for

regulatory purposes.[7–9] The assay is typically conducted

both with and without metabolic activation for each of the

five bacterial strains. For each bacterial strain, five or

more concentration levels of a compound and proper

concentration levels for the negative and positive controls

are determined by scientists. A positive control is required

for the validity of the assay but is not included in the

evaluation of the mutagenicity of a compound. A negative

control is needed to account for spontaneous reverse

mutation in the evaluation of the mutagenicity of the test

article. Historical control data are useful for further eva-

luation of positive effects associated with a compound.

Each dose level is tested in triplicate, and each of the

triplicate plates is prepared independently. Therefore, if

five concentrations are selected for each bacterial strain,

then a total of 50 sets of triplicate data from the

compound (five concentrations, two types of activation,

and five strains of bacteria) and 10 sets of triplicate data

Fig. 1 Description of the conduct of the Ames test.

Ames Test 29

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from each of the negative control and positive control are

the results of the assay.

The purpose of the Ames test is to evaluate the

mutagenic effects of a compound. A suitable selection of

the concentration levels of a compound for testing is

essential. Logarithmically spaced concentration levels are

determined by scientists in an attempt to capture an

increasing trend in the response. However, if the

concentration of the compound is too high, then one

would expect a downturn in the number of revertant

colonies as a result of toxicity. For determination of the

concentration levels for the Ames test, a compound is

assayed over a wide range of concentration levels up to

5000 mg/plate for each bacterial strain. Based on the

preliminary results, five to seven concentration levels are

then selected using a top concentration of 5000 mg/plate,

adjusted for toxicity. The highest concentration may be

very close to the toxic level.

ANALYSIS METHODS FORAMES TEST DATA

Proper analysis methods should account for various

sources of variability in the response. Therefore, one

needs to identify different sources of variability in

the assay data before considering the analysis. Based

on the variability and some assumptions, we discuss

various statistical and nonstatistical methods for the ana-

lysis of revertant colonies obtained from the Ames test.

Edler[10] and Mahon et al.[11] gave a good overview of

statistical methods for the Ames Salmonella test. For a

more recent review of statistical methods, see Lin.[12]

Here we will begin the discussion with some basic in-

formation on data in the next section. Then selected

methods will be discussed to bring about different ap-

proaches for the analysis of Ames test data. The me-

thods discussed in the subsequent sections are modified

two- and threefold rules, nonparametric methods, and

parametric methods.

Understanding Data

What is the distribution of the number of revertants from

the Ames test? Before suggesting an answer, let us

understand the data first and try to identify various

sources of variability in it. For each replicate plate, a

separate minimal agar mixture of the selected strain of

bacterial cells, the test article, and a solution of histidine,

tryptophan, and biotin is made in a tube. Therefore, the

numbers of revertants from the triplicate plates are in-

dependent. Because auxotrophs need to grow in a histi-

dine/tryptophan-sufficient environment, trace amounts of

these amino acids are supplied at the beginning of the test.

For each strain of bacteria, variability in the number of

revertants can be a result of the number of bacterial cells

that are plated at the beginning of the test, the amount of

histidine/tryptophan provided initially, the concentration

of the test article, the contents of the minimal agar, the

amount of S9 mix, the duration of the incubation time, or

other factors. In a laboratory, attempts are made to control

all factors so that changes in the revertant counts would

reflect only the effect of the test article through the con-

centration levels.

To demonstrate that a compound is not mutagenic,

one has to test it at sufficiently high concentrations to

rule out doubts that the bacterial cells may not have been

challenged enough. Pilot studies are usually conducted

first to select proper concentration levels for each strain of

bacteria. The final selection often includes concentration

levels that are very close to the toxicity threshold of the

bacterial cells. Consequently, one may observe a down-

turn in the number of revertants when some of the

concentration levels of a compound are higher than the

toxicity threshold of the bacterial cells.

Because the number of bacterial cells plated initially

is large (about 107) and the probability of a cell un-

dergoing a reverse mutation from auxotrophy to proto-

trophy is small, the resulting revertant counts of such

rare events may have a Poisson distribution. Does the

number of revertants X follow a Poisson distribution

p(X = x, l) where

pðX ¼ x; lÞ ¼ lxe�l

x!for x ¼ 0; 1; 2; . . . ð1Þ

and l is the mean rate of reverse mutation? One can

examine this either graphically or by performing a sta-

tistical test. To get a good assessment of the distribution

assumption, both approaches require more data than are

available from one assay in general. When a sufficient

amount of data is available, one can check this Poisson

assumption by plotting the sample variance against the

sample mean on a logarithmic scale. A linear relationship

with slope near one is an indication of Poisson distri-

bution. Or one can perform Fisher’s dispersion test[13] for

a sample of n counts, x1, x2, . . ., xn, which compares the

test statistic

Pni ¼ 1 ðxi � �xÞ2

�xð2Þ

to a chi-square distribution with n� 1 degrees of free-

dom, where �x is the average of the n revertant counts.

