Archtvu of
Arch. Toxicol. 38, 27-34 (1977)
TOXICOLOGY 9 by Springer-Verlag 1977
Small Numbers in Mutagenieity Tests* Alfred Grafe and Joachim Vollmar Medizinische Forschung, Boehringer Mannheim GmbH, Sandhofer Straf3e 112, D-6800 Mannheim 13, Federal Republic of Germany
Abstract. Experimental control material for statistical analysis of the results of the micronuclei test in the mouse (NMRI strain) and the Chinese hamster and for the host-mediated assay in the mouse (NMRI strain) using auxotrophic bacterial strains are presented. The binomial distribution of the micronuclei makes it possible to analyse the sample size according to the formula of Cochran and Cox (1957). For the host-mediated assay, the experimental principles are given which make it possible to evaluate the results obtained even with a weakly mutagenic, unknown substance. Critical points in comparative tests are not only the methodological questions, but also pharmacokinetic problems of the substance being tested which can only be clarified in the species used for the mutagenicity test. If this is ignored then even experimentally based findings can only be recorded as speculations. Key words: Mutagenicity tests - Micronuclei test - Host-mediated assay Comparative mutagenicity tests - Statistics in mutagenicity.
Zusammenfassung. Das experimenteUe Kontrollmaterial zur statistischen Auswertung der Ergebnisse des Mikrokerntests an der Maus (Stamm NMRI) und dem Chinesischen Hamster sowie des Host-mediated assay an der Maus (Stamm NMRI) bei Verwendung auxotropher Bakterienst/imme werden vorgelegt. Die binomiale Verteilung der Mikrokerne erm6glicht ihre Auswertung nach der Formel von Cochran und Cox (1957). F/ir den Host-mediated assay werden die experimentellen Grundlagen genannt, die eine Auswertbarkeit erzielter Ergebnisse auch mit schwach mutagenen unbekannten Substanzen erm6glichen. Kritische Punkte in Vergleichstesten sind nicht nur methodische Fragen sondern pharmakokinetische Probleme der Pr/ifsubstanz, die nur in der im Mu* Presented at the 3rd Meeting of the Gesellschaftf/Jr Umwelt-Mutationsforschung e. V., Neuherberg, July i-2, 1976
28
A. Grafe and J. Vollmar tagenit/itstest verwendeten Spezies aufgekl~irt werden k~Snnen. Werden diese Probleme ignoriert, dann sind auch experimentell begr/indete Feststellungen nur als Vermutungen zu bewerten.
The desire to be able to detect in our environment the greatest number of mutagenic factors in the shortest possible time led to the development of a series of test systems which, with the aid of checks using strongly mutagenic substances, were recommended as valuable for routine tests. However, what is of only minor importance in the development of a test method with known, strongly mutagenic agents becomes a problem in industrial routine tests with unknown substances, namely the reliability of the deductions. In this respect, we as scientists regard the two possible errors, i.e. declaring a mutagenic substance as non-mutagenic and a non-mutagenic substance as mutagenic, as being equally important. For each of the test systems used the question arises as to whether a test procedure developed with a strongly mutagenic substance can be adopted without alteration. This applies not only for the testing periods and doses of the substance to be tested, but also for the number of animals to be used, the bacterial nutrient media, the testing of the nuclei, etc. In addition, the procedure for evaluating the results obtained must also be critically analysed. In doing this, one rapidly realizes that the uncritical adoption of test methods developed with strongly mutagenic substances for mutagenicity testing of unknown substances contains a hidden, but marked risk of false assessment. The present paper is concerned with the micronuclei test in the mouse and Chinese hamster and with the host-mediated assay using auxotrophic bacterial strains. It is intended to show that it is necessary to get away from small numbers in order to achieve the reliability in the assessment of an unknown substance.
Materials and Methods Material
For all experiments mice of the NMRI strain and Chinese hamsters were used. At the start of the experiments, the weight of the mice was between 25 and 32 g and the age of the hamsters between 12 and 15 weeks.
Methods Micronuclei Test. The method used has been described by Schmid (1975). At least 10,000 polychro-
matic erythrocytes were tested per animal. Host-Mediated Assay. The test was carried out with the auxotrophic strain of Salmonellatyphimurium
G 46 (his-) using the singlepoint procedure (Gabridge and Legator, 1969; Propping et al., 1972) and a linear test (Grafe et al., 1975).
