lacI mutagenicity assay: statistical determination of sample size

Fundamental and Molecular Mechanisms of Mutagenesis

ELSEVIER

Mutation

Research

327 (1995) 201-208

Transgenic h/ZacI mutagenicity assay: statistical determination of sample size Janice D, Callahan a, Jay M. Short b2* ’ Callahan Associates Inc., 874 Candlelight Place, La Jolla. CA 92037, USA b Industrial BioCatalysis Inc., 505 Coast Blud., 4th floor, La Jolla, CA 92037, USA Received

21 April 1994; revised

17 November

1994; accepted

18 November 1994

Abstract Statistical analysis of the h/lucZ transgenic mutagenicity assay was used to determine optimal sample size and resource allocation in terms of number of animals and number of recovered target genes (recovered phage) required to demonstrate a statistically significant induction in mutant frequency. Statistical assumptions as applied to mutagenicity data are discussed for a number of frequently used statistical analyses. Log transformations are

suggested as a means of meeting statistical assumptions and examples are given on interpreting results of analyses of log transformed data. The data analyzed in this study indicate that 300 000 lambda plaques from each of five animals should be analyzed per treatment group in order to detect a doubling of mutant frequencies. Additional sensitivity is gained primarily through increase of animal number and not the number of phage rescued, due to inherent animal-to-animal variability. Keywords:

Big Blue @. , Lambda. , Log transformation;

Mutation;

1. Introduction

Recently developed transgenic animal systems utilizing recoverable shuttle vectors allow the rapid determination of tissue-specific mutant frequencies (Short et al., 1988; Gossen et al., 1989; Kohler et al., 1990, 1991). Such mutant frequency measurements can be valuable for estimating the genotoxicity of compounds. One such system for

Abbreviations: ANOVA,

forming units * Corresponding 4864. 0027-5107/95/$09.50

analysis

of variance;

pfu, plaque

author. Tel. (619) 551-4863; Fax (619) 551-

0 1995 Elsevier

SSDI 0027-5107(94)00191-X

Statistics; Variance component

measuring these frequencies is known as the Big Bluea Mouse Mutagenicity Assay (Kohler et al., 1991; reviewed in Provost et al., 1993). This system uses an E. coli lacl target gene and an cy-ZacZ reporter gene that is contained within a A phage shuttle vector and stably integrated as a head-to-tail concatemer of approximately 40 copies on mouse chromosome number four (Dycaico et al., 1994). Phenotypic mutations within the ZucI target gene are detected by recovering the A vector from isolated genomic DNA by mixing with in vitro A packaging extracts that excise the vector from the genomic DNA and package it as an infectious phage particle. These phage are then plated with E. coli cells in the

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J.D. Callahan, J.M. Short /Mutation Research 327 (1995) 201-208

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presence of the chromogenic indicator, 5-bromo4-chloro-3-indolyl-P-o-galactopyranoside (X-gal), to identify vectors containing a mutant target, lacl. Phage containing mutations within the lacl gene form blue plaques due to the expression of a facZ reporter gene while non-mutant phage form colorless plaques due to repression of the 1acZ reporter by the Lac repressor. A mutant frequency is determined from the number of mutant plaques divided by the total number of plaques analyzed. Although these mutant frequency measurements are relatively simple to obtain, there are a number of questions relating to the appropriate and/or optimal protocol for determining the mutant frequency. Some of the issues relating to assay variability for each step of the assay have recently been investigated by Piegorsch et al. (1994). In that study, no excess variability was found within packagings or within studies, however excess variability between animals was observed. In addition, experiments have been completed for the optimization and standardization of the color screening procedure that have lead to improved intra- (Rogers et al., 1995) and inter(Young et al., 1995) laboratory reproducibility. This study extends these analyses of the lambda/ZacZ system in order to gain insights into how to allocate resources between the number of animals and the number of plaques recovered per animal per tissue to determine mutant frequencies. More specifically, we address some of the statistical issues encountered and suggest solutions for some of the issues identified.