Stead et al.[14] reported no overdispersion in their expe-

rience, whereas Vollmar[15] and Margolin et al.[16] ob-

served overdispersion. Because each laboratory may have

30 Ames Test

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its unique features in conducting the assay and control-

ling the assay environment, an assessment of overdisper-

sion should be performed based on its own historical

data, and reevaluation should be performed periodically.

If the rate of reverse mutation l from replicate to

replicate is not a constant, then the excess of variability in

replicates over the mean would suggest that the revertant

counts are a random sample from a mixture of Poisson

distributions. For ease of further references in later

sections, we will follow the parameterization of Margo-

lin et al.[16] If l is a random variable with a gamma

distribution, then the revertant counts have a negative bi-

nomial distribution

pðX ¼ xjm; cÞ ¼ x þ c�1 � 1x

� �m

mþ c�1

� �x

� c�1

mþ c�1

� �c�1

for x ¼ 0; 1; 2; . . . ð3Þ

where c � 0 and m > 0. The mean of this distribution

is m, and the variance is m(1 + cm). The extra variability

in the Poisson counts is reflected by the dispersion

parameter c. Large values of c indicate inadequacy of

modeling without accounting for the extra variability in

the sampling.

Modified Two- and Threefold Rules

The two- and threefold rules declare a given test article to

have induced a positive response if a concentration-

related increase in the number of revertant colonies is at

least twice the control count for strains TA98, TA100, and

WP2uvrA or three times the control count for strains

TA1535 and TA1537.[17] The comparison is based on the

average number of revertants from the replicates for the

control and each concentration level. The treated averages

are compared to the control average. In the event that

there is a downturn in the number of revertants owing to

toxicity, the evaluation criteria are applied only to the

results at the nontoxic level.

Nonparametric Methods

Vollmar[15] examined the results from the European

Collaborative Ames-Test Study 1977–1978, and the plots

of log-range vs. log-mean indicated that the number of

revertants did not follow a Poisson distribution. Over-

dispersion was evident between laboratories as well as

within each laboratory. It was recommended that

nonparametric methods be applied to Ames test results.

Two rank-based tests were considered: the Jonckheere

test[18] for monotonic concentration effects and the

Kruskal–Wallis test[19] for other effects, including a

downturn at the toxic levels. Given 713 Ames test results,

the Jonckheere test was superior to the Kruskal–Wallis

test and was recommended as the routine statistical

method for qualitative evaluations. Vollmar pointed out

that, in general, three to five replicate samples were

necessary for achieving a statistical significance level

of 0.05.

Wahrendorf et al.[20] proposed a nonparametric

approach to the analysis of Ames test data. Assume that

there are K concentration levels with nk replicates at the

kth level and the total number of replicates is N. In their

approach, the concentration levels were arranged in K

increasing levels, with K = 1 for the control. For a

given j, 1 j K, the revertant counts from all K

concentration levels are assigned to one of the two

categories: 1 is the ‘‘below’’ category for levels 1� j; 2

is the ‘‘above’’ category for levels j + 1 to K. The

revertant counts are ranked from low to high. If there are

no concentration-related effects, then the sum of the

ranks, Lj, from the ‘‘below’’ category should be the

product of the midrank, (N + 1)/2, and the number of

observations in the ‘‘below’’ category. Define L as the

sum of the ‘‘below’’ categories corresponding to j for

1 j K� 1. If a compound does induce a positive

trend in the number of revertants, then the ranks in the

‘‘above’’ category would be relatively higher than those

in the ‘‘below’’ category. Therefore, positive trends are

associated with smaller values of L, and a test statistic for

positive trends is L. Wahrendorf et al. provided critical

values for L based on Monte Carlo simulations for

standard designs in their paper. Incorporating the

expectation, E0(L), and variance, Var0(L), of L under

the null hypothesis of no concentration-related effects,

the resulting standardized test T for the alternative hy-

pothesis of an increasing trend is a one-sided test:

T ¼ E0ðLÞ � LffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVar0ðLÞ

p ð4Þ

where E0(L) and Var0(L) are defined[20] by the total

sample N and sj, the number of observations in the

‘‘below’’ category for a given j as follows:

