1. Hojin Moon, Ph.D. E-mail: HMoon@nctr.fda.gov September 16, 2005
Statistical Methods for Testing Carcinogenic Potential of New Drugs in Animal Carcinogenicity Studies
Hojin Moon, Ph.D.
September 16, 2005
September 16, 2005

2. Collaborators Dr. Ralph L. Kodell – DBRA, NCTR, FDA
Dr. Hongshik Ahn – Brook
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

3. Animal Carcinogenicity Study
Studies are conducted to assess the oncogenic potential of chemicals encountered in food or drugs for the protection of public health
Studies often involve a problem of testing the statistical significance of a dose-response relationship among dose (treatment) groups.
Various statistical testing methods for a dose-response relationship (Ahn and Kodell, 1998)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

4. Animal Carcinogenicity Study
Typical Experimental Design:
A zero-dose control and 2 or 3 dose groups
50 or more animals (mice or rats) per sex/group
Exposure to a test agent at treatment groups of varying doses for the duration of a study
At least 18 months in mice, 24 months in rats (CDER, US FDA in Office of the Federal Register, 1985)
Multiple (interval) sacrifices or single terminal sacrifice
Age at death (survival time) and status (presence/absence) of specific tumor types
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

5. Animal Carcinogenicity Study
Methods:
Data with cause-of-death information assigned by pathologists (Peto type)
Data without cause-of-death information (Poly-k type)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

6. Animal Carcinogenicity Study
The statistical analysis of animal carcinogenicity data and the Peto COD controversy are current issues in the government-regulated pharmaceutical industry
(Lee et al., 2002; STP Peto Analysis Working Group, 2001, 2002; U.S. FDA, 2001)
Town Hall meetings were held in both June 2001 & June 2002 at the annual meetings of the STP to discuss issues surrounding COD assignment and implications for using the Peto test or the alternative Poly-3 test
Opinions of a number of statisticians (Lee et al., 2002)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

7. Dose-Related Trend Tests
Peto Test (Peto et al., 1980)
Recommended by IARC
Required for product registration in Europe
Commonly used in most pharmaceutical companies
Needed COD assigned by pathologists
Use of COD information has been controversial:
(Lagakos, 1982; Racine-Poon & Hoel, 1984; Lagakos & Louis, 1988; Kodell et al., 1995; Ahn et al., 2000; Moon et al., 2002; Moon et al., 2003)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

8. Dose-Related Trend Tests
Modifications of Peto’s Test
The Peto imputed COD test (Moon et al., 2002)
No COD required
Developed constrained NPMLE method to impute COD
Imputation of COD:
Solve the constrained NPMLE problem by implementing Newton-based method of Ahn, Moon, Kim and Kodell (2002)
The weight-adjusted Peto Test (Moon et al., 2004)
Use of Fleming-Harrington type weight adjustment (Fleming & Harrington, 1981)
Web-based sample size and power estimator (Moon et al, 2002)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

9. Dose-Related Trend Tests
Cochran-Armitage Trend Test (Cochran, 1954; Armitage, 1955)
To detect linear trend across dose groups in lifetime tumor incidence rates
Does not require COD
Requires an assumption under H0 that all animals are at equal risk of developing a tumor over the duration of a study
A problem for this test arises from the presence of treatment-induced mortality unrelated to the tumor of interest
The CA test is known to be sensitive to increase in treatment lethality and to fail to control the probability of a Type I error (Bailer & Portier, 1988; Mancuso et al., 2002; Moon et al., 2003)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

10. Cochran-Armitage Trend Test
Dose Group 1 2 …. g
Total
# w. T y1 y2 yg y.
# w/o T
N1 - y1
N2 - y2
Ng – yg
N - y.
# subjects N1 N2 Ng N
The CA test utilizes the tumor data pooled over the study duration for each group
Expected # w T in group
Dose level in group
Under the null hypothesis of equal tumor incidence rates among groups
Some treatments shorten overall survival -> decreased risks of tumor onset
Survival time is not utilized
Observed # w T in group
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