2. Materials

and methods

Data utilized in this analysis were derived from experiments by Rogers et al. (1994) and Provost et al. (1994). The procedures used to generate these data are summarized in the following sections. Animal handling B6C3Fl (Lambda LIZ: C57BL/6NTAC[LIZ] female x C3H/HeNTAC male) 7-9 week old

male mice used in these studies were raised in disease- and pathogen-free barrier facilities at Taconic Farms, NY. The animals were maintained on Teklad 4% (fat) mouse diet (Harlad Teklad). All animals used in these experiments were hemizygous for the transgene and were identified as transgenic through hybridization screening with a 32P-labeled lambda DNA probe against genomic DNA isolated from the tail. Animals were killed by cervical dislocation as dictated by the AVMA Panel on Euthanasia (1993) and all experiments were approved by the Institutional Animal Care and Use Committee. Tissue isolation and phage rescue Tissues (liver for the spontaneous study; spleen for the benzene study) were collected immediately from killed animals, wrapped in foil, and flash frozen in liquid nitrogen. DNA was isolated as previously described (Kohler et al., 1991) with minor modifications summarized below. Briefly, 0.25 cm3 tissue sections were dissociated in buffer with a Wheaton dounce homogenizer, then treated with proteinase K (2 mg/ml) and RNase ItTM (20 PI/ml) (Stratagene). Subsequently, samples were phenol/chloroform extracted and ethanol precipitated. The DNA samples were resuspended in Tris buffer (pH 7.5) at a final concentration of 0.5-l mg/ml and allowed to resuspend at room temperature for 24 h, and then stored at 4°C for up to 2 months. The DNA was packaged using a P-galactosidase deficient, single tube format packaging extract, TranspackTM, by incubating 8 ~1 of genomic DNA solution with 10 ~1 of extract at 30°C for 90 min. This was followed by adding an additional 10 ~1 of freshly thawed extract and incubating for an additional 90 min. The reaction was terminated by adding SM buffer to a final volume of 1 ml. E. coli and plating conditions SCS-8 Mcr deficient E. coli K12 cells (Kretz et al., 1991) were grown for 4 h to approximately with OD,,” = 1.5 in NZY medium supplemented maltose and Mg*+. An average of 15000 pfu were plated onto 25 cm* plates containing NZY medium with top agarose (35 ml) containing 1.5

J.D. Callahan, J.M. Short /Mutation

mg/ml of X-gal, as previously described (Rogers et al., 1995). Color control mutants CM-O and CM-l were plated in parallel to ensure screening conditions remained constant between experiments. In all experiments CM1 displayed a weak blue phenotype and the majority of the CM-O mutants were visible only with the red filter (Rogers et al., 1995). Data were generated by a single researcher using approximately 100 plates for screening of approximateIy 1.3 million pfu plated and screened per experiment over 2 days (one day plating; one day screening). Mutant

scoring procedure

All data used in this analysis were generated using coded samples that were unknown to the laboratory worker. Mutant scoring was performed as previously described and total numbers of phage plated were determined through dilution titration (Rogers et al., 19951. Spontaneous mutants were confirmed by replating. All mutant phage plaques were also isolated and stored as frozen stocks by mixing the isolated plaque with 500 ~1 of SM buffer, 50 ~1 of chloroform. Phage were allowed to elute one or more days at 4°C and, after the addition of DMSO to a final concentration of 7%, 100 ~1 of this phage solution was stored at - SO”C, as a purified frozen stock. Chemical dosing

Benzene was administered by oral gavage at 200 mg/ml, 400 mg/ml, or 750 mg/ml for five consecutive days. The spleens were harvested 14 days following the last administration, as described in the preceding Tissue isolation section. Statistical assumptions

