&address all correspondence to
Richard Wilson

Department of Physics

Cambridge MA 02459-1728

Tel: 617 495 3387

Wilson@huhepl.harvard.edu

April 19^th, 2000

We have used the CBDS database of the National Toxicology Program to study the difference between Absolute Risk and Relative Risk models for inter species and inter sex predictions of cancer risk. For no combination (class) of tumor and site is the prediction good for all chemicals. The variation in predicted risk between chemicals exceeds the difference in risks resulting from application of these two models. On the whole, it appears that relative risk is a better model.

In this paper we address key question in the quantitative assessment of cancer risks: how should one project chemically caused increase in cancer rate for one specific tumor at one specific site in one specific sex and species to increases in cancer rates in other site/sex/species combinations? And in particular how does that projection depend on the natural background rate in known and predicted sites?

Risk prediction across sex and especially across species should account for differences in the effective doses of chemicals delivered to target organs. Same dose of a chemical given to 30g mice and 500g rats would indeed result in different toxic effects. Therefore for each model the dose metric must be appropriately normalized. It is likely that there is only a small normalization necessary between sexes, but between species a weight adjustment may be necessary.

We discuss two models that are frequently used to support regulatory decisions. In the Absolute Risk (AR) model the increase of rate of a specific tumor at a specific site projects directly to an identical increase of the corresponding tumor at the corresponding site in the second species. In the Relative Risk (RR) model it is the fractional increase (relative to the natural background) that projects directly. The two models would give identical results if the background rates for known and predicted tumors were the same but can differ markedly if the background rates are very different. In neither model (AR or RR) do we expect that the prediction of tumors will be exact. There will of course be a statistical fluctuation because of the limited number of animals but also an additional variation because of differences in the behavior of specific chemicals.

Regulation has tended to use an absolute risk model (Anderson et al. 1983). For example, the US EPA has calculated a unit risk factor for the most sensitive species at the most sensitive site, and assumed that this factor applies to the other species.

RR model is rooted deeper both theoretically and practically. An absolute risk model is obvious nonsense in projecting prostate cancer from male to female or ovarian cancer from female to male, but the relative risk model correctly predicts zero in each case. Relative risk is the natural projection in multistage theories of cancer starting with that of Armitage and Doll (1954, 1957). The overall cancer rate is the product of the probabilities of a number of steps occurring. The chemical interacts with one of several stages, whereas the background influences all of them. A doubling (for example) of the background by changing sex, species, strain or environmental situation, would presumably nearly double the combined probability effect of all the stages other than the one affected by the chemical of concern and therefore double the overall cancer rate.

Storer et al. (1988) examined data of the cancers caused by exposing several strains of male and female mice to gamma rays from a cesium source. They found that the relative risk (RR) model fit better than absolute risk (AR) model in 5 out of 9 tumor types selected: lung, breast, liver, ovary and adrenal. Both models fitted myeloid leukemia and Harderian gland tumors, and neither model predicted thymic lymphoma and reticulum cell sarcoma well. This paper used the estimated RR of death from the RR model in mice to predict the RR of death in humans from 4 different tumor types of homogeneous origin (lung cancer, breast cancer, leukemia and liver tumors). This was compared to the RR found in the studies of cancer among Japanese A-bomb survivors (Pierce et al. 1996). There are no significant differences between the estimate from animal data and the estimate from human data.

Granath et al. (1999) used published data of bioassays of 4 genotoxic carcinogens (mutagens), ethylene oxide, acrylamide, and butadiene, to calculate a risk increment for all the sites (brain tumors, peritoneal mesothelioma, subcutis fibroma, mammary gland carcinoma, Harderian gland adenoma and carcinoma, uterine carcinoma, lung carcinoma, and mononuclear cell leukemia). Doses were compared by using a radiation-like dose in units rad*millimol*kg-1*h. Goodness of fit tests showed adequate concordance between observed numbers of primary neoplasms and the number predicted by the RR model but poor concordance with the AR model.

The method follows several procedures that have been used by this group over the last 10-15 years (Byrd et al. 1991, Linkov et al 1998, Gray et al. 1996). The Carcinogenesis Bioassay Database System (CBDS) produced by the National Toxicology Program is our data source. For a specific chemical, experiment is usually conducted on only one strain of a given species of rodent. Thus it is not possible to compare the effects on different strains as Storer et al. or Granath et al. were able to do. We can only ask whether the relative risk (RR) or the absolute risk (AR) model extrapolates better, for specific sites or specific chemical subgroups, between different sexes within a rodent species and between rodent species, in these long-term rodent bioassays. However in contrast to Storer et al. and Granath et al. we are able to study this for a large number of chemicals.

