National Center for Toxicological Research, U.S. Food and Drug Administration, Jefferson, Arkansas 72079
Received July 21, 2000; accepted October 6, 2000
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ABSTRACT |
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Key Words: dose response; tumorigenesis; trend test; body weight; Poly-3.
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INTRODUCTION |
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Seilkop (1995) uses historical control animal data to provide a relationship between tumor incidence and body weight, upon which tumor rate adjustments are based. This provides a procedure when historical data are available, and the tumor incidence relationship to body weight for the current chemical under test follows historical trends. Gaylor and Kodell (1999) divide the experimental data into body weight groups from the current bioassay and calculate dose-response statistics within groups. An overall test for a dose-response trend is computed by pooling the statistics across weight groups in the same manner as age-adjusted analyses are currently calculated. Gaylor and Kodell (1999) used the procedure of Peto et al. (1980) within body weight groups to adjust for differences in survival across dose groups. In this paper, the Poly-3 method (Bailer and Portier, 1988) is used to adjust for differences in survival among animals within body weight groups. This approach adjusts for the number of animals at risk, based on survival. The Poly-3 dose-response trend test for tumorigenicity, which allows for variability in the estimate of the number of animals at risk (Bieler and Williams, 1993
), is used in this paper. This procedure is computationally simpler than the procedure of Peto et al. (1980), but more importantly, the approach used in this paper does not require assigning whether or not the tumor of interest was the cause of death for each animal bearing that tumor type. Thus, this paper employs the simple technique of estimating dose-response trends within body weight strata, as proposed by Gaylor and Kodell (1999), to adjust tumor incidence associated with different body weights across doses, but employs the simpler Poly-3 method for adjusting for tumor incidence associated with different survival across doses without requiring the cause of death of tumor bearing animals. The weight adjustment approach is illustrated for 3 chemicals in which lower body weights in the high dose groups may be associated with lower tumor incidence.
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Trend Test Adjusted for Body Weight |
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The procedure to account for differences in tumor incidence due to differences in body weights across doses is accomplished by dividing the animals into body weight strata with approximately an equal number of animals in each stratum. Dose-response trends are estimated within each stratum and then pooled across body weight strata to obtain an overall dose-response trend test.
Let
i = 1, 2, ... , s denote the body weight stratum;
j = 1, 2, ... , g denote the dose group;
nij = the number of animals initially at risk in the jth dose of the ith body weight stratum;
ni = jnij
dij = the dose level of the jth dose which is the same value for each body weight stratum;
yij = the number of animals with tumors in the jth dose of the ith stratum;
yi = jyij
wijk = (tijk/T)3 sample size weight assigned the kth animal in the jth dose of the ith body weight stratum;
n'ij = k wijk = effective number of animals at risk in the jth dose of the ith stratum;
n'i = j n'ij
p'ij = yij/n'ij = tumor incidence adjusted for survival in the jth dose of the ith stratum;
aij = (n'ij)2/nij;
p'i = j yij/
j n'ij = yi/n'i.
For the control group di1 = 0, and to simplify calculations without loss of generality for test statistics, di2 can be set equal to one for the group of lowest dosed animals and the other dij can be scaled accordingly, relative to that group.
Following Bieler and Williams (1993), a weighted least squares estimate of the slope of the dose-response trend for the ith body weight stratum is
![]() | (1) |
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![]() | (2) |
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An overall estimate of the dose-response slope (b) is obtained by weighting the bi by the reciprocal of their variances
![]() | (3) |
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A test of the null hypothesis that dose has no effect on tumor incidence, i.e., true slope = 0, is derived in Appendix B.
![]() | (4) |
where Z is approximately a standard normal deviate and is the maximum difference between adjacent doses. Note that the continuity correction, negative term in the numerator, approximates the usual value of
/2 if the Ci are approximately equal.
If the continuity correction is not included, the approximate test given in Equation 4 may underestimate the true p value when the total number of tumor occurrences across dose groups is small. An alternative to the test in Equation 4
for small tumor frequencies (e.g., 10 or fewer tumor bearing animals) is to use an exact version of the test without the continuity correction (Kodell et al., 2000
).
In older animals, the body weight might be influenced by the presence of disease, particularly a growing tumor, rather than the occurrence of a tumor influenced by the body weight. Seilkop (1995) investigated body weights at different ages and used the body weight of the animals after one year in a study for adjustments. Turturro et al. (1993) show that body weights taken earlier than 12 months may have a higher correlation with tumor incidence at some tissue sites. For purposes of illustration, 12 month body weights are used here. For a given chemical, the animals are divided into 2, 3, 4, etc. weight groups, with approximately equal numbers of animals per weight group. As the numbers of weight groups are increased, the body weights within a group become more homogeneous, but the number of animals per dose-weight group become smaller. The number of weight groups is limited by the requirement to have animals in at least 2 dose groups in order to estimate the slope (dose-response trend) within each body weight stratum.