We began with a simple question on the optimal allocation of resources: Should an investigator using Big Blue@ study few animals with many plaques per animal or many animals with fewer plaques per animal? A sample size calculation depends on and requires answers to the following: (1) Analysis to be done (i.e., hypothesis to be tested) (2) Significance level of test (typically 0.05) (3) Power of the test (typically 0.80)

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(4) Size of effect to be found significantly different (5) Variability of data Which analysis is to be done is determined by the experimental design. For example, if means of two groups are to be compared, the analysis would be a t-test; if the number of groups is larger than two then the analysis would be an analysis of variance (ANOVA); a dose-response study could be analyzed with a Iinear regression. An estimate of the variability must be obtained either through a pilot study or from the literature. For this paper, two-tailed tests with significance level at 0.05 and power at 0.80 will be assumed. That leaves the effect size as the only requirement entirely up to the investigator. A very small effect can become statistically significant if the sample size is very large. The key is to choose an obtainable effect size that is scientifically meaningful. It is a waste of resources to establish and perform an experiment which proves a meaningless difference is statistically significant. An allocation of sample size depends on relative variabilities. In this paper, sample size allocation depends on the plate-to-plate within-animal variability compared to the animal-to-animal variability. The analyses considered in this paper were t-tests (comparing a treatment group to a control group), analyses of variance (comparing more than two treatment groups), and regressions (to characterize a dose response). Each of these statistical analyses is based upon similar assumptions, which were not met by the mutagenicity data without transformation, as discussed below. The primary statistical assumptions are independent observations, normality within a group and equal variability among groups. Equal numbers of observations per group will be assumed. For a t-test, these assumptions mean mutagenicity data from the untreated animals are normally distributed (i.e., bell-shaped or Gaussian), data from the treated animals are normally distributed, and these two sets of data have the same variance. For an analysis of variance with three treatments, say A, B, and C, the assump-

204

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tions mean normality within each of the three treatments and the variances of the three treatments must be equal. For a dose-response regression, each dose level is like an ANOVA treatment. The data must be normally distributed within each dose level, and the variances within each dose level must be equal. Mutagenicity data are usually skewed, and thus non-normal, due to a lower bound at zero and to occasional observations with a large number of mutants. However, the normality requirement is the less important of the two assumptions because a large sample size will usually cause this assumption to be met (this is called the Central Limit Theorem (Cramer, 1966, p. 213)). The equality-of-variance assumption is the more important of the two and it is also not met. Mutagenicity data are Poisson distributed or worse (Margolin et al., 1989). For Poisson data, the variance equals the mean (Cramer, 1966, p. 204). ‘Worse’ means the variance is even larger than that, as in the Ames assay (Margolin et al., 1989). So, when a treatment produces a higher level of mutants, the mean will be larger and thus the variance as well. Increasing variance with increasing mean implies inequality of variances among groups. An easy way to spot unequal variances is to plot the observed data on the y-axis versus the dose level on the x-axis. Variance increasing with mean results in a plot with a funnel shape. See the Results section (Fig. 1) for an example. A common solution for violation of the equalvariance assumption is to transform the data, for example, a log transformation. The log transformation is also a normalizing transformation; outlying observations are brought in closer to the mean. The log transformation will be used in this paper. Another important advantage of log transforming mutagenicity data is in measuring the effect size which is the change in the mutant frequency in response to an increase in dose, for example. Statistically, effect size is always measured by subtracting (an additive modeI); e.g., the effect of a treatment compared to a control is the mean mutant frequency with treatment minus the mean mutant frequency with no treatment. A re-

Research 327 (1995) 201-208

searcher looking for a doubling of the mutant frequency is interested in an effect measured by a ratio (a multiplicative model). However, a doubling of mutant frequency is a difference of lag(2) for log transformed mutant frequencies {log(2X) - log(X) = log(2X/X) = lag(2)). Thus, the log transformation converts a multiplicative model (a doubling) into an additive model (an increase of lag(2)). In other words, a significant increase in mutant frequency measured as a fold induction is dependent upon the absolute mutant frequency of the control since this determines the difference or effect size. However, when using log transformations this dependence is eliminated. This is useful and important for standardizing analyses of mutational data that can vary depending on, for example, animal, tissue, sex, chemical, expression time, and laboratory performing the assay. Those conditions affecting control levels will affect the statistical power of the analysis because doubling of a larger control is a larger difference and requires a larger sample size. However, this larger sample size is not required for log transformed analyses.