E0ðLÞ ¼ N þ 1

2

XK�1

j ¼ 1

sj ð5Þ

Var0ðLÞ ¼ N þ 1

2½XK�1

j ¼ 1

sjðN � sjÞ

þ 2XK�2

j ¼ 1

XK�1

k ¼ jþ1

sjðN � skÞ� ð6Þ

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The T statistic is approximated by a normal distribu-

tion. In addition to the test proposed in the foregoing,

Wahrendorf et al. also provided a calculation for the

probability q̂j that a revertant count from the ‘‘below’’

category is smaller than that from the ‘‘above’’ category

for a given j. Under the null hypothesis of no con-

centration-related effects, q̂j is expected to have a value

of 0.5. This probability gives insight to the change of

trends in the revertant counts and is helpful for further

understanding of the type and strength of the trends.

Parametric Modeling

Parametric methods include the following: 1) regression

on transformed data, assumed to be normally distribu-

ted;[21] 2) nonlinear regression on data assumed to be

Poisson distributed, either with or without extra variation,

using a full likelihood or quasi-likelihood approach; and

3) biologically based models incorporating extra-Poisson

variation.[15,22,23]

Linear regression on logarithmicallytransformed revertant counts

Chu et al.[21] at the In Vitro Program of the National

Cancer Institute (NCI)/National Toxicology Program

(NTP) evaluated the statistical methods for Ames test

data based on results from 2362 tests performed in four

laboratories on 17 test articles. In defining the screening

criteria for adequate data, they defined ‘‘toxic dose level’’

as ‘‘any dose level which was greater than the dose

eliciting the highest average response and which had

every response less than the lowest single response in the

highest average response dose level.’’ Evidence of

toxicity is a decrease in the number of revertants after

reaching the toxic level. Therefore, when a downturn is

present in the revertant counts and the peak mean

revertant count occurs at concentration level ci, then the

toxic levels are those concentration levels, cj, for j > i,

that have all revertant counts smaller than the lowest

revertant count at concentration level ci.

Once the toxic concentration levels are identified,

evaluation of the mutagenic effects will be based on data

obtained in the nontoxic concentration range. One

approach to the statistical evaluation of the mutagenic

effects is regressing the logarithmically transformed

revertant count on the logarithmically transformed

concentration level.[21] Because the control concentration

level is 0 and the log transformation of 0 does not exist,

the recommendation was to increase all concentration

levels by 1. The validity of this regression approach lies in

the appropriateness of the normality assumption resulting

from the log transformation on the revertant counts.

Mutagenicity is established by a statistically significant

positive slope of the regression line. Chu et al. required a

test to have at least five concentration levels, including a

negative control, and each with a minimum of two

replicates. When concentration levels are approximately

equally spaced, instead of adding 1 to all concentration

levels to allow for the log transformation on the 0

concentration level, an alternative was recommended by

Margolin et al.[24] The concentration level of the negative

control is selected so that all concentration levels are

equally spaced on the logarithmic scale.

Nonlinear regression on revertant counts

Although rare events are often modeled by Poisson

models, and it seems reasonable to consider the small

number of revertants in about 10 million bacterial cells a

Poisson random variable, there are statistical concerns in

the assumption of simple Poisson distribution. Evidence

of extra-Poisson variation was observed by some, but not

all. Because replicates are required at each concentration

level, accumulating historical control data for examina-

tion of the adequacy of the Poisson assumption is

essential. Under the Poisson assumption, the revertant

counts can be modeled by a generalized linear model[25]

with Poisson distribution and logarithmic link. Positive

trends in the treated groups can be tested in a sequential

fashion by a trend test[26] if identifying the concentration

level associated with no observable effect is of interest.

For laboratories that exhibit extra-Poisson variation in the

historical control data, the generalized linear model can

be adjusted using a quasi-likelihood method for the extra-

Poisson variation. The extra-Poisson variation is

accounted for by including an extra factor in the variance

of the model. The extra factor can be estimated by the

square root of Pearson’s chi-square divided by the degrees

of freedom. This analysis can be carried out using PROC

GENMOD in SAS.[27]

If the mean rate for reverse mutation, l, in Eq. 1 is a

random variable with gamma distribution, then the

posterior distribution of the revertant counts is a negative

binomial distribution as in Eq. 3. Thus, the extra-Poisson

variation can be incorporated in the modeling and

evaluation of the mutagenicity of a compound using a

full likelihood approach.

