Statistical Aspects of the Design, Analysis, and Interpretation of Chronic Rodent Carcinogenicity Studies of Pharmaceuticals

Administrative draft guidance, not enacted legislation. This captured publisher edition preserves the listed document and attachments; later developments are not independently consolidated.

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Guidance for Industry
Statistical Aspects of the Design,
Analysis, and Interpretation of Chronic
Rodent Carcinogenicity Studies of
Pharmaceuticals
DRAFT GUIDANCE
This guidance document is being distributed for comment purposes only.
Comments and suggestions regarding this draft document should be submitted within 90 days of publication in the
Federal Register of the notice announcing the availability of the draft guidance. Submit comments to Dockets
Management Branch (HFA-305), Food and Drug Administration, 12420 Parklawn Dr., rm. 1-23, Rockville, MD
20857. All comments should be identified with the docket number listed in the notice of availability.
For questions regarding this draft document contact (CDER) Karl K. Lin, Ph.D., 301-827-3093, e-mail link
@cder.fda.gov.
U.S. Department of Health and Human Services
Food and Drug Administration
Center for Drug Evaluation and Research (CDER)
May 2001
Pharm/Tox

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Guidance for Industry
Statistical Aspects of the Design,
Analysis, and Interpretation of Chronic
Rodent Carcinogenicity Studies of
Pharmaceuticals
Additional copies are available from:
Office of Training and Communications
Division of Communications Management
Drug Information Branch, HFD-210
Center for Drug Evaluation and Research (CDER)
5600 Fishers Lane
Rockville, MD 20857
(Tel) 301-827-4573
(Internet) http://www.fda.gov/cder/guidance/index.htm
U.S. Department of Health and Human Services
Food and Drug Administration
Center for Drug Evaluation and Research (CDER)
May 2001
Pharm/Tox

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TABLE OF CONTENTS
I. INTRODUCTION................................................................................................................................................................1
II. BACKGROUND...................................................................................................................................................................1
III. VALIDITY OF THE DESIGN......................................................................................................................................2
IV. METHODS OF STATISTICAL ANALYSIS ...........................................................................................................4
A. AN OVERVIEW OF COMPLEXITIES OF STATISTICAL ANALYSIS OF TUMOR DATA..................................................... 4
B. ADJUSTMENT OF TUMOR RATES FOR INTERCURRENT MORTALITY............................................................................ 6
C. STATISTICAL ANALYSIS OF TUMOR DATA WITH INFORMATION ABOUT CAUSE OF DEATH, TUMOR LETHALITY,
BUT WITHOUT MULTIPLE SACRIFICES...................................................................................................................................... 8
1. Role of the Tumor in Animal’s Death (Contexts of Observation of Tumor Types).............................................8
2. Statistical Analysis of Incidental Tumors...................................................................................................................9
3. Statistical Analysis of Fatal Tumors.........................................................................................................................15
4. Statistical Analysis of Tumors Observed in Both Incidental and Fatal Contexts.............................................16
5. Statistical Analysis of Mortality Independent Tumors...........................................................................................16
6. Exact Methods..............................................................................................................................................................17
D. STATISTICAL ANALYSIS OF DATA WITHOUT INFORMATION ABOUT CAUSE OF DEATH AND WITHOUT
MULTIPLE SACRIFICES.............................................................................................................................................................. 21
E. STATISTICAL ANALYSIS OF DATA FROM STUDIES WITH DUAL CONTROLS............................................................ 25
V. INTERPRETATION OF STUDY RESULTS.............................................................................................................26
A. ADJUSTMENT FOR THE EFFECT OF MULTIPLE TESTS (CONTROL OVER FALSE POSITIVE ERROR)........................ 27
B. CONTROL OVER FALSE NEGATIVE ERROR.................................................................................................................... 30
C. THE USE OF HISTORICAL CONTROL DATA ................................................................................................................... 30
D. EVALUATION OF VALIDITY OF DESIGNS OF NEGATIVE STUDIES............................................................................... 32
VI. PRESENTATION OF RESULTS AND DATA SUBMISSION........................................................................32
REFERENCES .............................................................................................................................................................................38

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Guidance for Industry1
1
Statistical Aspects of the Design, Analysis, and Interpretation of	2
Chronic Rodent Carcinogenicity Studies of Pharmaceuticals	3
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I. INTRODUCTION	19
20
This document is intended to provide guidance to sponsors on the design of animal	21
carcinogenicity experiments, methods of statistical analysis of tumor data, interpretation of study	22
results, presentation of data and results in reports, and the submission of tumor data to FDA	23
statistical reviewers at the Food and Drug Administration (FDA). A brief background	24
description of the operation of statistical review of carcinogenicity studies in FDA's Center for	25
Drug Evaluation and Research (CDER) is given in section II. A discussion of the validity of the	26
design of the experiment is given in Section III. Section IV discusses methods of statistical	27
analysis. Section V discusses how the results should be interpreted, and Section VI discusses	28
data presentation and submission.	29
30
31
II. BACKGROUND	32
33
Assessment of the risk of drug exposure in humans includes an assessment of carcinogenicity in	34
tests in rodents. The Division of Biometrics in the Office of Biostatistics, Center for Drug	35
Evaluation and Research (CDER), Food and Drug Administration (FDA), is responsible for	36
conducting statistical reviews of long-term animal (rodent) carcinogenicity studies of	37
pharmaceuticals submitted by drug sponsors to FDA. In a carcinogenicity study of a new drug	38
using a series of increasing dose levels, statistical tests for positive trends in tumor rates are	39
usually of greatest interest, but as discussed in this document, in some situations, pairwise	40
comparisons are considered to be more indicative of drug effects than trend tests.	41
42
1 This guidance has been prepared by the Office of Biostatistics with the participation of the Office of Review
Management, Center for Drug Evaluation and Research (CDER), Food and Drug Administration.
This draft guidance, when finalized, will represent the Food and Drug Administration's current
thinking on this topic. It does not create or confer any rights for or on any person and does not
operate to bind FDA or the public. An alternative approach may be used if such approach
satisfies the requirements of the applicable statutes and regulations.

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In statistical reviews of carcinogenicity studies, statisticians evaluate the validity of the designs	43
and the appropriateness of methods of data analysis used by the sponsor. They also use raw	44
study data in electronic form to perform additional statistical analyses.	45
46
The recommendations that follow are based on FDA’s assessment of current literature,	47
consultations with outside experts, and internal research.	48
49
50
III. VALIDITY OF THE DESIGN	51
52
Many factors determine the adequacy of a carcinogenicity study, including the species and strain	53
of the animals, sample size, dose selection, method of allocation of animals, route of	54
administration, animal care and diet, caging, drug stability, and study duration. Of particular	55
interest to statisticians are the methods used to allocate animals to treatment groups and caging	56
rotation, the determination of sample size, and the duration of the study.	57
58
Although not generally a statistical issue, dose selection is particularly critical. The premise of	59
carcinogenicity testing most directly applicable to genotoxic mechanisms (when there may not	60
be a pharmacological threshold, or identification of a threshold is difficult) is that long exposure	61
duration and large doses in a small number of animals will be informative about the much	62
smaller risks of lower doses and shorter durations of exposure in humans. As a result, the	63
general goal should be to maximize rodent exposure by testing at maximum tolerated doses.	64
65
The International Conference on Harmonization (ICH) guidance entitled S1C Dose Selection for	66
Carcinogenicity Studies of Pharmaceuticals (S1C) is an internationally accepted guidance for	67
dose selection for carcinogenicity studies, and sponsors are advised to consult this document.	68
The guidance allows for approaches to high dose selection based on toxicity endpoints (Sontag,	69
Page, and Saffiotti 1976; Chu, Cueto, and Ward 1981), pharmacokinetic endpoints (multiple of	70
maximum human exposure), pharmacodynamic endpoints, and maximal feasible dose. For	71
further clarification, the appropriate medical review division should be consulted.2
72
73
Randomization should be used to allocate animals to treatment groups. Random assignment of	74
experimental animals to different treatment groups allows the assumption that treatments will not	75
be continually favored or handicapped by extraneous sources of variation over which the	76
experimenter has no control (i.e., that possible bias will be minimized).	77
78
One area where bias can still be introduced, however, is in the microscopic evaluation of tissues.	79
Currently, open or nonblinded microscopic evaluation of tissues from experimental animals is	80
the routine practice adopted by veterinary pathologists in the generation of histopathological data	81
in carcinogenicity studies. Veterinary pathologists do not favor blinded readings of slides of	82
2 Sponsors can seek CDER’s advance concurrence on carcinogenicity protocols and should consult other available
guidance (e.g., ICH guidances S1A, S1B, S1C, S1C(R)). In addition, a draft guidance titled Carcinogenicity Study
Protocal Submissions published in November 2000. Once finalized, that guidance will represent the Agency's
thinking on that topic.

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animal tissues/organs because they believe that blinded reading results in loss of information	83
critical to interpretation, such as the ability to relate observations in different tissues.	84
Furthermore, they argue that the variables constitute the baseline that defines the experimental	85
control and that it is impractical to perform blinded slide readings because there are so many	86
tissues from each animal. Mistakes can be easily made when assigning, opening codes, and	87
recording results in blinded reading (Iatropoulos 1988; Prasse et al. 1986). There are others,	88
however, who have argued that blinded evaluation should be used to prevent the bias that can be	89
introduced by the pathologists’ knowledge of the treatment groups of the tested animals (Temple,	90
Fairweather, Glocklin, and O'Neill 1988). Certainly, blinded re-readings are common in close or	91
disputed cases.	92
93
The number of animals remaining in a study for the full duration is an important statistical	94
consideration. A sufficient number of animals should be used in an experiment to ensure	95
reasonable power of statistical tests to detect true carcinogenic effects. It has been recommended	96
that each dose and concurrent control group contain at least 50-60 animals of each sex. If	97
interim sacrifices are planned, the initial number of animals should be increased by the number	98
of animals scheduled for interim sacrifice. Prior assignments of treatment and designations for	99
sacrifice of the animals should be made (Bannasch et al. 1986).	100
101
Animals are usually exposed to the test substance for essentially their entire normal life span,	102
generally 24 months for rats and mice. The vast majority of carcinogenicity studies of	103
pharmaceuticals using rats that are submitted to CDER for review have durations of 24 months	104
and have reasonable survival. The duration of mouse studies ranges from 18 to 24 months, with	105
many lasting only 18 or 21 months even though they have very low mortality at terminal	106
sacrifice. One reason for using shorter durations in mouse studies appears to be a 1985 federal	107
government publication stating that carcinogenicity studies should be conducted at least 18	108
months in mice and 24 months in rats (OFR 1985). The publication, however, goes on to say	109
that a longer duration may be appropriate if cumulative mortality at the planned terminal	110
sacrifice is low. CDER recommends that drug sponsors also conduct mouse studies for 24	111
months, unless there is excessive mortality as described below. Results of a recent study of the	112
effect of shortened duration on the statistical power of carcinogenicity studies by Kodell, Lin,	113
Thorn, and Chen (2000) support the CDER recommendation. The study showed that stopping at	114
18 months would reduce power to an unacceptable level for a variety of models of the	115
tumorigenicity, and that the loss of power is too great to warrant an early stopping at 21 months,	116
absent effects on survival.	117
118
However, early termination of a study for mortality, even if unavoidable, may render a study	119
uninformative, leaving too few animals living long enough to represent adequate exposure to the	120
chemical. This is especially important in the evaluation of the design validity of a negative	121
study. In general, a 50 percent survival rate to weeks 80 to 90 of the 50 initial animals in any	122
treatment group is considered adequate. The percentage can be lower or higher if the number of	123
animals used in each treatment/sex group is larger or smaller than 50, but between 20 to 30	124
animals should be still alive during these weeks (Lin and Ali 1994). Whether a study could be	125
terminated before the scheduled termination date if the survival of any treatment group goes	126
below 50 percent or 20 to 30 surviving animals (provided that sufficient numbers of animals	127