11. The Poly-k Trend Test Appropriate alternative to the Peto-type test
No COD required
Adopted by NTP as its official test for carcinogenicity
Survival-adjusted quantal-response procedure that takes dose-group differences in intercurrent mortality (all deaths other than those resulting from a tumor of interest) into account.
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

12. The Poly-k Trend Test Bailer & Portier (1988)
Proposed the Poly-3 test, which made an adjustment of the CA test by using a fractional weighting scheme
# at risk in group
where
(time-at-risk weight for the kth animal in group i)
Replace Ni with ri in calculating ZCA
First mentioned the Poly-k test without specifying how to obtain k
Recommended k=3 following evaluation of neoplasm onset time distribution in control F344 rats and B6C3F1 mice (Portier et al., 1986)
The Poly-k test with correct k -> Superior operating characteristics to the Poly-3 test
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

13. The Poly-k Trend Test Bieler & Williams (1993) Objectives
Further modified the CA test by an adjustment of the variance estimation of the test statistic using the delta method (Woodruff, 1971)
Showed that the Bailer-Portier Poly-3 test is anticonservative for low tumor incidence rates and for high treatment toxicity
Characteristics of the BP Poly-3 test and the BW Poly-3 test can be found in Chen et al. (2000)
Objectives
The Poly-k statistic: asymptotically normal under H0 of equal tumor incidence rates among groups (Bieler & Williams, 1993)
Valid only if the correct value of k is used
Develop the method of bootstrap resampling to estimate the empirical distribution of the test statistic and corresponding critical value of the Poly-k test while taking into account the presence of competing risks
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

14. Generalized Poly-k Test
Moon et al. (2003)
Proposed a method for estimating k for data with interval sacrifices (interim sacrifices and a terminal sacrifice)
Estimation of the poly-k based empirical lifetime cumulative tumor incidence rate, a function of k
Estimation of cumulative tumor incidence rate (Kodell & Ahn, 1997)
Equate two estimate and find k
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

15. Generalized Poly-k Test
Moon et al. (2005) – Bootstrap-based age-adjusted Poly-k test
Improving the Poly-k test for data with a single terminal sacrifice
Estimation of k for single sacrifice data is more difficult than that for data with interval sacrifices due to lack of information on tumor development among live animals before the termination of the experiment
Propose a method of bootstrap-based age-adjusted resampling to improve the Poly-k test via a modification of the permutation method of Farrar & Crump (1990), which was used for exact statistical tests
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

16. Objectives
Develop the method of bootstrap resampling to estimate the empirical distribution of the test statistic and corresponding critical value of the Poly-k test while taking into account the presence of competing risks that are possible COD
We attempt to keep the CRSR using an age-adjusted resampling scheme as well as to preserve the tumor incidence rates under H0 and to assess the significance of the Poly-k test
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

17. Bootstrap Method . . . . . X = (x1, x2, …, xn) Data Set T(X) Bootstrap
Bootstrap
X*1
X*2
X*B
Samples
T(X*1)
T(X*2)
T(X*B)
Replicates
100(1-α)th percentile: CR(X)
Reject H0 if T(X) ≥ CR(X)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

18. Bootstrap Method Suitable for data with the same CRSR
When the CRSR is different across dose groups in the original data, the bootstrap samples from the pooled data may not reflect the CRSR of each group, while satisfying the null distribution of equal tumor incidence rate across groups
Need to modify the bootstrap method in order to preserve the survival rates in each dose group
Develop an age-adjusted scheme
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

19. Age-adjusted Bootstrap Scheme
X = (x1, x2, …, xn)
Data Set
T(X)
Age-adjusted scheme
I(I,m); i=1,….,G; m=1,….,Mi
Samples
X*1
X*2
X*B
Bootstrap
T(X*1)
T(X*2)
T(X*B)
Replicates
Bootstrap
100(1-α)th percentile: CR(X);
Reject H0 if T(X) ≥ CR(X)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