The basic procedure is to pick a tumor site/type combination (hereinafter called class) in which the chemical produces a statistically significant increase of tumors, and to project the anticipated tumor rate in the other sex and in both sexes of the other species using each of the Absolute risk (AR) and Relative Risk (RR) models. We then compared the predicted number of tumors with the number of tumors actually observed.

Database and Selection of Chemicals

The CBDS consists of experiments finished by 1983 on 18 strains of rodents. In each experiment, there are usually 3 dose groups with 50 animals in each group. The CBDS includes a total of 587 bioassays (some chemicals had been tested in more than one bioassay). Most of these bioassays have data for both male and female animals. In this study, we consider only experiments on B6C3F1 mice and Fisher344 rats, which are the most often used strains of rodents in the National Toxicology Program long term bioassays.

We used tumor classification system developed and presented in Byrd et al. (1991), Gray et al. (1996) and Linkov et al. (1998) with 102 categories which include both tumor types and tumor locations. The following modifications suggested originally by Dr J. Haseman were made: (i) The class 7 for Liver adenoma and class 64 for liver carcinoma were modified very slightly to better separate benign and malignant tumors (Linkov et al. 1999), and (ii) Class 10 (Pituitary adenoma) and class 36 (Chromophobe adenoma) are left out of analysis because the pituitary tumors were not diagnosed consistently across time and experiments. Thus there are a total of 100 tumor classes under consideration in this paper.

We tested for carcinogenicity at any site using the Cochran-Armitage trend test with a significance value of P<0.02 as the criterion. By insisting that we start with a very significant response in one group we avoid having too many random responses. Then we selected chemicals that induced a significant increase in any tumor rate in any of the four sex/species combinations (male mice (MM), female mice (FM), male rats (MR), and female rats (FR)).

For each chemical with significant response, we fitted a simple model using a Maximum Likelihood Method:

R(d) = 1-(1-a )*exp[- b *d/(1-a )] (1)

R(d) is the lifetime risk of developing cancer at dose d, a is the background tumor rate, b is the cancer potency, and d is the dose in mg/[kg(body weight)*day]. To extrapolate to other sex/species, the following method was applied. For example, to extrapolate from MM to FM by AR and RR model:

AR: projected b _{j, fm} = b _{j, mm} (2)

RR: projected b _{j, fm} = (b _{j, mm}/a _{j, mm})* a _{j, fm} (3)

Here j denotes the responding tumor category. The underlying assumption is that doses are equivalent within species (between MM and FM) in the units mg/[kg(body weight)*day]. In some tumor classes, there are frequently no tumors for as specific sex/species group so that predictions based on relative risk become meaningless. Therefore we use the historical control rate (averaged over all bioassays) for each class and each sex/species. Thus in the equation above, a _{j, mm} and a _{j, fm} are the historical control rates.

Then we predicted lifetime risk R(d) and the number of tumor-bearing animals in other sex/species, for each dose group (denoted by i) of the same chemical, by RR and AR model, using equation (i) and the equation below.

N(d_i) _j = R(d_i)_j,fm * A-Den_{i j, fm} (4)

N(d_i) _j denotes predicted number of tumor-bearing animal if dose i was applied.

A-Den_{i j, fm} is the number of animals in the dose group i in FM experiment examined for tumor j.

For each of the AR and RR models, we plot the predicted vs. observed number of animals with the specific class of tumor under study. The same procedure was followed to project between species (mice to rats or vice versa), with the use of a interspecies conversion factor based on metabolic processes, which is the ratio of body weight raised to the power of 0.25 (Rhomberg 1994, US EPA 1992).

Further detail of the calculation is in the appendix.

In order to investigate the relative merits of RR and AR models, we examined the ratio of observed number of tumor-bearing animals to the predicted number (i.e. N(d_i) _j in (4)) obtained by RR and AR model (denoted by R = [Obs/Pred]). Since neither of the observed and predicted number can be negative, the ratio is constrained to a value greater then or equal to 0. This leads us to paramertization any distribution of values of R as a lognormal distribution. The log transformation automatically eliminated from the analysis those cases with a value R=0 (i.e. the observed number of tumor-bearing animals is zero). Since we can not tell by the ratio how far away the prediction is from the zero observation, those cases were addressed separately.