3. Results Analysis of the induced data

In order to study the variance in treated studies, benzene was selected as a test mutagen for analysis of the suspected target organ, spleen. This compound is carcinogenic in rodents (IARC, 1982) and has demonstrated genotoxicity (Harper and Legator, 1987). Although the specific compound chosen for this analysis is not critical for the points of discussion, this compound does exhibit a mutagenic induction profile that is similar in terms of the funnel-shaped profile to that obtained using other compounds (Mirsalis et al., 1993; Provost et al., 1993, 1994; Provost and Short, 1994). Fig. 1 displays a plot of mutant frequency observations as a function of dose, indicated with an asterisk. There were four observations for each dose level. Some observations were so close that only one point can be seen on the graph. These data exhibit a funnel shape. The spread at the 750 mg/kg dose level is over twice

J.D. Callahan, J.M. Short /Mutation

0

100

200

300

Treatment

l

.

l

400 (Benzene.

500

600

700

800

mg/kg)

Frequency

Log(Frequency)

Fig. 1. Plot of frequency versus dose showing funnel effect. At the bottom is a plot of log (frequency) showing equal variances.

the spread at zero dose. At the bottom of the graph are displayed the log transformed data with a dot for the plot symbol. Although the relative size of the means has been maintained, the log transformed data have nearly equal variabilities. An ANOVA was used to determine if the system responded in a measurable way to high doses of toxic chemicals. The result of an ANOVA is either no differences (all means are the same) or there are at least two means different from each other. The ANOVA found significant differences, p = 0.019. The root mean square error, the average within-group standard deviation, was 0.101. A Dunnett’s multiple comparison (Miller, 1980) found both the 400 and the 750 mg/kg dose level groups were significantly different from the control group. No difference was found between the 200 mg/kg dose level and the control

Research 327 (1995) 201-208

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group. The conclusion from this analysis is that there is a measurable effect due to increased dose levels. The difference between the mean log transformed 750 mg/kg dose level data and the mean log transformed control data was 0.23044. Ten to the power 0.23044 is 1.70, indicating that the high dose level mutant frequency was 1.7 times the control rate. Ten to the power 0.23044 was used because the transformation was log base 10. Note that logarithms to any base can be used, but that base is raised to the power to find the frequency multiple. For example, if natural logs (log base e) had been used, then e to the power 0.23044 would give the frequency multiple. For illustrative purposes, the same analysis was performed on non-transformed mutant frequencies. This analysis was also significant, p = 0.0217, but the Dunnett’s multiple comparisons (Miller, 1980) found differences only between the 750 mg/kg dose level group and the control group. The 400 mg/kg dose group was not significantly different from the control group. Comparing results of the two analyses shows that not only does the log transformation meet the assumptions, it yields a more sensitive analysis, i.e., a smaller p-value and two dose groups significantly different from the control group. Depending on the induction profile and mechanism, dose-response data are often analyzed with a regression to estimate the increase in mutant frequency per increase in dose. The data discussed above were also analyzed with regression to illustrate interpreting regression results from log transformed data. Dose levels were scaled by dividing by 100 and a straight line was fitted. Note, an intercept term must always be included when fitting to log transformed data. The fitted regression equation was the following: logro(mutant

frequency)