20. Example
Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups ID
Group 1
Group 2
Group 3
Group 4 A 74 B
145 C
176 D
185 E
243 F
300 G
316 H
324 I
340 J
341 K
343 L
345 M
351 N
385
…..
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

21. Example
Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups ID
Group 1
Group 2
Group 3
Group 4 A 74 B
145 C
176 D
185 E
243 F
300 G
316 H
324 I
340 J
341 K
343 L
345 M
351 N
385
…..
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

22. Example
Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups ID
Group 1
Group 2
Group 3
Group 4 A 74 B
145 C
176 D
185 E
243 F
300 G
316 H
324 I
340 J
341 K
343 L
345 M
351 N
385
…..
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

23. Example
Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups ID
Group 1
Group 2
Group 3
Group 4 A 74 B
145 C
176 D
185 E
243 F
300 G
316 H
324 I
340 J
341 K
343 L
345 M
351 N
385
…..
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

24. Simulation Study
To evaluate the improvement of the proposed test in terms of the robustness to a variety of tumor onset distributions
Typical bioassay design according to standard designs of NTP
4 dose groups (dose levels: 0, 1, 2 and 4) of 50 animals each
Experimental duration of 2 yrs.
A single terminal sacrifice at the end of the experiment
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

25. Simulation Study
Illustration of illness and death with possible transitions (Kodell & Nelson, 1980)
Normal
Tumor (T1)
Death from Competing Risks (T3)
Death from Tumor (TD)
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

26. Simulation Study Modeling T1: Time to tumor onset
S(t) = exp[-θδ(t/tmax)k]
T2: Time after onset until death from the tumor
Q(t) = exp[-φ(γ1t+ γ2t γ3)]
T3: Time to death from a competing risk
The same form as Q(t)
φ is selected to reflect tumor lethality
T1 + T2 = TD: Time to death from the tumor of interest
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

27. Simulation Study Tumor onset distributions: Tumor rates:
Weibull tumor onset distribution with shape parameter k = 1.5, 3.0 and 6.0
Tumor rates:
.05, .15 and .30 for the control
Size evaluation:
tumor rates are the same across dose groups
Power evaluation:
tumor rates for the highest dose group by 104 weeks: 5, 3 and 2 times the background tumor rates of .05, .15 and .30, respectively
CRSR (from NTP feeding studies, Haseman et al., 1998)
(.6, .6, .6, .6); (.6, .5, .4, .3); (.6, .6, .5, .2); (.5, .5, .5, .2); (.5, .6, .5, .4); (.5, .7, .6, .4); (.5, .7, .6, .5)
5000 simulated data sets; α = .05 significance level;
For each data set, 5000 bootstrap samples
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

28. Simulation Study
Size & Power Evaluation with 5000 simulated data sets, 5000 bootstrap samples for each data set and 5% nominal significance level TR
CRSR
Weibull 1.5
Weibull 3.0
Weibull 6.0 B N .3
.6,.6,.6,.6
.053
.050
.054
.055
.052
.5,.5,.5,.2
.044
.066
.041
.040
.021
.6,.6,.5,.2
.036
.072
.033
.037
.018
.6,.5,.4,.3
.047
.069
.043
.045
.024
.5,.6,.5,.4
.049
.048
.5,.7,.6,.4
.046
.5,.7,.6,.5
.051
.918
.934
.908
.923
.893
.904
.837
.932
.781
.847
.725
.667
.790
.939
.734
.846
.668
.638
.864
.938
.825
.884
.773
.748
.886
.929
.868
.895
.834
.819
.881
.930
.856
.892
.817
.810
.927
.909
.859
.865
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

29. Example The 2-yr Gavage Study of Furan
Furan (C4H4O), a clear and colorless liquid, serves primarily as an intermediate in the synthesis and preparation of numerous organic compounds (NTP, 1993)
Toxicology and carcinogenesis studies were conducted by administering furan in corn oil by gavage to groups of F344/N rats and B6C3F1 mice of each sex for 2 yrs
Furan was nominated by the NCI for evaluation of carcinogenic potential due to its large production volume and use, and because of the potential for widespread human exposure to a variety of furan-containing compounds
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