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were exposed through week 80 to 90) depends on the situation. For example, there is no reason	128
to stop a study if the survival of only the low-dose group and/or the medium-dose group is	129
altered, because the control vs. high-dose comparison will still be informative. If the survival of	130
the high-dose group falls below 50 percent or 20-30 surviving animals after week 80, the study	131
should be continued, either stopping dosing of animals in the high-dose group or terminating	132
only the high-dose group, because the comparison of at least the control and low/middle doses	133
would still be informative (the high-dose comparison would depend on the situation). A study	134
could be terminated early if the survival of the control group (or groups) goes below 50 percent	135
or 20-30 surviving animals after weeks 80 to 90, as the later comparisons would not be	136
informative. Others have suggested, for example, that an experiment be terminated early when	137
the survival of the control or the low-dose group is reduced to 20-25 percent of the original	138
number of animals. If the mortality is increased only in the high-dose group, consideration can	139
be given to early termination of that group (OFR 1985).3 Because early study termination poses	140
complex problems, it is strongly recommended that a decision to terminate a study or a study	141
group early be made with input from the Center and the medical division responsible for the	142
review of the associated application.	143
144
If in discussions with CDER, the Center approves the early termination of a study under this	145
recommendation, the study’s sponsor can be assured that the study will be considered by the	146
Center as valid in terms of adequate duration of drug exposure.	147
148
149
IV. METHODS OF STATISTICAL ANALYSIS	150
151
A. An Overview of Complexities of Statistical Analysis of Tumor Data	152
153
The primary purpose of a long-term rodent carcinogenicity study of a new drug is to	154
evaluate the oncogenic potential of the drug when it is administered to animals for most	155
of their normal life span. The drug, however, may effect the mortality of different	156
treatment groups. Test animals living longer are more likely to develop tumors than	157
those dying early, as demonstrated by examples in the next section, and comparisons of	158
tumor incidence rates among treatment groups based solely on the crude proportions of	159
animals with tumors and failure to consider the rates at which animals develop tumors	160
can cause serious bias in the analysis (Petro et al. 1980; McKight and Crowley 1984; Gart	161
et al. 1986). Therefore, it is essential to make adjustment for the differences in mortality	162
among treatment groups in the analysis of tumor data.	163
164
Tumor incidence (i.e., the rate of tumor onset among the previously tumor-free	165
population) is the most appropriate measure of tumorigenesis for two reasons (Dinse	166
1994; McKight and Crowley 1984; and Malani and Van Ryzin 1988): (1) the tumor	167
incidence rate reduces biases in the crude incidence proportion of animals with tumors	168
that could arise from differences in mortality by adjusting for time differences and by	169
conditioning the rate at each time point on the likelihood that an animal is still alive, and	170
3 This article also appeared in Gart, J.J., D. Krewski, P. N. Lee, R. E. Tarone, and J. Wahrendorf, 1986, U.S.
Interagency Staff Group on Carcinogens.

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(2) unlike the death rate with or from tumors, the tumor incidence rate does not confound	171
information about the course of tumors with information about the onset of tumors. Most	172
tumors except those such as skin and mammary tumors, which can be detected by	173
palpation and visual inspection, are occult and discovered only at the time of the animal’s	174
death. The exact tumor onset times are unknown.	175
176
The analysis of tumor data is complicated when adjustments are made for differences in	177
mortality among treatment groups because of the lack of the observable onset time of	178
occult tumors discussed above. A huge number of statistical procedures aiming to deal	179
with these complexities have been proposed in the literature. They followed, in general,	180
the strategy that “without direct observations of the tumor onset times, the desired	181
survival adjustment usually is accomplished by making assumptions concerning tumor	182
lethality, cause of death, multiple sacrifices, or parametric models” (Dinse 1994).	183
184
The prevalence method (Hoel and Walburg 1972; Peto et al. 1980), the death-rate method	185
(Tarone 1975; Peto et al. 1980), and the onset-rate (Peto et al. 1980), discussed in Section	186
C below, for analyzing nonlethal, lethal, and observable tumors, respectively, are based	187
on an assumption, or information about tumor lethality. The Peto test (Peto et al. 1980),	188
also discussed in Section C, for analyzing data of a tumor that is considered nonlethal to a	189
subset of animals and lethal to the rest of the animals is also based on an assumption or	190
information as to whether the tumor caused an animal’s death. The analyses will become	191
biased if the assumption or information on tumor lethality and cause of death is not valid	192
or accurate (Dinse 1994).	193
194
Data from carcinogenicity studies do not always contain information of tumor lethality	195
and cause of death. Even when such information is provided, the difficulty and	196
subjectivity in the determination of cause of death and lethality of a tumor may render the	197
information too inaccurate and unobjective to allow valid analysis using the above	198
statistical methods. Another way of analyzing the tumor incidence rates without relying	199
on the tumor lethality and cause-of-death information is to use a design with multiple	200
sacrifices at different time points. Without cause-of-death information or simplifying	201
assumptions, multiple sacrifices of groups of animals are necessary to identify tumor	202
incidence rates of occult tumors from the bioassay data (McKight and Crowley 1984;	203
Kodell and Ahn 1997; Dinse 1994). Statistical methods have been proposed for	204
analyzing tumor incidence rates on the information from multiple sacrifices rather than	205
on the information on cause of death and tumor lethality.4 In reality, however, very few	206
studies are conducted with multiple sacrifices because of the cost and complexity	207
involved. Since it is rarely used in practice, no recommendations on analysis of data with	208
multiple sacrifices are given in this guidance.	209
210
4 See, for example, Berlin, Brodsky, and Clifford 1979; Dewanji and Kalbfleisch 1986; Portier and Dinse 1987;
Dinse 1988; Malani and Van Ryzin 1988; Willams and Portier 1992; Malani and Lu 1993; Ahn and Kodell 1995;
Kodell and Ahn 1996 and 1997; and Ahn, Kodell, and Moon 2000)

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Finally, for data from bioassays with no information (or assumptions) regarding tumor	211
lethality or cause-of-death and no interval sacrifices, Dinse (1991) and Lindsey and Ryan	212
(1993 and 1994) have proposed survival-adjusted statistical tests that focus on tumor	213
incidence for dose-related trends by making some parametric assumptions. Dinse’s test	214
is based on the assumption of a constant difference between the death rates of animals	215
with and without a tumor while Lindsey and Ryan’s test assumes a constant ratio for	216
those death rates. Recently, other statistical procedures of this type have been proposed	217
in the literature for dealing with the complexities of analysis of tumor data. Those	218
procedures do not require data on tumor lethality and cause of death, or the use of	219
multiple sacrifices. Among those procedures, the poly-3 (in general poly-k) tests (Bieler	220
and Portier 1988; Dinse 1994), and the ratio trend test (a modified poly-k test) (Bieler and	221
Williams 1993; Dinse 1994) have been most extensively studied and shown to perform	222
well under actual study conditions. Detailed discussions of the poly-k tests and the ratio	223
trend test are given in Section D.	224
225
Some of the recently proposed statistical procedures, such as those described by Kodell,	226
Pearce, Turturro, and Ahn (1997), and Moon, Ahn, and Kodell (2000), deal with the	227
complexities of the tumor data analysis from a somewhat different direction. These	228
procedures use a constrained nonparametric maximum likelihood estimation method to	229
impute (estimate) incidence rates of fatal tumors and nonfatal tumors for time intervals	230
preceding the final time interval of terminal sacrifice. These procedures do not require	231
tumor lethality and cause-of-death information and are applicable to studies with only a	232
single sacrifice. The imputed tumor incidence rates can then be used in the death-rate	233
method, prevalence method, or the Peto test. The properties of these procedures have not	234
yet been widely studied, and they involve extensive computations.	235
236
B. Adjustment of Tumor Rates for Intercurrent Mortality	237
238
Intercurrent mortality refers to all deaths other than those resulting from a tumor being	239
analyzed for evidence of carcinogenicity. Like human beings, older rodents have a many	240
fold higher probability of developing or dying of tumors than those of a younger age.	241
Therefore, in the analysis of tumor data, it is essential to identify and adjust for possible	242
differences in intercurrent mortality among treatment groups to eliminate or reduce biases	243
caused by these differences. It has been pointed out that “the effects of differences in	244
longevity on numbers of tumor-bearing animals can be very substantial, and so, whether	245
or not they (the effects) appear to be, they should routinely be corrected when presenting	246
experimental results” (Peto et al. 1980). The following examples demonstrate this point.	247
248
Example 1 (Peto et al. 1980). Consider a mouse study consisting of one control group	249
and one treated group of 100 animals each. A very toxic but not carcinogenic new drug	250
is administered to the animals in the diet for 2 years. Assume that the spontaneous	251
incidental tumor rates for both groups are 30 percent at 15 months and 80 percent at 18	252
months and that the mortality rates at 15 months for the control and the treated groups are	253
20 percent and 60 percent, respectively, due to the toxicity of the drug. The results of this	254
experiment are summarized in Table 1.	255

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256
Table 1: Effects of Differences in Mortality on Tumor Incidence Rates, Example 1	257
258
Control Treated
T D % T D %
15 Months 6 20 30 18 60 30
18 Months 64 80 80 32 40 80
Totals 70 100 70 50 100 50
Note: T = Incidental Tumors Found at Necropsy. D = Deaths	259
260
261
If one looks only at the overall tumor incidence rates of the control and the treated groups	262
(70 percent and 50 percent, respectively) without considering the significantly higher	263
early deaths in the treated group caused by the toxicity of this new drug, one can	264
misinterpret the apparent significance (p = 0.002, 1-tailed) as showing a decrease in the	265
treated group in this tumor type. The one-tailed p-value is 0.5, however, showing no	266
effect of treatment when the survival-adjusted prevalence method is used.	267
268
Example 2 (Gart, Krewski, Lee, Tarone, and Wahrendorf 1986). Assume that the design	269
used in this experiment is the same as the one used in the experiment in Example 1.	270
Also, assume that the tested new drug in this example induces an incidental tumor that	271
does not directly or indirectly cause animal deaths, in addition to having severe toxicity	272
as in the previous example. Assume further that the incidental tumor prevalence rates for	273
the control and treated groups are 5 percent and 20 percent, respectively, before 15	274
months of age, and 30 percent and 70 percent, respectively, after 15 months of age; and	275
that the mortality rates at 15 months are 20 percent and 90 percent for the control and the	276
treated groups, respectively. The results of this experiment are summarized in Table 2.	277
278
279
Table 2: Effects of Differences in Mortality on Tumor Incidence Rates, Example 2	280
281
Control Treated
T D % T D %
Before 15
Months 1 20 5 18 90 20
After 15
Months 24 80 30 7 10 70
Totals 25 100 25 25 100 25
Note: T = Incidental Tumors Found at Necropsy. D = Deaths	282
283
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The age-specific tumor incidence rates are significantly higher in the treated group than	285
those in the control group. The survival-adjusted prevalence method yielded a one-tailed	286
p-value of 0.003, revealing a clear tumorigenic effect of the new drug. The overall tumor	287
incidence rates, however, are 25 percent for the two groups. Without adjusting the	288
significantly higher early mortality in the treated group, the positive finding would be	289
missed.	290
291
Peto et al. (1980) recommend that, whether or not survival among treatment groups is	292
significantly different, tumor rates should routinely be adjusted for survival when	293
presenting experimental results. The Cox test (Cox 1972; Thomas, Breslow, and Gart	294
1977; Gart et al. 1986); the generalized Wilcoxon or Kruskal-Wallis test (Breslow 1970;	295
Gehan 1965; Thomas, Breslow, and Gart 1977); and the Tarone trend tests (Cox 1959;	296
Peto et al. 1980; Tarone 1975) are routinely used to test for heterogeneity in survival	297
distributions and significant dose-response relationships (trends) in survival.	298
299
300
C. Statistical Analysis of Tumor Data With Information About Cause of Death,	301
Tumor Lethality, but Without Multiple Sacrifices	302
303
1. Role of the Tumor in Animal’s Death (Contexts of Observation of Tumor	304
Types)	305
306
One way to choose the appropriate survival-adjusted methods in the analysis of	307
tumor data is to base analysis on the role that a tumor plays in causing the	308
animal’s death. Tumors can be classified as incidental, fatal, and mortality	309
independent or (observable) according to the contexts of observation described in	310
Peto et al. (1980). Tumors that are not directly or are indirectly responsible for an	311
animal’s death, but are merely observed at the autopsy of the animal after it has	312
died of an unrelated cause, are said to have been observed in an incidental	313
context. Tumors that kill the animal, either directly or indirectly, are said to have	314
been observed in a fatal context. Tumors, such as skin tumors, for which	315
detection occurs at times other than when the animal dies are said to have been	316
observed in a mortality independent (or observable) context. To apply a survival-	317
adjusted method correctly based on such information, it is essential that the role of	318
a tumor in an animal’s death (or the context of observation of a tumor) be	319
determined as accurately as possible.	320
321
Different statistical techniques have been proposed for analyzing data of tumors	322
when information about the role of a tumor in causing death is available. For	323
example, the prevalence method, the death rate method, and the onset rate method	324
are recommended for analyzing data on tumors observed in incidental, fatal, and	325
mortality independent contexts of observation, respectively (Peto et al. (1980)).	326
In that paper, Peto et al. demonstrate the possible biases resulting from	327
misclassification of incidental tumors as fatal tumors, or of fatal tumors as	328
incidental tumors.	329
330

