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DRAFT GUIDANCE
This guidance document is being distributed for comment purposes only.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Federal Register of the notice announcing the availability of the draft guidance.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 Animals 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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1
Guidance for Industry
1
Statistical Aspects of the Design, Analysis, and Interpretation of
2
Chronic Rodent Carcinogenicity Studies of Pharmaceuticals
3
4
5
6
7
This draft guidance, when finalized, will represent the Food and Drug Administration's current
8
thinking on this topic.  It does not create or confer any rights for or on any person and does not
9
10 operate to bind FDA or the public.  An alternative approach may be used if such approach
11 satisfies the requirements of the applicable statutes and regulations.
12
13
14
15
16
17
18
19 I.  INTRODUCTION
20
21 This document is intended to provide guidance to sponsors on the design of animal
22 carcinogenicity experiments, methods of statistical analysis of tumor data, interpretation of study
23 results, presentation of data and results in reports, and the submission of tumor data to FDA
24 statistical reviewers at the Food and Drug Administration (FDA).  A brief background
25 description of the operation of statistical review of carcinogenicity studies in FDA's Center for
26 Drug Evaluation and Research (CDER) is given in section II.  A discussion of the validity of the
27 design of the experiment is given in Section III.  Section IV discusses methods of statistical
28 analysis.  Section V discusses how the results should be interpreted, and Section VI discusses
29 data presentation and submission.
30
31
32 II.  BACKGROUND
33
34 Assessment of the risk of drug exposure in humans includes an assessment of carcinogenicity in
35 tests in rodents.  The Division of Biometrics in the Office of Biostatistics, Center for Drug
36 Evaluation and Research (CDER), Food and Drug Administration (FDA), is responsible for
37 conducting statistical reviews of long-term animal (rodent) carcinogenicity studies of
38 pharmaceuticals submitted by drug sponsors to FDA.  In a carcinogenicity study of a new drug
39 using a series of increasing dose levels, statistical tests for positive trends in tumor rates are
40 usually of greatest interest, but as discussed in this document, in some situations, pairwise
41 comparisons are considered to be more indicative of drug effects than trend tests.
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.
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43 In statistical reviews of carcinogenicity studies, statisticians evaluate the validity of the designs
44 and the appropriateness of methods of data analysis used by the sponsor.  They also use raw
45 study data in electronic form to perform additional statistical analyses.
46
47 The recommendations that follow are based on FDAs assessment of current literature,
48 consultations with outside experts, and internal research.
49
50
51 III.  VALIDITY OF THE DESIGN
52
53 Many factors determine the adequacy of a carcinogenicity study, including the species and strain
54 of the animals, sample size, dose selection, method of allocation of animals, route of
55 administration, animal care and diet, caging, drug stability, and study duration.  Of particular
56 interest to statisticians are the methods used to allocate animals to treatment groups and caging
57 rotation, the determination of sample size, and the duration of the study.
58
59 Although not generally a statistical issue, dose selection is particularly critical.  The premise of
60 carcinogenicity testing most directly applicable to genotoxic mechanisms (when there may not
61 be a pharmacological threshold, or identification of a threshold is difficult) is that long exposure
62 duration and large doses in a small number of animals will be informative about the much
63 smaller risks of lower doses and shorter durations of exposure in humans.  As a result, the
64 general goal should be to maximize rodent exposure by testing at maximum tolerated doses.
65
66 The International Conference on Harmonization (ICH) guidance entitled S1C Dose Selection for
67 Carcinogenicity Studies of Pharmaceuticals (S1C) is an internationally accepted guidance for
68 dose selection for carcinogenicity studies, and sponsors are advised to consult this document.
69 The guidance allows for approaches to high dose selection based on toxicity endpoints (Sontag,
70 Page, and Saffiotti 1976; Chu, Cueto, and Ward 1981), pharmacokinetic endpoints (multiple of
71 maximum human exposure), pharmacodynamic endpoints, and maximal feasible dose.   For
72 further clarification, the appropriate medical review division should be consulted.2
73
74 Randomization should be used to allocate animals to treatment groups.  Random assignment of
75 experimental animals to different treatment groups allows the assumption that treatments will not
76 be continually favored or handicapped by extraneous sources of variation over which the
77 experimenter has no control (i.e., that possible bias will be minimized).
