September 16, 2005 Statistical Methods for Testing Carcinogenic Potential of New Drugs in Animal Carcinogenicity Studies Hojin Moon, Ph.D. HMoonnctr.fda.gov.

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


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)


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)


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)


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


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.


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


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


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


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


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


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)


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


ExampleExample


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

……....



ExampleExample


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

……....



ExampleExample


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

……....



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


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


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


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


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


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


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


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.

September 16, 2005 Statistical Methods for Testing Carcinogenic Potential of New Drugs in Animal Carcinogenicity Studies Hojin Moon, Ph.D. HMoonnctr.fda.gov.

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