Small Numbers in Mutagenicity Tests
29
Statistical Analysis. The statistical analysis to answer the question, "What is the lowest number of animals that must be used in the micronuclei test and the host-mediated assay?" is based on the following experimental material. 1. Micronuclei test in the mouse (NMRI strain): 5 males and 5 females, each with 25,000 polychromatic erythrocytes; 3 males and 3 females, each with 10,000 polychromatic erythrocytes. 2. Micronuclei test, Chinese hamster: 5 males and 5 females, each with 25,000 polychromatic erythrocytes; 7 males and 4 females, each with 10,000 polychromatic erythrocytes. 3. Host-mediated assay in the mouse (NMRI strain): 295 control animals included in 13 experiments were evaluated. In the micronuclei test, the binomial distribution of the micronuclei was tested with the aid of the X 2 test and the approximate estimation of the sample size was carried out according to a formular given by Cochran and Cox (1957). For the host-mediated assay, the sample size was calculated with the aid of a non-central tdistribution (Mace, 1964).
Experimental Section Micronuclei Test For the micronuclei analysis of bone marrow preparations, Schmid (1975) recommends 1000 polychromatic erythrocytes per animal with 5 animals per dose. Whilst he recommends, it is true, an increase in the size of the experiment in certain cases, he does not give any definite numbers. Miller (1973) recommended the testing of 2 0 0 0 - 5 0 0 0 erythrocytes, but limited the n u m b e r of animals to 2 - 3 animals per dose level. Weber et al. (1975) came to the conclusion, after testing strongly mutagenic substances, that one should test at least 5 animals and 2000 polychromatic cells each if one wishes to demonstrate a doubling of the micronuclei in comparison with controls as a mutagenic substance effect. As these recommendations are not based on experimental and statistical grounds we attempted with experiments in mice and Chinese hamsters by statistical analysis of the results to provide a basis for the necessary extent of the micronuclei test. F o r the micronuclei, which were found in 310,000 polychromatic erythrocytes from mice and in 360,000 from Chinese hamsters, there was homogeneity in the animal material. Table 1. Extent of the micronucleianalysis in polychromatic erythrocytes of mice (NMRI) and Chinese hamsters with a probability of error of 0.05 Spontaneous rate %
0.05 0.1 0.2 0.3
Number of polychromatic erythrocytes to be examined with an increase in the spontaneous rate by a factor of a 2
3
4
5
6
63,000 31,500 15,700 10,500
20,200 10,100 5,030 3,350
10,800 5,400 2,690 1,790
7,070 3,530 1,760 1,170
5,140 2,570 1,280 851
a The values have been calculated by Dipl.-Math.J. Kr/iger, HumangenetischesInstitut der Universit~it Heidelberg, and are taken from a comprehensive table
30
A. Grafe and J. Vollmar
As the micronuclei can be regarded as being binomially distributed both in the N M R I mice and in the Chinese hamsters, the sample size was calculated by the formula given by Cochran and Cox (1957). The numbers of polychromatic erythrocytes given for the test are minimum values for a selected probability of error of 0.05. In both of the species tested by us, the spontaneous rate was about 0.08%. If one follows Schmid's proposals, then we could demonstrate a substance-induced 5-fold increase in micronuclei as a significant difference. In Miller's opinion in 3 • 5000 polychromatic erythrocytes it would be possible to detect an increase by a factor of 3, whilst we were able, following the recommendation of Legator's group, to demonstrate doubling only with a spontaneous rate of 0.3% and higher. Until it will be possible to clarify experimentally the question of how the various factors influence the necessary number of animals, we shall test 6 animals per dose.