Since our data is the combination of projections, tumor categories, chemicals and dose groups, we would like to compare RR and AR models under some more specific scenarios each of which addresses specific group of projections (here the term projection means predicting from one sex/species to another sex/species) or chemicals. The following scenarios were examined: (i) within projections (ii) within projections groups with different background rates; (iii) within specific sites; (iv) in a specific class of chemicals - chlorinated hydrocarbons; and (v) in mutagenic chemicals. We separated liver tumors (liver adenoma and hepatocellular carcinoma) and non-liver tumor since liver tumor has been found quite different from other kinds of tumor. In each scenario we studied the distribution of R = [Obs/Pred], and the number of cases with ratio in the range between 0.1 and 10 or log-ratio in the range of –1 to 1.

There are 12 projections (extrapolations) from one of the four MM, FM, MR, and FR to the three others. In 65 classes out of our classification of 100-tumor classes at least one chemical shows a statistically significant increase of tumors, contributed by 209 chemicals. Most chemicals are counted twice as there is a projection for the tumor rate at each dose. This leads to 3206 combinations of projection/site/experiment/dose, among which 636 have 0 observed tumor-bearing animal. There are 1631 combinations on non-liver tumors.

The initial results were expressed in 802 graphs (each with a different category by projection or tumor class). But most of these are uninteresting, either because there was no difference between the two models, the data are not scattered or neither model fitted well. We show 4 characteristic ones. Firstly we show in figure 1 a projection of cancer from tumors in Male Mice (MM) at site (class) 3 (GI papilloma) to Female Mice (FM) in the same site. For this site the background rate is similar in both Male and Female Mice so that the absolute and relative risk projections are similar also. On the ordinate is the predicted number of tumors and on the abcissa is the measured number of tumors. Each point on the graph represents a response to an individual chemical. The 45-degree line is the identity line, which suggests the ideal prediction. It is clear that there is more scatter about the 45 degree line than given by statistical fluctuation showing already the major limitation of our method.

Figure 2 (site 7, liver adenoma) is a typical case where the backgrounds for Male and Female mice differ and therefore the absolute and relative risk predictions differ. The graph shows that RR model tends to under-predict, while AR model over-predicted more often. Figure 2 shows respiratory, oral adenoma in the same projection. AR predictions seem cluster more closely around the identity line, while RR model under-predicts more often.

Figure 3 from Male Mice to Male Rats shows, by contrast, that for liver carcinoma (class 64) absolute risk predicts better. Finally figure 4, Male Mice to Male Rats, for skin squamous carcinoma (class51) neither model predicts well.

The ratio, R = [Obs/Pred]), of the observed and the predicted number of tumor-bearing animals was examined. Table 1 shows the geometric mean and geometric standard deviation of the ratio for AR and RR model, grouped by projection, in all tumors other than liver tumors. Liver tumors because of their peculiarities in the animal bioassay (Gray et al. 2000) were considered separately. All the projections except the AR prediction from FR to MR can be described by a log normal distribution. At a significance level of P < 0.05, tests for mean log R = 0 could not be rejected in 6 and 2 out of 12 projections for RR and AR model respectively. Table 2 shows that overall, both models were more likely to over-predict than under-predict. AR was less likely to under predict than RR.

Extreme over or under-predictions are especially interesting in judging relative model performances. We define extreme in this context as being off by a factor of 10 [log R >= 1]. There was a total of 17 extremely under-predicted projection/site/experiment/dose by AR, and 51 by RR. 98 cases were over-predicted (0<R<=0.1) by AR and 51 by RR. A large fraction of the extreme values occurred in interspecies extrapolation. MR to FM tended to result in most extreme under-prediction among all projection (23% in AR and 20% in RR).