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Examples |
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Initially, 50 animals were started in each dose group. The calculations of the numbers of animals at risk, adjusted for mortality before the presence of a tumor or the terminal sacrifice by the Poly-3 technique proposed by Bailer and Portier (1988), were 45.9, 43.6, 42.6, and 44.0 for the 0, 1250, 2500, and 5000 ppm doses, respectively. The lifetime incidences of mammary fibroadenoma, unadjusted for body weight differences, were 17/45.9, 15/43.6, 19/42.6, and 19/44.0, respectively, showing no dose-response trend. However, e.g., when the animals were stratified into 3 body groups, the number of animals with tumors divided by the Poly-3 number of animals at risk gave the survival and weight-adjusted mammary fibroadenoma incidence rates in Table 1.
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If a comparison of this result is made to the body weight-adjusted analysis using a trend test based on Peto et al. (1980), note that Gaylor and Kodell (1999) reported 2-sided p values.
O-Nitroanisole.
Female B6C3F1 mice were administered O-nitroanisole in the diet at 0, 666, 2000, and 6000-ppm concentrations in a National Toxicology Program (1993) study. At 12 months, the average body weights were 44g, 43g, 38g, and 25g, respectively. Initially, 50 animals were started on the study in each dose group. The calculations of the number of animals at risk, adjusted for mortality before the presence of tumor or the terminal sacrifice, were 45.7, 44.8, 46.5, and 47.8 for the respective dose groups, by the Poly-3 technique proposed by Bailer and Portier (1988). The lifetime incidence of hepatocellular adenoma or carcinoma, unadjusted for body weight difference, were 17/45.7, 21/44.8, 37/46.5, and 20/47.8 at 0, 666, 2000, and 6000 ppm, respectively, showing no dose-response trend. However, when the animals were divided into 3 body weight groups, e.g., the Poly-3 survival adjusted liver tumor incidence rates are given in Table 4.
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There was no overlap in body weights between the controls and the high dose group; thus, a comparison of these 2 groups is meaningless. This may be an indication that 6000 ppm exceeded the maximum tolerated dose.
Doxylamine succinate.
Jackson and Blackwell (1993) present the results of a 2-year carcinogenicity study conducted at the National Center for Toxicological Research, in which Fischer 344 rats were administered 0, 500, 1000, and 2000 ppm of doxylamine succinate in the diet. The average body weights for female rats, after 12 months on the study, were 295, 282, 263, and 229g in the 0, 500, 1000, and 2000 ppm groups, respectively. If ignoring the decreases in body weight with higher doses, results show a highly significant negative dose-response trend for mammary tumors. The Poly-3 survival-adjusted lifetime incidence rates for mammary fibroadenomas were 21/47.0, 18/46.5, 7/43.9, and 3/45.7, respectively. When the animals were divided into 4 body weight groups, the negative dose-response trend was greatly diminished (Table 6).
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Even when the dose-response trend tests were adjusted for lower body weights as dose increased, the negative trend appeared to remain. This suggests that doxylamine succinate may cause a decrease in mammary tumors by a mechanism in addition to or in conjunction with a reduction in body weight.
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DISCUSSION |
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The procedure proposed in this paper divides the animals into body weight groups and calculates dose-response trend statistics within these groups. An overall test for a dose-response trend is calculated by pooling the test statistics across body weight groups, in the same manner as age-adjusted analyses are often calculated. Hence, no external data to the bioassay or additional assumptions are required. The dose-response trend tests used in this paper follow the procedures of Bieler and Williams (1993), using Poly-3 adjustments for survival. However, body weight stratification can be used for any statistical dose-response test. The proposed test for trend pools results across body weight groups weighted inversely by their estimated variances.
When a chemical causes an increase in body weight and subsequent increase in tumor incidence, the analysis stratified body weight will tend to decrease a spurious positive dose-response trend, and hence decrease the statistical significance, if any, of a positive dose-response trend. When a chemical causes a decrease in body weight and a subsequent decrease in tumor incidence, the analysis within body weight groups will tend to disclose an increase in the dose-response trend. For example, without an adjustment for differing body weights across dose groups, p-nitrobenzoic acid did not exhibit a dose-response trend for mammary fibroadenoma. However, when animals were sorted into body weight groups, there is statistical evidence of an effect of p-nitrobenzoic acid on mammary fibroadenoma (Table 2). Seilkop (1995) also found increases in mammary tumors, when compared to historical controls, with the same 12-month body weights.