Host-Mediated Assay In the method published by Gabridge and Legator (1969), which was recommended as a rapid test, both mice and bacteria were used. Mice exhibit a wide range of variation not only with regard to the bacterial multiplication, but also in their reaction to the chemical substances, which can be seen from any toxicity test. The results of the host-mediated assay are furthermore affected by the errors of bacterial counting. As both errors can be determined, the unknown factors to be investigated are concentrated on the properties of the test substance. This generally rarely has an exclusive mutagenic activity. More often pharmacological, toxicological and antibacterial properties may be present in varying degrees and can affect the test for mutagenic action in many ways. It should be stated from the very start that the results of mutagenic tests in hostmediated assay using bacteria is of doubtful worth if only 3 or 4 animals per group are used and no description of the experimental procedure is given that could be repeated. But how many animals are actually necessary? We investigated this by means of the results that we have obtained over a period of 3 years under our experimental conditions, i.e. the same strain of animals, the same laboratory assistant. The error of bacterial counting at 0.90 probability was 10% using > 5 test plates/animal. The logarithmic bacterial counts of the N M R I strain had an average standard deviation of S ~ 0.20. The results of the sample size analyses are shown in the Tables 2 and 3. With given probabilities of error the necessary number of animals increases with increasing variability of the animal material and decreasing mutagenicity of the test substance. The use of small numbers of animals is only justified when a strongly mutagenic substance is tested with a very reliable bacterial count in a species with a low degree of variability. With a constant variability of the animal material the necessary number of animals rises with reduced probabilities of error and reduced mutagenicity of the substance being tested. The use of a low number of animals is only possible if a
Small Numbers in Mutagenicity Tests
31
Table 2. Relationship between the variability of the mouse strain NMRI, the mutation factor and the necessary number of animals in the host-mediated assay --
S
Necessary number of animals for a mutation factor
0.10 0.15 0.20 0.25 0.30
15 33 58 91 130
Probabilities of error
7 14 24 37 52 rx =
=
5 9 15 23 33
4 7 12 18 25
4 6 10 14 20
4 4 6 9 13
0.05
Table 3. Relationship between the probabilities of error, the mutation factor and the necessary number of animals of the mouse strain NMRI
Probability of error
Necessary number of animals with a mutation factor of
a
2
= /l)
3
4
5
6
10
strongly mutagenic substance is tested with the usual probability of error of 0.05 or if only a low reliability of the assessment is required.
Discussion From the statistical analysis of the results of the micronuclei test and the hostmediated assay we come to the conclusion that for both of these test procedures there does not exist a fixed number for the sample size of animals. The number of animals required depends on several factors. In the micronuclei test it is mainly the spontaneous rate in the control animals. When using mice and Chinese hamsters the microscopic determination of micronuclei is scarely subjected to error, assuming that a trained assistant carries out the microscopy. In the host-mediated assay, the results are compounded with further uncertainty owing to the error in bacterial counting. Anyone who wishes to assess the presence or absence of mutagenicity of an unknown substance must know these errors before he starts to test the substance. Only then he can decide what is the minimum number of animals at a chosen probability of error that is necessary in order to be able to determine a weak mutagenic action of an unknown substance. If one should be required to give such a number for both test systems, then from our experience the following must be said:
32
A. Grafe and J. Vollmar
Micronuclei Test In the mutagenicity test for micronuclei using mice or Chinese hamsters 6 animals per experimental group should be used until more precise data on the necessary number of animals has been obtained. The number of polychromatic erythrocytes required can be calculated by the formula of Cochran and Cox (1957). With probabilities of error o~ =/~ = 0.05 and a spontaneous rate of 0.1% this would be, for a treatment dose and an equally large control, a total of at least 12x 5000 = 60,000 polychromatic erythrocytes if one wishes to demonstrate a doubling in the mutation factor. The time necessary for such an investigation is about 3 - 4 working days.
Host-Mediated Assay The possibilities of error in the host-mediated assay are, in contrast to the micronuclei test, increased by the error in bacterial counting. This error must be known before one starts to test the substance as this also has an influence on the determination of the variability of the animal material. The variability in turn has a considerable influence on the necessary number of animals. The following Table 4 shows the numbers of animals per group that are necessary for the host-mediated assay under achievable conditions. The statistical basis for the host-mediated assay will be reported in special publications (Lorenz et al., 1977 and VoUmar et al. in prep.). With acceptable probabilities of error of 0.05 we are, under our working conditions, at best in the position to detect a mutagenic effect of the substance if the substance-induced mutation factor is at least 3, as we have to keep the total number of animals per day to less than 50. If we are unable to employ more than two assistants for this purpose, then the mutation factor 4 is the achievable limit - and this is usually the case. This means 15 animals per group. The numbers of animals given in the literature assume a considerably lesser degree of variability in the animals than that in the NMRI strain, an almost errorfree bacterial count and a mutation factor of at least 8. As these three conditions are not given simultaneously, the correctness of the conclusions drawn in the corresponding papers and publications with the use of lower numbers of animals must be subjected to doubt. Numbers of animals of less than 10 per substance dose must be regarded as low, if precise data on the errors involved are not reported.