Table 1 also revealed some clues of the difference between intra- and interspecies extrapolations. Among projections from a specific sex/species, intraspecies extrapolation always has a GM closer to 1 and a smallest Geometric Standard Deviation (GSD) then interspecise extrapolations, by both AR and RR models. For example, comparing the three projections from FM, projection from FM to MM appears to be the better, by both AR and RR models. The only exception is the projection from MR to FR by AR model. The GSD is relatively small but the GM is far from 1, which is worse than MR to other sex/species by AR model is. However, RR model appears to work well for projection from MR to FR (see also Figure 5). Projection from MM to MR shows great variation in both models. The Geometric Mean (GM) is far less than 1, which shows overall over-prediction by both models (Figure 6).

Table 2 reveals some clues of the difference between intra- and inter-species extrapolations. From the comparison of FM to MM, FM to FR and FM to MR, it is obvious that the fraction of extreme predictions (10 fold larger or smaller) is highest in cross species and gender extrapolation. The projection from MM to MR was an extreme case. The percentage of extreme prediction in this projection was 23% by AR and 16% by RR. However, there was not a clear sign indicating AR and RR was distinguishable in any of the 12 projections (Figures 5-10).

Table 3 shows the results of goodness of fit test. Cases of zero observed tumor-bearing animals were included in the tests. Among the 12 projections, extrapolation by RR model from MR to FR and from FR to MM passed the test at 0.05 significant level. AR model did not show sufficient fit in any projection.

Since the underlying difference of the two models is whether chemical carcinogens induce responses by interacting with background mechanism in rodent species, it is necessary to investigate how the background rate affect the prediction. We first dichotomized all predictions into whether the background rate of the first sex/species is higher or lower than the predicted sex/species. When predicting from sex/species with relatively lower background rate to those with higher background rate, both AR and RR over-predicted, with geometric mean of 0.44 and 0.43. The GSD was similar. When predicting in the opposite direction (i.e. from sex/species with a higher background rate than the predicted sex/species), AR over-predicted (GM=0.60) while RR under-predicted (GM=1.38). Both geometric means were different from 1. However, when measured potency in FM was used to predict responses in other sex/species, with higher background rate in FM than in others, RR model appeared to be better than AR model. We could not tell the difference of the two models in the category of low to high background rate. Different results were found in projections from FR to other sex/species. When predicting from FR in tumor sites that FR have a lower background rate than the predicted sex/species, the GM of R=[Obs/Pred] is 0.97 and 0.56, the GSD is 2.37 and 2.40 for AR and RR model, respectively (Table 4, Figures 6 and 7).

In about half of the 65 classes of tumor/site, the distributions of the ratio of observed to predicted tumor-bearing animal were similar in both AR and RR models. In the other half of the classes there were not enough data to distinguish between the two models. The background rates differ remarkably for liver tumors and therefor we pay special attention to liver tumors. For liver adenoma, the results we found are intermediate between the AR prediction and RR prediction. For liver carcinoma the AR model seemed to work better (Figure 7 and 8).

In about half of the 65 sites, AR and RR predictions did not differ a lot. The distributions of ratio of observed to predicted tumor-bearing animal by each model were quite similar in location and spread. In the other half sites there were not enough data to distinguish between the two models.

The background rates differ markedly for liver tumors and therefor we pay special attention to liver tumors. For liver adenoma, all projections together, the results we found are intermediate between the AR prediction and the RR prediction. The GM is 0.57 and 0.59 for AR and RR model respectively. For hepatocellular carcinoma GM is 0.62 for AR model and 1.00 for RR model, with similar GSD for the two models (Figures 8 and 9).

We compared the goodness of fit of RR and AR for liver adenoma and hepatocellular carcinoma respectively, by the sex/species of which its measured potency served as the base of projection (i.e. projections from MM to all other sex/species, from FM to all other sex/species, etc.). For liver adenoma, neither model have sufficient fit in any of the 4 groups with different base sex/species of projection. For hepatocellular carcinoma, AR model appeared to be better than RR model in projections from FR(p-value(AR)=0.14, p-value(RR)=0, df=5). Both models fit when projecting from MR to other sex/species (p-value(AR)=0.52, p-value(RR)=0.45, df=4). Neither model fit when projecting from responses in hepatocellular carcinoma in male or female mice. We further examine the goodness of fit in each of the 12 projections. However, in most projections, there were not enough cases to conduct goodness of fit test with sufficient resolution. Only the projection from FR to MR showed a slightly better fit of RR model in liver adenoma (df=4, p-value(RR)=0.09, p-value(AR)=0.02).

We hope that if one could find a correlation of chemicals and sites that have similar modes of action between species, a better comparison could be made. We therefore looked at two specific classes of chemicals.