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The determination of whether a tumor is incidental, fatal or mortality independent	331
is often difficult, especially for the first two classifications, as it is often hard to	332
tell whether a tumor caused an animal’s death. According to Haseman (1999), in	333
practice, a continuum exists between these two extremes: many tumors contribute	334
ultimately to an animal’s death, but are not instantly (or even rapidly lethal).	335
Such tumors technically are neither incidental nor fatal, and it remains unclear	336
how such tumors should be regarded. Even if the information on the	337
circumstances of individual animals and tumors is reliable and available, it is	338
overly simplistic to assume that all tumors of a given type are 100 percent fatal or	339
100 percent incidental. It is likely that there will be a mixture of incidental and	340
fatal tumors.	341
342
As noted above, alternative survival-adjusted statistical procedures that do not	343
need such information have been developed and used for tumor data analysis.	344
Some of the procedures are discussed briefly in the Section IV.C.1 and in detail in	345
Section IV.D. The alternative procedures should be used to replace the	346
procedures proposed by Peto et al. (1980) in the analysis of tumor data when there	347
is no information available or the information is not accurate enough to perform a	348
meaningful statistical analysis.	349
350
2. Statistical Analysis of Incidental Tumors	351
352
The prevalence method described in the paper by Peto et al. (1980) should be	353
used in testing for positive trends in prevalence rates of incidental tumors. The	354
method is described briefly here.	355
356
The method focuses on the age-specific tumor prevalence rates to correct for	357
intercurrent mortality differences among treatment groups in the test for positive	358
trends or differences in incidental tumors. The experiment period is partitioned	359
into a set of intervals plus interim (if any) and terminal sacrifices. The incidental	360
tumors are then stratified by those intervals of survival times. The selection of the	361
partitions of the experiment period does not matter very much as long as the	362
intervals are “not so short that the prevalence of incidental tumors in the autopsies	363
they contain is unstable, nor yet so large that the real prevalence in the first half of	364
one interval could differ markedly from the real prevalence in the second half”	365
(Peto, et al. 1980).	366
367
In each time interval, for each group, the observed and the expected numbers of	368
animals with a particular tumor type found in necropsies are compared. The	369
expected number is calculated under the null hypothesis that there is no dose-	370
related trend. Finally, the differences between the observed and the expected	371
numbers of animals found with the tumor type after their deaths are combined	372
across all time intervals to yield an overall test statistic using the method	373
described in a paper by Mantel and Haenszel (1959).	374
375

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The following derivation of the Peto prevalence test statistic uses the notations in	376
Table 3. Let the experiment period be partitioned into the following m intervals	377
I1, I2, …, Im. As mentioned before, interim (if any) and terminal sacrifices should	378
be treated as separate intervals.	379
380
Let Rk be the number of animals that have not died of the tumor type of interest	381
but come to autopsy in time interval k, Pik be the proportion of Rk in group i, and	382
Oik be the observed number of autopsied animals in group i and interval k found	383
to have the incidental tumor type.	384
385
Define O.k = ∑iOik.	386
387
The number of autopsied animals expected to have the particular incidental tumor	388
in group i and interval k, under the null hypothesis that there is no treatment	389
effect, is:	390
391
Eik = O.k Pik.	392
393
The variance-covariance of (Oik – Eik) and (Ojk – Ejk) is:	394
395
Vijk = αk Pik(δ ij – Pjk)	396
397
where	398
399
αk = O.k(Rk - O.k) / (Rk – 1)	400
and	401
402
1 if i = j,	403
δij =	404
0 otherwise	405
406
Define	407
408
Oi = ∑k Oik	409
410
Ei = ∑k Vijk.	411
412
and Vij = ∑k Vijk.	413
414
The test statistic T for the positive trend in the incidental tumor is defined as:	415
416
T = ∑i Di (Oi – Ei)	417
418
with estimated variance	419
420

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V(T) = ∑i∑j Di Dj Vij	421
422
where Di is the dose level of the ith group.	423
424
Under the null hypothesis of equal prevalence rates among the treatment groups,	425
the statistic	426
427
Z = T / [V(T)]1/2
428
429
is approximately distributed as a standard normal.	430

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Table 3: Notations Used in the Derivation of Peto Prevalence Test Statistics	431
432
Group 0 1 . . . i . . . r	Interval
Dose D0 D1 . . . Di . . . Dr
Sum
I1 R1 O01 O11 . . . Oi1 . . . Or1 O.1
P01 P11 . . . Pi1 . . . Pr1 P.1
I2 R2 O02 O12 . . . Oi2 . . . Or2 O.2
P02 P12 . . . Pi2 . . . Pr2 P.2
. . . . . . . . . . . . .
.
. . . . . . . .
.
. . . . .
. . . . . . . . . . . . .
Ik Rk O0k O1k . . . Oik . . . Ork O.k
P0k P1k . . . Pik . . . Prk P.k
. . . . . . . . . . . . .
.
. . . . . . . . . . . . .
. . . . . . . . . . . . .
Im Rm O0m O1m . . . Oim . . . Orm O.m
P0m P1m . . . Pim . . . Prm P.m
433
Notes:	434
Rk: Number of animals that have not died of the tumor type of interest, but come to autopsy in time interval k.	435
Pik: Proportion of Rk in group i.	436
Oik: Observed number of autopsied animals in group i and interval k found to have the incidental tumor type.	437
O.k: 3iOik.	438
439
440

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As noted above, to use the prevalence method, the experimental period should be	441
partitioned into a set of intervals plus interim (if any) and terminal sacrifices. The	442
following partitions (in weeks) are used most often by statisticians in CDER in 2-	443
year studies: (1) 0 – 50, 51 – 80, 81 – 104, interim sacrifice (if any), and terminal	444
sacrifice; (2) 0 – 52, 53 – 78, 79 – 92, 93 – 104, interim sacrifice (if any), and	445
terminal sacrifice (proposed by National Toxicology Program); and (3) partition	446
determined by the ad hoc runs procedure described in Peto et al. (1980).	447
448
The data for liver hepatocellular adenoma in male mice from a carcinogenicity	449
study are used as an example to explain the prevalence method for testing the	450
positive trend in tumor rates of an incidental tumor. There were four treatment	451
groups. The control group had 100 animals, the three treated had 50 animals	452
each. The dose levels used were 0, 10, 20, and 40 mg/kg/day for the control,	453
low-, medium-, and high-dose groups, respectively. The study lasted for 106	454
weeks. In this example, the study period was partitioned into four intervals, 0 –	455
50, 51 – 80, 81 – 106, and terminal sacrifice. The numbers of animals died and	456
necropsied, and the numbers of necropsied animals with liver hepatocellular	457
adenoma by treatment group in each interval are included in Table 4.	458
459
460
Table 4: Data of Liver Hepatocellular Adenoma of Male Mice	461
462
Groups
Control Low Medium High
Time
Intervals
(Weeks)
T N % T N % T N % T N %
0 – 50 0 6 0 0 2 0 0 2 0 0 4 0
51 – 80 1 26 4 1 18 6 3 17 18 1 13 8
81 – 106 4 37 11 2 14 14 2 14 14 7 19 37
Terminal
Sacrifice
2 31 6 5 16 31 3 17 18 4 14 29
Total 7 100 7 8 50 16 8 50 16 12 50 24
Notes: T = Number of necropsies with the above tumor.	463
N = Number of necropsies during a time interval.	464
% = Percent of necropsies with the above tumor.	465
466
467
The observed incidences and the expected incidences of the tumor type calculated	468
under the null hypothesis that there is no trend (or drug induced increase) are	469
shown in Table 5. The expected tumor rates in each interval were calculated in	470
the following way. First, the tumor rate for the interval using data of all treatment	471
groups in the interval was estimated. For example, the estimated tumor rate for	472

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the interval 51 – 80 weeks was 6/74 = 0.0811. Second, the expected incidences	473
for individual groups in the interval were calculated by multiplying the numbers	474
of necropsies by the estimated tumor rate. For the interval 51 – 80 weeks, the	475
expected tumor rates for the control, low-, medium-, and high-dose groups were	476
26x(6/74)=2.11, 18x(6/74)=1.46, 17x(6/74)=1.38, and 13x(6/74)=1.05,	477
respectively.	478
479
Table 5: Observed and Expected Tumor Incidences Liver	480
Hepatocellular Adenoma of Male Mice	481
482
Groups	Time
Intervals
(Weeks)
Observed &
Expected
Incidences Control Low Medium High
Observed 0 0 0 0	0 – 50
Expected 0 0 0 0
Observed 1 1 3 1	51 – 80
Expected 2.11 1.46 1.38 1.05
Observed 4 2 2 7
Expected 6.61 2.50 2.50 3.39
Observed 2 5 3 4	Terminal
Sacrifice Expected 5.56 2.87 3.05 2.51
Observed 7 8 8 12	Total
Expected 14.28 6.83 6.93 6.95
Note: The expected tumor incidences were calculated under the null hypothesis that	483
there is no trend.	484
485
486
The test statistics T’s and their variances V(T)’s for the data of the 5 intervals	487
calculated by the formulas listed above are included in Table 6. It is noted that	488
the first interval, 0 - 50 weeks, did not contribute anything to the overall test result	489
since none of the 14 animals that died during the first time interval developed	490
liver hepatocellular adenoma. The overall result shows a statistically significant	491
positive trend in tumor rates of this tumor (with one-sided p-value 0.002).	492
493
494
495
496

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Table 6: Test Statistics, Their Variances, z-values, and P-value of	497
Peto Prevalence Analysis of Incidental Tumors	498
499
Liver Hepatocellular Adenoma of Male Mice	500
Time
Intervals
(Weeks)
T-Stat
T
Variance of
T-Stat
V(T)
T
z = ----------
[V(T)]0.5
P-Value
0 - 50 - - - -
51 - 80 25.6756 1116.583 0.7683 0.2211
81 - 106 129.2857 3091.314 2.3253 0.0100
Term. Sacr. 79.7435 2445.855 1.6124 0.0534
Overall Total 234.7048 6653.752 2.8773 0.0020
Note: The z and p-value columns do not add up to the totals. The z and p-value of	501
overall total row were calculated based on the T and V(T) of the row.	502
503
504
Also as noted above, this method used normal approximation in the test for	505
positive trend or difference in tumor prevalence rates. The accuracy of the normal	506
approximation depends on the number of tumor occurrences in each group in each	507
interval, the number of intervals used in the partitioning, and the mortality	508
patterns. The approximation may not be stable and reliable when the numbers of	509
tumor occurrences across treatment groups are small. In this situation, an exact	510
permutation trend test based on an extension of the hypergeometric distribution	511
(to be discussed in Subsection III.C.6) should be used to test for the positive trend	512
in tumor prevalence rates.	513
514
3. Statistical Analysis of Fatal Tumors	515
516
It is recommended that the death rate method described in Peto et al. (1980) be	517
routinely used to test for the positive trend or difference in incidence of tumors	518
observed in a fatal context.	519
520
The notations of Subsection III.C.2 with some modifications will be used in this	521
section to derive the test statistic of the death rate method. Now let t1 <t2 < …<tm	522
be the time points when one or more animals died of the fatal tumor of interest.	523
These time points are used to replace the intervals used in the prevalence method.	524
The notations in Table 3 are redefined as follows:	525
526
Rk: The number of animals at risk of all groups just before tk.	527
528
Pik: (The same as in the prevalence method) Proportion of Rk in Group i.	529
530

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Oik: Observed number of animals in Group i dying of the fatal tumor of	531
interest at time tk.	532
533
O.k = ∑i Oik.	534
535
As in the prevalence method, the test statistic T for the positive trend in the fatal	536
tumor is defined as:	537
538
T = ∑i Di(Oi – Ei)	539
540
with estimated variance	541
542
V(T) = ∑i∑j Di Dj Vij.	543
544
where Di, Oi, Ei, and Vij are defined similarly as in Subsection III. C.2.	545
546
Under the null hypothesis of equal tumor rates across the treatment groups, the	547
statistic	548
549
Z = T / [V(T)]1/2
550
551
is distributed approximately as standard normal.	552
553
4. Statistical Analysis of Tumors Observed in Both Incidental and Fatal	554
Contexts	555
556
When a tumor is fatal for some animals and is incidental for other animals in the	557
experiment, data for the incidental and fatal tumors should be analyzed separately	558
by the prevalence and the death rate methods. Results from the different methods	559
can then be combined to yield an overall result. The combined overall result can	560
be obtained simply by adding together either the separate observed frequencies,	561
the expected frequencies, and the variances, or the separate T statistics and their	562
variances (Peto et al. 1980).	563
564
5. Statistical Analysis of Mortality Independent Tumors	565
566
Tumors that are mortality independent, such as skin tumors and mammary gland	567
tumors, which are visible and/or can be detected by palpation in living animals,	568
are analyzed by CDER statistical reviewers using the onset rate method. The	569
onset rate method for mortality independent tumors and the death rate method for	570
fatal tumors are essentially the same in principle except that the endpoint in the	571
onset rate method is the occurrence of such a tumor (e.g., skin tumor reaching	572
some prescpecified size) rather than the time or cause of the animal’s death.	573
574