Biologically based models

Nonmonotonicity observed as a downturn in the revertant

counts is not uncommon in practice. Bacterial cells

subject to toxicity are inhibited from full expression of

mutagenicity. Once a definition of a toxic concentration

level is established, then one can eliminate the toxic

concentration levels and model the mutagenic effects of a

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compound using the remaining data. An alternative to this

two-step modeling approach is to model both mutageni-

city and toxicity of a compound simultaneously. Margolin

et al.[16] developed biologically based models for model-

ing the mutagenicity and toxicity while accounting for the

extra variation in the Poisson distribution in the revertant

counts from the Ames test. The choice of their models

depends on the number of generations the bacterial cells

have for their histidine/tryptophan supply, the number

of generations the compound is mutagenic, and the num-

ber of generations the compound is toxic. Two basic

assumptions of the biologically based models are that

mutagenic and toxic effects are independent, and dura-

tions of bacterial cells, being mutagenic and toxic, are

not affected by the concentration of the compound. The

mean, m, of the negative binomial distribution, is related

to the number of bacterial cells exposed to the test article,

N0, and the probability of resulting a revertant colony

when exposed to the compound at concentration level d,

P(d), as

m ¼ N0PðdÞ ð7Þ

We will discuss the two simplest cases, when the bacterial

cells have enough histidine/tryptophan supply for just one

generation and the compound is mutagenic for one

generation. The first case is when the compound is toxic

for one generation. The second case is when it is toxic for

infinitely many generations. If a compound is toxic only

for one generation, then P(d) is

PðdÞ ¼ ð1 � e�ðaþbdÞÞe�gd ð8Þ

where a and b are positive and g is nonnegative. However,

if it has long-lasting toxicity, then P(d) is

PðdÞ ¼ ð1 � e�ðaþbdÞÞ½2 � e�gd�þ ð9Þ

where [y] + = max(y, 0). The spontaneous reverse

mutation rate, mutagenicity, and toxicity are modeled

through parameters a, b, and g. The evaluation of the

Ames data is based on Models 8 and 9 in combination

with Eq. 7 and the negative binomial distribution in Eq. 3

through parameters a, b, g, and c. If there is no toxicity,

then g = 0 and Models 8 and 9 are identical. Mutage-

nicity of a compound is evaluated by testing the null

hypothesis of H0:b = 0 against the alternative of

Ha:b > 0. Margolin et al.[16] approximated the distri-

bution of the ratio of the maximum likelihood estimate of

b, b̂, and its standard error, SEðb̂Þ, by a standard normal

distribution. The SEðb̂Þ was obtained based on the Fisher

information matrix evaluated at the maximum likelihood

estimates of a, b, g, and c. However, further research by

Margolin et al.[22] identified problems with the two

models. Inflated Type I error rates were reported for both

models. Their proposal to contain the Type I error rates

was performing a pretest on g = 0 to identify the

presence of toxicity. The pretest of H0:g = 0 against

Ha:g > 0 is a likelihood ratio test:

lg ¼ 2ðLða; b; g; cÞ � Lða; b; 0; cÞÞ ð10Þ

where L(a, b, g; c) is the maximum of the log-likelihood

of the data. If the toxicity is not supported by the data,

then the mutagenicity parameter b will be tested by the

likelihood ratio test in Eq. 10 constrained on g = 0:

lg ¼ 2ðLða; b; 0; cÞ � Lða; 0; 0; cÞÞ ð11Þ

Otherwise, the mutagenicity parameter b will be tested by

lg ¼ 2ðLða; b; g; cÞ � Lða; 0; g; cÞÞ ð12Þ

Histidine/tryptophan is necessary for the growth of

auxotrophic cells. In the biologically based models

described in the foregoing, amino acid diffusion was not

considered and each cell will have a local supply of the

essential amino acid. However, if the amino acids do

diffuse through the plate agar, then the revertant counts

should be a function of the amount of histidine/tryptophan

as well. Krewski et al.[23] proposed to generalize the

biologically based models by Margolin et al.[16] to allow

for diffusion of the amino acids in an agar plate.

DISCUSSION

The original and modified two- or threefold rules are

simple to use and have been compared to other methods in

Refs. [21,28]. Chu et al.[21] reported favorable perform-

ance of the modified twofold rule based on results from

2362 tests performed in four laboratories on 17 test

articles. Define the false positive and false negative as

follows:

False positive = negative tests determined by consensus

of microbiologists that is concluded positive using the

decision rule.

False negative = positive tests determined by consensus

of microbiologists that is concluded negative using the

decision rule.

Among the methods that gave higher false-positive

conclusions than false-negative conclusions is the modi-

fied twofold rule, which gave 4.1% false-positive and

1.8% false-negative results and the positive linear trend

test described in the section ‘‘Linear Regression on

Logarithmically Transformed Revertant Counts,’’ which

gave 20.0% false-positives and 0.4% false-negative

results. If the modified twofold rule is supplemented

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with a modified threefold rule, one would expect the

proportion of false positives to decrease further.