= 0.0350 + 0.514

where D = dose level. This equation fit significantly, p = 0.0044, root mean square error = 0.104. A regression equation from log,, transformed data is interpreted in the following way: the rate multiplier is 10 raised to the power S where S is the slope of the regression line. For this data, 10 to the power 0.035 equals 1.0839, meaning for every increase in dose of 100 mg/kg,

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the frequency multiplier was 1.0839. Or, for every increase in dose of 100 mg/kg, the mutant frequency increased by (1.0839 - 1) X 100 = 8.39%. Note that this frequency increase of 8.39% does not depend on the value of mutant frequency at the lower dose level. The equation can be further used in the following ways: Expected

mean

frequency

at dose = 200:

mean mutant frequency = 5.98

at dose = 750:

~00.035x2+0.514

Expected

mutant =

3.84

1()0.035x7.5+0.514

Frequency

multiple

between

and dose = 200: .5.98/3.&I which can also be calculated 100.035x(7.5-2) = 1.56.

dose = 750 = 1.56 as:

Thus, to find the frequency multiple between two dose levels, take 10 to the power (the slope of the regression equation times the difference in the dose levels). This is what is meant by a multiplicative model-it automatically yields the frequency multiples. Analysis of the spontaneous mutation data The data from several similar experiments designed to measure spontaneous mutant frequency were analyzed to determine sample size, all yielding a similar conclusion. The data from one representative study of 10 animals all 7-9 weeks of age is presented (Piegorsch et al., 1994; Rogers et al., 1995). The original question was how to allocate resources between the number of plaques and the number of animals. Typically a researcher would perform an experiment and score all the plates produced from that experiment. It

Table 1 Variance Number

components of plaques

as a function counted

of the total number Variances Between

100000 200 000 300 000 400 000 500 000

0.0054 0.0069 0.0071 0.0032 0.0059

of plaques

of log transformed animals

was decided to use units of approximately 100 000 plaques and allocate resources between the number of units per animal and the total number of animals per treatment group. Each datum is the log transformed ratio of the number of mutants divided by the number of plaques counted in one experiment. We will call this the log mutant ratio. The purpose of allocating sample size is to minimize the variance of the effect being tested. Since log transformation has equalized variabilities between treatment groups, the variance of one treatment-group mean is being minimized. A treatment-group mean was calculated by averaging the log mutant ratios over units measured per animal and then averaging those averages over all animals. The variance of this mean is the following:

where U = the number of units per animal, A = the number of animals and a2 = variance. The variance of this mean can be minimized by increasing ZJ if the unit-within-an-animal variance is larger, or by increasing A if animal-toanimal variance is larger. Notice that increasing the number of units only reduces the first term on the right side of the equation above. After some point, increasing U further has no further effect on a:,,,. To optimize A and U simultaneously we need to estimate unit-within-an-animal variability and animal-to-animal variability. The technique to do this is called variance components analysis Gearle, 1971). Variance components were estimated for liver tissue data. Table 1 displays these components. Data for these calculations came from 10 animals