78
79 One area where bias can still be introduced, however, is in the microscopic evaluation of tissues.
80 Currently, open or nonblinded microscopic evaluation of tissues from experimental animals is
81 the routine practice adopted by veterinary pathologists in the generation of histopathological data
82 in carcinogenicity studies.  Veterinary pathologists do not favor blinded readings of slides of
                                                                
2 Sponsors can seek CDERs 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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83 animal tissues/organs because they believe that blinded reading results in loss of information
84 critical to interpretation, such as the ability to relate observations in different tissues.
85 Furthermore, they argue that the variables constitute the baseline that defines the experimental
86 control and that it is impractical to perform blinded slide readings because there are so many
87 tissues from each animal.  Mistakes can be easily made when assigning, opening codes, and
88 recording results in blinded reading (Iatropoulos 1988; Prasse et al. 1986).  There are others,
89 however, who have argued that blinded evaluation should be used to prevent the bias that can be
90 introduced by the pathologists knowledge of the treatment groups of the tested animals (Temple,
91 Fairweather, Glocklin, and O'Neill 1988).  Certainly, blinded re-readings are common in close or
92 disputed cases.
93
94 The number of animals remaining in a study for the full duration is an important statistical
95 consideration.  A sufficient number of animals should be used in an experiment to ensure
96 reasonable power of statistical tests to detect true carcinogenic effects.  It has been recommended
97 that each dose and concurrent control group contain at least 50-60 animals of each sex.  If
98 interim sacrifices are planned, the initial number of animals should be increased by the number
99 of animals scheduled for interim sacrifice.  Prior assignments of treatment and designations for
100 sacrifice of the animals should be made (Bannasch et al. 1986).
101
102 Animals are usually exposed to the test substance for essentially their entire normal life span,
103 generally 24 months for rats and mice.  The vast majority of carcinogenicity studies of
104 pharmaceuticals using rats that are submitted to CDER for review have durations of 24 months
105 and have reasonable survival. The duration of mouse studies ranges from 18 to 24 months, with
106 many lasting only 18 or 21 months even though they have very low mortality at terminal
107 sacrifice.  One reason for using shorter durations in mouse studies appears to be a 1985 federal
108 government publication stating that carcinogenicity studies should be conducted at least 18
109 months in mice and 24 months in rats (OFR 1985).  The publication, however, goes on to say
110 that a longer duration may be appropriate if cumulative mortality at the planned terminal
111 sacrifice is low.  CDER recommends that drug sponsors also conduct mouse studies for 24
112 months, unless there is excessive mortality as described below.  Results of a recent study of the
113 effect of shortened duration on the statistical power of carcinogenicity studies by Kodell, Lin,
114 Thorn, and Chen (2000) support the CDER recommendation.  The study showed that stopping at
115 18 months would reduce power to an unacceptable level for a variety of models of the
116 tumorigenicity, and that the loss of power is too great to warrant an early stopping at 21 months,
117 absent effects on survival.
118
119 However, early termination of a study for mortality, even if unavoidable, may render a study
120 uninformative, leaving too few animals living long enough to represent adequate exposure to the
121 chemical.  This is especially important in the evaluation of the design validity of a negative
122 study.  In general, a 50 percent survival rate to weeks 80 to 90 of the 50 initial animals in any
123 treatment group is considered adequate.  The percentage can be lower or higher if the number of
124 animals used in each treatment/sex group is larger or smaller than 50, but between 20 to 30
125 animals should be still alive during these weeks (Lin and Ali 1994).  Whether a study could be
126 terminated before the scheduled termination date if the survival of any treatment group goes
127 below 50 percent or 20 to 30 surviving animals (provided that sufficient numbers of animals
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128 were exposed through week 80 to 90) depends on the situation.  For example, there is no reason
129 to stop a study if the survival of only the low-dose group and/or the medium-dose group is
130 altered, because the control vs. high-dose comparison will still be informative.  If the survival of
131 the high-dose group falls below 50 percent or 20-30 surviving animals after week 80, the study
132 should be continued, either stopping dosing of animals in the high-dose group or terminating
133 only the high-dose group, because the comparison of at least the control and low/middle doses
134 would still be informative (the high-dose comparison would depend on the situation).  A study
135 could be terminated early if the survival of the control group (or groups) goes below 50 percent
136 or 20-30 surviving animals after weeks 80 to 90, as the later comparisons would not be
137 informative.  Others have suggested, for example, that an experiment be terminated early when
138 the survival of the control or the low-dose group is reduced to 20-25 percent of the original
139 number of animals.  If the mortality is increased only in the high-dose group, consideration can
140 be given to early termination of that group (OFR 1985).3  Because early study termination poses
141 complex problems, it is strongly recommended that a decision to terminate a study or a study
142 group early be made with input from the Center and the medical division responsible for the
143 review of the associated application.
