Risk Analysis, Vol. 12, No. 4, 1992

Comparison of the Dependence of the TD,, on Maximum Tolerated Dose for Mutagens and Nonmutagens Gay Goodrnanl4 and Richard Wilson' Received July 10, 1991; revised June 25, 1992

The relationship between the minimum TD,, (i-e., the TD,, measured at the most sensitive site) and the maximum dose administered (maxD) in rodent carcinogenicity bioassays was investigated separately for mice and rats. The relationship between log(l/D,,) and log(l/maxD) was analyzed as a function of (1) mutagenicity and (2) the statistical significance cutoff for selecting the minimum TD,, values. For rat bioassays, the variance of l o g ( l ~ , , )is larger and the correlation of log(l/ TD,,) with log(l/maxD) is weaker for mutagens than for nonmutagens, suggesting that the relationship between minimum TD,, and MTD is, in general, stronger for nonmutagens than for mutagens. The difference in correlation does not depend on the TD,, statistical significance cutoff, but the difference in variance is not significant for the most stringently selected dataset. For mouse bioassays, no significant mutagen/nonmutagen differences in log( lRD5,,) variance are found. A significantly weaker correlation of log(l/TD,,) with log(l/maxD) for mutagens in comparison to nonmutagens occurs only for the dataset with minimum TD,, chosen at the least stringent level, suggesting that this difference may be due to chance variation. We also looked for changes in correlation and regression parameters as a function of mutagenic potency in Salmonella; the variance of l o g ( l ~ , , ) and its correlation with log(l/maxD) are not found to vary in a consistent manner. Taken as a whole, our results indicate that (1) mutagenicity is a determinant of the TD,d maxD relationship in rats and (2) any effect that mutagenicity may exert on the TD,dmaxD relationship in mice is unimportant. A pseudo-single-dose model, equivalent to that analyzed by Bernstein et al. (Fundurn. Appl. Toxicol. 5, 79-86, 1985), was imposed upon the experimental data in order to determine the extent to which the resultant artificial datasets reproduce the mutagen/ nonmutagen differences in sample variance. We discovered that this model does not approximate the actual distribution of log(l/TD,,) vs. log(l/maxD) closely enough to be useful for examining artifacts in the relationship between these two variables. KEY WORDS: Carcinogenic potency; TDS,; toxicity; mutagenic; genotoxic; rodent carcinogenicity bioassay; dose-response; simulation.

acute toxicity (LDs0) or the inverse of the maximum tolerated dose (MTD), has been described by several authors.('-*) The correlation has been found to take the form log@) = rn-log(l/MTD), where rn = 1. Part of the correlation is attributable to a bias inherent in the carcinogenicity bioassay: the carcinogenic potencies of compounds which are highly toxic and only weakly carcinogenic cannot be determined in a dose group of 50100 animals, since at the MTD such compounds would not produce a measurable excess of tumors.(*) In other

1. INTRODUCTION The existence of a correlation between carcinogenic potency (p or ln(2)/TD5,) and toxicity, measured as the

' Department of Physics, Harvard University, Cambridge, Massachusetts 02138. Harvard School of Public Health, Boston, Massachusetts 02115. ' Present address: Gradient Corporation, 44 Brattle Street, Cambridge, Massachusetts 02138. To whom all corrcspondence should be addresscd.

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0272-4332/92/1200-0525$06.50/1 Q 1992 Socicly for Risk Analysis