counted,

in liver tissue from 10 B6C3Fl

animals

data Within 0.0292 0.0159 0.0094 0.0077 0.0042

animal

Total variance (between + within) 0.0346 0.0228 0.0165 0.0109 0.0101

J.D. Callahan, J.M. Short /Mutation

with approximately 10 units scored per animal. These were summed until the total number of plaques just exceeded the count in the first column of Table 1 and then log,, of the mutant frequency was taken. In this fashion 10 replicates of 100000 plaques per animal were generated, five replicates of 200 000 plaques per animal were generated, and so forth up to two replicates of 500 000 plaques. For some animals there were not enough plaques scored in the experiment to exceed 500000 twice. Table 1 can be used to select the optimal number of plaques scored per animal. We used two criteria: approximate equality of the between-animal variance and the within-animal variance, and a leveling of the within-animal variance. Comparing the between-animal variance to within-animal variance in Table 1, a less than 50% difference is observed when 300000 plaques have been analyzed. In addition, there is less than a 50% decrease from the 300000 plaque level in total variance for both 400000 and 500000 plaques counted. Decreases of less than 50% are well within normal variability of variances, and therefore, there is minimal gain in seeking these small reductions in variance. On the basis of these parameters, 300000 was selected as the number of plaques to be scored. The total variance of each observation per animal is 0.0071 + 0.0094 which equals 0.0165. Since the standard deviation is the square root of the variance, the standard deviation is the square root of 0.0165 or 0.13. (Note that this compares well with the root mean square error values in the previous section.) This standard deviation can be used to calculate a sample size. As an example, we generated sample sizes for two-tailed t-tests (comparing two groups), significance level = 0.05, power = 0.80. Table 2 contains the sample sizes for detecting six frequency multiples with three different standard deviations, the 0.13 as discussed above, and a smaller and a larger standard deviation that bracket the standard deviations in Table 1. The column titled ‘Difference in logs’ contains log base 10 of the frequency multiple. For example, assuming a standard deviation of 0.13 and a frequency multiple of 2, the required sample size is five animals

Research 327 (1995) 2OI-208 Table 2 Number of animals

per group

Frequency multiple

Difference in logs

1.25 1.5 1.75 2 3 4

0.0969 0.1761 0.243 0.301 0.4771 cl.4

207

to detect

frequency

Standard

deviation

0.10

0.13

Sample 18 7 4 4 3 2

multiples

0.20

size per group 30 10 6 5 3 3

68 22 12 9 4 4

per group. Laboratories obtaining variabilities larger than those presented in this paper (Table 1) should either use sample sizes from the larger standard deviation in Table 2 or perform a similar sample size calculation.

4. Conclusions Statistical assumptions should be investigated before performing statistical analysis of mutagenicity data. Mutagenicity data frequently violate assumptions of normality and homogeneous variances. Log transforming the mutant frequency values and analyzing the transformed data solves these problems and gives a more sensitive analysis. In addition, the multiplicative model is more appealing to the researcher than an additive model because the effect being sought is often a frequency multiple. While the log transformation is the first and simplest approach to solving violation of statistical assumptions and dealing with multiplicative models, more sophisticated techniques may occasionally be required. Based on this analysis, 300000 plaques from each of five animals should be analyzed per treatment group in order to detect a doubling of mutant frequencies. If known strong mutagens are used as positive controls, the investigator may be looking for a greater than two-fold effect and could then analyze fewer animals per group. If weaker effects are to be observed, the number of animals should be increased. In general, increasing the number of plaques analyzed will not increase sensitivity due to the greater animal-to-

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J.D. Callahan, J.M. Short /Mutation Research 327 (19951 201-208

animal variation in mutant frequency. These results are based on comparing a single treatment group to a single control group. Further calculations would be required if additional treatment groups at varying dose levels and/or expression times are desired because it may be possible to decrease the number of animals per group when studying more than two groups. Finally, while these and other statistical analyses are important early steps for study design, researchers will ultimately need to consider other factors including: cell proliferation rates, half-life of adduct removal, metabolic differences, and influences such as route of exposure for each tissue analyzed to determine significance of the response observed.

Acknowledgements

This work was supported in part by NIEHS grants 5R44ES04484-03 and ROlES04’728. We wish to thank Dr. Barry Glickman for his comments during the preparation of the manuscript and the reviewers for their helpful comments.