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In the onset rate method, all those animals that, although still alive, have	575
developed the particular mortality independent tumor and hence are no longer at	576
risk for such a tumor are excluded from the calculation of the numbers of animals	577
at risk. The Rk, Pik, and Oik described in Section III.C.3 are now redefined as	578
follows for the onset rate method:	579
580
Rk: The number of animals alive and free of the mortality independent	581
tumor of interest in all groups just before tk.	582
583
Pik: (The same as in the death rate method) Proportion of Rk in Group i.	584
585
Oik: Observed number of animals in Group i found to have developed	586
the mortality independent tumor of interest at time tk.	587
588
The test statistic T and its estimated variance V(T) are the same as those defined	589
in the death rate method.	590
591
6. Exact Methods	592
593
As noted in previous sections, the prevalence method, the death rate method, and	594
the onset rate method used normal approximation in the test for the positive trend	595
in tumor incidence rates. Mortality patterns, the number of intervals used in the	596
partitioning of the study period, and the numbers and patterns of tumor	597
occurrence in each individual interval have effects on the accuracy of the normal	598
approximation. It is also well known that the approximation results may not be	599
stable and reliable, and tend to underestimate the exact p-values when the total	600
numbers of tumor occurrence across treatment groups are small (Ali 1990). In	601
this situation, the exact permutation trend test should be used to test for the	602
positive trend (Gart et al. 1986; Goldberg 1985). The exact permutation trend test	603
is a generalization of the Fisher’s exact test to a sequence of 2x(r+1) tables. The	604
exact permutation trend test procedure described below is for tumors observed in	605
an incidental context. However, the positive trends in incidence rates of tumors	606
observed in a fatal or in a mortality independent context can be tested in a similar	607
way. In those cases, the number of 2x(r+1) tables will be equal to the number of	608
time points when one or more animals died of a particular fatal tumor, or when	609
one or more animals developed a particular mortality independent tumor.	610
Fairweather et al. (1998) contains a discussion on the limitations of applying	611
exact methods to fatal tumors.	612
613
The exact method is derived by conditioning on the row and column marginal	614
totals of each of the 2x(r+1) tables formed from the partitioned data set of Table	615
3. Consider the k-th interval Ik (in Table 3) and rewrite it as in Table 7. Let the	616
column totals C0k, C1k, …, Crk and the row totals O.k and A.k be fixed. Define Pik	617
= Cik/Rk. Then the quantities Eik = O.kPik, Vijk = αk Pik(δij-Pjk), Ei, and V(T)	618
(defined in Subsection III.C.2) are all known constants.	619
620

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621
622
Table 7: The Data in the k-th Time Interval Ik Is Written as a 2 x (r + 1) Table	623
624
Group 0 1 . . . i . . . r
Dose D0 Dl . . . Di . . . Dr Total
# w tumor O0k Olk . . . Oik . . . Ork O.k
# w/o tumor A0k Alk . . . Aik . . . Ark A.k
Total C0k Clk . . . Cik . . . Crk Rk
625
626
627
Now let y be the observed value of Y = ∑DiOi, where Oi = ∑kOik, the total	628
number of tumor bearing animals of the tumor of interest in treatment group i.	629
Then (under conditioning on the column and row marginal totals in each table)	630
the observed significance level or	631
632
p-value = P[∑DiOi>=y] = P(∑iDi ∑kOik>=y) = P(∑k∑iDiOik>=y)	633
634
= P(∑kYk>=∑yk) = P(Y>=y),	635
636
where Y = ∑Yk = ∑k∑iDiOik and y = ∑yk, the observed value of Y.	637
638
This p-value (P(Y>=y) is computed from the exact permutational distribution of	639
Y. Given the observed row and column marginal totals in a 2x(r+1) table, all	640
possible tables having the same marginal totals can be generated. Let Sk	641
(k=1,2,…,K) be the set of all such tables generated from the k-th observed table.	642
From a set of K tables taking one from each Sk and assuming independence	643
between the K tables, the above expression for the p-value can now be written as	644
645
p-value = ∑[P(Y1 = yi) … P(Yk = yk)]	646
647
where yk =∑iDiOik (k=1,2,…,K), the sum is over all sets of K tables such that	648
yi+y2+…+yk >=y, the observed value of Y, and P(Yk=yk) is the conditional	649
probability given the marginal totals in the k-th table, i.e.,	650

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651
P(Yk=yk) = C
O
C
O
0k
0k
1k
1k


 




 

 

 . . . C
O
rk
rk


 

 


R
O
k
k


 

	652
653
654
Example (Lin and Ali 1994). Consider an experiment with 3 treatment groups	655
(control, low-, and high-dose) with dose levels D0=0, D1=1, and D2=2,	656
respectively. Suppose the study period is partitioned into the intervals 0-50, 51-	657
80, 81-104 weeks, and the terminal sacrifice week. Consider a tumor type	658
(classified as incidental) with data in Table 8.	659
660
661
662
Table 8: Hypothetical Tumor Data for Exact Permutation Trend Test	663
664
Time intv.
Dose levels
0 1 2 Total
0 - 50 O
C
0 0 0
1 3 3
0
7
51 - 80 O
C
0 0 0
4 5 7
0
16
81 - 104 O
C
0 0 2
10 12 15
2
37
Term. Sacr. O
C
0 1 0
35 30 25
1
90
O = observed tumor count, C = number of animals necropsied	665
666
667
668
Since all the observed tumor counts (i.e., O’s) in the first two time intervals are	669
zeros, the data for these intervals will not contribute anything to the test statistic,	670
and these intervals may be ignored. The observed subtables formed from the last	671
two intervals are given in Table 9.	672
673
Now, generate all possible tables from observed subtable 1. Since the marginal	674
totals are fixed, these tables may be generated by distributing the total tumor	675
frequency O.1(=2) among the three treatment groups. Thus, each table will	676
correspond to a configuration of this distribution of O.1. The configurations, the	677
values of Y1, and the P(Y1=y1) are shown in Table 10.	678
679
680
681

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Table 9: Observed Subtables From the Above Hypothetical Tumor Data	682
Observed subtable 1 Observed subtable 2
Dose 0 1 2 Total Dose 0 1 2 Total
O 0 0 2 2=O.1 O 0 1 0 1=O.2
A 10 12 13 35=A.1 A 35 29 25 89=A.2
C 10 12 15 37=R1 C 35 30 25 90=R2
683
684
685
Table 10: All Possible Configurations of o.1 and the	686
Corresponding Hypergeometric Probabilities	687
Configurations y1 P(Y1=y1)
0, 0, 2
0, 2, 0
2, 0, 0
0, 1, 1
1, 0, 1
1, 1, 0
4
2
0
3
2
1
.15766
.09910
.06757
.27027
.22523
.18018
688
689
To illustrate the computation of y1 and P(Y1=y1) consider the last row. Here y1=	690
D0x1 + D1 x1 + D2 x0 = 0x1 + 1x1 + 2x0 = 1, and	691
692
P(Y1=1) = 10
1
12
1


 




 

 

 . . . 15
0


 

 


37
2


 

 = 0.18018	693
694
The configurations and probabilities obtained from observed subtable 2 are given	695
in Table 11.	696
697
Note that the first configuration (0,0,2) in Table 8 corresponds to the observed	698
subtable 1 with a value of y1= (0x0)+(2x2)=4 and a probability of .15766, and the	699
second configuration (0,1,0) in Table 8 corresponds to the observed subtable 2	700
with a value of y2= (0x0)+(1x1)+(0x0)=1 and a probability of .33333. Thus, the	701
observed value of y = y1+y2 = 4+1=5. Now the exact p-value (right-tailed) is	702
calculated as follows:	703
704
705
P(Y = Y1+Y2 >=5) = P(Y1=4,Y2=1)+P(Y1=4, Y2=2)+P(Y1=3, Y2=2)	706
707
= .15766 x .33333 + .15766 x .27778 + .27027 x .27778	708
709

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= .17142	710
711
712
713
Table 11: All Possible Configurations of O.2 and the	714
Corresponding Hypergeometric Probabilities	715
Configurations y1 P(Y1=y1)
0, 0, 1
0, 1, 0
1, 0, 0
2
1
0
.27778
.33333
.38889
716
717
For the purpose of comparison, it should be noted that the normal approximated	718
p-value for the data set in the above example is .0927.	719
720
721
D. Statistical Analysis of Data Without Information About Cause of Death and	722
Without Multiple Sacrifices	723
724
As noted previously, in the analysis of tumor data, it is essential to identify and adjust for	725
possible differences in intercurrent mortality among treatment groups to eliminate or	726
reduce biases caused by these differences. It is also necessary for the analysis to	727
appropriately account for tumor lethality. The widely used prevalence method, the death	728
rate method, and the onset rate methods for analyzing incidental, fatal, and mortality	729
independent tumors, respectively, described in previous sections rely on good	730
information on tumor lethality and cause of death. There are situations in which sponsors	731
have not included tumor lethality and cause of death information in their statistical	732
analyses and electronic data sets. Under those situations, statistical reviewers in CDER	733
either treated all tumors as incidental or relied on cause of death assessments by the	734
reviewing pharmacologists and toxicologists in the Center. There are consequences in	735
misclassifying tumors as lethal or not in survival adjusted statistical tests. The prevalence	736
method will reject the null hypothesis of no positive trend less frequently than it should	737
as the lethality of a tumor increases (Peto et al. 1980; Dinse 1994). This will increase the	738
probability of failing to detect true carcinogens.	739
740
The Bailer-Portier poly-3, and poly-6 (in general poly-k) tests (Bailer and Portier 1988;	741
Dinse 1994) have been proposed for testing linear trends in tumor rates. These tests are	742
basically modifications of the survival unadjusted Cochran-Armitage test (Cochran 1954;	743
Armitage 1955, 1971) for linear trend in tumor rate. If the entire study period is	744
considered as one interval, the data for a particular tumor type will be in the form of	745
Table 12. The notations in Table 12 to be used to explain these tests are the same as	746
those in Table 7 except that the k-th interval now is the entire study period. The second	747
subscript, k, for the k-th interval was dropped from the notations.	748
749

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750
Table 12: The Data Using the Entire Study Period as an Interval	751
752
Group 0 1 . . . i . . . r
Dose D0 Dl . . . Di . . . Dr Total
# w. tumor O0 Ol . . . Oi . . . Or O
# w/o tumor A0 Al . . . A i . . . Ar A
Total C0 Cl . . . Ci . . . Cr R
753
754
755
756
The Cochran-Armitage test statistic for linear tend in tumor rate is defined as (Armitage	757
1955):	758
759
R { R ∑ OiDi – O ∑ Ci Di } 2
760
χCA2 = --------------------------------------------------------- or	761
O (R – O) { R ∑ Ci Di2 – { ∑ Ci Di) 2 }	762
763
764
{ ∑ Di (Oi – Ei) }	765
= ---------------------------------------	766
∑ Ei Di2 – ( ∑ Ei Di) 2 / O	767
768
Where O = ∑ Oi, A = ∑ Ai, R= ∑ Ci, Ei = O Ci / R.	769
770
The test statistic χCA2 is distributed approximately as χ2 on one degree of freedom.	771
772
The Cochran-Armitage linear trend test is based on a binomial assumption that all	773
animals in the same treatment group have the same risk of developing the tumor over the	774
duration of the study. However, as noted previously, the animal’s risk of developing the	775
tumor increases as study time increases. The assumption is thus no longer valid if some	776
animals die earlier than others. It has been shown that as long as the mortality patterns	777
are similar across treatment groups, the Cochran-Armitage test is still valid, although it	778
may be slightly less efficient than a survival adjusted test (Dinse 1994). However, if the	779
mortality patterns are different across treatment groups, the Cochran-Armitage test can	780
give very misleading results.	781
782
The Bailer-Portier poly-3 test adjusts for differences in mortality among treatment groups	783
by modifying the number of animals at risk in the denominators in the calculations of	784
overall tumor rates in the Cochran-Armitage test to reflect “less-than-whole-animal	785
contributions for decreased survival” (Bailer and Portier 1988). The modification is	786