Goodman and Wilson

526

words, if m < < 1, then p is too small to determine in standard bioassays. But a compound at the opposite end of the spectrum, one which is highly carcinogenic relative to its toxicity (i.e., rn > > l), could certainly be identified under the same bioassay conditions and would appear as an exception to the correlation. In fact, chemicals with m > > 1 are rarely identified, most likely because few exist. Their absence amounts to evidence that, in general, carcinogenicity observed under conditions of the rodent bioassay is related to t0~icity.c~) In lifetime rodent bioassays, compounds are tested at the highest practicable dose (i.e., at or near the MTD) in order to maximize the probability that a significant site-specific excess of tumors will appear. It has been suggested that events corollary or consequent to toxicity may mediate some of the carcinogenicity observed in rodent bioassays conducted at the MTD.(9Jo)Many compounds might be carcinogenic at high doses primarily due to their cytotoxicity, for example, via production of endogenous mutagens (e.g., oxygen radicals) or increased cell proliferation.(lCl2) For several nongenotoxic compounds, the evidence suggests that tumorigenesis occurs only when the dose is high enough to produce quantifiable tissue damage at the tumor target site; saccharin induction of bladder tumors in male rats is a notable example of a species-specific, organ-specific carcinogenic response that only occurs above a threshold dose.(13) This is not to say that toxicity of necessity mediates carcinogenicity for every nongenotoxic carcinogen. Nongenotoxic compounds which control or interfere with the regulation of cell division (e.g., certain hormones and phorbol esters) are tumorigenic at subtoxic doses. It is also clear that toxicity is not a sufficient condition for carcinogenicity, since some compounds tested in rodent bioassays produce site-specific toxic effects following chronic administration at the MTD without showing any evidence of carcinogenicity at this or other sites.(14)An example is benzoin, which can produce hyperplasia of the adrenal medulla in male rats without being tumorigenic in the adrenal gland or elsewhere.(15) Is the carcinogenic potency of a genotoxic chemical as measured in the rodent bioassay a function of the chemical's ability to produce toxic effects other than genotoxicity? We attempt to address this question by determining whether the relationship between carcinogenic potency and MTD is weaker for mutagenic than for nonmutagenic agents. The maximum dose administered (maxD) in a bioassay is usually fixed at the MTD, and consequently may be used as a surrogate for the MTD.(4.S)In this work, we determine whether the dependence of TD,, on maxD is different for mutagenic

and nonmutagenic carcinogens. We also look at the relationship between TD,, and MaxD in Salmonella mutagens as a function of one measure of mutagenic potency (Le., lowest effective dose). 2. METHODS

Two sets of chemical compounds were studied. One group consisted of 222 compounds tested by the National Cancer InstituteDIational Toxicology Program (NCVNTP), and tabulated according to "structural alerts" (WA) and mutagenicity (M) to Salmonella by Ashby and Tennant.(16) Compounds positive for both S/A and M were designated by these authors as + / + , compounds negative for S/A and M were classified as -/-, and so forth. Concordant compounds (Le., those designated + / + or - / - ) were classified as mutagenic or nonmutagenic, respectively. The nonconcordant - / -t compounds were classified as mutagens. For the nonconcordant + / - compounds, our assignment of mutagenicity or nonmutagenicity was based upon (1) mutagenicity in Salmonella tests not considered by Ashby and Tennant, (2) mutagenicity in other bacterial systems, or (3) mutagenicity in some eukaryotic in vitro test, using MRC Monographs Supplement 6(17)as a reference. If positive for S/A and untested for genotoxicity (+/?), the chemical was classified as mutagenic. In this manner, we categorized 117 compounds as nonmutagens and 100 as mutagens. The five compounds which we did not classify and which were not included in our analyses were negative for S/A and untested for genotoxicity ( - /?). The second set consisted of 245 chemical compounds which had tested positive for mutagenicity in various Salmonella strains and for which quantitative information (i.e., the mean number of revertant colonies per plate at each dose level) was available. All data were from studies published by Zeiger and associates.(18-20) From these data we estimated, for each chemical, the lowest effective dose (LED) in each test, and took the geometric mean of the LED over all tests. The LED was taken to be the lowest dose at which the number of revertants was above background and there was a positive dose-response with increasing dose. The compounds were divided into three groups according to their geometric mean LED: low (LED < 10 mg), intermediate (10 mg s LED < 100 mg), high (LED 2 100 mg). This is only the most simplistic of several possible measures of Salmonella mutagenicity. Better approaches