References Cramer, H. (1966) Mathematical Methods of Statistics, Princeton University Press, Princeton, NJ. Dycaico, M., P.L. Kretz, G.S. Provost, K. Lundberg, D. Ardourel, B. Rogers and J.M. Short (1994) Transgenic mice and rats for mutagenicity testing, Mutation Res., 290. l-18. Gossen. J.A., W.J.F. de Leeuw, C.H.T. Tan, E.C. Zwarthoff, F. Berends, P.H.M. Lohman, D.L. Knook and J. Vijg (1989) Efficient rescue of integrated shuttle vectors from transgenic mice: a model for studying mutations in vivo, Proc. Natl. Acad. Sci. USA. 86, 7971-7975. Harper, B.L. and MS. Legator (1987) Pyridine prevents the clastogenicity of benzene but not of benzo[alpyrene or cyclophosphamide, Mutation Res., 179, 23-31. IARC (1982) Monographs on the Evaluation of the Carcinogenic Risk of Chemicals to Man, Vol. 29: Benzene, IARC, Lyon, pp. 93-148. Kohler, S.W., G.S. Provost, P.L. Kretz, M.J. Dycaico, J.A.

Sorge, D.L. Putman and J.M. Short (1990) Development of a short-term, in vivo mutagenesis assay: the effects of methylation on the recovery of a lambda phage shuttle vector from transgenic mice, Nucleic Acids Res., 18, 30073013. Kohler, S.W., G.S. Provost, A. Fieck, P.L. Kretz, W.O. Bullock, D.L. Putman and J.M. Short (1991) Spectra of spontaneous and induced mutations in the lad gene in transgenie mice, Proc. Nat]. Acad. Sci. USA, 88, 7958-7962. Kretz, P.L., S.W. Kohler and J.M. Short (1991) Identification and characterization of a gene responsible for inhibiting propagation of methylated DNA sequence in mcrA, mcrE2 Escherichia coli strains, J. Bacterial., 173, 4707-4716. Margolin, B.H.. B.S. Kim and K.J. Risko (1989) The Ames Salmonella /microsome mutagenicity assay: issues of inference and validation, J. Am. Statist. Assoc., 84, 651-661. Miller, R.G. (1980) Simultaneous Statistical Inference, 2nd edn., Springer Verlag, New York. Mirsalis, J.A., G.S. Provost, C.D. Matthews, R.T. Hamner, J.E. Schindleer, K.G. O’Loughlin, J.T. MacGregor and J.M. Short (1993) Induction of hepatic mutations in lad transgenic mice, Mutagenesis, 8, 265-271. Piegorsch, W.W., A.C. Lockhart, B.H. Margolin, K.R. Tindall, N.J. Gorelick, J.M. Short, G.J. Carr and M.D. Shelby (1994) Sources of variability in data from a lad transgenic mouse mutation assay, Environ. Mol. Mutagen., 23, 17-31. Provost, G.S. and J.M. Short (1994) Characterization of mutations induced by ethylnitrosourea in seminiferous tubule germ cells of transgenic B6C3Fl mice, Proc. Natl. Acad. Sci. USA, in press. Provost, G.S., P.L. Kretz, T.T. Hamner, C.D. Matthews, B.J. Rogers, KS. Lundberg, M.J. Dycaico and J.M. Short (1993) Transgenic systems for in vivo mutation analysis, Mutation Res., 288, 133-149. Provost, G.S., J.C. Mirsalis, P.L. Kretz, B.J. Rogers, Y.K. Tran, M.J. Dycaico and J.M. Short (1994) Validation studies of the lambda/Iacl transgenic mouse assay, Toxicologist, 14, 246. Rogers, B.J., G.S. Provost, R.R. Young, D.L. Putman and J.M. Short (1995) Intralaboratory optimizaton and standardization of mutant screening conditions used for a lambda/lacl transgenic mouse mutagenesis assay, Mutation Res., 327, 57-66. Searle, S.R. (1971) Linear Models, John Wiley and Sons, New York. Short, J.M., S.W. Kohler, W.D. Huse and J.A. Sorge (1988) A transgenic model for the identification of genetic lesions, Fed. Proc., 8515a. Young, R., B.J. Rogers, G.S. Provost, J.M. Short and D.L. Putman (1995) Interlab comparison: liver spontaneous mutant frequency from lambda/lacl transgenic mice (Big Blue’). Mutation Res., 327, 67-73.