Dose-Response Trend Tests for Tumorigenesis Adjusted for Differences in Survival and Body Weight across Doses

David W. Gaylor1 and Ralph L. Kodell

National Center for Toxicological Research, U.S. Food and Drug Administration, Jefferson, Arkansas 72079

Received July 21, 2000; accepted October 6, 2000


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
A relationship between rodent body weight and tumor incidence for some tissue/organ sites has been demonstrated in many studies. It is not uncommon for a chemical tested for carcinogenicity to also affect body weight due to toxicity and/or food consumption. In such cases, comparisons of tumor incidence may be biased by body weight differences across dose groups. A simple procedure was investigated for reducing this bias. This procedure divides the animals into a few groups on the basis of body weight. Body weight at 12 months was used, before the appearance of a tumor was likely to affect body weight. Statistics for dose-response trend tests are calculated within body weight strata and pooled to obtain an overall dose-response trend test. This procedure is analogous to stratifying animals on the basis of age at the time of removal from a study to account for differences in ages of animals across dose groups that can affect comparisons of tumor incidence. In this paper, differences in survival times of animals were adjusted by the Poly-3 technique used by the National Toxicology Program. This technique does not require the assignment of cause of death. Several examples from rodent chronic bioassays were investigated, where the high dose group had reduced body weights and associated reductions in tumor incidence. When we analyzed the data by body weight strata, some positive dose-response trends for tumor incidence were demonstrated. In one case, the body weight adjusted analysis indicated that a negative dose-response trend in tumor incidence was a real effect in addition to a body weight reduction. These examples indicate that it is important to consider the effects of body weight changes as low as 10%, and perhaps less, as possibly being caused by chemicals in 2-year bioassays for carcinogenesis. The simple procedure of analyzing tumor incidence within body weight strata can reduce the bias introduced by body weight differences across dose groups.

Key Words: dose response; tumorigenesis; trend test; body weight; Poly-3.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
Numerous studies have shown a positive correlation between rodent body weight and tumor incidence for some tissue sites (e.g., Kari and Abdo, 1995; Tannenbaum, 1940; Turturro et al., 1993). Hart and Turturro (1997) provide an overview of dietary intake, body weight, and tumor incidence. Gaylor and Kodell (1999) summarize potential mechanisms that relate tumor incidence to body weight. When toxicity or reduced food consumption results in lowered body weights as dosage increases, this could artificially result in reduced tumor incidence with dose. On the other hand, chemicals with therapeutic and/or nutritional components may result in higher body weights with increased dose, which could artificially inflate tumor rates.

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, 1988Go) 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, 1993Go), 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.


    Trend Test Adjusted for Body Weight
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
It has been recognized for several decades that tumor rates increase dramatically with age. Differences in survival across dose groups in a chronic bioassay can affect tumor rates and bias dose-response trend tests. Bailer and Portier (1988) introduced a procedure that adjusts for differences in survival without requiring the cause of death of tumor bearing animals. Their Poly-3 procedure incorporates a weighting scheme that allows fractional values for animals not at full risk for tumor development. This weighting scheme essentially modifies the denominators of the crude estimates of lifetime tumor incidence to approximate the total number of animals at risk in each group. The weight given an animal is w = (t/T)3, where T is the time of final sacrifice for the bioassay and t is the time of removal for an animal. If an animal lives to the end of the bioassay, it receives a full weight of one. An animal that gets a tumor of interest also counts as a full animal, regardless of the time of observance of the tumor. No assumption is required concerning the lethality of the tumor. The adjusted number of animals at risk in a group is n' = {Sigma}w, and the age-adjusted tumor incidence is (y/n') where y is the number of animals in the group that develop the tumor of interest.

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 = {Sigma}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 = {Sigma}jyij

wijk = (tijk/T)3 sample size weight assigned the kth animal in the jth dose of the ith body weight stratum;

n'ij = {Sigma}k wijk = effective number of animals at risk in the jth dose of the ith stratum;

n'i = {Sigma}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 = {Sigma}j yij/{Sigma}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)


Following Bieler and Williams (1993), the approximate variance of bi, which considers n'ij a random variable (see Appendix A), is


(2)

An overall estimate of the dose-response slope (b) is obtained by weighting the bi by the reciprocal of their variances


(3)

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 {Delta} is the maximum difference between adjacent doses. Note that the continuity correction, negative term in the numerator, approximates the usual value of {Delta}/2 if the Ci are approximately equal.

If the continuity correction is not included, the approximate test given in Equation 4Go 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 4Go 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., 2000Go).

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.


    Examples
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
p-Nitrobenzoic acid.
In the first example, data from the National Toxicology Program (1994) 2-year bioassay for p-nitrobenzoic acid are used to illustrate the weight stratification process for dose-response tests for carcinogenicity. In this study, the average body weights for female rats at 12 months were 271, 269, 260, and 243g in the 0, 1250, 2500, and 5000 ppm dietary groups, respectively. The high dose group weighed just 10% less than the control group. Seilkop (1995) and Turturro et al. (1993) indicate that mammary tumor incidence in female Fischer 344 rats is correlated with 12 month body weight. Hence, a weight-adjusted, dose-response analysis was conducted for mammary fibroadenoma.