527

Mutagen/Nonrnutagen Comparisons entail estimation of initial slopes from linear(21)or nonlinear(22)models and use of more sophisticated methods for combining results of multiple data set^.(^^) Thus, our results based on the LED should not be taken as representing a definitive answer to the question of whether mutagenic potency influences the TD,, relationship. The minimum TD,,s at a given level of statistical significance were taken from the Carcinogenic Potency Database (CPDB) of Gold ef (For the NCI/NTP compounds, the experiments yielding the appropriate minimum TD,, values were not necessarily those performed by the NCUNTP. Note that “ N C I N P dataset” here refers to the CPDB tabulation of all pertinent experimental results for these compounds and does not imply that the data came exclusively from NCIMTP experiments.) Data were taken only from those experiments which the original authors concluded were positive for carcinogenicity. Data from combined sites (tumorbearing animals, abbreviated in the CPDB as tba or TBA) were ignored. We did not perform analyses separately for males and females; we took the minimum TDSosfor the given rodent species, irrespective of sex. Only oral and inhalation routes were considered. If the tumor incidence in the control group for a given site was greater than 60%, then the TD,, at that site was disregarded. The TD,, values were chosen to satisfy one of four criteria for statistical significance:p < 0 . 0 1 , ~< 0.025, p < 0.05, orp < 0.1. We shall refer to the data selected according to these criteria as sets A, B, C, and D, respectively. The designated maxD is the highest dose in the experiment from which the minimum TDSowas derived.

2.1. Tests for Similarity If the relationship between two variables x and y is such that y is linearly dependent on x , and if y is a random effect factor (i.e., normally distributed for a given value ofx) andx is either a fixed-effect or random-effect factor, then simple linear regression analysis is appropriate. On the other hand, if the relationship between y and x is not one of dependence and if both variables are random-effect factors, then correlation analysis is appropriate.27 The Kolmogorov-Smirnov one-sample test(28) was used to test the goodness of fit to a normal distribution for both Iog(l/TD,,) and log(l/maxD) from set D; the test was made separately for mouse mutagens, rat mutagens, mouse nonmutagens, and mouse nonmutagens. The distributions of log(lKD,,) and log(l/maxD) for all four species/mutagenicitygroups were found not to differ significantly from the normal: all p values were

0.5 or greater. (Statgraphics was used for this analysis.) Therefore, in the study of the relationship between log(1/ TD,,) and log(l/maxD), it is reasonable to use either regression or correlation analysis. Linear regression analysis permits comparisons of slopes (i.e., functional relationships) in addition to variances (i.e., goodness of fit to the model). By convention, the variance calculated pertains to the variation in the dependent variable, y log(llTD,,)). However, we might just as well postulate that x log(l/maxD)) is the dependent variable and then calculate the variance accordingly as the variation in x . On the other hand, the correlation coefficient is a measure of the variation of both y and x . Therefore, by comparing correlation coefficients, one obtains information about the variation in x that is not present in the variance calculation for regression of y on x. In the comparison of two datasets, if the correlation coefficients but not the variances are found to differ significantly, then the discrepancy may be interpreted as being the consequence of differences in the variance of x with respect toy. A dummy variable method was used to test the null hypothesis that a given pair of regression lines are coin~ i d e n t . (The ~ ~ )datasets were combined and linear regression was performed for the model: y

=

bo

+ b$ + ~ 1 +6 C&

wherey = log(l/TD,,),x = log(l/maxD), and 6 = 0 for one dataset, 6 = 1 for the second. A t-test was made of the probability that either of the coefficients c, or c2 is significantly different from zero. If c1 # 0, then the regression intercepts differ; if c2 # 0, then the regression slopes differ. [SAS software was used for this and all of the following analyses. Two measures were considered significantly different if the hypothesis that they are equal (i.e., the null hypothesis), was rejected with 2 95% confidence.] The residual mean square [i.e., the variance after taking into account the dependence of y on x (here referred to simply as the “variance”)] was calculated; this is often written as If the variances s: and st for datasets 1 and 2 are assumed to have x2 distributions, then for comparison of the two variances, an F test may be performed to determine the confidence with which we can reject the null hypothesis, H,: (a: = at), in favor of the alternative hypothesis, H,:(a: # ag), where aZ is the underlying variance. The observed value r of the underlying correlation coefficient p may be transformed to a new, approximately normal variable z,., defined by z, = X[In(l

+ r) - ln(1 - r)]

Goodman and Wilson

528 For comparison of two values rl and r, obtained from independent samples of size n , and n,, the variable Z is defined as

where I

1

1

The Z statistic was evaluated in terms of a standard normal distribution, yielding the probability of observing as extreme a value of Z if the null hypothesis, H,: (pl = p,) is 2.2. Pseudo-Single-Dose Experiments