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made by defining a new number of animals at risk for each treatment group. The number	787
of animals at risk for the i-th treatment group C*i is defined as	788
789
C* i = ∑ W ij	790
791
where w ij the weight for the j-th animal in the i-th treatment group, and the sum is over	792
all animals in the group.	793
794
Bailer and Portier (1988) proposed the weight w ij as follows:	795
796
w ij = 1 to animals dying with the tumor, and	797
798
w ij = ( tij / tsacr )3 to animals dying without the tumor	799
800
where tij is the time of death of the j-th animal in the i-th treatment group, and tsacr is the	801
time of terminal sacrifice.	802
803
The power of 3 used in the weighting is from the observation that tumor incidence can be	804
modeled as a polynomial of order 3. Similarly the poly-6 test (or the general poly-k test)	805
assigns the weight w ij = (tij / t sacr )6 (or w ij = ( tij / tsacr )k ) to animals dying without	806
the tumor when the tumor incidence is close to a polynomial of order 6 (or order k).	807
808
The class of Bailer-Portier poly-k tests are carried out by replacing the Ci’s by the new	809
numbers of animals at risk C*i’s in the calculation of the above Cochran-Armitage test	810
statistic.	811
812
The class of Bailer-Portier poly-k tests adjust differences in survival, do not need the	813
information about cause of death, and call for only a (the terminal) sacrifice. Results of	814
simulation studies by Bailer and Portier (1988), and Dinse (1994) show that the tests	815
performed very well under many conditions simulated. They are also relatively robust to	816
(not affected greatly by) tumor lethality.	817
818
Bieler and Williams (1993) pointed out that, since animal survival time is generally not a	819
fixed quantity, the numerators and denominators of the adjusted quantal response	820
estimates	821
822
p*i = Oi / C*i	823
824
are both subject to random variation.	825
826
Bieler and Williams (1993) proposed a test called the ratio trend test (also called Bieler-	827
Williams poly-3 test), which is another modification to the Cochran-Armitage linear	828
trend test. The ratio trend test employs the adjusted quantal response rates calculated in	829
Bailer and Portier (1988) and the delta method (Woodruff 1971) in the estimation of the	830
variance of the adjusted quantal response rates p*i = Oi / C*i.	831

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832
The computational formula for Bieler-Williams ratio trend (modified C-A) test statistic is	833
given as follows:	834
835
836
∑ mi p*i Di – (∑ miDi) (∑mi p*i) / ∑mi	837
χ2BW = ----------------------------------------------------	838
{c [∑ mi Di 2 - (∑ mi Di )2 / ∑ mi]}1/2
839
840
where	841
842
c = ∑∑ (rij – ri.)2 / [R – (r + 1)]	843
844
mi = (CI*)2 / Ci	845
846
rij = yij - p* wij	847
848
ri. = ∑ rij / Ci	849
850
yij = tumor response indicator (0 = absent at death, 1 = present at death) for the jth	851
animal in the ith group.	852
853
Bieler and Williams (1993) showed that the Bailer-Portier poly-3 trend test is anti-	854
conservative when tumor incidence rates are low and treatment toxicity is high. Their	855
study also showed that for tumors with low background rates, the ratio trend test (Bieler-	856
Williams poly-3 test) yielded actual Type I errors close to the nominal levels used and	857
was observed to be less sensitive than the Bailer-Portier poly-3 trend test to	858
misspecification of the shape of tumor incidence function and the magnitude of treatment	859
toxicity.	860
861
A more recent simulation study by Chen, Lin, Juque, and Arani (2000) showed the	862
following additional results about the characteristics of the Bailer-Portier poly-3 and the	863
ratio trend tests (Bieler-William poly-3 test). For individual tumor types, the two tests for	864
trend yield attained Type I errors around the nominal levels (5 percent and 1 percent) for	865
tumors with spontaneous rates in the range between 2 percent to 20 percent. When	866
spontaneous rates are below the range, the two tests become conservative (i.e., less likely	867
to show statistically significant results). For tumors with spontaneous rates above 20	868
percent to 60 percent (the upper rate used in the simulation), the ratio trend test still	869
maintains the attained Type I error rates close to the nominal levels, but the Bailer-Portier	870
poly-3 test becomes more and more conservative as the rates go up. The introduction of	871
the compound symmetric correlation structure (although a not very realistic structure)	872
among tumors corrects the problem of conservativeness somewhat in the Bailer-Portier	873
poly-3 test, but the patterns of conservativeness continue to exist.	874
875

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The ratio trend test (Bieler-William poly-3 test), like the Bailer-Portier poly-3 test,	876
adjusts differences in survival, does not need the information about cause of death, and	877
results only in a (the terminal) sacrifice. Results of simulation studies (Bieler and	878
Williams 1993; Chen, Lin, Huque, and Arani 2000) show that the tests performed very	879
well under many simulated conditions. It is also shown to be relatively robust to (not	880
affected greatly by) tumor lethality, misspecification of the shape of tumor incidence	881
function, and the magnitude of treatment toxicity. The ratio trend test (Bieler-William	882
poly-3 test) should be used to replace the asymptotic tests that depend on the information	883
of tumor lethality and cause of death when the information is unavailable.	884
885
Theoretically, exact versions of the class of tests can be developed for testing data of	886
studies with small numbers of tumor bearing animals by applying the test procedures to	887
all possible permuted configurations of the outcome. However, because these tests use	888
risk sets based on all animals in each treatment group, the computations involved in the	889
exact tests will be extensive. Therefore, for studies with small numbers of tumor bearing	890
animals, the current practice of treating them as incidental tumors and applying the exact	891
permutation trend test should continue.	892
893
E. Statistical Analysis of Data From Studies With Dual Controls	894
895
There are two categories of studies with dual control groups. The first category usually	896
consists of studies using an untreated control group and a vehicle control group (Category	897
A). Other variations of nonidentically treated, nondrug treatment controls groups are also	898
occasionally used and are included in Category A for statistical purposes. The second	899
category (Category B) includes studies that use two identical control groups (Society for	900
Toxicology 1982; Haseman, Winbush, and O’Donnell 1986).	901
902
The main reasons for using two differently treated controls, generally an untreated	903
control and a vehicle control in a study in Category A are to determine whether the	904
vehicle has effects on tumor incidence and pattern, body weight, and food consumption	905
(in dietary studies) on the test animals, and to make sure that the control animals are	906
subjected to the same influences (e.g., gavage or injection) as the drug treated animals, so	907
that all animals will be subject to equal physiological response and stress (i.e., to isolate	908
the treatment effect from other possible effects) (Gart et al. 1986; Dayan 1988).	909
910
There are arguments for and against using two identical control groups in a study	911
(Category B). The arguments for this design are that the results from the two identical	912
controls can be used as a mechanism for identifying the extent of control variability (Gart	913
et al. 1986) and the results can be used to help evaluate the biological significance of	914
increases in tumor incidence in the treated groups (i.e., true increases versus noise).	915
From the biological perspective, the dual control data can be viewed as equivalent to	916
having contemporary historical data. In this case, consideration of other appropriate	917
historical control data is essential if the results with the two contemporary controls are	918
different. As described below, however, there may be difficulties in statistical analysis of	919
data from a study using this design.	920

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Statisticians and pharmacologists/toxicologists should decide collaboratively which of the	921
two control groups is appropriate for the analysis of data from a study in Category A.	922
Ordinarily, analyses of data of the vehicle control and the treated groups are the most	923
meaningful assessment of drug effect. Even in this case, however, the untreated control	924
can give information about spontaneous variability. There are other situations in which	925
three analyses – control 1 versus treated groups, control 2 versus treated groups, and	926
control 1 plus control 2 versus treated groups – are performed. Because concerns about	927
the possible effects of the vehicle substance on the test animals are the reason for using	928
the vehicle control in addition to the untreated control, it is also of interest to compare the	929
mortality, tumor rates, body weight, and food consumption (in dietary studies) between	930
the two control groups.	931
932
Data from dual identical control groups may or may not be combined for statistical	933
analysis of data. If comparisons of the controls for Category B studies show no large	934
differences in mortality and tumor rate, the data from the two control groups are usually	935
combined to form a single control group in subsequent analyses (Haseman et al. 1990).	936
If the data show evidence of differences in mortality or tumor incidence between the	937
identical controls, three tests – control 1 versus treated groups, control 2 versus treated	938
groups, and control 1 plus control 2 versus treated groups – for each tumor/organ	939
combination should be carried out.	940
941
In the second case, the question of how to interpret the results of a study in Category B	942
can be approached from two perspectives. First, a trend or a difference in tumor rate	943
could be considered significant only if it is significant for both of the controls. The basis	944
for this conclusion would be that a real finding should be reproducible. Alternatively, the	945
trend or the difference in tumor rate between groups could be considered significant as	946
long as any one of the three tests (i.e., drug vs. control 1, drug vs. control 2, and drug vs.	947
pooled control) either control and pooled control shows a significant result, assuming that	948
most carcinogenicity studies are relatively under powered. The first approach is	949
conservative in the sense that the null hypothesis will be rejected less often. The second	950
approach, on the other hand, will result in an increased false positive rate.	951
952
Currently, no good information exists about how to appropriately adjust the significance	953
levels for the above two approaches to maintain the 10 percent overall false positive rate	954
used by the Center. In general, the test result could be regarded as providing only	955
equivocal evidence of a positive finding unless all the three tests yield consistent results	956
(i.e., all statistically significant or all not statistically significant) (Haseman et al. 1990).	957
In such instances, from a biological prospective it is particularly important to evaluate the	958
control response relative to a historical control.	959
960
961
V. INTERPRETATION OF STUDY RESULTS	962
963
Interpreting results of carcinogenicity experiments is a complex process, and there are risks of	964
both false negative and false positive results. The relatively small number of animals used and	965

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low tumor incidence rates can result in the failure to detect the carcinogenicity of a drug (i.e., a	966
false negative). Because of the large number of comparisons involved (usually 2 species, 2	967
sexes, and 30 or more tissues examined), a great potential exists for finding statistically	968
significant positive trends or treatment-placebo differences due to chance alone (i.e., a false	969
positive). Therefore, it is important that an overall evaluation of the carcinogenic potential of a	970
drug take into account the multiplicity of statistical tests of significance for both trends and	971
pairwise comparisons. The evaluation should also make use of historical information and other	972
information related to biological relevance (e.g., positive findings at the same site in the other	973
sex and/or in the other species, and evidence of increased preneoplastic lesions at the target	974
organs/tissues).	975
976
A. Adjustment for the Effect of Multiple Tests (Control Over False Positive	977
Error)	978
979
It is well known that, for a multi-group study (e.g., 3 doses and placebo), trend tests are	980
more powerful (i.e., more likely to detect an effect) than pairwise comparisons. Tests for	981
trend instead of pairwise comparison tests between control and high-dose groups are	982
therefore the primary tests in the evaluation of drug related increases in tumor rate.	983
984
Statistical and nonstatistical procedures have been proposed for controlling the overall	985
false positive rate. Surveys of some of those procedures can be found in Lin and Ali	986
(1994), and Fairweather et al. (1998). In this guidance document, only the statistical	987
decision rules for controlling the overall false positive rates associated with trend tests	988
and pairwise comparisons used by the Center in interpreting the final results of	989
carcinogenicity studies are discussed. The decision rules were developed based on	990
historical control data of CD rats and CD mice (strains that are most widely used in	991
studies of pharmaceuticals) to achieve an overall false positive rate of around 10 percent	992
for the standard two-species, two-sex in-vivo studies and the alternative ICH one-species,	993
two-sex in-vivo studies.	994
995
In the past, statisticians in CDER used the statistical decision rule described in Haseman	996
(1983) in tests for significance of trends in tumor incidence. The decision rule was	997
originally developed for pairwise comparison tests in tumor incidence between the	998
control and the high-dose groups and was derived from results of carcinogenicity studies	999
conducted at National Toxicology Program (NTP). Strains of Fischer 344 rats and	1000
B6C3F1 mice were used in the NTP studies. Like most studies of pharmaceuticals, four	1001
treatment/sex groups with 50 animals in each group were used in the NTP studies. All of	1002
the NTP studies lasted for 2 years. The decision rule tests the significant differences in	1003
tumor incidence between the control and the dose groups at 0.05 level for rare tumors and	1004
at 0.01 level for common tumors. A tumor type with a background rate of 1 percent or	1005
less is classified as rare by Haseman; more frequent tumors are classified as common.	1006
Haseman’s original study and a second study using more recent data with higher tumor	1007
rates show that the use of this decision rule in the control-high pairwise comparison tests	1008
would results in an overall false positive rate between 7 to 8 percent and between 10 to	1009
11 percent, respectively (Haseman 1983, 1984a, 1991).	1010