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 1Go.


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TABLE 1 p-Nitrobenzoic Acid Administered to Female Fischer 344 Rats for Two Years in Feed
 
The 2 lower body weight groups indicate a dose-response trend. The overall test result across the 3 body weight groups is given in Table 2Go.


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TABLE 2 Estimates of Dose-Response Slope (b), Slope Test Statistic (Zc), and one-Sided p Value for Mammary Fibroadenoma in Female Fischer 344 Rats Administered p-Nitrobenzoic Acid in the Diet
 
The animals were divided into 2, 3, 4, 6, and 12 body weight groups, with nearly equal numbers per group, and slopes (dose-response trends) and variances of the slopes were calculated within each body weight stratum. Weighted averages of the slopes were calculated from Equation 3Go and tested for significant differences from zero using Equation 4Go. The results are summarized in Table 2Go. With 2 weight groups, the body weight ranges were from 217–259 g and 260–319 g at 12 months. With such diverse body weights within these 2 groups, no improvement was obtained over using no stratification of body weights. With 12 body weight groups, many of the groups had a weight range of only 5 grams. No demonstrable difference in tumor incidence would be expected among animals within these groups. Hence, more body weight groups were not examined. Also, as the number of body weight groups is increased, the number of animals per body weight-dose group decreases and frequently is zero. Thus, it is not uncommon, with a large number of body weight groups, to have animals for only 2 doses within a body weight group. In the comparison of the controls with the high dose group (Table 3Go), it was not possible to obtain 12 body weight groups with animals in both the controls and high dose groups. Three adjacent weight groups had to be pooled, resulting in 9 body weight groups. From the estimated slope (b), using Equation 3Go, the estimated difference between the control and 5000-ppm high-dose groups was 5000 x b (Table 3Go).


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TABLE 3 Estimates of the Difference in Mammary Fibroadenoma Incidence between the Controls and Female Fischer 344 Rats Fed 5000 ppm p-Nitrobenzoic Acid in the Diet
 
In this study, failure to recognize the lowered incidence of mammary fibroadenomas in the high dose group associated with lower body weights results in no detection of a dose-response trend. Accounting for differences in body weight across doses, by examining dose-response trends within body weight strata, resulted in a dose-response slope about 3 times larger than the unadjusted slope. The adjusted slope achieved a one-sided p value of 0.02 when 12 relatively homogeneous body weight groups were used (Table 2Go).

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 4Go.


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TABLE 4 O-Nitroanisole Administered to Female B6C3F1 Mice for Two Years in Feed
 
A dose response is apparent in the 2 larger body weight groups. Combined over the three body weight groups, the dose response has a one-sided p value of less than 0.01 (Table 5Go).


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TABLE 5 Estimates of Dose-response Slope (b), Slope Test Statistic (Zc), and One-Sided p Value for Hepatocellular Adenoma or Carcinoma in B6C3F1 Female Mice Administered O-Nitroanisole in the Diet
 
The results of using up to 4 body weight groups are summarized in Table 5Go. Ignoring the decreased liver tumor incidence associated with lower body weights in the higher dose groups failed to show the tumorigenicity of o-nitroanisole.

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 6Go).


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TABLE 6 Doxylamine Succinate Administered to Female Fischer 344 Rats for Two Years in Feed
 
The results of using up to 4 body weight groups are summarized in Table 7Go. Adjusting for the decreased mammary fibroadenoma incidence associated with lower body weights in the higher dose groups diminishes the negative dose-response trend.


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TABLE 7 Estimates of Dose-Response Slope (b), Slope Test Statistic (Zc), and One-Sided p Value for a Negative Trend for Mammary Fibroadenoma in Fischer 344 rats Fed Doxylamine in the Diet
 
There was such small overlap in similar body weights between the control group (3 animals) and the high dose group (9 animals) that a comparison of their incidence rates would be meaningless.

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.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
Several studies have shown a positive correlation for some tissue sites between rodent body weight and tumor incidence. This indicates that weight-adjusted comparisons of tumor rates are needed when animal body weights differ across dose groups. A standard covariance analysis of tumor incidence and body weight may not be appropriate because the treatment (chemical) also causes the difference in body weights. Seilkop (1995) uses historical tumor rates from control animals to provide a relationship between tumor incidence and body weight upon which tumor rate adjustments are made. This requires that the current study follow historical norms, if they are available.

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 2Go). 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, 1997Go). 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.


    APPENDIX A
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
Variance of bi
From Equation 9 of Bieler and Williams (1993) with n'ij treated as a random variable, the variance of p'ij is approximately


(A1)

From the Taylor's series expansion of p'ij, the variance of p'ij is approximately

(A2)

where


and based on a Poisson distribution approximation,


Substituting the above values into (A2) gives

(A3)

where aij = (n'ij)2/nij.