We calculated a carcinogenic potency based on partial data from the bioassay as follows. For each experiment that provided a minimum TD,, value under the particular selection criterion (A, ByC, and D), we noted the control group tumor incidence a,, the maximum tumor incidence a,, and the total number of animals n, and n,, in the control and maxD groups, respectively. A carcinogenic potency based on this pseudo-single-dose experiment was calculated as

shown for Zeiger dataset A because the high LED group contains too few points to be representative. Table I shows the results of obtaining the leastsquares fit to the normal error linear regression model for log(lRD,,) vs. log(l/maxD). The slope ( + SD), intercept, variance (s2), and number of points (n) are given for each N C I N P and Zeiger dataset. The slopes for mutagens and nonmutagens (NCI/ NTP data) and for compounds with low, intermediate, and high LEDs (Zeiger data) were compared. For mouse data, the slopes are uniformly larger for the mutagens than the nonmutagens, but the difference is significant only for mouse dataset A (199.5% confidence). Visual inspection of Fig. 1A suggests that this difference may be attributable to the points with l/maxD > -10( m a g d a y ) - ' . For rat data, no significant mutagen/ nonmutagen slope differences are observed. The low/ medium and mediumhigh LED comparisons also do not demonstrate any significant differences in slope. Variances for NCI/NTP mutagens and nonmutagens and for Zeiger mutagens as a function of LED are also shown in Table I. In every painvise mutagednonmutagen comparison, the variance is greater for the mutagens than the nonmutagens, although the difference is significant only for three rat datasets: B, C and D ( 2 95% confidence). Pairwise comparison between LED groups reveals no significant differences. 3.2. Correlation of log(l/TD,,) and log(l/maxD)

Note that this is the same formula for potency used by in their simulation of the results of Bernstein et single-dose bioassays. Log@) was plotted against log( 1/ maxD), and both linear regression and correlation analyses were performed. 3. RESULTS AND DISCUSSION

3.1. Regression of log(l/TD,,) on log(l/maxD)

For the NCVNTP data, log(lrD,,,) vs. log(l/maxD) is plotted for mice (Fig. 1A and B) and for rats (Fig. 1C and D), with different symbols for mutagenic and nonmutagenic compounds. Data shown are from the two extremes of TD,, statistical significance, set A (Fig. 1A and C) and set D (Fig. 1B and D). For set B of the Zeiger mutagens, Iog(l/TD,,) vs. log(l/maxD) is plotted for mice (Fig. 2A) and for rats (Fig. 2B) with different symbols for the low, intermediate, and high LED groups. Data are not

In Table I we also show the coefficient of correlation (r) of log(l/TD,,) and log(l/maxD) for each NCI/ NTP and Zeiger dataset. The correlation coefficients are uniformly smaller for the mutagens than the nonmutagens, although the difference is not always significant. We find that in all three cases where there is a significant difference in variance, there is also a significant difference in correlation coefficient (i.e., for the mutagen/ nonmutagen comparison based on the maxD for rat datasets ByC, and D). In three cases where no significant difference in variances occurs, there is nevertheless a significant difference in correlation coefficient: the mutagenhonmutagen comparisons based on the maxD for mouse dataset D and rat dataset A and the medium/high LED comparison for mice. With respect to the mouse mutagen/nonmutagen comparison, we interpret the single observation of a significant mutagenhonmutagen difference in correlation coefficients for mouse dataset D as possibly attributable to chance variation consistent with the performance of multiple tests. However, for the rat mutagenhonmutagen comparison, a significant difference in correlation coefficients is found for all four

Mutagen/Nonmutagen Comparisons

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rat datasets (A, B, C, and D), indicating that the difference is nonspurious. For the low/medium/high LED comparisons, the medium LED dataset is significantly less correlated than the high LED dataset. However, since the difference between the low and high LED datasets is not similarly significant, the mediumhigh difference is best explained as being due to chance variation.

the correlation coefficient tends to decrease for both mutagens and nonmutagens (Table I). Thus, comparison of the variance (or correlation) for mutagens and nonmutagens chosen at different significance levels would yield an artifactual difference. This obsewation suggests that it is important to choose minimum TD,, values at the same level of significance when comparing the TD5dmaxD relationship for mutagens and nonmutagens.