For situations where there is no convincing evidence

for the assumptions of Poisson distribution, overdisper-

sion in the Poisson distribution, and the normality distri-

bution of the transformed data, the nonparametric me-

thods discussed in the section ‘‘Nonparametric

Methods’’—namely, the Jonckheere test and the method

proposed by Wahrendorf et al.—seem plausible. The

latter also provide a descriptive quantity for assessment of

the types of increasing trends and the possibility of down-

turn due to toxicity. An example of revertant counts of

strain TA100 in triplicate of (66, 82, 64), (66, 73, 87), (89,

84, 86),(76, 83, 87), (87, 103, 91), and (89, 98, 82) cor-

responding to the concentration levels of 0, 10, 30, 50, 100,

and 300 mg per plate, respectively, was taken from Stead

et al.[14] The nonparametric method by Wahrendorf

concluded a highly significant mutagenic effect with

p value = 0.0028 based on normal approximation and

p = 0.0016 based on critical values established by

Monte Carlo simulations. If the modified twofold rule

were applied to the data, no mutagenic effects would

be concluded.

Parametric methods with the assumptions of Poisson

distribution with or without extra variation and negative

binomial distribution of the revertant counts utilize sta-

tistical tools in modeling the counts for mutagenicity,

toxicity, and dispersion, whereas the modified twofold

rule calls only for simple averages of the revertant counts.

Although the modified twofold rule demonstrated good

agreement with the consensus of the microbiologists in

the NCI/NTP study,[21] it was considered too conservative

by statisticians in general. It is clear that if the statistical

methods are adopted, then there will be a great deal of

statistically significant findings than using the modified

twofold and threefold rules. To address the differences in

the mutagenicity of compounds using statistical evalu-

ation and biological evaluation, several issues merit

further discussion here:

1. The use of historical control data.

2. The toxicity threshold of a bacterial cell to a test

article.

3. Extra-Poisson variation in the revertant counts.

4. The amount of histidine/tryptophan provided.

5. The relationship between statistical significance and

biological significance.

Clearly, these issues are all interrelated and, therefore,

the discussion may not be in the order listed here.

Because, in practice, most laboratories conduct Ames

tests in triplicate, it is difficult to identify if extra-Poisson

variation is present in the revertant counts within each

experiment. A historical database for negative control

data should be a must for examining the assumption of

excessive variation in the revertant counts. In addition,

a historical database can provide a base range for the

evaluation of compounds that may yield statistical sig-

nificance that is not biologically important. Because there

may be variations among various laboratories, it is best

for each laboratory to establish its own database for the

historical negative control.

The toxicity threshold of a bacterial cell to a test article

may be determined using the rule described by Chu et al.

or by 50–90% lethality. In other words, the number of

revertants in the treated plates has to be reasonably low to

indicate a toxic effect. Statistical methods can then be

applied without modeling the toxic effects. However, if

the rules are not accepted by the regulatory agencies,

statistical modeling may be the best way to determine the

presence of the toxic effects.

Biologically based models for different combinations

of mutagenicity and toxicity lead to different models.

How one determines the number of generations that the

trace amino acid supply will last, the number of gene-

rations the compound will be mutagenic, and the number

of generations the compound will be toxic is unclear.

CONCLUSION

At this point, no consensus has been reached on statistical

methods for analyzing and interpreting the Ames data.

This is reflected in the ICH guideline for genotoxi-

city,[5,29,30] which does not mention any statistical me-

thods for the evaluation of the test results. Considering

the small set of numbers that the Ames test provides for

each bacterial strain, statistical methods designed to

evaluate the mutagenic effects should reflect the bio-

logical significance to be of any help to microbiologists.

Statistical methods that find biologically small increases

statistically significant with small p values are not

desirable and may slow the development of a compound

unnecessarily. Any statistical methods recommended for

the routine data analysis for the Ames test should be

validated by a collection of compounds with known

mutagenicity. A historical database is a must in the

evaluation of the mutagenicity of compounds and should

be established in each laboratory. When a historical

database is not available, nonparametric approaches may

be a better choice than parametric methods. Statistical

methods should support microbiologists’ findings when

the effects, mutagenic or nonmutagenic, are clear, and

should guide scientists when the effects are not clear.

Because the modified twofold and threefold rules seem to

agree well with the consensus of microbiologists,[21]

further work in this area is needed to compare the

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proposed statistical methods with the modified twofold

and threefold rules based on known compounds.

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