144
145 If in discussions with CDER, the Center approves the early termination of a study under this
146 recommendation, the studys sponsor can be assured that the study will be considered by the
147 Center as valid in terms of adequate duration of drug exposure.
148
149
150 IV.  METHODS OF STATISTICAL ANALYSIS
151
152 A.  An Overview of Complexities of Statistical Analysis of Tumor Data
153
154 The primary purpose of a long-term rodent carcinogenicity study of a new drug is to
155 evaluate the oncogenic potential of the drug when it is administered to animals for most
156 of their normal life span.  The drug, however, may effect the mortality of different
157 treatment groups.  Test animals living longer are more likely to develop tumors than
158 those dying early, as demonstrated by examples in the next section, and comparisons of
159 tumor incidence rates among treatment groups based solely on the crude proportions of
160 animals with tumors and failure to consider the rates at which animals develop tumors
161 can cause serious bias in the analysis (Petro et al. 1980; McKight and Crowley 1984; Gart
162 et al. 1986).  Therefore, it is essential to make adjustment for the differences in mortality
163 among treatment groups in the analysis of tumor data.
164
165 Tumor incidence (i.e., the rate of tumor onset among the previously tumor-free
166 population) is the most appropriate measure of tumorigenesis for two reasons (Dinse
167 1994; McKight and Crowley 1984; and Malani and Van Ryzin 1988):  (1) the tumor
168 incidence rate reduces biases in the crude incidence proportion of animals with tumors
169 that could arise from differences in mortality by adjusting for time differences and by
170 conditioning the rate at each time point on the likelihood that an animal is still alive, and
                                                                
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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171 (2) unlike the death rate with or from tumors, the tumor incidence rate does not confound
172 information about the course of tumors with information about the onset of tumors.  Most
173 tumors except those such as skin and mammary tumors, which can be detected by
174 palpation and visual inspection, are occult and discovered only at the time of the animals
175 death.  The exact tumor onset times are unknown.
176
177 The analysis of tumor data is complicated when adjustments are made for differences in
178 mortality among treatment groups because of the lack of the observable onset time of
179 occult tumors discussed above.  A huge number of statistical procedures aiming to deal
180 with these complexities have been proposed in the literature.  They followed, in general,
181 the strategy that without direct observations of the tumor onset times, the desired
182 survival adjustment usually is accomplished by making assumptions concerning tumor
183 lethality, cause of death, multiple sacrifices, or parametric models (Dinse 1994).
184
185 The prevalence method (Hoel and Walburg 1972; Peto et al. 1980), the death-rate method
186 (Tarone 1975; Peto et al. 1980), and the onset-rate (Peto et al. 1980), discussed in Section
187 C below, for analyzing nonlethal, lethal, and observable tumors, respectively, are based
188 on an assumption, or information about tumor lethality.  The Peto test (Peto et al. 1980),
189 also discussed in Section C, for analyzing data of a tumor that is considered nonlethal to a
190 subset of animals and lethal to the rest of the animals is also based on an assumption or
191 information as to whether the tumor caused an animals death.  The analyses will become
192 biased if the assumption or information on tumor lethality and cause of death is not valid
193 or accurate (Dinse 1994).