3.3. TD,, Significance Level: Effect on Variance and Correlation Coefficient

3.4. Pseudo-Single-Dose Experiments

As the stringency for selection of minimum TD,, values is lowered fromp < 0.01 (set A) t o p < 0.1 (set D), the variance for the maxD regression tends to increase and

Linear regression was performed for each pseudosingle-dose experimental dataset; the variances are given in Table 11. As in the complete experiments, in the pseudo

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experiments the variances of the mutagens are uniformly larger than those of the nonmutagens. However, there is no significant difference between any pair of mutagen/ nonmutagen variances obtained in the pseudo experiments; by contrast, in the complete experiments (Table I), the pairwise variance differences are significant for rat datasets B, C , and D. The failure of the pseudosingle-dose experiments to replicate the significant differences in mutagednonmutagen variance found with the complete experiments indicates that the former are not an ideal surrogate for the latter. Also shown in Table I1 is a comparison of mutagen/

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nonmutagen correlation coefficients for the pseudo-single-dose experimental datasets. There are significant differences for three mouse datasets: A (2 99% confidence) and B and C (195% confidence), and for rat datasets B, C , and D ( 295% confidence). By contrast, the complete experiments yield significant mutagednonmutagen differences in correlation coefficient for mouse dataset D and rat datasets A, B, C, and D. Thus, while the overall mutagenhonmutagen differences in variance are diminished in the pseudo-singledose experiments relative to the complete experiments, the opposite is true for the differences in correlation coefficient. As explained in general terms in the Methods section, the discrepancy between pseudo and complete interpreted as being the consequence of differences in the log(l/maxD) variance of mutagens and/or nonmutagens between the pseudo and complete datasets. This may be because differences in tumor response between mutagens and nonmutagens appear in the sub-maxD dose groups more often than in the maxD dose group. For both mutagens and nonmutagens, at the maxD the tumor response might be converging toward the same apparent dependence on toxicity. It has been argued by Rieth and S t a ~ ( *that ~ ) since the range of maxDs spans over six orders of magnitude while the possible range of finite and significantly nonzero single-dose values of carcinogenic potency p at a given maxD is, according to Bemstein et ~ l . (confined ~) to a 30-fold range around l/maxD, then a high degree of correlation between p and maxD is inevitable. But this conclusion masks the fact that the analysis of Bernstein er al. was based not on actual values of p, but on values that are obtainable in a single-dose experiment. The pseudo-single-dose model described here, which is equivalent to that analyzed by Bernstein et al., does not approximate the actual distribution of l o g ( l ~ , , )vs log(1/ maxD) closely enough to be useful for examining artifacts in the relationship between these two quantities. 4. CONCLUSIONS

If the relationship between carcinogenicity and toxicity is different for mutagens and nonmutagens, then one might expect the strength of the relationship to depend quantitatively on mutagenicity (e.g., on the LED). This is not what we found. However, the LED also does not correlate well with minimum TDso for these same compounds (unpublished data). The finding that the LED

MutagedNonmutagen Comparisons

531

Table I. Linear Regression and Correlation of log(l/TD,,) vs. log(l/maxD) for NCI/NTP Mutagens and Nonmutagens and for Zeiger Mutagensa Data NCINTP carcinogens Mutagens, mice

Nonmutagens, mice

TDw A B C D A

B Mutagens, rats

Nonmutagens, rats

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Abbreviations: TD,,, statistical significance cutoff for TD, values (A, p < 0.01; B, p < 0.025; C, p < 0.05; D,p < 0.1); r, observed correlation coefficient; sz, observed variance; n, number of compounds in the dataset. Statistical significance of the parameter differences for the same-species, same TD,,-significance-cutoff comparison between mutagens and nonmutagens: *, probability is < 5% that the true value is the same for nonmutagens; **, probability is < 1% that the true value is the same for nonmutagens, ***, probability is < 0.5% that the true value is the same for the dataset consisting of mutagens and nonmutagens combined. Statistical significance of the correlation coefficient differences for the same-species comparison between mutagens with low, intermediate (mid), and high LED values: +, probability is < 0.5% that the true value is the same for the high LED dataset B.

