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Appendix F
Correlation Between Carcinogenic Potency and the Maximum Tolerated Dose: Implications for Risk Assessment
D. Krewski,1,2 D.W. Gaylor3, A.P. Soms4,5 & M. Szyszkowicz1
Current practice in carcinogen bioassay calls for exposure of experimental animals at doses up to the maximum tolerated dose (MTD). Such studies have been used to compute measures of carcinogenic potency such as the TD50 as well as unit risk factors such as q*/1 for predicting low dose risks. Recent studies have indicated that these measures of carcinogenic potency are highly correlated with the MTD. Carcinogenic potency has also been shown to be correlated with indicators of mutagenicity and toxicity. Correlation of the MTDs for rats and mice implies a corresponding correlation in TD50 values for these two species. The implications of these results for cancer risk assessment are examined in light of the large variation in potency among chemicals known to induce tumors in rodents.
1. Introduction
Carcinogen bioassay is an important source of information on the potential carcinogenic effects of chemicals. Current practice involves the exposure of animals at doses up to the maximum tolerated dose
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(MTD), defined as that dose which can be administered to rodents over the course of a lifetime without appreciably altering body weight or survival other than as a result of tumor occurrence (Munro, 1977). High doses such as the MTD are used to enhance tumor response rates, thereby increasing the likelihood of observing elevated tumor occurrence rates in a small sample of experimental animals. In this regard, Haseman (1985) has shown that more than two-thirds of the carcinogenic effects detected in feeding studies conducted under the U.S. National Toxicology Program (NTP) would have been missed if the highest dose had been restricted to one-half of the MTD.
The use of such high doses in animal cancer tests has been the subject of considerable debate (cf. McConnell, 1989). In particular, it has been argued that biochemical and physiological distortions occurring at high doses may lead to toxicity-induced carcinogenic effects that might not be expected to occur at lower doses (Carr & Kolbye, 1991; Clayson et al., 1992). Ames & Gold (1990) have suggested that high dose stimulation of mitogenesis will enhance mutagenesis, leading to the identification of rodent carcinogens that may not present a human health risk. Apostolou (1990) questioned the necessity of using the MTD in animal cancer tests on the grounds that many human carcinogens can be identified in animal tests at doses of one-half of the MTD or less.
Suggestions for redefining the high dose to be used in animal cancer tests to circumvent these issues have been made (Apostolou, 1990; Carr & Kolbye, 1991). Clayson et al. (1992) considered such proposals, but recommended retaining the MTD, while recognizing that nongenotoxic carcinogens that appear to be effective in animals only at high doses may not present a risk to humans exposed to much lower doses (cf. Butter-worth, 1990). Since the definition of the maximum dose to be used in animal cancer tests is of secondary importance for our present purposes, we make no attempt to resolve this issue here. Instead, the reader is referred to the recent report by the National Research Council (1992), which considers the definition of the maximum dose to be used in detail.
The completion of several hundred bioassays over the past two decades has resulted in the availability of a large data base that may be used in global analyses of bioassay data. Recent analyses have revealed that the MTD is highly correlated with quantitative measures of carcinogenic potency such as the TD50 (Bernstein et al., 1985; Reith and Starr, 1989a), defined as the dose that reduces the proportion of tumor-free animals by 50% (Peto et al., 1984).
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Since the maximum dose tested (MDT) in carcinogen bioassay may not always correspond to the maximum tolerated dose (MTD), we note that it may be more appropriate to claim that carcinogenic potency is correlated with the MDT rather than the MTD. However, since highest dose tested in most studies approximates the MTD, we will not always distinguish between the MDT and the MTD in what follows.
Carcinogenic potency has also been shown to be correlated with various measures of toxicity and mutagenic potential (Travis et al., 1990a). The MTD for rats has also been shown to be correlated with the MTD for mice, for carcinogens that are effective in both species, thereby implying a correlation between the TD50 values for these two species (Crouch and Wilson, 1979; Reith and Starr, 1989b).
These meta-analytic results have important implications for carcinogenic risk assessment. The correlation between the MTD and TD50 has led to suggestions that the latter measure of carcinogenic potency is simply an artifact of the experimental design specifying the highest dose to be used in the bioassay (Bernstein et al., 1985) and of the use of an essentially linear dose-response model to estimate the TD50 (Kodell et al., 1990). The existence of such a correlation has also led to suggestions that preliminary estimates of cancer risk may be derived from the MTD in the absence of carcinogen bioassay data (Gaylor, 1989).