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1011
Concerns have been raised that applying the rule described by Haseman (1983) to	1012
analyses of trend tests would lead to an excessive overall false positive error rate as data	1013
from all treatment groups are used in the tests and considerably lower tumor rates can	1014
yield a wrongly significant result. Results from recent studies within and outside FDA	1015
show that this concern is valid. Based on studies conducted by CDER and NTP, the	1016
overall false positive error resulting from interpreting trend tests by use of the above	1017
decision rule is about twice as large as that associated with control-high pairwise	1018
comparison tests.	1019
1020
Based on recent studies using real historical control data of CD mice and CD rats from	1021
Charles River Laboratory and simulation studies conducted internally and in	1022
collaboration with NTP, a new statistical decision rule for tests for a positive trend in	1023
tumor incidence has been developed. This new decision rule tests the positive trend in	1024
incidence rates in rare and common tumors at 0.025 and 0.005 levels of significance,	1025
respectively. The new decision rule achieves an overall false positive rate of around 10	1026
percent in a standard two-species and two-sex study (Lin 1995, 1997; Lin and Rahman	1027
1998a, 1998b). The 10 percent overall false positive rate is seen by CDER statisticians as	1028
appropriate in a new drug regulatory setting.	1029
1030
Regulatory statistical literature emphasizes methods for testing for positive trends in	1031
tumor rate (Lin 1988, 2000); Lin and Ali 1994; Chen and Gaylor 1986; Dinse and	1032
Haseman 1986; and Dinse and Lagokos 1983). There are situations, however, in which	1033
pairwise comparisons between control and individual treated groups may be more	1034
appropriate than trend tests because trend tests assume that a carcinogenic effect is	1035
related to doses or systemic exposure weights, or ranks. The assumption may be true for	1036
simple direct acting carcinogens in studies not complicated by excessive toxicity.	1037
However, there are many cases in which the response is to a drug metabolite, is mediated	1038
through a receptor (or enzyme) that may be saturated even at the low dose, is	1039
compounded by dose-related toxicity, or is complicated by other nonlinear effects. Under	1040
those situations, pairwise comparisons may be appropriate and the decision rule described	1041
in Haseman (1983) should be used in interpreting the results of the pairwise comparison	1042
tests.	1043
1044
Sponsors should conduct both trend tests and pairwise comparison tests and present the	1045
results of these two types of tests in the formats used in Table 15. A recent complication	1046
to the use of the trend test is the choice by a sponsor not to do histopathologic evaluation	1047
of all treatment groups. Although studies conducted using this design have been	1048
evaluated by CDER, such an approach is not usually recommended.	1049
1050
The high cost (between 1 and 2 million dollars) and long time (a minimum of 3 years) it	1051
takes to conduct a standard long-term, in-vivo carcinogenicity study and the increased	1052
insight into the mechanisms of carcinogenicity provided by advances in molecular	1053
biology have led to alternative in-vivo approaches to the assessment of carcinogenicity.	1054
The International Conference on Harmonization (ICH) has developed guidance for use in	1055

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the United States and in other regions entitled S1B Testing for Carcinogenicity of	1056
Pharmaceuticals (1998). This guidance outlines experimental approaches to the	1057
evaluation of carcinogenic potential that may obviate the need for the routine use of two	1058
long-term rodent carcinogenicity studies and allows for the alternative approach of	1059
conducting one long-term rodent carcinogenicity study together with a short- or medium-	1060
term rodent test. The short- or medium-term rodent test systems include such studies as	1061
initiation-promotion in rodents, transgenic rodents, or newborn rodents, which provide	1062
rapid observation of carcinogenic endpoints in-vivo. In general, these studies do not	1063
produce false positive results because tumor background rates are very low. False	1064
positives therefore arise primarily from the 2-year rodent study. Results from an agency	1065
study using historical control data of CD rats and CD mice (Lin 1997; Lin and Rahman	1066
1998b) showed that the use of significance levels of 0.05 and 0.01 in tests for positive	1067
trend in incidence rates of rare tumors and common tumors, respectively, will result in an	1068
overall false positive rate around 10 percent in a study in which only one 2-year rodent	1069
bioassay (plus the shorter rodent study) is conducted.	1070
1071
The decision rules for testing positive trend or differences between control and individual	1072
treated groups in incidence rates for standard studies using two species and two sexes as	1073
well as studies following ICH guidance and using only one 2-year rodent bioassay are	1074
summarized in Table 13.	1075
1076
The developed decision rules for tests for positive trend and for difference in pairwise	1077
comparisons are based on the proposition that the carcinogenic effect of a drug is	1078
considered positive if one or more tumor types tested in any of the four experiments (or	1079
two experiments under an alternative ICH study) of species/sex combination show a	1080
significant positive trend in tumor incidence rates (or one or more tumor types show a	1081
significant difference in tumor incidence rates when the results of the control-high	1082
pairwise comparisons are used in the final interpretation). The decision rules were	1083
developed assuming the use of the two-species-and-two-sex (or one-species-and-two-sex)	1084
standard design of a two-year study with 50 animals in each of the four treatment/sex	1085
groups.	1086
1087

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Table 13: Statistical Decision Rules for Controlling the Overall False	1088
Positive Rates Associated With Tests for Positive Trend or With	1089
Control-High Pairwise Comparisons in Tumor Incidences to	1090
Around 10 Percent in Carcinogenicity Studies of Pharmaceuticals	1091
1092
1093
Tests for Positive Trend Control-High Pairwise
Comparisons
Standard 2-Year Studies
with 2 Species and 2 Sexes
Common and rare tumors
are tested at 0.005 and 0.025
significance levels,
respectively.
Common and rare tumors
are tested at 0.01 and 0.05
significance levels, respectively.
Alternative ICH Studies
(One Two-Year Study in
One Species and One Short-
or Medium-Term Study,
Two Sexes)
Common and rare tumors
are tested at 0.01 and 0.05
significance levels,
respectively.
Under development and not yet
available.
1094
1095
1096
B. Control Over False Negative Error	1097
1098
To make sure that the false negative rate is not excessive, reviewing pharmacologists,	1099
pathologists, and medical officers evaluate the adequacy of the gross and histological	1100
examination of both control and treated groups, the adequacy of the dose selection, the	1101
duration of the experiment in relation to the normal life span of the tested animals, and	1102
the survival of animals in the study.	1103
1104
C. The Use of Historical Control Data	1105
1106
The concurrent control group is always the most appropriate and important in testing	1107
drug related increases in tumor rates in a carcinogenicity experiment. However, if used	1108
appropriately, historical control data can be very valuable in the final interpretation of the	1109
study results. Large differences between studies can result from differences in	1110
nomenclature, pathologists reading slides, the specific animal strain used and laboratory	1111
conditions. It is therefore extremely important that the historical control data chosen be	1112
from studies comparable to the current study, generally recent studies from the same	1113
laboratory using the same strain of rodent.	1114
1115
Historical control data are particularly useful in classifying tumors as rare or common. A	1116
statistically significant increase in a rare tumor is unlikely as a chance occurrence so that	1117
it is critical to decide whether a tumor is rare or not. Rare tumors are generally tested	1118
with less stringent statistical decision rules (see Table 13). Historical control data can	1119
also be used as a quality control mechanism for a carcinogenicity experiment by	1120
assessing the reasonableness of the spontaneous tumor rates in the concurrent control	1121

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group (Haseman 1984b; Haseman, Huff, and Boorman 1984), and for evaluation of	1122
disparate findings in dual concurrent controls.	1123
1124
For common tumors, in cases of marginally significant trends or differences, historical	1125
control data can help investigators determine whether the findings are real or false	1126
positives. Historical control data can also help investigators determine whether	1127
nonsignificant findings in rare tumors are true negative or false negative results due to the	1128
lack of power in the statistical tests used. A widely used informal method is to determine	1129
whether the tumor rates in the treated groups in the experiment are within the range of	1130
reliable historical control data. If they are, a marginally significant finding for a common	1131
tumor may be discounted as resulting from a random occurrence of a low concurrent	1132
control rate. Similarly, a nonsignificant increase for a rare tumor can be considered truly	1133
negative if the treated tumor rates are within the historical range.	1134
1135
The above informal method of using historical control data in the interpretation of	1136
statistical test results is not very satisfactory because the range of historical control rates	1137
is usually too wide. This is especially true in situations in which the historical tumor	1138
rates of most studies used are clustered together, but a few other studies give rates far	1139
away from the cluster. When the range of historical control data is simply calculated as	1140
the difference between the maximum and the minimum of the historical control rates.	1141
The range does not consider the shape of the distribution of the rates. The upper	1142
confidence intervals for binomial proportions constructed by the methods described in	1143
Louis (1981), Blyth (1986), Vollset (1993), Jovanovic and Viana (1996), and Jovanovic	1144
and Levy (1997) should probably replace the historical range in the above informal	1145
method.	1146
1147
In addition to the informal use of historical control data in the interpretation of the	1148
statistical testing results mentioned above, more formal statistical procedures have been	1149
proposed that allow the incorporation of appropriate historical control data in tests for	1150
trend in tumor rate. For example, Tarone (1982), Hoel (1983), Hoel and Yanagawa	1151
(1986), Tamura and Young (1986, 1987), and Prentice et al. (1992) proposed some	1152
empirical procedures using the beta-binomial distribution to model historical control	1153
tumor rates and to derive approximate and exact tests for trend. The results from those	1154
studies show that the incorporation of the historical control data improves the power of	1155
the tests. The greatest improvement of power is shown in the tests of rare tumors.	1156
Dempster et al (1983) proposed a Bayesian procedure to incorporate historical control	1157
data into statistical analysis. The procedure uses the assumption that the logits of the	1158
historical control tumor rates were normally distributed.	1159
1160
These formal statistical procedures work well in situations in which historical data from a	1161
large number of studies with relatively large control groups are available to provide	1162
reliable estimations of the parameters of the prior distributions. However, the maximum	1163
likelihood estimators (MLEs) of the prior parameters were shown to be unstable, and the	1164
distributions of the MLEs were skewed to the right (i.e., with bunching above the mean	1165
and a long tail below the mean). The skewness was severe in cases in which only	1166

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historical data of a few small control groups were available. The skewness of the MLEs	1167
inflated the Type I error of the tests. Also, these procedures were developed to	1168
incorporate historical control data into the Cochran-Armitage test for linear trend in	1169
tumor incidence. Since the Cochran-Armitage test is a survival-unadjusted procedure,	1170
these procedures cannot be applied to studies with significant differences in survival	1171
among treatment groups. Recently, Ibrahim and Ryan (1996) developed a method for	1172
incorporating historical control information into survival-adjusted tests for trend in tumor	1173
incidence. When using this method, the study period should be partitioned into intervals.	1174
In each interval, the multinomial distribution should be used to model the observed	1175
numbers of animals dying with the tumor, and Dirichlet distribution should be used as the	1176
prior distribution for the historical control tumor rates. This method applies only to fatal	1177
tumors.	1178
1179
D. Evaluation of Validity of Designs of Negative Studies	1180
1181
In negative or equivocal studies, that is, studies for which either the sponsor’s or FDA’s	1182
statisticians detected no statistically significant positive trend or difference in tumor rate,	1183
the statistical reviewers will perform a further evaluation of the validity of the design of	1184
the experiment to see if there were sufficient numbers of animals living long enough to	1185
provide adequate exposure to the chemical and to be at risk of forming late-developing	1186
tumors. The reviewers also want to see if the doses used were adequate to present a	1187
reasonable tumor challenge to the tested animals (Haseman 1985).	1188
1189
As a rule of thumb, a 50 percent survival rate of the 50 initial animals in any treatment	1190
group between weeks 80 to 90 of a 2-year study would be considered to yield a sufficient	1191
number of animals with adequate exposure. The percentage can be lower or higher if the	1192
number of animals used in each treatment/sex group is larger or smaller than 50, but	1193
between 20 to 30 animals should be still alive during these weeks.	1194
1195
The adequacy of doses selected and of the animal tumor challenge in long-term	1196
carcinogenicity experiments is evaluated by pharmacologists and the CDER	1197
Carcinogenicity Assessment Committee (CAC) based on the previously described ICH	1198
approaches as well as on the results of the long-term carcinogenicity experiments. To	1199
assist the evaluation, CDER statistical reviewers are often asked to provide analyses of	1200
body weight and mortality differences and, occasionally, other differences between	1201
treated and control groups.	1202
1203
1204
VI. PRESENTATION OF RESULTS AND DATA SUBMISSION	1205
1206
To facilitate the statistical reviews, sponsors should present study results and data in such a way	1207
that FDA statistical reviewers are able to verify the sponsors’ calculations, to validate their	1208
statistical methods, and to trace back the sponsors’ conclusions through their summaries and	1209
analyses of the raw data (FDA 1987).	1210
1211