Table 4. Necessary number of animals per group in the host-mediated assay under achievable test conditions s
0.20
Probabilities of error ~r = [~
Necessarynumber of animals for a mutation factor of 2
3
4
5
6
7
8
9
10
0.05
58
24
15
12
10
8
7
7
6
Small Numbers in Mutagenicity Tests
33
But not only the results that are obtained with one test method must be doubted if necessary experimental principles are not observed. If one compares two test methods with the aid of substances which exert their mutagenic action on the same organ, then the experimental principles for both methods must be worked out and observed. Even more difficult are comparative tests with methods which exert their actions on different organs. For this, not only the methodological conditions must be developed, but also a thorough knowledge of the substance itself is necessary. This applies not only to precise knowledge of the site of mutagenic action of the test substance, but also, to the same degree, for its quantitative distribution in those organs that are to be used for the test. Pharmacokinetic studies show us an interplay of the various factors that act within the body on a substance that has been administered and it is therefore impossible to draw analogous conclusions on the organ behaviour of a substance from that of its effect on another. Similarly, it is also impossible to draw conclusions on the behaviour of a substance in one species from that of its behaviour in another. There is neither an even distribution of the substance in the body nor are there constant concentrations in the individual organs (Steiner and Garbe, 1976). If one wishes to compare the sensitivities of test methods, then one is obliged to determine the concentrations of the substance at the time of the test in the organs used for the test. If one does not do this (and this is generally the case), then the results are merely a claim or even a false assessment if no statistical significant mutagenic effect was found. In summary, it can be said that the in vivo testing of unknown substances for possible mutagenic action requires, not only in the micronuclei test and host-mediated assay, a carefully observation of the experimental principle so that a result is not only obtained, but can also be evaluated. If these conditions are ignored, then even experimentally based findings can only be recorded as speculations.
References Cochran, W. G., Cox, G. M.: Experimental designs. New York-London: Wiley 1957 Gabridge, M. G., Legator, M. S.: A host-mediated microbial assay for the detection of mutagenic compounds. Proc. Soc. exp. Biol. (N.Y.) 130, 831-834 (1969) Grafe, A., Lorenz, R. J., Vollmar, J.: Testing the mutagenic potency of chemical substances in a linear host-mediated assay. I. Experimental microbiological basis. Mutation Res. 31, 205-216 (1975) Lorenz, R. J., Vollmar, J., Grafe, A.: Testing the mutagenic potency of chemical substances in a linear host-mediated assay. II. Comparison with the conventional host-mediated assay and statistical evaluation of the data. Mutation Res. (in press) (1977) Mace, A. E.: Sample size determination, pp. 77-80. New York: Reinhold 1964 Miller, R. C.: The micronucleus test as an in vivo cytogenetic method. Environm. Hlth Perspektives 6, 167--170 (1973) Propping, P., R6hrborn, G., Buselmaier, W.: Comparative investigations on the chemical induction of point mutations and dominant lethal mutations in mice. Molec. gen. Genet. 117, 197-209 (1972) Schmid, W.: Der Mikrokerntest. DFG, Mutagenit~itspr/ifung 1975. Kommission f/Jr Mutagenit~itsfragen, Mitteilung III, S. 53-61
34
A. Grafe and J. Vollmar
Steiner, K., Garbe, A.: Organverteilung von 14C-Pramiverin im Organismus der Ratte. ArzneimittelForsch. 26, 709-716 (1976) Vollmar, J., Grafe, A.: The micronuclei test. In: Statistics in testing mutagenicity (J. Vollmar, R. J. Lorenz, eds.). Stuttgart: Fischer 1977 Weber, E., Bidwell, K., Legator, M. S.: An evaluation of the micronuclei test using triethylenemelamine, trimethylphospbate, hycanthone and niridazole. Mutation Res. 28, 101-106 (1975) Received December 21, 1976
Arch. Toxicol. 38, 27-34 (1977)
TOXICOLOGY 9 by Springer-Verlag 1977
Small Numbers in Mutagenieity Tests* Alfred Grafe and Joachim Vollmar Medizinische Forschung, Boehringer Mannheim GmbH, Sandhofer Straf3e 112, D-6800 Mannheim 13, Federal Republic of Germany
Abstract. Experimental control material for statistical analysis of the results of the micronuclei test in the mouse (NMRI strain) and the Chinese hamster and for the host-mediated assay in the mouse (NMRI strain) using auxotrophic bacterial strains are presented. The binomial distribution of the micronuclei makes it possible to analyse the sample size according to the formula of Cochran and Cox (1957). For the host-mediated assay, the experimental principles are given which make it possible to evaluate the results obtained even with a weakly mutagenic, unknown substance. Critical points in comparative tests are not only the methodological questions, but also pharmacokinetic problems of the substance being tested which can only be clarified in the species used for the mutagenicity test. If this is ignored then even experimentally based findings can only be recorded as speculations. Key words: Mutagenicity tests - Micronuclei test - Host-mediated assay Comparative mutagenicity tests - Statistics in mutagenicity.