In this paper, we examine these and other issues involved in the use of carcinogen bioassay data for risk assessment purposes. In section 2, we discuss measures of carcinogenic potency proposed in the literature. The reasons for the apparent correlation between the MDT and carcinogenic potency are explored in section 3. The prediction of the TD50 on the basis of indicators of subchronic toxicity and genotoxicity is discussed in section 4, along with the calculation of preliminary estimates of cancer risk based on the MTD. Evidence for interspecies correlation in carcinogenic potency is reviewed in section 5. Our conclusions regarding the implications of these results for carcinogenic risk assessment are presented in section 6.
2. Carcinogenic Potency
2.1 Measures of Carcinogenic Potency
Barr (1985) has reviewed a number of proposed measures of carci-
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nogenic potency. Such indices provide a quantitative measure of carcinogenic potential, which may be used to rank the relative potency of different carcinogens. A widely used measure of potency is the TD50 proposed by Peto et al. (1984). Application of the TD50 in ranking chemical carcinogens has recently been discussed by Woodward et al. (1991); the TD50 also represents a primary component of the multifactor ranking scheme proposed by Nesnow (1990). Letting P(d) denote the probability of a tumor occurring in an individual exposed to dose d, the TD50 is defined as the dose d that satisfies the equation
where R(d) is the extra risk over background at dose d. Thus, the TD50 is the dose for which the extra risk is equal to 50% or, equivalently, the dose at which the proportion of tumor-free animals is reduced by one-half.
The TD50 may be estimated on the basis of tumor response rates observed in laboratory studies involving a series of increasing dose levels. Sawyer et al. (1984) employ an essentially linear one-stage dose-response model for this purpose, with
The slope parameter ß in this one-hit model is related to the TD50 by
and has been used as a measure of potency by Crouch and Wilson (1981). To accommodate curvature, however, a nonlinear model such as the multi-stage (Armitage, 1985)
(qi = 0) or Weibull (Kodell et al., 1991)
(a, ß, k > 0) may be more appropriate. We note that the Weibull mod-
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el is not being proposed for purposes of low dose risk estimation; rather, it is a relatively simple yet flexible model that allows for curvature in the observable response range.
Another measure of potency, which has been used by the U.S. Environmental Protection Agency (1986), is the estimate of the linear term q1 in the multi-stage model. Since the extra risk is approximated by
at low doses, the value of q1 may be used to estimate the risk associated with environmental exposures to a dose d of a carcinogen. In practice, an upper confidence limit q1* on the value of q1 (Crump, 1984a) is used due to the instability of the maximum likelihood estimate of the linear term in the multi-stage model. This application is commonly referred to as the linearized multistage (LMS) model.
Estimates of q1* have been criticized on the grounds that they require extrapolation of data well below the experimentally observable tumor response range. The TD50, on the other hand, does not require low dose extrapolation, but does not lead directly to estimates of risk at environmental exposure levels. Since an added risk of 50% will not always be achieved at the MTD, estimation of the TD50 may also require extrapolation outside the experimental dose range, albeit to a lesser degree than with q1*. Of 217 bioassays considered by Krewski et al. (1990b), for example, 65 of the TD50 values exceeded the MDT (cf. Munro, 1990). The need to extrapolate above the experimental dose range can be reduced by the use of a lower quantile of the dose-response curve, such as the TD25 employed by Allen et al. (1988a). (Note that the TD25 will not generally be equal to one-half of the TD50 in the presence of curvilinear dose-response.)
Arguments in favor of the use of an even lower quantile of the dose-response curve can be made. Crump (1984b) introduced the notion of a benchmmark dose for toxicological risk assessment, which corresponds to a quantile such as the TD10. This benchmark dose is not strongly dependent on the dose-response model used to describe the data (Krewski et al., 1990a), and will likely lead to rankings similar to the TD50 or TD 25. Cogliano (1986) has recently shown that the TD10 is highly correlated with q1*; the TD10 could then be used as a starting point for linear extrapolation to lower doses, thereby providing a single index for
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potency ranking and low dose risk assessment. Other investigators have previously proposed linear extrapolation from the TD01 for low dose risk estimation (Mantel & Bryan, 1961; Van Ryzin, 1980; Farmer et al., 1982; Gaylor, 1983).