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In the sponsor’s report, in addition to the volumes containing study data of individual animals, a	1212
statistical analysis section should be included containing summary statistics of the study data,	1213
results of statistical analyses of the data, results and findings, and main conclusions of the study.	1214
In the statistical analysis section, the sponsor should include descriptions of the statistical	1215
procedures used and pertinent literature references. The descriptions of statistical methodology	1216
and references are particularly important if the sponsor decides to use designs and methods of	1217
analysis and interpretation other than those recommended in this guidance document.	1218
1219
Tables 14, 15, and 16 include examples of formats for presenting summaries and results of	1220
analyses of survival and tumor data. Presentations of data summaries and analyses results should	1221
be made for each species/sex combination. Descriptive statistics such as mean, standard	1222
deviation, and range, which are important in characterizing the distinctive and essential features	1223
of a study, should also be reported by species/sex combination. Graphics that are useful and	1224
informative in presenting study results should be used to display summary data, especially	1225
summary statistics over time.	1226
1227
Two sets of formats and specifications were previously used regularly by the Divisions of	1228
Biometrics, Office of Biostatistics. They were (a) the Divisions of Biometric Formats and	1229
Specifications for Submission of Animal Carcinogenicity Study Data, and (b) the Submitters	1230
Toxicological Uniform Data Information Exchange Standard (STUDIES). Because mistakes	1231
have often been made by sponsors in data sets using the STUDIES formats, the Office of	1232
Biostatistics now recommends that sponsors submit the data sets in the simpler divisions of	1233
biometrics formats and specifications described in Lin (1998). Discussions of the statistical	1234
analyses on which the formats were developed can be found in Lin (1998).	1235
1236
Data sets described in the above Divisions of Biometrics formats and specifications document	1237
are divided into two groups, Group A and Group B, depending on whether the data will be used	1238
immediately in the statistical review and evaluation of the carcinogenicity studies. Group A	1239
includes data sets that are always used by statisticians performing a statistical review and	1240
evaluation of the carcinogenicity studies. Group B includes data sets that may be used by	1241
medical officers, pharmacologists, toxicologists, and statisticians in their final interpretations of	1242
the study results. Sponsors are urged to submit the two groups of data sets together with their	1243
original, initial submissions of the hardcopy NDA or IND. However, if a sponsor under some	1244
special circumstances cannot submit the two groups of data sets together, the Group A data sets	1245
should be submitted first.	1246
1247
The FDA has issued a guidance document (1999) to encourage and assist drug applicants in	1248
submitting an electronic archival copy of a new drug applications (NDAs), including	1249
amendments and supplements. The Agency’s effort to encourage applicants to submit	1250
applications electronically is an integrated part of the Agency’s Electronic Records; Electronic	1251
Signatures regulation (Electronic Records; Electronic Signatures, Office Federal Register, March	1252
20, 1997). The above submission of data from carcinogenicity studies to statisticians should be a	1253
part of an electronic NDA. The information in the formats and specifications, discussed above,	1254
have been incorporated into the Agency’s guidance on regulatory submission of electronic	1255
applications (FDA 1999). Drug sponsors should follow the guidance and recommendations	1256

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included in the nonclinical pharmacology and toxicology section of the guidance in their	1257
preparation and submission of electronic carcinogenicity study data.	1258
1259
Table 14: Example Format for Showing Summary of Deaths and Sacrifices of Male Mice	1260
1261	1262
Control Low Medium High	1263
Week E D S N NP E D S N NP E D S N NP E D S N NP	1264	1265
34 70 -- -- -- -- 70 -- -- -- -- 70 -- -- -- -- 70 -- -- -- --	1266
1267
35 70 1 1 1 1 70 -- -- -- -- 70 -- -- -- -- 70 -- -- -- --	1268
36 68 -- -- -- -- 70 1 -- -- 1 70 -- -- -- -- 70 -- -- -- --	1269
1270
39 68 -- -- -- -- 69 -- -- -- -- 70 -- -- -- -- 70 1 -- 1 --	1271
1272
41 68 -- -- -- -- 69 -- -- -- -- 70 1 -- -- 1 69 -- -- -- --	1273
1274
43 68 -- -- -- -- 69 -- -- -- -- 69 1 -- 1 -- 69 -- -- -- --	1275
1276
49 68 -- -- -- -- 69 -- -- -- -- 68 -- -- -- -- 69 1 -- -- --	1277
1278
52* 68 -- 10 10 -- 69 -- 10 10 -- 68 -- 10 10 -- 68 -- 10 10 --	1279
1280
53 58 1 -- 1 -- 59 -- -- -- -- 58 -- -- -- -- 58 -- -- -- --	1281
1282
58 57 -- -- -- -- 59 -- -- -- -- 58 3 -- 3 -- 58 -- -- -- --	1283
1284
62 57 1 -- 1 -- 59 -- -- -- -- 55 -- -- -- -- 58 1 -- 1 --	1285
1286
65 56 -- -- -- -- 59 -- -- -- -- 55 -- -- -- -- 57 1 -- 1 --	1287
1288
70 56 -- -- -- -- 59 -- -- -- -- 55 3 -- 3 -- 56 1 -- 1 --	1289
1290
71 56 -- 1 1 -- 59 1 1 2 -- 52 1 -- 1 -- 55 -- -- -- --	1291
1292
(Continue to the end of the study)	1293
1294
Term* 41 2 39 41 -- 40 -- 40 40 -- 36 -- 36 -- -- 38 1 37 36 2	1295	1296
Mean	1297
survival 668 680 650 632	1298	1299 Notes: E = Number of animals entering the period; D = Deaths; S = Sacrificed moribund;	1300
N = At least one tissue was examined microscopically; NP = No tissues were examined	1301
microscopically; * = Scheduled and terminal sacrifices.	1302
1303
1304

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Table 15: Example Format for Showing Summary of Incidences and Results of	1305
Statistical Tests (P-values) of Neoplastic Lesions (in Male Mice)	1306
1307	1308
Organ/Tissue Control Low Medium High	1309
And Tumor	1310	1311
1312
Number of animals at the beginning 50 50 50 50	1313
1314
Liver (40) (45) (50) (43)	1315
1316
Hepatocellular adenoma 4 5 7 10	1317
(Context of obser. of the tumor)#
1318
1319
Unadjusted P-values##:	1320
Exact test P= P= P= P=	1321
Asymptotic test P= P= P= P=	1322
Hepatocellular carcinoma 2 2 5 3	1323
(Context of obser. of the tumor)#
1324
1325
Unadjusted P-values##:	1326
Exact test P= P= P= P=	1327
Asymptotic test P= P= P= P=	1328
Hemangioma 0 0 2 3	1329
(Context of obser. of the tumor)#
1330
1331
Unadjusted P-values##:	1332
Exact test P= P= P= P=	1333
Asymptotic test P= P= P= P=	1334
Hepatoma 0 1 1 2	1335
(Context of obser. of the tumor)#
1336
1337
Unadjusted P-values##:	1338
Exact test P= P= P= P=	1339
Asymptotic test P= P= P= P=	1340
1341	1342 See the footnotes on next page.	1343

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Table 15 (Continued): Example Format for Showing Summary of Incidences and	1344
Results of Statistical Tests (P-values) of Neoplastic Lesions (in Male Mice)	1345
1346	1347
Organ/Tissue Control Low Medium High	1348
And Tumor	1349	1350
1351
Lung (45) (47) (49) (45)	1352
1353
Bronchiolar/alveolar adenoma 2 1 4 8	1354
(Context of obser. of the tumor)#
1355
1356
Unadjusted P-values##:	1357
Exact test P= P= P= P=	1358
Asymptotic test P= P= P= P=	1359
1360
Bronchiolar/alveolar carcinoma 2 2 5 4	1361
(Context of obser. of the tumor)#
1362
1363
Unadjusted P-values##:	1364
Exact test P= P= P= P=	1365
Asymptotic test P= P= P= P=	1366
1367
1368
(List the numbers of animals with the tissues examined,	1369
overall tumor incidences, and the p-values of trend	1370
tests and pairwise comparisons for all organs/tissues and tumo rs.)	1371
1372
1373
Notes: Numbers in parentheses are numbers of animals with the tissues examined	1374
microscopically.	1375
The p-values under the control group are from trend tests.	1376
The p-values under each dosed group are from pairwise comparisons between that dosed	1377
group and the control group.	1378 #Contexts of observation of the tumor, if information is available, should be one of the	1379
four possibilities: fatal, incidental, mortality independent, and mixture of fatal and	1380
incidental. Use N.A. to indicate that the information is not available.	1381 ##Unadjusted P-values are the p-values unadjusted for effect of multiple tests.	1382
1383
1384
1385

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Table 16: Example Format for Showing Historical Control Data (in Male Rats)	1386
1387
The historical control data are based on the carcinogenicity studies conducted at XYZ	1388
Laboratory between 1995 and 2000.	1389
1390
Species: Mouse, Sex: Male, Strain: Crl:CD-1 Mice	1391	1392
1393
Historical Control Incidences	1394
Studies Tumor type 1 Tumor type 2 . . . Tumor type T	1395	1396
1397
Study #1 (1992) 1/49 4/49 . . . 8/50	1398
1399
Study #2 (1992) 1/50 3/50 . . . 4/50	1400
1401
. . . . . . .	1402
. . . . . . .	1403
. . . . . . .	1404
1405
Study #n (1996) 0/50 2/50 . . . 5/50	1406
1407
Total 2/347 23/417 . . . 34/417	1408
1409
Standard	1410
Deviation 1.0% 3,2% . . . 4.0%	1411
1412
Range 0%-2% 0%-10% . . . 3%-17%	1413
1414
1415
1416
1417

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1418
1419
REFERENCES	1420
1421
Ahn, H., and R.L. Kodell (1995), “Estimation and Testing of Tumor Incidence Rates in	1422
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1424
Ahn, H., and R.L. Kodell, and H. Moon (2000), "Attribution of Tumor Lethality and Estimation	1425
of Time to Onset of Occult Tumors in the Absence of Cause-of-Death Information," Applied	1426
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1428
Ali, M.W. (1990) "Exact Versus Asymptotic Tests of Trend of Tumor Prevalence in	1429
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Armitage, P. (1955), “Tests for Linear Trends in Proportions and Frequencies,” Biometrics, 11,	1433
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1435
Armitage, P. (1971), Statistical Methods in Medical Research, John Wiley, New York.	1436
1437
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1440
Bannasch, P., R.A. Griesemer, F. Anders, B. Becker, J.R. Cabral, G.D. Porta, V.J. Feron, D.	1441
Henschler, N. Ito, R. Kroes, P.N. Magee, B. McKnight, U. Mohr, R. Montesano, N.P. Napalkov,	1442
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Bieler, G.S., and R.L. Williams (1993), “Ratio Estimates, the Delta Method, and Quantal	1451
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Blyth, C.R. (1986), "Approximate Binomial Confidence Limits," Journal of American Statistical	1454
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1456
Breslow, N. (1970), "A Generalized Kruskal-Wallis Test for Comparing K Samples Subject to	1457
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1462

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Chen, J.J., and D.W. Gaylor (1986), "The Upper Percentiles of the Distribution of the Logrank	1463
Statistics for Small Numbers of Tumors," Communications in Statistics - Simulation and	1464
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1466
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1469
Cochran, W. (1954), “Some Methods for Strengthening the Common χ2 Tests,” Biometrics, 10,	1470
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1472
Cox, D.R. (1959), "The Analysis of Exponentially Distributed Life-times with Two Types of	1473
Failures," Journal of Royal Statistical Society, Series B, 21, 4121-421.	1474
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Cox, D.R. (1972), "Regression Models and Life Tables (with discussion)," Journal of Royal	1476
Statistical Society, Series B, 34, 187-220.	1477
1478
Dayan, A.D. (1988), “Biological Assumptions in Analysis of the Bioassay,” in Carcinogenicity,	1479
The Design, Analysis and Interpretation of Long-Term Animal Studies, an International Life	1480
Sciences Institute (ILSI) monograph, edited by H,C. Grice and J.L. Ciminera, Springer-Verlag,	1481
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1483
Dempster, A.P., M.R. Selwyn, and B.J. Weeks (1983), “Combining Historical and Randomized	1484
Controls for Assessing Trends in Proportions,” Journal of the American Statistical Association,	1485
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1487
Dewanji, Anup and J.D. Kalbfleisch (1986), "Nonparametric Methods for Survival/Sacrifice	1488
Experiments," Biometrics, 42, 325-341.	1489
1490
Dinse. G.E. (1988), "Estimating Tumor Incidence Rates in Animal Carcinogenicity	1491
Experiments," Biometrics, 44, 405-415.	1492
1493
Dinse, G.E. (1991), "Constant Risk Differences in the Analysis of Animal Tumorigenicity Data,"	1494
Biometrics, 47, 681-700.	1495
1496
Dinse, G.E. (1994), "A Comparison of Tumor Incidence Analyses Applicable in Single-	1497
Sacrifice Animal Experiments," Statistics in Medicine, 13, 689-708.	1498
1499
Dinse, G.E., and J.K. Haseman (1986), "Logistic Regression Analysis of Incidental-Tumor Data	1500
from Animal Carcinogenicity Experiments," Fundamental and Applied Toxicology, 6, 751-770.	1501
1502
Dinse, G.E., and S.W. Lagokos (1983), "Regression Analysis of Tumor Prevalence Data," The	1503
Journal of the Royal Statistical Society, Series C, 32, 236-248.	1504
1505
Fairweather, W.R., A. Bhattacharyya, P.P. Ceuppens, G. Heimann, L.A. Hothorn, R.L. Kodell,	1506
K.K. Lin, H. Mager, B.J. Middleton, W. Slob, K.A. Soper, N. Stallard, J. Ventre, and J. Wright	1507