Zusammenfassung. Das experimenteUe Kontrollmaterial zur statistischen Auswertung der Ergebnisse des Mikrokerntests an der Maus (Stamm NMRI) und dem Chinesischen Hamster sowie des Host-mediated assay an der Maus (Stamm NMRI) bei Verwendung auxotropher Bakterienst/imme werden vorgelegt. Die binomiale Verteilung der Mikrokerne erm6glicht ihre Auswertung nach der Formel von Cochran und Cox (1957). F/ir den Host-mediated assay werden die experimentellen Grundlagen genannt, die eine Auswertbarkeit erzielter Ergebnisse auch mit schwach mutagenen unbekannten Substanzen erm6glichen. Kritische Punkte in Vergleichstesten sind nicht nur methodische Fragen sondern pharmakokinetische Probleme der Pr/ifsubstanz, die nur in der im Mu* Presented at the 3rd Meeting of the Gesellschaftf/Jr Umwelt-Mutationsforschung e. V., Neuherberg, July i-2, 1976
28
A. Grafe and J. Vollmar tagenit/itstest verwendeten Spezies aufgekl~irt werden k~Snnen. Werden diese Probleme ignoriert, dann sind auch experimentell begr/indete Feststellungen nur als Vermutungen zu bewerten.
The desire to be able to detect in our environment the greatest number of mutagenic factors in the shortest possible time led to the development of a series of test systems which, with the aid of checks using strongly mutagenic substances, were recommended as valuable for routine tests. However, what is of only minor importance in the development of a test method with known, strongly mutagenic agents becomes a problem in industrial routine tests with unknown substances, namely the reliability of the deductions. In this respect, we as scientists regard the two possible errors, i.e. declaring a mutagenic substance as non-mutagenic and a non-mutagenic substance as mutagenic, as being equally important. For each of the test systems used the question arises as to whether a test procedure developed with a strongly mutagenic substance can be adopted without alteration. This applies not only for the testing periods and doses of the substance to be tested, but also for the number of animals to be used, the bacterial nutrient media, the testing of the nuclei, etc. In addition, the procedure for evaluating the results obtained must also be critically analysed. In doing this, one rapidly realizes that the uncritical adoption of test methods developed with strongly mutagenic substances for mutagenicity testing of unknown substances contains a hidden, but marked risk of false assessment. The present paper is concerned with the micronuclei test in the mouse and Chinese hamster and with the host-mediated assay using auxotrophic bacterial strains. It is intended to show that it is necessary to get away from small numbers in order to achieve the reliability in the assessment of an unknown substance.
Materials and Methods Material
For all experiments mice of the NMRI strain and Chinese hamsters were used. At the start of the experiments, the weight of the mice was between 25 and 32 g and the age of the hamsters between 12 and 15 weeks.
Methods Micronuclei Test. The method used has been described by Schmid (1975). At least 10,000 polychro-
matic erythrocytes were tested per animal. Host-Mediated Assay. The test was carried out with the auxotrophic strain of Salmonellatyphimurium
G 46 (his-) using the singlepoint procedure (Gabridge and Legator, 1969; Propping et al., 1972) and a linear test (Grafe et al., 1975).