Another approach to estimating low dose risks is the model-free extrapolation (MFX) method proposed by Krewski et al. (1991a). This procedure assumes only that the dose-response curve is linear at low doses, and is based on a series of secant approximations to the slope of the dose-response curve obtained by linear interpolation between points in the low dose region and controls. Upper confidence limits on the slope of the dose-response curve based on MFX are generally close to the values of q1* obtained from the LMS model. If the dose-response curve is actually sublinear at low doses, the MFX method still provides an upper bound on low dose risks.
In practice, estimation of measures of carcinogenic potency such as the TD50 is not as straightforward as might appear from the preceding discussion. Ideally, estimation of the TD50 should take into account both intercurrent mortality in long-term animal studies and, when available, cause of death information (Finkelstein & Ryan, 1987; Finkelstein, 1991). Sawyer et al. (1984) propose methods for adjusting for intercurrent mortality with rapidly lethal tumors; Portier & Hoel (1987) show that estimates of the TD50 may be biased when the assumption of rapid tumor lethality is not satisfied. Dewanji et al. (1992) proposed a Weibull model that can be used for this purpose, provided that the survival times of individual animals are available for analysis. Bailar & Portier (1992) also use a Weibull model in estimating carcinogenic potency.
2.2 Carcinogenic Potency Database (CPDB)
Gold et al. (1984, 1986a, 1987, 1990) have tabulated the TD50 values for a large number of chemicals which have induced tumors in laboratory animals in their Carcinogenic Potency Database (CPDB). The TD50 values were calculated using statistical methods developed by Sawyer et al. (1984) and Peto et al. (1984) using a one-stage model. All TD 50 values are expressed in common units of mg/kg body weight/day, adjusted to a standard two year rodent lifetime, and corrected for intercurrent mortality whenever individual animal data was available (Gold et al.,
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1986b). When the level of exposure was not constant throughout the study period, a time-weighted average daily dose was used to determine the TD50. Although more precise methods of estimating carcinogenic potency with time-dependent exposure patterns are available (Murdoch & Krewski, 1988), this is not critical for our present purposes (cf. Murdoch et al., 1992).
The CPDB includes data on over 3700 experiments on 975 different chemicals conducted under the National Cancer Institute/National Toxicology Program and by other investigators who have reported their results in the scientific literature (Gold et al., 1989). For each chemical, the CPDB may include studies done on different sexes, species and strains; by various routes of exposure; or under other experimental conditions. For each experiment, the doses and crude tumor response rates for each lesion demonstrating evidence of a dose-related effect are provided, thereby affording the opportunity for secondary analyses of the experimental results.
2.3 Variation in Carcinogen Potency
The CPDB includes data on potent chemical carcinogens such as 2,3,7,8-tetraclorodibenzo-p-dioxin (TCDD), as well as less potent compounds such as DDT. Gold et al. (1984) noted that the TD50 value in the CPDB for chemicals inducing tumors in rats varied by seven orders of magnitude or 10 million-fold.
In studying the distribution of carcinogenic potency, Rulis (1986) noted that the TD50 values for 343 rodent carcinogens selected from the CPDB were roughly lognormally distributed. (In cases where more than one experiment was done on the same chemical or where more than one lesion was dose-related in a single study, the minimum TD50 value was used in this analysis.) Similar distributions have been observed using other subsets of the CPDB (Krewski et al., 1990b). For example, consider the distribution of TD50 values shown in Figure 1a for 191 of the 217 compounds considered previously by Krewski et al. (1990b). These compounds were selected to satisfy a number of criteria, including the requirements that the experiment have at least two doses in addition to unexposed controls and demonstrate clear evidence of carcinogenicity. The 26 experiments omitted from the current analysis included only one
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FIGURE 1a Variation in carcinogenic potency of 191 chemical carcinogens selected from the CPDB.
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nonzero dose level, which precluded the use of the Weibull model to estimate the TD50 (see annex A for a detailed discussion of this issue). The median TD50 based on the fitted lognormal distribution was approximately 29 mg/kg/day, with 10th and 90th percentiles of 0.5 and 896 mg/kg/day, respectively. Although the inter-decile range is limited to a range of potencies of about 2,000-fold, the observed potencies again vary by more than eight orders of magnitude due in large part to the very low TD50 value for TCDD.