Equating this result to Equation A1Go 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 4Go. Under the null hypothesis of no dose effect, p'ij = p'i, for all j. Hence, Equation A4Go becomes

(A5)

Replacing (n'ij/n'ij) by the average of the (n'ij/n'ij) weighted by nij gives

(A6)
as used in Equations 2–4GoGoGo for V(bi), b, and the test statistic, ZC, respectively.


    APPENDIX B
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
Dose-Response Trend Test
The overall estimate (b) of the weighted slopes within body weight strata is given in Equation 3Go. The variance of b is,

(B1)

From Equation 2Go, V(bi) = Ci/deni, giving,

(B2)

The ratio of b to is distributed approximately as a standardized normal deviate,

(B3)

The Z-score is adjusted further by the continuity correction,

(B4)

where {Delta} is the maximum difference in dose between 2 adjacent doses. Note that the continuity correction term approximates the usual value of {Delta}/2 if the Ci are approximately equal.


    ACKNOWLEDGMENTS
 
The authors wish to thank Dr. Richard Hailey, National Institute of Environmental Health Sciences, Research Triangle Park, NC, for providing the 12-month body weights of animals from the National Toxicology Program bioassay on p-nitrobenzoic acid and o-nitroanisole.


    NOTES
 
1 To whom correspondence should be sent at Sciences International, Inc., 13815 Abinger Court, Little Rock, AR 72212. E-mail: dgaylor{at}sciences.com. Back


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 Trend Test Adjusted for...
 Examples
 DISCUSSION
 APPENDIX A
 APPENDIX B
 REFERENCES
 
Ames, B. N., and Gold, L. S. (1990). Chemical carcinogenesis: Too many rodent carcinogens. Proc. Natl. Acad. Sci. U.S.A. 87, 7772–7776.[Abstract]

Bailer, A. J., and Portier, C. J. (1988). Effects of treatment-induced mortality and tumor-induced mortality on tests for carcinogenicity in small samples. Biometrics 44, 417–431.[ISI][Medline]

Bieler, G. S., and Williams, R. L. (1993). Ratio estimates, the delta method, and quantal response tests for increased carcinogenicity. Biometrics 49, 793–801.[ISI][Medline]

Gaylor, D. W., and Kodell, R. L. (1999). Dose-response trend tests for tumorigenesis adjusted for body weight. Toxicol. Sci. 49, 318–323.[Abstract]

Hart, R. W., and Turturro, A. (1997). Dietary restrictions and cancer. Environ. Health Perspect. 105(Suppl.), 989–992.[ISI][Medline]

Jackson, C. D., and Blackwell, B.-N. (1993).Two-year toxicity study of doxylamine succinate in the Fischer 344 rat. J. Amer. College Toxicol. 12, 1–11.[ISI]

Kari, F., and Abdo, K. (1995). The sensitivity of the NTP bioassay for carcinogen hazard evaluation can be modulated by caloric restriction. In Dietary Restriction: Implications for the Design and Interpretation of Toxicity and Carcinogenic Studies. (R. Hart, D. Neumann, and R. Robertson, Eds.). ILSI Press, Washington, DC.

Kodell, R. L., Lin, K. K., Thorn, B. T., and Chen, J. J. (2000). Bioassays of shortened duration for drugs: Statistical implications. Toxicol. Sci. 55, 415–432.[Abstract/Free Full Text]

National Toxicology Program (1993). Toxicology and Carcinogenesis Studies of O-Nitroanisole in F344/N Rats and B6C3F1 Mice. NTP Tech. Rpt. 416. National Institute of Environmental Health Sciences, Research Triangle Park, NC.

National Toxicology Program (1994). Toxicology and Carcinogenesis Studies of p-Nitrobenzoic Acid in F344/N Rats and B6C3F1 Mice. NTP Tech. Rpt. 442. National Institute of Environmental Health Sciences, Research Triangle Park, NC.

Peto, R. Pike, M. C., Day, N. E., Gray, R. G., Lee, P. N., Parish, S., Peto, J., Richards, S., and Wahrendorf, J. (1980). Guidelines for simple, sensitive significance test for carcinogenesis effects in long-term animal experiments. IARC Monographs, Supplement 2, pp. 311–426. International Agency for Research on Cancer. Lyon, France.

Seilkop, S. K. (1995). The effect of body weight on tumor incidence and carcinogenicity testing in B6C3F1 mice and F344 rats. Fundam. Appl. Toxicol. 24, 247–259.[ISI][Medline]

Tannenbaum, A. (1940). The initiation and growth of tumors. I: Effects of underfeeding. Amer. J. Cancer 38, 335–350.

Turturro, A., Duffy, P. H., and Hart, R. W. (1993).Modulation of toxicity by diet and dietary macronutrient restriction. Mutat. Res. 295, 151–164.[ISI][Medline]





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