Small Numbers in Mutagenicity Tests
29
Statistical Analysis. The statistical analysis to answer the question, "What is the lowest number of animals that must be used in the micronuclei test and the host-mediated assay?" is based on the following experimental material. 1. Micronuclei test in the mouse (NMRI strain): 5 males and 5 females, each with 25,000 polychromatic erythrocytes; 3 males and 3 females, each with 10,000 polychromatic erythrocytes. 2. Micronuclei test, Chinese hamster: 5 males and 5 females, each with 25,000 polychromatic erythrocytes; 7 males and 4 females, each with 10,000 polychromatic erythrocytes. 3. Host-mediated assay in the mouse (NMRI strain): 295 control animals included in 13 experiments were evaluated. In the micronuclei test, the binomial distribution of the micronuclei was tested with the aid of the X 2 test and the approximate estimation of the sample size was carried out according to a formular given by Cochran and Cox (1957). For the host-mediated assay, the sample size was calculated with the aid of a non-central tdistribution (Mace, 1964).
Experimental Section Micronuclei Test For the micronuclei analysis of bone marrow preparations, Schmid (1975) recommends 1000 polychromatic erythrocytes per animal with 5 animals per dose. Whilst he recommends, it is true, an increase in the size of the experiment in certain cases, he does not give any definite numbers. Miller (1973) recommended the testing of 2 0 0 0 - 5 0 0 0 erythrocytes, but limited the n u m b e r of animals to 2 - 3 animals per dose level. Weber et al. (1975) came to the conclusion, after testing strongly mutagenic substances, that one should test at least 5 animals and 2000 polychromatic cells each if one wishes to demonstrate a doubling of the micronuclei in comparison with controls as a mutagenic substance effect. As these recommendations are not based on experimental and statistical grounds we attempted with experiments in mice and Chinese hamsters by statistical analysis of the results to provide a basis for the necessary extent of the micronuclei test. F o r the micronuclei, which were found in 310,000 polychromatic erythrocytes from mice and in 360,000 from Chinese hamsters, there was homogeneity in the animal material. Table 1. Extent of the micronucleianalysis in polychromatic erythrocytes of mice (NMRI) and Chinese hamsters with a probability of error of 0.05 Spontaneous rate %
0.05 0.1 0.2 0.3
Number of polychromatic erythrocytes to be examined with an increase in the spontaneous rate by a factor of a 2
3
4
5
6
63,000 31,500 15,700 10,500
20,200 10,100 5,030 3,350
10,800 5,400 2,690 1,790
7,070 3,530 1,760 1,170
5,140 2,570 1,280 851
a The values have been calculated by Dipl.-Math.J. Kr/iger, HumangenetischesInstitut der Universit~it Heidelberg, and are taken from a comprehensive table
30
A. Grafe and J. Vollmar
As the micronuclei can be regarded as being binomially distributed both in the N M R I mice and in the Chinese hamsters, the sample size was calculated by the formula given by Cochran and Cox (1957). The numbers of polychromatic erythrocytes given for the test are minimum values for a selected probability of error of 0.05. In both of the species tested by us, the spontaneous rate was about 0.08%. If one follows Schmid's proposals, then we could demonstrate a substance-induced 5-fold increase in micronuclei as a significant difference. In Miller's opinion in 3 • 5000 polychromatic erythrocytes it would be possible to detect an increase by a factor of 3, whilst we were able, following the recommendation of Legator's group, to demonstrate doubling only with a spontaneous rate of 0.3% and higher. Until it will be possible to clarify experimentally the question of how the various factors influence the necessary number of animals, we shall test 6 animals per dose.