Rulis (1986) suggested that this distribution of carcinogenic potency could be used to establish a level of exposure below which regulatory attention would not be required. Such a threshold of regulation would be established on the basis of a lower quantile of the distribution of TD50s, on the assumption that a new untested chemical would be unlikely to be more potent than most known animal carcinogens (Munro, 1990). This concept has also been considered by Zeise et al. (1984).
The distribution of TD50s in Figure 1a is subject to overdispersion, since each individual TD50 is subject to experimental error. The distribution of true TD50s may be determined using the shrinkage estimators described in annex B. This technique adjusts for overdispersion by ''shrinking" each estimated TD50 towards the mean TD50 on a logarithmic scale, using a shrinkage factor determined by the relative magnitude of the variation within and between experiments (see annex B for details). Due to the large variation in TD50s noted in different studies, and the comparatively small standard error for individual TD50s, application of the shrinkage estimator in this case reduces the variance of the logarithm (base 10) of the TD50 from 2 = 2.2 to 2 = 1.8 (Figure 1b).
2.4 Classification of Carcinogens
Based on an evaluation of 237 chemical carcinogens tested in the U.S. National Toxicology Program, Rosenkranz & Ennever (1990) showed that carcinogens that are active at multiple sites in more than one species tend to be more potent than carcinogens that affect a single species or a single tissue. McGregor (1992) recently examined the characteristics of chemical carcinogens in different categories used by the International Agency for Research on Cancer to classify the strength of evidence for carcinogenicity. Carcinogens in Group 1 (known human carcinogens) tended to be more potent in rodents than carcinogens in Group 2A (probable
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FIGURE 1b Variation in carcinogenic potency of 191 chemical carcinogens selected from the CPDB.
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human carcinogen), Group 2B (possible human carcinogens), and Group 3 (unclassifiable with respect to human carcinogenicity).
Rosenkranz & Ennever (1990) also showed that genotoxic carcinogens that demonstrated mutagenic effects in the Salmonella assay were, on average, more potent than nongenotoxic carcinogens that tested negative in Salmonella. Human carcinogens also appear to be predominantly genotoxic (Shelby et al., 1988; Bartsch & Malaveille, 1989).
Based on an examination of the potency of carcinogens evaluated by the International Agency for Research on Cancer, McGregor (1992) concluded that there did not appear to be a strong association between carcinogenic potency in rodents and genotoxicity. It was noted that the most potent rodent carcinogen (TCDD) is apparently nongenotoxic, whereas one of the least potent rodent carcinogens (phenacetin) is mutagenic in the Salmonella assay.
3. Correlation Between TD50 and the MTD
3.1 Empirical Correlations
Several investigators have noted a marked correlation between carcinogenic potency and the MDT (Bernstein et al., 1985; Gaylor, 1989; Krewski et al., 1989; Reith & Starr, 1989a). To demonstrate this relationship, we reanalyzed data in the CPDB on the 191 chemical carcinogens discussed in section 2.3. Following Gold et al. (1984), we first used the one-stage model to estimate the TD50 for each carcinogen based on the crude proportion of animals developing tumors at each dose (Figure 2a). To allow for curvilinear dose-response, the TD50 was also estimated using both the multistage and Weibull models (Figures 2b and 2c respectively). These estimates of carcinogenic potency values are all adjusted to a standard two year rodent lifetime as described in annex C. In each case, there is a strong positive association between the TD50 and the MDT, indicating that the most potent carcinogens in the database are those with the smallest MDTs.
The Pearson correlation coefficients between log10(TD50) and log10 (MDT) are 0.924, 0.952 or 0.821, depending on whether the one-stage, multistage or Weibull model is used to estimate the TD50. Note that the multistage model, which provides for curvature, yields a higher
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Estimates of V(k), V (log10b) and Cov (log10b, k) can be obtained using RISK 81 (Krewski and Vany Ryan, 1981).