Gold et al. (1991) had separated out chlorinated hydrocarbons to see whether this class of chemicals display unique characteristics. Therefore we investigated the possibility that these extreme projections were caused by this specific group of chemicals. We compared the percentage of chlorinated hydrocarbons contributing to the extreme prediction the percentage of all chemicals. 208 chemicals contributed to one or more of our predictions (zero observation excluded), of which 65 (31%) were chlorinated compounds. 25 chemicals gave an extreme prediction [Log [Ratio]>=1] of which 8 (32%) were chlorinated chemicals. Among the 82 chemicals that have less extreme predictions [Log [R]<=-1], 25 (31%) were chlorinated (Table 5). Thus the chlorinated hydrocarbons were not, as a group, contributing to the scatter of our results.

We investigated the possibility that the predictions would work better for mutagens (genotoxins) than for non mutagens. We used the mutagenicity calls from Zeiger (1987), which included 224 chemicals that had been tested on carcinogencity and mutagenicity. However, only 63 chemicals in our data set were mutagens according to the mutagenicity calls. Others were non-mutagens or not tested. Combining all predictions on these 63 chemicals did not show obvious difference between AR and RR (Figure 9). The location and spread of AR and RR are similar. RR is approximately symmetric, with thicker tails than AR in either side of 1. AR has a relatively thicker tail in the left side than right side, implying slightly more over-predict.

For over 25 years (e.g. Crouch and Wilson 1979) it has been noted that the correlation between cancer potencies in different species seems to be better if the site is not specified. In the context of this paper, this implies that the variability between the combination of chemical and site is very important. Chemicals are not equally toxic to all sex/species, even for the same tumor site. In our database, a chemical usually had only one experiment in one sex/species with an average of one control group and two dose groups. Thus we were unable to look at a single chemical on a specific tumor site since there would not be enough data. Even though we could combine data of a specific chemical across several tumor sites, the mechanisms that the chemical induces tumor might vary from site to site. While we unavoidably incorporate a mixture of factors (such as chemicals, sites, intra- and interspecies projections) in order to have enough data, it may wipe off the distinction between AR and RR.

There are a total of 646 cases where the number of tumors in that class was zero although both models predicted a response. Some might be double counted for the same predicted sex/species/experiment/site/dose. Zero observation may be due to small sample size (number of animal examined), low background rate, low response rate, or the combination. Figure 9 showed that in our data, most of the zero observations came from a sample size of about the average number of animal of the usual experiment design. It is likely that these zero observation were due to low background rate or/and low response rate to chemicals. We are unable to distinguish AR and RR models by the ratio of observed number to predicted number. A chi-square goodness-of-fit test may be applied for all zero and non-zero observation data. But we have to solve the problem that 0 and 1 account for a huge percentage of data such that we could not assign cells of equal probability to compare the distribution of observation and prediction.

For small predicted and observed numbers of tumors a bias is evident. The predicted numbers are too high for either model. We believe that this occurs because we have based the prediction on a statistically significant increase in tumor rates in the first sex/species. The demand for statistical significance forces the number to be at the upper end of a statistical fluctuation. Our criteria also rule out the enrollment of chemicals that are not carcinogens in the first sex/species but indeed are carcinogenic to other sex/species. The impact of our criteria of selecting "carcinogens" needs further investigation.

In some sites, such as liver adenoma, the control rate increased over time. The use of a fixed historical control rate for all experiments might lead to underestimation of cancer potency in experiments conducted in earlier years and over estimation for those during later years in our database.

The absolute risk model has long been used in regulating chemical carcinogens based upon rodent bioassay data. A large problem arises because the rodent species used in many carcinogenicity bioassays (the B63F1 mouse) was specifically chosen for the high sensitivity of the liver to carcinogens this is also associated with high background rates. Since the background tumor rates of liver tumors in humans is ½% compared with that in mice of over 10%, using an absolute risk model will give a prediction of human cancer rates 20 times that of the prediction by the relative risk model. Based on the same rationale, the estimated acceptable exposure levels in human from the two models would be different by the same factor. Since liver tumors are the most common response in rodent bioassays (e.g. Gold et al. 1991), deciding the correct model to use is important for proper regulation.

