Statistical Methods for Testing Carcinogenic Potential of New Drugs in Animal Carcinogenicity Studies

1
Statistical Methods for Testing Carcinogenic
Potential of New Drugs in Animal Carcinogenicity
Studies

• Hojin Moon, Ph.D.
• E-mail HMoon_at_nctr.fda.gov
• September 16, 2005

2
Collaborators

• Dr. Ralph L. Kodell DBRA, NCTR, FDA
• Dr. Hongshik Ahn SUNY_at_Stony Brook

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)

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

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)

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)

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)

8
Dose-Related Trend Tests

• Modifications of Petos 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)
• http//biostatistics.mdanderson.org/ACSS

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)

10
Cochran-Armitage Trend Test
Dose Group Dose Group Dose Group Dose Group 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 -gt
  decreased risks of tumor onset
• Survival time is not utilized

• Observed w T in group

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.

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 k3 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 -gt Superior
  operating characteristics to the Poly-3 test

13
The Poly-k 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-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

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

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

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

17
Bootstrap Method
100(1-a)th percentile CR(X)
Reject H0 if T(X) CR(X)
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

19
Age-adjusted Bootstrap Scheme
Age-adjusted scheme I(I,m) i1,.,G m1,.,Mi
. . . . .
Samples
. . . . .
X1
X2
XB
Bootstrap
Replicates
. . . . .
T(X1)
T(X2)
T(XB)
Bootstrap
100(1-a)th percentile CR(X)
Reject H0 if T(X) CR(X)
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
.. .. .. .. ..
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
.. .. .. .. ..
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
.. .. .. .. ..
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
.. .. .. .. ..
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

25
Simulation Study

• Illustration of illness and death with possible
  transitions (Kodell Nelson, 1980)

Tumor (T1)
Normal
Death from Tumor (TD)
Death from Competing Risks (T3)
26
Simulation Study

• Modeling
• T1 Time to tumor onset
• S(t) exp-?d(t/tmax)k
• T2 Time after onset until death from the tumor
• Q(t) exp-f(?1t ?2t ?3)
• T3 Time to death from a competing risk
• The same form as Q(t)
• f is selected to reflect tumor lethality
• T1 T2 TD Time to death from the tumor of
  interest

27
Simulation Study

• Tumor onset distributions
• 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 a .05 significance
  level
• For each data set, 5000 bootstrap samples

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 1.5 Weibull 3.0 Weibull 3.0 Weibull 6.0 Weibull 6.0
TR CRSR B N B N B N
.3 .6,.6,.6,.6 .053 .050 .054 .050 .055 .052
.3 .5,.5,.5,.2 .044 .066 .044 .041 .040 .021
.3 .6,.6,.5,.2 .036 .072 .033 .037 .033 .018
.3 .6,.5,.4,.3 .047 .069 .043 .045 .040 .024
.3 .5,.6,.5,.4 .049 .055 .050 .048 .048 .037
.3 .5,.7,.6,.4 .046 .053 .048 .046 .045 .036
.3 .5,.7,.6,.5 .054 .050 .051 .047 .054 .044
.3 .6,.6,.6,.6 .918 .934 .908 .923 .893 .904
.3 .5,.5,.5,.2 .837 .932 .781 .847 .725 .667
.3 .6,.6,.5,.2 .790 .939 .734 .846 .668 .638
.3 .6,.5,.4,.3 .864 .938 .825 .884 .773 .748
.3 .5,.6,.5,.4 .886 .929 .868 .895 .834 .819
.3 .5,.7,.6,.4 .881 .930 .856 .892 .817 .810
.3 .5,.7,.6,.5 .904 .927 .884 .909 .859 .865
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

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Example

• Female F344/N rats
• 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

31
Data
Group Animal Tumor Pathology
Livera Vehicle Control 1(0), 2(16), 3(0), 4(34)
Livera 2 mg/kg 1(1), 2(17), 3(1), 4(31)
Livera 4 mg/kg 1(3), 2(19), 3(3), 4(25)
Livera 8 mg/kg 1(4), 2(27), 3(6), 4(13)
Lungb Vehicle Control 1(3), 2(14), 3(4), 4(29)
Lungb 8 mg/kg 1(4), 2(24), 3(3),4(19)
Lungb 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
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 1.6449 (plt.001) 2.0141 (plt.001)
0,2,4 2.7705 1.6449 (p.003) 1.9584 (p.004)
0,2,8 4.3559 1.6449 (plt.001) 1.9584 (plt.001)
0,4,8 3.6632 1.6449 (plt.001) 1.8214 (plt.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 (plt.001) 1.7423 (plt.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

33

• 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 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

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
  Petos test can not be implemented

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, 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 Pathologys position on
  statistical methods for rodent carcinogenicity
  studies. Toxicologic Pathology, 29(6), 670-672.
• STP Peto Analysis Working Group (2002). The
  Society of Toxicological Pathologys
  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.

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Ongoing Research

• Developing improved survival-adjusted statistical
  tests in long-term tumorigenicity bioassays (NCTR
  E07171.01)
• Developing estimators for hazard identification
  in long-term tumorigenicity bioassays (NCTR
  E07172.01)
• Developing statistical procedures for
  incorporating dose-response-model uncertainty
  into microbial risk assessment (NCTR E07045.01)
• 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 E07061.01)

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.

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

39
Frequency Tabulation of number of mice in the
ED01 study
Dose (ppm) NTP intervals (days) Fatal tumors assigned by pathologists Natural Death Natural Death Sacrifice Sacrifice
Dose (ppm) NTP intervals (days) Fatal tumors assigned by pathologists With tumor Without tumor Tumor present No tumor present
0 0-364 0 0 9 0 0
0 365-546 0 0 15 0 0
0 547-644 1 1 34 0 0
0 645-726 1 1 60 7 137
30 0-364 0 0 17 0 0
30 365-546 0 2 42 0 0
30 547-644 1 6 67 0 0
30 645-726 2 7 84 22 279
35 0-364 0 1 9 0 0
35 365-546 3 3 31 0 0
35 547-644 1 1 55 0 0
35 645-726 0 1 80 18 192
45 0-364 0 0 7 0 0
45 365-546 1 1 13 0 0
45 547-644 3 5 43 0 0
45 645-726 2 3 66 19 132