For female B6C3F1 mice administered o-nitroanisole, the decrease in body weight at the high dose and accompanying low incidence of hepatocellular tumors resulted in no dose-response trend. However, when the data were analyzed by weight groups, a highly significant dose-response trend was noted. Seilkop (1995) also found increases in the incidence of liver tumors when compared to historical controls, with the same average 12-month body weights.
For doxylamine succinate administered to female Fischer 344 rats, the negative dose-response trend for mammary tumors remains even after the weight adjusted analysis. This indicates that doxylamine succinate may have a beneficial effect for mammary tumors in addition to or in conjunction with the effect from body weight reduction.
Ames and Gold (1990) suggest that lower body weight may indicate cytotoxicity which could cause compensatory cell proliferation providing increased opportunities for mutations, and as a result artificially inflate tumor incidence at high doses. Analysis of tumor incidence results by body weight strata should also adjust for such a negative association between tumor incidence and body weight.
This paper does not address the issue of when it is necessary to account for differences in body weight across dose groups. In the example with p-nitrobenzoic acid, substantial effects on dose-response trend tests were obtained with a 10% difference in body weights. Seilkop (1995) and Turturro et al. (1993) show effects on tumor incidence for body weight differences less than 10%. Since stratifying by body weight is a simple procedure that imposes no additional assumptions, it can be applied universally. No information is lost in those cases where body weight has no influence.
Much of the data indicating a relationship between body weight and tumor incidence come from caloric restriction studies. Suggested mechanisms for influencing tumor incidence appear to be related to caloric intake rather than body weight (Hart and Turturro, 1997). Body weight serves as a simple, direct surrogate for dietary intake. It might be of interest for future research to investigate if stratifying on dietary intake and body weight provide similar results.
Any procedure to adjust for body weight changes must make the assumption that a body weight change has the same impact on tumor incidence regardless of the cause. For example, the implicit assumption is that a similar decrease in body weight due to reduced caloric intake or chemical toxicity has a similar effect on tumor incidence.
It appears that the animals should be divided into as many weight groups as possible and still maintain some animals in most dose groups in each weight group. When there is little overlap in body weights between the control animals and the high dose animals, as was the case with o-nitroanisole and doxylamine, only a few body weight groups may be feasible.
It could be argued that corrections of tumor incidence for body weight changes should not be made. If this is part of the mechanism through which a chemical influences tumor rate, perhaps it should contribute accordingly to the risk. On the other hand, it can be argued that at low doses body weights may not differ from unexposed control levels and, therefore, tumor rates should be adjusted for their effects at higher doses. The adjusted trend test proposed here to accommodate differences in body weight across dose groups is similar to adjusted trend tests commonly in use to accommodate differences in noncancer mortality across dose groups.
The above examples indicate that it is absolutely important to consider the differences in tumor incidence resulting from body weight differences caused by chemicals in 2-year bioassays for carcinogenesis. Such effects on tumor incidence can be significant even in studies where average body weight differences are 10% or perhaps less. The simple procedure of dividing the animals into a few groups stratified by body weight (12-month body weight was used in these analyses) and pooling dose-response trend statistics from body weight groups provides an easy method to adjust for body weight differences across dose groups.
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APPENDIX A |
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![]() | (A1) |
From the Taylor's series expansion of p'ij, the variance of p'ij is approximately
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where
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and based on a Poisson distribution approximation,
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Substituting the above values into (A2) gives
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where aij = (n'ij)2/nij.
Equating this result to Equation A1 gives
![]() | (A4) |
Following the approach of Bieler and Williams (1993), the test of the hypothesis of no dose effect, i.e., true slope = 0, contains the term Ci in Equation 4. Under the null hypothesis of no dose effect, p'ij = p'i, for all j. Hence, Equation A4
becomes
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Replacing (n'ij/n'ij) by the average of the (n'ij/n'ij) weighted by nij gives
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APPENDIX B |
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![]() | (B1) |
From Equation 2, V(bi) = Ci/deni, giving,
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The ratio of b to is distributed approximately as a standardized normal deviate,
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The Z-score is adjusted further by the continuity correction,
![]() | (B4) |
where is the maximum difference in dose between 2 adjacent doses. Note that the continuity correction term approximates the usual value of
/2 if the Ci are approximately equal.
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ACKNOWLEDGMENTS |
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NOTES |
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REFERENCES |
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