30. Example Female F344/N rats Male B6C3F1 mice
Evaluation of carcinogenic potential on incidences of cholangiocarcinoma or hepatocellular neoplasms of the liver
Groups of 50 rats were administered 2, 4 or 8 mg furan per kg body weight in corn oil by gavage 5 days per week for 2 yrs
Male B6C3F1 mice
Evaluation of carcinogenic potential on incidences of adenocarcinoma or alveolar/bronchiolar adenoma of the lung.
Groups of 50 mice received doses of 8 or 15 mg/kg furan 5 days per week for 2 yrs
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

31. Animal Tumor Pathology
Data
Group
Animal Tumor Pathology
Livera
Vehicle Control
1(0), 2(16), 3(0), 4(34)
2 mg/kg
1(1), 2(17), 3(1), 4(31)
4 mg/kg
1(3), 2(19), 3(3), 4(25)
8 mg/kg
1(4), 2(27), 3(6), 4(13)
Lungb
1(3), 2(14), 3(4), 4(29)
1(4), 2(24), 3(3),4(19)
15 mg/kg
1(7), 2(23), 3(6), 4(14)
aCholangiocarcinoma or hepatocellular neoplasms of the liver in female F344/N rats
bAdenocarcinoma or alveolar/bronchiolar adenoma of the lung in male B6C3F1 mice
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

32. Test results on the carcinogenic activity of furan in female F344/N rats based on increased incidences of cholangiocarcinoma and hepatocellular neoplasms of the liver (Reject when T(X) ≥ CR(X))
mg/kg
T(X)aBW
CR(X)bNormal
CR(X)cBootstrap
Overall
4.1617
(p<.001)
(p<.001)
0,2,4
2.7705
(p=.003)
(p=.004)
0,2,8
4.3559
(p<.001)
0,4,8
3.6632
(p<.001)
0,2
1.4641
(p=.072)
(p=.040)
0,4
2.6542
(p=.004)
(p=.001)
0,8
3.8420
(p<.001)
aThe BWP3 test statistic obtained from the data
bStandard normal critical value at the significance level .05
cCritical value estimated by the 95th percentile of T(X)’s from our method
NTP concluded that under the conditions of these 2-yr gavage studies, there was clear evidence of carcinogenic activity of furan in female F344/N rats based on increased incidences of cholangiocarcinoma and hepatocellular neoplasms of the liver
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

33. Our test results agree with the conclusions from NTP
Test results on the carcinogenic potential of furan on incidences of adenocarcinoma and alveolar/bronchiolar adenoma of the lung in male B6C3F1 mice (Reject when T(X) ≥ CR(X))
mg/kg
T(X)aBW
CR(X)bNormal
CR(X)cBootstrap
Overall
1.6995
(p=.045)
(p=.058)
0,15
1.6805
(p=.046)
(p=.052)
0,8
.2229
(p=.41)
(p=.53)
aThe BWP3 test statistic obtained from the data
bStandard normal critical value at the significance level .05
cCritical value estimated by the 95th percentile of T(X)’s from our method
Our test results agree with the conclusions from NTP
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

34. Significance
The statistical analysis of tumorigenicity data from animal bioassays remains an important regulatory issue to FDA and the pharmaceutical industry
The present research will build to further refine the Poly-k test in order to make it more broadly competitive with the Peto test
The improved Poly-k test for dose-related trend will be robust to a variety of tumor onset distributions.
It will control the false positive rate better than the Poly-3 test, thus having enhanced performance in identifying dose-related trends.
With no information on COD or tumor lethality, the improved version can be used confidently when Peto’s test can not be implemented
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