In setting standards for radiation exposure the Absolute Risk (AR) model was used for many years. Radiation Risk estimates are dominated by studies of the Hiroshima Nagasaki survivors (the LSS50 cohort) where the dose was given in 1945 and cancer rates are measured subsequently. It is assumed for example that the cancer rates thus obtained for Japanese (who have a high natural incidence of stomach cancer but a low natural incidence of colon cancer) apply to other countries. Another important difference is not between different species or sex but between tumor rates at different ages. If the radiation dose given at age 25 adds a certain amount to the cancer incidence as seen 30 years later, (and this amount is 50% of the cancer incidence at age 25) how does that increase apply to someone exposed at age 10 getting cancer 50 years later? Is the cancer increased by the same absolute amount or is it increased by the same amount relative to the natural incidence at age 10? In 1970, one did not know (NAS 1970). Since 1970 two to three times more (excess) radiation induced cancers have appeared in the LSS50 cohort than the absolute risk model would have predicted (except for leukemia where no excess cancers have appeared). Thus the relative risk model is now preferred for radiation protection calculations.

Generally speaking, the AR model is more conservative (gives a higher calculated risk to human beings) than RR model in two senses. Firstly AR is less likely to under-predict under most circumstances. In the setting of extrapolating from FM to others when the background rate of FM is higher than the predicted sex/species, RR is superior to AR. In that setting, AR on average predicted about 2.4 time the observed number, and RR predictions matched the corresponding observation better than AR. Though RR is still more likely to under-predict than AR. Predicting from a high to a low background rate is the context that we always encounter when assessing human cancer risk from results of rodent bioassays. From a policy point of view, more information is needed to assure that the use of RR in specific settings would lead to more accurate assessment than AR.

The work would not have been possible by the work of the many individuals who prepared the CBDS database. The work was funded by gifts to Harvard University from Pfizer Inc. and Zeneca Corporation to whom the authors are grateful. The authors thank Dr. John S. Evans for valuable comments and Mr. Sidney Atwood for technical assistance.

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The Observed number of tumors in Female Mice (FM) in site/tumor class 3 (GI papilloma) compared to the number projected from the measured potency in Male Mice (MM). Absolute Risk open circles, Relative Risk closed triangles. The line is the exact prediction. The spread about the line shows the inherent limitations of this study.

The Observed number of tumors in Male Rats (MR) in site/tumor class 7 (liver adenoma) compared to the number projected from the measured potency in Male Mice (MM). Absolute Risk open circles, Relative Risk closed triangles. The line is the exact prediction. It can be seen that the relative risk works better.

The Observed number of tumors in Male Rats (MR) in site/tumor class 64 (liver carcinoma compared to the number projected from the measured potency in Male Mice (MM). Absolute Risk open circles, Relative Risk closed triangles. The line is the exact prediction. Absolute risk works better.

The Observed number of tumors in Female Rats (FR) in site/tumor class 51 (squamous skin carcinoma) compared to the number projected from the measured potency in Male Mice (MM). Absolute Risk open circles, Relative Risk closed triangles. The line is the exact prediction. Neither model works well.

The distribution of the Ratio R = [Obs/Pred] for prediction of female rat (FR) tumors from male rat (MR) tumor rates; all non-liver tumors.

The distribution of the Ratio R = [Obs/Pred] for prediction of male rat (MR) tumors from male mice (MM) tumors; all non-liver tumors.

Figure 7

The distribution of the Ratio R = [Obs/Pred] for prediction at any other sex/species from female mice (FM) tumors; high background rate to low background rate only. All non-liver tumors. Zero observations excluded.

The distribution of the Ratio R = [Obs/Pred] for prediction at any other sex/species from female rat (FR) tumors; low background rate to high background rate only. All non-liver tumors. Zero observations excluded.

Figure 9

The distribution of the Ratio R = [Obs/Pred] for prediction of Liver adenoma (class 7) at any sex/species from any other species or sex; all non zero observations.

Figure 10

The distribution of the Ratio R = [Obs/Pred] for prediction of hepatocellular carcinoma (class 64) at any sex/species from any other species or sex; all non-zero observations.

Figure 11

The distribution of the Ratio R = [Obs/Pred] for all predictions for mutagenic compounds only.

[Obs/AR] is the ratio of observed to predicted number by AR model.

[Obs/RR] is the ratio of observed to predicted number by RR model.

Cases with Obs=0 are excluded due to log transformation.