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September 16, 2005September 16, 2005
Statistical Methods for Testing Statistical Methods for Testing Carcinogenic Potential of New Drugs Carcinogenic Potential of New Drugs
in Animal Carcinogenicity Studiesin Animal Carcinogenicity Studies
Hojin MoonHojin Moon, Ph.D., Ph.D.E-mail: [email protected]
SeptemberSeptember 16,16, 200 20055
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
CollaboratorsCollaborators
Dr. Ralph L. Kodell – DBRA, NCTR, FDADr. Ralph L. Kodell – DBRA, NCTR, FDADr. Hongshik Ahn – SUNY@Stony BrookDr. Hongshik Ahn – SUNY@Stony Brook
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Animal Carcinogenicity StudyAnimal 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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Animal Carcinogenicity Animal Carcinogenicity StudyStudy
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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Dose-Related Trend TestsDose-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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Cochran-Armitage Trend Test Cochran-Armitage Trend Test Dose GroupDose Group
11 22 …….. gg TotalTotal
# w. T# w. T yy11 yy22 …….. yygg y.y.
# w/o T# w/o T NN11 - y - y11 NN22 - y - y22 …….. NNgg – y – ygg N - y.N - y.
# subjects# subjects NN11 NN22 …….. NNgg NN)/.(: NNyEi ii 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
iyi :
, gi iii EydX 1 )(
idi :
NdNdddNNNyNyV igi i
gi ii /)()()]}1(/[.).({ 11
2 ,
Observed # w T in group
VXZCA /
)1,0(: NZH CAo
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
The Poly-The Poly-kk Trend Test 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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
The Poly-The Poly-kk Trend Test 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
iNk iki wri 1:
tumor with dies if
otherwise max
1
)/( 3ttikik
w
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
The Poly-The Poly-kk Trend Test Trend Test Bieler & Williams (1993)
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-The Poly-kk statistic: asymptotically normal under H statistic: asymptotically normal under H00
of equal tumor incidence rates among groups (Bieler of equal tumor incidence rates among groups (Bieler & Williams, 1993)& Williams, 1993)
Valid only if the correct value of Valid only if the correct value of kk is used is used Develop the method of bootstrap resampling to Develop the method of bootstrap resampling to
estimate the empirical distribution of the test estimate the empirical distribution of the test statistic and corresponding critical value of the Poly-statistic and corresponding critical value of the Poly-kk test while taking into account the presence of test while taking into account the presence of competing riskscompeting risks
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Generalized Poly-Generalized Poly-kk Test 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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Generalized Poly-Generalized Poly-kk Test 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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Age-adjusted Bootstrap Scheme
X = (xX = (x11, x, x22, …, x, …, xnn))Data Set
T(X)
Samples
Replicates
. . . . .
Bootstrap XX*1*1 XX*2*2 XX*B*B
. . . . .
. . . . .
T(X*1) T(XT(X*2*2)) T(XT(X*B*B))Bootstrap
Age-adjusted scheme
I(I,m); i=1,….,G; m=1,….,Mi
100(1-100(1-αα))th percentile: percentile: CR(X)CR(X); ;
RejectReject H H00 if if T(X) ≥ T(X) ≥ CR(X)CR(X)
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
ExampleExample
IDID Group 1Group 1 Group 2Group 2 Group 3Group 3 Group 4Group 4
AA 7474
BB 145145
CC 176176
DD 185185
EE 243243
FF 300300
GG 316316
HH 324324
II 340340
JJ 341341
KK 343343
LL 345345
MM 351351
NN 385385
……....
• Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
ExampleExample
IDID Group 1Group 1 Group 2Group 2 Group 3Group 3 Group 4Group 4
AA 7474
BB 145145
CC 176176
DD 185185
EE 243243
FF 300300
GG 316316
HH 324324
II 340340
JJ 341341
KK 343343
LL 345345
MM 351351
NN 385385
……....
• Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
ExampleExample
IDID Group 1Group 1 Group 2Group 2 Group 3Group 3 Group 4Group 4
AA 7474
BB 145145
CC 176176
DD 185185
EE 243243
FF 300300
GG 316316
HH 324324
II 340340
JJ 341341
KK 343343
LL 345345
MM 351351
NN 385385
……....
• Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
ExampleExample
IDID Group 1Group 1 Group 2Group 2 Group 3Group 3 Group 4Group 4
AA 7474
BB 145145
CC 176176
DD 185185
EE 243243
FF 300300
GG 316316
HH 324324
II 340340
JJ 341341
KK 343343
LL 345345
MM 351351
NN 385385
……....
• Death times (in days) in a hypothetical animal carcinogenicity data set with 4 groups
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Simulation StudySimulation 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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Simulation StudySimulation Study Tumor onset distributions:Tumor onset distributions:
Weibull tumor onset distribution with shape parameter Weibull tumor onset distribution with shape parameter kk = 1.5, = 1.5, 3.0 and 6.03.0 and 6.0
Tumor rates: Tumor rates: .05, .15 and .30 for the control.05, .15 and .30 for the control
Size evaluation: Size evaluation: tumor rates are the same across dose groupstumor rates are the same across dose groups
Power evaluation: Power evaluation: tumor rates for the highest dose group by 104 weeks: 5, 3 and 2 tumor rates for the highest dose group by 104 weeks: 5, 3 and 2
times the background tumor rates of .05, .15 and .30, times the background tumor rates of .05, .15 and .30, respectivelyrespectively
CRSR (from NTP feeding studies, Haseman et al., 1998)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); (.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)(.5, .6, .5, .4); (.5, .7, .6, .4); (.5, .7, .6, .5) 5000 simulated data sets; 5000 simulated data sets; αα = .05 significance level; = .05 significance level; For each data set, 5000 bootstrap samplesFor each data set, 5000 bootstrap samples
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
Simulation StudySimulation Study Size & Power Evaluation with 5000 simulated data sets, 5000 bootstrap
samples for each data set and 5% nominal significance levelTR CRSR Weibull 1.5 Weibull 3.0 Weibull 6.0
B N B N B N
.3 .6,.6,.6,.6 .053 .050 .054 .050 .055 .052
.5,.5,.5,.2 .044 .066 .044 .041 .040 .021
.6,.6,.5,.2 .036 .072 .033 .037 .033 .018
.6,.5,.4,.3 .047 .069 .043 .045 .040 .024
.5,.6,.5,.4 .049 .055 .050 .048 .048 .037
.5,.7,.6,.4 .046 .053 .048 .046 .045 .036
.5,.7,.6,.5 .054 .050 .051 .047 .054 .044
.3 .6,.6,.6,.6 .918 .934 .908 .923 .893 .904
.5,.5,.5,.2 .837 .932 .781 .847 .725 .667
.6,.6,.5,.2 .790 .939 .734 .846 .668 .638
.6,.5,.4,.3 .864 .938 .825 .884 .773 .748
.5,.6,.5,.4 .886 .929 .868 .895 .834 .819
.5,.7,.6,.4 .881 .930 .856 .892 .817 .810
.5,.7,.6,.5 .904 .927 .884 .909 .859 .865
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
ExampleExample
The 2-yr Gavage Study of FuranThe 2-yr Gavage Study of Furan Furan (CFuran (C44HH44O), a clear and colorless liquid, serves O), a clear and colorless liquid, serves
primarily as an intermediate in the synthesis and primarily as an intermediate in the synthesis and preparation of numerous organic compounds (NTP, preparation of numerous organic compounds (NTP, 1993)1993)
Toxicology and carcinogenesis studies were Toxicology and carcinogenesis studies were conducted by administering furan in corn oil by conducted by administering furan in corn oil by gavage to groups of F344/N rats and B6C3Fgavage to groups of F344/N rats and B6C3F11 mice of mice of each sex for 2 yrseach sex for 2 yrs
Furan was nominated by the NCI for evaluation of Furan was nominated by the NCI for evaluation of carcinogenic potential due to its large production carcinogenic potential due to its large production volume and use, and because of the potential for volume and use, and because of the potential for widespread human exposure to a variety of furan-widespread human exposure to a variety of furan-containing compoundscontaining compounds
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
ExampleExample
Female F344/N ratsFemale F344/N rats Evaluation of carcinogenic potential on incidences of Evaluation of carcinogenic potential on incidences of
cholangiocarcinoma or hepatocellular neoplasms of cholangiocarcinoma or hepatocellular neoplasms of the liver the liver
Groups of 50 rats were administered 2, 4 or 8 mg Groups of 50 rats were administered 2, 4 or 8 mg furan per kg body weight in corn oil by gavage 5 days furan per kg body weight in corn oil by gavage 5 days per week for 2 yrsper week for 2 yrs
Male B6C3FMale B6C3F11 mice mice Evaluation of carcinogenic potential on incidences of Evaluation of carcinogenic potential on incidences of
adenocarcinoma or alveolar/bronchiolar adenoma of adenocarcinoma or alveolar/bronchiolar adenoma of the lung.the lung.