Host-Mediated Assay In the method published by Gabridge and Legator (1969), which was recommended as a rapid test, both mice and bacteria were used. Mice exhibit a wide range of variation not only with regard to the bacterial multiplication, but also in their reaction to the chemical substances, which can be seen from any toxicity test. The results of the host-mediated assay are furthermore affected by the errors of bacterial counting. As both errors can be determined, the unknown factors to be investigated are concentrated on the properties of the test substance. This generally rarely has an exclusive mutagenic activity. More often pharmacological, toxicological and antibacterial properties may be present in varying degrees and can affect the test for mutagenic action in many ways. It should be stated from the very start that the results of mutagenic tests in hostmediated assay using bacteria is of doubtful worth if only 3 or 4 animals per group are used and no description of the experimental procedure is given that could be repeated. But how many animals are actually necessary? We investigated this by means of the results that we have obtained over a period of 3 years under our experimental conditions, i.e. the same strain of animals, the same laboratory assistant. The error of bacterial counting at 0.90 probability was 10% using > 5 test plates/animal. The logarithmic bacterial counts of the N M R I strain had an average standard deviation of S ~ 0.20. The results of the sample size analyses are shown in the Tables 2 and 3. With given probabilities of error the necessary number of animals increases with increasing variability of the animal material and decreasing mutagenicity of the test substance. The use of small numbers of animals is only justified when a strongly mutagenic substance is tested with a very reliable bacterial count in a species with a low degree of variability. With a constant variability of the animal material the necessary number of animals rises with reduced probabilities of error and reduced mutagenicity of the substance being tested. The use of a low number of animals is only possible if a
Small Numbers in Mutagenicity Tests
31
Table 2. Relationship between the variability of the mouse strain NMRI, the mutation factor and the necessary number of animals in the host-mediated assay --
S
Necessary number of animals for a mutation factor
0.10 0.15 0.20 0.25 0.30
15 33 58 91 130
Probabilities of error
7 14 24 37 52 rx =
=
5 9 15 23 33
4 7 12 18 25
4 6 10 14 20
4 4 6 9 13
0.05
Table 3. Relationship between the probabilities of error, the mutation factor and the necessary number of animals of the mouse strain NMRI
Probability of error
Necessary number of animals with a mutation factor of
a
2
= /l)
3
4
5
6
10
strongly mutagenic substance is tested with the usual probability of error of 0.05 or if only a low reliability of the assessment is required.
Discussion From the statistical analysis of the results of the micronuclei test and the hostmediated assay we come to the conclusion that for both of these test procedures there does not exist a fixed number for the sample size of animals. The number of animals required depends on several factors. In the micronuclei test it is mainly the spontaneous rate in the control animals. When using mice and Chinese hamsters the microscopic determination of micronuclei is scarely subjected to error, assuming that a trained assistant carries out the microscopy. In the host-mediated assay, the results are compounded with further uncertainty owing to the error in bacterial counting. Anyone who wishes to assess the presence or absence of mutagenicity of an unknown substance must know these errors before he starts to test the substance. Only then he can decide what is the minimum number of animals at a chosen probability of error that is necessary in order to be able to determine a weak mutagenic action of an unknown substance. If one should be required to give such a number for both test systems, then from our experience the following must be said:
32
A. Grafe and J. Vollmar
Micronuclei Test In the mutagenicity test for micronuclei using mice or Chinese hamsters 6 animals per experimental group should be used until more precise data on the necessary number of animals has been obtained. The number of polychromatic erythrocytes required can be calculated by the formula of Cochran and Cox (1957). With probabilities of error o~ =/~ = 0.05 and a spontaneous rate of 0.1% this would be, for a treatment dose and an equally large control, a total of at least 12x 5000 = 60,000 polychromatic erythrocytes if one wishes to demonstrate a doubling in the mutation factor. The time necessary for such an investigation is about 3 - 4 working days.
Host-Mediated Assay The possibilities of error in the host-mediated assay are, in contrast to the micronuclei test, increased by the error in bacterial counting. This error must be known before one starts to test the substance as this also has an influence on the determination of the variability of the animal material. The variability in turn has a considerable influence on the necessary number of animals. The following Table 4 shows the numbers of animals per group that are necessary for the host-mediated assay under achievable conditions. The statistical basis for the host-mediated assay will be reported in special publications (Lorenz et al., 1977 and VoUmar et al. in prep.). With acceptable probabilities of error of 0.05 we are, under our working conditions, at best in the position to detect a mutagenic effect of the substance if the substance-induced mutation factor is at least 3, as we have to keep the total number of animals per day to less than 50. If we are unable to employ more than two assistants for this purpose, then the mutation factor 4 is the achievable limit - and this is usually the case. This means 15 animals per group. The numbers of animals given in the literature assume a considerably lesser degree of variability in the animals than that in the NMRI strain, an almost errorfree bacterial count and a mutation factor of at least 8. As these three conditions are not given simultaneously, the correctness of the conclusions drawn in the corresponding papers and publications with the use of lower numbers of animals must be subjected to doubt. Numbers of animals of less than 10 per substance dose must be regarded as low, if precise data on the errors involved are not reported.