35. References
Ahn H, Kodell RL (1998). Analysis of long-term carcinogenicity studies. In Design and Analysis of Animal Studies in Pharmaceutical Development, Chow SC, Liu JP (eds). Marcel Dekker, Inc.: New York,
Armitage P (1955). Tests for linear trends in proportions and frequencies. Biometrics, 11,
Bailer AJ, Portier CJ (1988). Effects of treatment-induced mortality and tumor-induced mortality on tests for carcinogenicity in small samples. Biometrics, 44,
Bieler GS, Williams RL (1993). Ratio estimates, the delta method, and quantal response tests for increased carcinogenicity. Biometrics, 49,
Chen JJ, Lin KK, Huque MF, Arani RB (2000). Weighted p-value for animals carcinogenicity trend test. Biometrics, 56,
Cochran WG (1954). Some methods for strengthening the common x2 tests. Biometrics, 10,
Lee PN, Fry JS, Fairweather WR, Haseman JK, Kodell RL, Chen JJ et al. (2002). Current issues: statistical methods for carcinogenicity studies. Toxicologic Pathology, 30,
Mancuso JY, Ahn H, Chen JJ, Mancuso JP (2002). Age-adjusted exact trend tests in the event of rare occurrences. Biometrics, 58,
Moon H, Ahn H, Kodell RL, Lee JJ (2003). Estimation of k for the poly-k test. Statistics in Medicine, 22,
National Toxicology Program (1993). Toxicology and carcinogenesis studies of furan in F344/N rats and B6C3F1 mice (Gavage studies). NTP Technical Report, 402, Research Triangle Park, NC.
STP Peto Analysis Working Group (2001). The Society of Toxicological Pathology’s position on statistical methods for rodent carcinogenicity studies. Toxicologic Pathology, 29(6),
STP Peto Analysis Working Group (2002). The Society of Toxicological Pathology’s recommendations on rodent carcinogenicity studies. Toxicologic Pathology, 30,
U.S. FDA (2001). Guidance for industry: statistical aspects of the design, analysis, and interpretation of chronic rodent carcinogenicity studies of pharmaceuticals. Federal Register, 66(89),
Woodruff RS (1971). A simple method for approximating the variance of a complicated estimate. Journal of the American Statistical Association, 66,

36. Ongoing Research
Developing improved survival-adjusted statistical tests in long-term tumorigenicity bioassays (NCTR E )
Developing estimators for hazard identification in long-term tumorigenicity bioassays (NCTR E )
Developing statistical procedures for incorporating dose-response-model uncertainty into microbial risk assessment (NCTR E )
Developing statistical tests for distinguishing tumor frequency risks (effect on the number of induced tumors) from tumor latency risks (effect on their times to observation) in mutiple-tumor photococarcinogenicity studies (NCTR E )
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

37. Abstract
Researches in carcinogenicity have been actively conducted to understand the carcinogenic potential of chemicals exposed to humans. Long-term and animal-intensive carcinogenic studies have been performed to extrapolate carcinogenic risks in humans from exposure to drugs and food tainted. In this seminar, we discuss recent development of improved survival-adjusted and age-adjusted dose-related trend tests to achieve improved robustness to a variety of tumor onset distributions. We consider extensions of the survival-adjusted Cochran-Armitage test, known as the Poly-k test, to improve the robustness not only to the effects of differential mortality across groups but also to various tumor onset distributions. The Cochran-Armitage test is routinely applied for detecting a linear trend in the incidence of a tumor of interest across dose groups. We examine our recently developed statistical methods with real data sets including National Toxicology Program data sets to evaluate a dose-related trend of a test substance on the incidence of neoplasms.
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

38. Animal Carcinogenicity Data from the ED01 Study - NCTR
To find the carcinogenic effect of feeding 2-AAF to female mice (Littlefield et al., 1980)
A subset (low dose groups) of data with a single sacrifice was obtained
To test dose-related trend of the liver tumor incidence
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration

39. Frequency Tabulation of number of mice in the ED01 study
Dose (ppm)
NTP intervals (days)
Fatal tumors assigned by pathologists
Natural Death
Sacrifice
With tumor
Without tumor
Tumor present
No tumor present
0-364 9 15 1 34 60 7
137 30 17 2 42 6 67 84 22
279 35 3 31 55 80 18
192 45 13 5 43 66 19
132
September 16, 2005
National Center for Toxicological Research, U.S. Food and Drug Administration