Groups of 50 mice received doses of 8 or 15 mg/kg Groups of 50 mice received doses of 8 or 15 mg/kg furan 5 days per week for 2 yrsfuran 5 days per week for 2 yrs
September 16, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
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)b
Normal CR(X)cBootstrap
Overall 4.1617 1.6449 (p<.001) 2.0141 (p<.001)
0,2,4 2.7705 1.6449 (p=.003) 1.9584 (p=.004)
0,2,8 4.3559 1.6449 (p<.001) 1.9584 (p<.001)
0,4,8 3.6632 1.6449 (p<.001) 1.8214 (p<.001)
0,2 1.4641 1.6449 (p=.072) 1.4625 (p=.040)
0,4 2.6542 1.6449 (p=.004) 1.5905 (p=.001)
0,8 3.8420 1.6449 (p<.001) 1.7423 (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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
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)b
Normal CR(X)cBootstrap
Overall 1.6995 1.6449 (p=.045) 1.7774 (p=.058)
0,15 1.6805 1.6449 (p=.046) 1.6938 (p=.052)
0,8 .2229 1.6449 (p=.41) 1.9248 (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, 2005September 16, 2005 National Center for Toxicological Research, U.S. Food and Drug AdministrationNational Center for Toxicological Research, U.S. Food and Drug Administration
SignificanceSignificance 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
ReferencesReferences 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, 259-289.
Armitage P (1955). Tests for linear trends in proportions and frequencies. Biometrics, 11, 375-386.
Bailer AJ, Portier CJ (1988). Effects of treatment-induced mortality and tumor-induced mortality on tests for carcinogenicity in small samples. Biometrics, 44, 417-431.
Bieler GS, Williams RL (1993). Ratio estimates, the delta method, and quantal response tests for increased carcinogenicity. Biometrics, 49, 793-801.
Chen JJ, Lin KK, Huque MF, Arani RB (2000). Weighted p-value for animals carcinogenicity trend test. Biometrics, 56, 596-592.
Cochran WG (1954). Some methods for strengthening the common x2 tests. Biometrics, 10, 417-451.
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, 403-414.
Mancuso JY, Ahn H, Chen JJ, Mancuso JP (2002). Age-adjusted exact trend tests in the event of rare occurrences. Biometrics, 58, 403-412.
Moon H, Ahn H, Kodell RL, Lee JJ (2003). Estimation of k for the poly-k test. Statistics in Medicine, 22, 2619-2636.
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), 670-672.
STP Peto Analysis Working Group (2002). The Society of Toxicological Pathology’s recommendations on rodent carcinogenicity studies. Toxicologic Pathology, 30, 415-418.
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), 23266-23267.
Woodruff RS (1971). A simple method for approximating the variance of a complicated estimate. Journal of the American Statistical Association, 66, 411-414.