Table 4. Necessary number of animals per group in the host-mediated assay under achievable test conditions s
0.20
Probabilities of error ~r = [~
Necessarynumber of animals for a mutation factor of 2
3
4
5
6
7
8
9
10
0.05
58
24
15
12
10
8
7
7
6
Small Numbers in Mutagenicity Tests
33
But not only the results that are obtained with one test method must be doubted if necessary experimental principles are not observed. If one compares two test methods with the aid of substances which exert their mutagenic action on the same organ, then the experimental principles for both methods must be worked out and observed. Even more difficult are comparative tests with methods which exert their actions on different organs. For this, not only the methodological conditions must be developed, but also a thorough knowledge of the substance itself is necessary. This applies not only to precise knowledge of the site of mutagenic action of the test substance, but also, to the same degree, for its quantitative distribution in those organs that are to be used for the test. Pharmacokinetic studies show us an interplay of the various factors that act within the body on a substance that has been administered and it is therefore impossible to draw analogous conclusions on the organ behaviour of a substance from that of its effect on another. Similarly, it is also impossible to draw conclusions on the behaviour of a substance in one species from that of its behaviour in another. There is neither an even distribution of the substance in the body nor are there constant concentrations in the individual organs (Steiner and Garbe, 1976). If one wishes to compare the sensitivities of test methods, then one is obliged to determine the concentrations of the substance at the time of the test in the organs used for the test. If one does not do this (and this is generally the case), then the results are merely a claim or even a false assessment if no statistical significant mutagenic effect was found. In summary, it can be said that the in vivo testing of unknown substances for possible mutagenic action requires, not only in the micronuclei test and host-mediated assay, a carefully observation of the experimental principle so that a result is not only obtained, but can also be evaluated. If these conditions are ignored, then even experimentally based findings can only be recorded as speculations.
References Cochran, W. G., Cox, G. M.: Experimental designs. New York-London: Wiley 1957 Gabridge, M. G., Legator, M. S.: A host-mediated microbial assay for the detection of mutagenic compounds. Proc. Soc. exp. Biol. (N.Y.) 130, 831-834 (1969) Grafe, A., Lorenz, R. J., Vollmar, J.: Testing the mutagenic potency of chemical substances in a linear host-mediated assay. I. Experimental microbiological basis. Mutation Res. 31, 205-216 (1975) Lorenz, R. J., Vollmar, J., Grafe, A.: Testing the mutagenic potency of chemical substances in a linear host-mediated assay. II. Comparison with the conventional host-mediated assay and statistical evaluation of the data. Mutation Res. (in press) (1977) Mace, A. E.: Sample size determination, pp. 77-80. New York: Reinhold 1964 Miller, R. C.: The micronucleus test as an in vivo cytogenetic method. Environm. Hlth Perspektives 6, 167--170 (1973) Propping, P., R6hrborn, G., Buselmaier, W.: Comparative investigations on the chemical induction of point mutations and dominant lethal mutations in mice. Molec. gen. Genet. 117, 197-209 (1972) Schmid, W.: Der Mikrokerntest. DFG, Mutagenit~itspr/ifung 1975. Kommission f/Jr Mutagenit~itsfragen, Mitteilung III, S. 53-61
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A. Grafe and J. Vollmar
Steiner, K., Garbe, A.: Organverteilung von 14C-Pramiverin im Organismus der Ratte. ArzneimittelForsch. 26, 709-716 (1976) Vollmar, J., Grafe, A.: The micronuclei test. In: Statistics in testing mutagenicity (J. Vollmar, R. J. Lorenz, eds.). Stuttgart: Fischer 1977 Weber, E., Bidwell, K., Legator, M. S.: An evaluation of the micronuclei test using triethylenemelamine, trimethylphospbate, hycanthone and niridazole. Mutation Res. 28, 101-106 (1975) Received December 21, 1976