Rather than discard the 69 data sets for which mle's could not be obtained, we chose to fit a Weibull model to each of these data sets using a fixed value of the shape parameter k. In this regard, we first separated the 69 data sets into two subgroups based on their overall shape. A value of k = 1.7 was used for the 42 data sets that demonstrated clear upward curvature, this being the median value of k observed among the 68 of the 122 data sets for which k > 1. Similarly, a value of k = 0.55 was used for the 27 data sets exhibiting downward curvature, this being the median value of the 54 of the 122 data sets for which k < 1. The variance of log10TD*/50 was then estimated using (A.9), with k treated as an estimated rather than a known parameter. Allowance for some degree of uncertainty in the value of k is desirable in order not to severely underestimate the variance of log10TD*/50 (cf. annex B).
The 26 data sets in which only a control and single dose group were available were not used here since no information on the shape of the dose-response curve is available.
Annex B. Shrinkage Estimators of the Distribution of Carcinogenic Potency
The distribution of TD50 values for a series of chemical carcinogens provides useful information on the variation in carcinogenic potency. Because each estimate of the true TD50 for a specific chemical is subject to estimation error, the distribution of estimated potency values will exhibit greater dispersion than the distribution of true potency values (TD50s). This overdispersion may be eliminated using empirical Bayes shrinkage estimators (Louis, 1984).
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Let Y = log10TD50 and suppose that E(Y) = µ = log10TD50, with V(Y) = s2. Let Y1,…, Yn denote the logarithms of the estimated TD50 values for a series of n chemical carcinogens. We suppose that Yi is normally distributed with mean µi and variance si2. We further suppose that µi are normally distributed with mean µ and variance t2 where t2 reflects the variance among the µi. Our objective is to estimate µ and t2, and hence describe the lognormal distribution of unknown TD50 values.
Noting that
an estimator of t2 is
where and is the estimator of V(log10TD50) based on (A.9).
The shrinkage estimator of µi is given by
where represents an estimator of the intrastudy correlation, is an estimator of the overall mean of the log potency distribution, and
is designed to protect against overadjustment for overdispersion. In general < 1, so that the estimators of the µi are obtained by
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"shrinking" the Yi toward the mean . The estimators of µi have the correct dispersion in that
In fitting the Weibull model in (A.1), we found that the estimate of the variance of the log10TD*50 based on (A.9) appeared to be excessively large in a small number of cases. In order not to underestimate the between-study variability based on (B.2), we used a trimmed mean S*si2/n*, in which the largest and smallest 10% of the observed values of si2 were omitted (Hampel et al., 1986, p. 79). Specifically, the summation S* covers only those n* = 153 observations falling in the central 80% of the distribution of the si2.
Annex C: Adjustment of Potency Values for Less than Lifetime Exposure
In order to ensure that TD50 values for different chemicals are comparable, some adjustment for differences in the duration of the experimental period is desirable. Gold et al. (1984) adjusted TD50 values by a multiplicative factor of f2, where f represents the fraction of a two year period encompassed by the study period. This effectively scales the TD50 values to a standard two year rodent lifetime. Specifically, we have
where the TD50 denotes the estimate of carcinogenic potency based on the observed data for the actual experimental period, and denotes the standardized value.
To motivate the use of the adjustment factor f2, consider the extended Weibull model
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depending on both dose d and time t. Under this model, the TD50(t) evaluated at time t is given by
Thus, the ratio of TD50's at two distinct times t1 and t2 is
where f = t1/t2. In the CPDB, Gold et al. (1984) use a one-stage model with k = 1 and set p = 2 based on empirical observations reported by Peto et al. (1984), leading to their adjustment factor f2. In our applications of the Weibull model in (A.1), we will use a similar adjustment factor of f2/k to standardize TD50 values to a two year rodent lifetime.
For a multi-stage model of the form
allowing for the effects of both dose d and time t, the TD50 at time t is obtained as the solution of the equation
It follows that the standardized value of the TD50 is obtained as the solution of the equation
As with the Weibull model, we set p = 2 in the applications considered in this paper.
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Annex D. Correlation Between TD50 and MTD
In this annex, we derive an analytical expression for the correlation between the TD50 and the MTD. To this end, suppose that the probability P(d) of a tumor occurring in an animal exposed to dose D = MTD satisfies the Weibull model
in (2.5), where the background parameter α > 0 and the shape parameter k > 0 are known. This is a generalization of the one-stage model used by Bernstein et al. (1985) in which k = 1.