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(1998), “Biostatistical Methodology in Carcinogenicity Studies,” Drug Information Journal, 32,	1508
401-421.	1509
1510
Food and Drug Administration (FDA), (1987), Guideline for the Format and Content of the	1511
Nonclinical/Pharmacology/Toxicology Section of An Application.	1512
1513
FDA (1997), Formats and Specifications for Submission of Animal Carcinogenicity Study Data,	1514
Divisions of Biometrics I, II, III, and IV, Center for Drug Evaluation and Research. Rockville,	1515
Maryland; March 12, 1997.	1516
1517
FDA (1999), Guidance for Industry, Providing Regulatory Submissions in Electronic Formats ---	1518
NDAs, Center for Drug Evaluation and Research.	1519
1520
Gart, J.J., D. Krewski, P.N. Lee, R.E. Tarone, and J. Wahrendorf (1986), Statistical Methods in	1521
Cancer Research, Volume III - The Design and Analysis of Lo ng-Term Animal Experiments,	1522
International Agency for Research on Cancer, World Health Organization.	1523
1524
Gehan, E.A. (1965), "A Generalized Wilcoxon Test for Comparing K Samples Subject to	1525
Unequal Patterns of Censorship," Biometrika, 52, 203-223.	1526
1527
Goldberg, K.M. (1985), "An Algorithm for Computing An Exact Trend Test for Multiple 2 x K	1528
Contingency Tables," a paper presented at Symposium On Long-Term Animal Carcinogenicity	1529
Studies.	1530
1531
Haseman, J.K. (1983), "A Reexamination of False-Positive Rates for Carcinogenesis Studies,"	1532
Fundamental and Applied Toxicology, 3, 334-339.	1533
1534
Haseman, J.K. (1984a), "Statistical Issues in the Design, Analysis and Interpretation of Animal	1535
Carcinogenicity Studies," Environmental Health Perspective, 58, 385-392.	1536
1537
Haseman, J.K. (1984b), “Use of Historical Control Data in Carcinogenicity Studies in Rodents,”	1538
Toxicologic Pathology, 12, 126-135.	1539
1540
Haseman, J.K. (1985), "Issues in Carcinogenicity Testing: Dose Selection," Fundamental and	1541
Applied Toxicology, 5, 66-78.	1542
1543
Haseman, J.K. (1991), a personal communication to Robert Temple, M.D., CDER, FDA.	1544
1545
Haseman, J.K., J. Huff, and G.A. Boorman (1984), "Use of Historical Control Data in	1546
Carcinogenicity Studies in Rodents," Toxicologic Pathology, 12, 126-135.	1547
1548
Haseman, J.K., J.S. Winbush, and M.W. O’Donnell (1986), “Use of Dual Control Groups to	1549
Estimate False Positive Rates in Laboratory Animal Carcinogenicity Studies,” Fundamental and	1550
Applied Toxicology, 7, 573-584.	1551
1552

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Haseman, J.K., G. Hajian, K.S. Crump, M.R. Selwyn, and K.E. Peace (1990), “Dual Control	1553
Groups in Rodent Carcinogenicity Studies,” in Statistical Issues in Drug Research and	1554
Development, K. E. Peace, Editor, Marcel Dekker, New York.	1555
1556
Haseman, J.K. (1999), personal communication to the author.	1557
1558
Hoel, D.G. (1983), “Conditional Two Sample Tests with Historical Controls,” in Contributions	1559
to Statistics, P.K. Sen, Editor, North-Holland Publishing Company.	1560
1561
Hoel, D.G., and T. Yanagawa (1986), “Incorporating Historical Controls in Testing for a Trend	1562
in Proportions,” Journal of the American Statistical Association, 81, 1095-1099.	1563
1564
Hoel, D., and H. Walburg (1972), “Statistical Analysis of Survival Experiments,” Journal of the	1565
National Cancer Institute, 49, 361-372.	1566
1567
Iatropoulos, M.J. (1988), “Society of Toxicologic Pathologists Position Paper: “Blinded”	1568
Microscopic Examination of Tissues from Toxicologic or Oncogenic Studies,” in	1569
Carcinogenicity, The Design, Analysis, and Interpretation of Tong-Term Animal Studies, edited	1570
by H.C. Grice and J.L. Ciminera, ILSI Monographs, Spring-Verlag, New York.	1571
1572
ICH (1995), S1C Dose Selection for Carcinogenicity Studies of Pharmaceuticals, ICH - S1C.	1573
1574
ICH (1998), S1B Testing for Carcinogenicity of Pharmaceuticals, ICH - S1B, Federal Register,	1575
vol. 63, 8983-8986, 1998.	1576
1577
Ibrahim, J.G., and L.M. Ryan (1996), "Use of Historical Controls in Time-Adjusted Trend Tests	1578
for Carcinogenicity," Biometrics, 52, 1478-1485.	1579
1580
Jovanovic, B.D. and M.A.G. Viana (1996), “Upper Confidence Bounds for Binomial Probability	1581
in Safety Evaluation,” American Statistical Association 1996 Proceedings of the	1582
Biopharmaceutical Section, 140-144.	1583
1584
Jovanovic, B.D. and P.S. Levy (1997), "A Look at the Rule of Three," The American	1585
Statistician, 51, No.2, 137-139.	1586
1587
Kodell, R.L., and H. Ahn (1996), "Nonparametric Trend Test for the Cumulative Tumor	1588
Incidence Rates," Communications in Statistics - Theory and Methods, 25, 1677- 1692.	1589
1590
Kodell, R.L., and H. Ahn (1997), "An Age-Adjusted Trend Test for the Tumor Incidence Rate,"	1591
Biometrics, 53, 1467-1474.	1592
1593
Kodell, R.L., B.A. Pearce, A. Turturro, and H. Ahn (1997), "An Age-Adjusted Trend Test for the	1594
Tumor Incidence Rate for Single-Sacrifice Experiments," Drug Information Journal, 31, 471-	1595
487.	1596
1597

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Kodell, R.L., K.K. Lin, B.T. Thorn, and J.J. Chen (2000), “Bioassays of Shortened Duration for	1598
Drugs: Statistical Implications,” Toxicological Sciences, 55, 415-432.	1599
1600
Lin, K.K. (1988), "Peto Prevalence Method Versus Regression Methods in Analyzing Incidental	1601
Tumor Data from Animal Carcinogenicity Experiments: An Empirical Study," in the 1988	1602
American Statistical Association Annual Meeting Proceedings (Biopharmaceutical Section),	1603
New Orleans, Louisiana.	1604
1605
Lin, K.K. (1995), “A Regulatory Perspective on Statistical Methods for Analyzing New Drug	1606
Carcinogenicity Study Data,” Bio/Pharam Quarterly, Vol. 1, Issue 2, 18-20.	1607
1608
Lin, K.K. (1997), “Control of Overall False Positive Rates in Animal Carcinogenicity Studies of	1609
Pharmaceuticals,” presented at 1997 FDA Forum on Regulatory Sciences, December 8-9, 1997,	1610
Bethesda, Maryland.	1611
1612
Lin, K.K. (2000), “Carcinogenicity Studies of Pharmaceuticals,” in Encyclopedia of	1613
Biopharmaceutical Statistics, edited by S.C. Chow, Marcel Dekker, New York, 88-103.	1614
1615
Lin, K.K., and M.W. Ali (1994), "Statistical Review and Evaluation of Animal Tumorigenicity	1616
Studies," in Statistics in the Pharmaceutical Industry, Second Edition, Revised and Expanded,	1617
edited by C.R. Buncher and J.Y. Tsay, Marcel Dekker, Inc., New York.	1618
1619
Lin, K. K. and M. A. Rahman (1998a), “Overall False Positive Rates in Tests for Linear Trend in	1620
Tumor Incidence in Animal Carcinogenicity Studies of New Drugs,” Journal of Pharmaceutical	1621
Statistics, with discussions, 8(1), 1-22.	1622
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Lin, K. K. and M. A. Rahman (1998b), “False Positive Rates in Tests for Trend and Differences	1624
in Tumor incidence in Animal Carcinogenicity Studies of Pharmaceuticals under ICH Guidance	1625
S1B,” unpublished report, Division of Biometrics 2, Center for Drug Evaluation and Research,	1626
Food and Drug Administration.	1627
1628
Lin, K.K. (1998), “CDER/FDA Formats for Submission of Animal Carcinogenicity Study	1629
Data,” Drug Information Journal, 32, 43-52.	1630
1631
Lindsey, J., and L. Ryan (1993), "A Three-State Multiplicative Model for Rodent	1632
Tumorigenicity Experiments," Journal of Royal Statistical Society, Series C, 42, 283-300.	1633
1634
Lindsey, J., and L. Ryan (1994), "A Comparison of Continuous- and Discrete-Time Three-State	1635
Models for Rodent Tumorigenicity Experiments," Environmental Health Perspectives, 102	1636
(Suppl. 1), 9-17.	1637
1638
Louis, T.A. (1981), "Confidence Intervals for a Binomial Parameter After Observing No	1639
Success," The American Statistician, 35, No. 3, 154-154.	1640
1641
Malani, H.M., and J. Van Ryzin (1988), "Comparison of Two Treatments in Animal	1642
Carcinogenicity Experiments," Journal of American Statistical Association, 83, 1171-1177.	1643

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1644
Mantel, N., and W. Haenszel (1959), "Statistical Aspects of the Analysis of Data from	1645
Retrospective Studies of Disease," Journal of National Cancer Research, 22, 719-748.	1646
1647
Malani, H.M., and Y. Lu (1993), "Animal Carcinogenicity Experiments with and without Series	1648
Sacrifices," Communications in Statistics - Theory and Methods, 22, 1557-1584.	1649
1650
McKnight, B., and J. Crowley (1984), "Tests for Differences in Tumor Incidence Based on	1651
Animal Carcinogenesis Experiments," Journal of American Statistical Association, 79, 639-648.	1652
1653
Moon, H., H. Ahn, and R.L. Kodell (2000), "Testing Incidence of Occult Tumors by Attributing	1654
Tumor Lethality in the Absence of Cause-of-Death Information," submitted to Biometrics.	1655
1656
OFR (Office of the Federal Register), (1985), "Chemical Carcinogens; A Review of the Science	1657
and Its Associated Principles," in Part II, Office of Science and Technology Policy, Federal	1658
Register, March 14, 1985, 47-58.	1659
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OFR, (1995), “Dose Selection for Carcinogenicity Studies of Pharmaceuticals,” in Part III,	1661
Department of Health and Human Services, Food and Drug Administration, Federal Register,	1662
March 1, 1995, Vol. 60, No. 40, 11278-11281.	1663
1664
OFR, (1997), “Electronic Records; Electronic Signatures,” Federal Register, March 20, 1997.	1665
1666
Peto, R., M.C. Pike, N.E. Day, R.G. Gray, P.N. Lee, S. Parish, J. Peto, S. Richards, and J.	1667
Wahrendorf (1980), "Guidelines for Simple, Sensitive Significance Tests for Carcinogenic	1668
Effects in Long-term Animal Experiments," in Long-term and Short-term Screening Assays for	1669
Carcinogens: An Critical Appraisal, World Health Organization.	1670
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Portier, C.J., and G.E. Dinse (1987), "Semiparametric Analysis of Tumor Incidence Rates in	1672
Survival/Sacrifice Experiments," Biometrics, 43, 107-114.	1673
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Prasse, K. (1986), “Letter to the Editor (on blinded microscopic evaluation of slides from	1675
toxicity and carcinogenicity studies),” Toxicology and Applied Pharmacology, 83, 184-185.	1676
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Prentice, R.L., R.T. Smythe, D.Krewski, and M.Mason (1992), "On the Use of Historical Control	1678
Data to Estimate Dose Response Trends in Quantal Bioassay," Biometrics, 48, 459-478.	1679
1680
Society for Toxicology (1982), “Animal Data in Harzard Evaluation: Paths and Pitfalls,”	1681
Fundamental and Applied Toxicology, 2,101-107.	1682
1683
Sontag, J.A., N.P. Page, and U. Saffiotti (1976), Guidelines for Carcinogen Bioassay in Small	1684
Rodents, Carcinogenesis Technical Report, DHEW Publication (NIH), 76-801.	1685
1686
Tamura, R.N, and S.S. Young (1986), “The Incorporation of Historical Information in Tests of	1687
Proportions: Simulation Study of Tarone’s Procedure,” Biometrics, 42, 343-349.	1688
1689

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Tamura, R.N, and S.S. Young (1987), “A Stabilized Moment Estimator for the Beta-Binomial	1690
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