is not a determinant of the TDJmaxD relationship is in line with the hypothesis that the carcinogenicity of mutagens is not typically a function of the ability to produce point mutations.(M)This view is corroborated by the wellknown observation of relatively poor qualitative (yedno) concordance between mutagenicity in the Ames test and carcinogenicity in rodent bioas~ays.(~l) We have found differences in variance and correlation coefficient in the relationship between log(l/TDs0) and log(l/maxD) for mutagens vs. nonmutagens tested in rats and mice; for rats only, the difference is statistically significant. The differences may be smaller for

mice for reasons that have to do with the fact that mouse liver is the most frequent tumor target tissue in lifetime carcinogenicity b i o a s s a y ~ ( and ~ ~ ) the fact that spontaneous liver tumor rates are high for some mouse strains.(33) One explanation is that in the B6C3F1 strain typically used, several nonmutagens appear to be able to induce activation of liver cell oncogenes,(32)suggesting that a population of liver cells may exist normally in a preinitiated state. Our findings are consistent with the hypothesis that, even for most mutagens, at high doses carcinogenicity is induced via mechanisms associated with or corollaly

Goodman and Wilson

532 Table 11. Lincar Regression and Correlation of log(l/TD,,) vs. log( l/maxD)for Pseudo-Single-Dose Experiments Based on Datasets of NCIMTP Mutagens and Nonrnutagens“

NCI/NTP carcinogens, Pscudo-singlc-dose experiments ~~

Mutagens, mice

A B C D A B C D A B C D A B C D

Nonmutagens, mice

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0.127 0.177 0.191 0.200 0.130 0.182 0.183 0.187 0.160 0.218 0.225 0.268 0.108 0.142 0.156 0.195

54 60 67 72 45 53 59 69 50 60 65 68 25 29 44 50

mutagens or nonmutagens at much lower doses. However, our results do not suggest that the rodent bioassay leads to artifactual determination of high-dose carcinogenic potencies. With respect to the interspecies (rodent to human) extrapolation of high-dose potencies, existing evidence on a limited number of compounds suggests that rodent TD50 values are not inconsistent with observed rates of cancer in occupationally and medically exposed humans.(35)

NOTE The names of the compounds corresponding to the points in Fig. 1 and 2, their CAS numbers, and the values of log(l/maxD) and l ~ g ( l i T D , ~are ) available as an Appendix upon request from the first author (G.G.).

ACKNOWLEDGMENTS

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Abbreviations: See Table I legend. Statistical significance of the parameter diffcrences for the same-species, same TD,,-significancecutoff comparison between mutagens and nonmutagens: ’, probability is < 5% that the true value is the same for nonrnutagens; **, probability is < 1% that the true value is the same for nonmutagens.

to toxicity. Our findings are also consistent with a number of other hypotheses which follow from the suggestion that the so-called nonmutagens are actually mutagenic; discussion of the pros and cons of these latter hypotheses is beyond the scope of this paper. Since there is considerable overlap in the TD,~maxD distributions of mutagens and nonmutagens, the observed overall differences in variance and correlation coefficient are not large enough to be useful for predictive purposes. The quantitative information to be gained from the relationship between the MTD and the TD,, at the most sensitive site increases with the statistical significance level at which the most sensitive site is chosen; hence, the information is limited ultimately by the number of animals per dose group in the bioassays. In this we concur with much of what Bernstein et u Z . ( ~ ) and Rieth and Stan(*’) have previously concluded. The limiting influence of dose group size is revealed in greater detail by our Monte Carlo simulation of rodent carcinogenicity bioassay outcomes.(34) Our finding that minimum TDso values depend on the maxD in a similar fashion for mutagens and nonmutagens supports the argument against using rodent bioassay results for predicting carcinogenic potencies of

Dr. Wilson was supported by an Interagency Personnel Agreement with the U.S. Food and Drug Administration. Dr. Goodman was supported by gifts to Harvard University from Monsanto, Gillette, Bristol-Myers, and Rohm & Haas, and by cooperative agreement CR812699 from the U.S. Environmental Protection Agency to the Programs in Environmental Health and Public Policy at the Harvard School of Public Health.

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