Suppose that x of the n animals exposed to dose D develop tumors. Since and k are assumed known, β may be estimated by
where p0 = P(0) describes the spontaneous response rate. This leads to an estimate
of the TD50.
The estimate of β is appropriate for r ≤ x ≤ n-1. The lower limit of x = r is the minimum value of x that would lead to a statistically significant result at a nominal significance level of 0 < γ < 1; the value of r is determined from the fact that in the absence of a treatment effect at dose D, x follows the binomial distribution Bin (50, P(D)). The upper limit of x = n-1 is included since β, and hence TD50, is undefined for x = n.
The constraint x ≤ n-1 implies that
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whereas x ≤ r implies
We wish to find the correlation between Y = logeTD50 and X = log eD. (Although the correlation will be identical using logarithms to the base 10, the derivation of the correlation given here is simpler using natural logarithms.) Suppose now that W = TD50 follows a uniform distribution on the interval [a,b], reflecting the fact that given the value D of the MTD, the estimated value of the TD50 is unrelated to the MTD. Suppose further that X follows some distribution with mean µ and variance σ2. Although Bernstein et al. (1985) observed that the empirical distribution of X is approximately normal, the correlation between Y and X does not depend on the distribution of X other than through its variance σ2.
To calculate corr (Y, X), note that
and
where
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and
Thus we have
with V(X) = σ2. Noting that
where µ = E(X), we have
This leads to the desired result:
It can be shown that h2 - h12 + 1 ≥ 0, so that 0 < ρ ≤ 1. It can also be shown that ρ ↓ [σ2/(σ2 + 1)]1/2 as k ↓ 0, and that r 1 as k → ∞. Thus [σ2/(σ2 + 1)]1/2 ≤ ρ ≤ 1. In the limiting case as n → ∞, (D. 13) reduces to
The values of the correlation coefficient ρ in (D.13) as a function of
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the sample size n are shown in Table 1. (Note that the values of h1 and h2 are implicit functions of n.) These results are based on a one-stage model (k = 1) with a spontaneous response rate p0 = 0.10, and a nominal significance level of γ = 0.05 with r = 10 in the case n = 50. The value of σ2 = V(logeMTD) = 8.196 is based on the variance of the MTD of the 191 experiments considered previously by Krewski et al. (1990b). Using common logarithms, V(log10MTD) = 1.546.
The dependency of the correlations between log10TD50 and logeMTD on the Weilbull shape parameter k is illustrated in Table 2 for a sample size of n = 50. These results, including the limiting cases as k → 0 or ∞, are also based on (D.13). Note that the correlation remains high regardless of the value of k.
Annex E: Correlation Between TD50s For Rats and Mice
In this annex, we derive analytical expressions for the correlation between TD50 values for rats and mice. Letting Yrats and Ymice denote the logarithms (basee) of the estimated TD50s for rats and mice, we seek an expression for ρ = Corr(Yrats, Ymice). Following Bernstein et al. (1985) we assume initially that the MTD for rats is directly proportional to that for mice, with
Using the notation of annex D, we will denote the logarithms of the MTDs for rats and mice by Xrats and Xmice, so that
Note that (E.2) implies that V(Xrats) = V(Xmice) = σ2
As in annex D, we assume that the TD50s for rats and mice are uniformly distributed about their respective MTDs. From (D.10), we may then write
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where h1 and h2 are the same for rats and mice since g1 and g2 defined in (D.4) and (D.5) respectively are the same for rats and mice. Assuming that Yrats and Ymice are conditionally independent, given MTDmice (and hence MTDrats from (D.1)), we have
Hence
where ρ = Corr(Yrats, Xrats) is given in (D.13) of annex D. Based on the n = 127 compounds from the CPDB considered in section 6.1, we find σ2rats = 10.065 ≈ σ2mice = 8.873. For σ2 = 10, we have ρ = 0.943.
The assumption (D.1) of strict proportionality between MTDrats and MTDmice can be relaxed. Let V(Xrats) = σ2rats and V(Xmice) = σ2mice . As in (D.3), we have
and
Assuming Yrats and Ymice are conditionally independent, given Xrats and Xmice, we have
and hence
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For the n = 127 compounds considered in section 6.1, we estimate Cov (Xrats, Xmice) = 7.638, and ρ = 0.763
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Representative terms from entire chapter:
low dose