194
195 Data from carcinogenicity studies do not always contain information of tumor lethality
196 and cause of death.  Even when such information is provided, the difficulty and
197 subjectivity in the determination of cause of death and lethality of a tumor may render the
198 information too inaccurate and unobjective to allow valid analysis using the above
199 statistical methods.  Another way of analyzing the tumor incidence rates without relying
200 on the tumor lethality and cause-of-death information is to use a design with multiple
201 sacrifices at different time points.  Without cause-of-death information or simplifying
202 assumptions, multiple sacrifices of groups of animals are necessary to identify tumor
203 incidence rates of occult tumors from the bioassay data (McKight and Crowley 1984;
204 Kodell and Ahn 1997; Dinse 1994).  Statistical methods have been proposed for
205 analyzing tumor incidence rates on the information from multiple sacrifices rather than
206 on the information on cause of death and tumor lethality.4  In reality, however, very few
207 studies are conducted with multiple sacrifices because of the cost and complexity
208 involved.  Since it is rarely used in practice, no recommendations on analysis of data with
209 multiple sacrifices are given in this guidance.
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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211 Finally, for data from bioassays with no information (or assumptions) regarding tumor
212 lethality or cause-of-death and no interval sacrifices, Dinse (1991) and Lindsey and Ryan
213 (1993 and 1994) have proposed survival-adjusted statistical tests that focus on tumor
214 incidence for dose-related trends by making some parametric assumptions.  Dinses test
215 is based on the assumption of a constant difference between the death rates of animals
216 with and without a tumor while Lindsey and Ryans test assumes a constant ratio for
217 those death rates.  Recently, other statistical procedures of this type have been proposed
218 in the literature for dealing with the complexities of analysis of tumor data.  Those
219 procedures do not require data on tumor lethality and cause of death, or the use of
220 multiple sacrifices.  Among those procedures, the poly-3 (in general poly-k) tests (Bieler
221 and Portier 1988; Dinse 1994), and the ratio trend test (a modified poly-k test) (Bieler and
222 Williams 1993; Dinse 1994) have been most extensively studied and shown to perform
223 well under actual study conditions.  Detailed discussions of the poly-k tests and the ratio
224 trend test are given in Section D.
225
226 Some of the recently proposed statistical procedures, such as those described by Kodell,
227 Pearce, Turturro, and Ahn (1997), and Moon, Ahn, and Kodell (2000), deal with the
228 complexities of the tumor data analysis from a somewhat different direction.  These
229 procedures use a constrained nonparametric maximum likelihood estimation method to
230 impute (estimate) incidence rates of fatal tumors and nonfatal tumors for time intervals
231 preceding the final time interval of terminal sacrifice.  These procedures do not require
232 tumor lethality and cause-of-death information and are applicable to studies with only a
233 single sacrifice.  The imputed tumor incidence rates can then be used in the death-rate
234 method, prevalence method, or the Peto test.  The properties of these procedures have not
235 yet been widely studied, and they involve extensive computations.
236
237 B.  Adjustment of Tumor Rates for Intercurrent Mortality
238
239 Intercurrent mortality refers to all deaths other than those resulting from a tumor being
240 analyzed for evidence of carcinogenicity.  Like human beings, older rodents have a many
241 fold higher probability of developing or dying of tumors than those of a younger age.
242 Therefore, in the analysis of tumor data, it is essential to identify and adjust for possible
243 differences in intercurrent mortality among treatment groups to eliminate or reduce biases
244 caused by these differences.  It has been pointed out that the effects of differences in
245 longevity on numbers of tumor-bearing animals can be very substantial, and so, whether
246 or not they (the effects) appear to be, they should routinely be corrected when presenting
247 experimental results (Peto et al. 1980).  The following examples demonstrate this point.
248
249 Example 1 (Peto et al. 1980).  Consider a mouse study consisting of one control group
250 and one treated group of 100 animals each.  A very toxic but not carcinogenic new drug
251 is administered to the animals in the diet for 2 years.  Assume that the spontaneous
252 incidental tumor rates for both groups are 30 percent at 15 months and 80 percent at 18
253 months and that the mortality rates at 15 months for the control and the treated groups are
254 20 percent and 60 percent, respectively, due to the toxicity of the drug.  The results of this
255 experiment are summarized in Table 1.
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256
257 Table 1: Effects of Differences in Mortality on Tumor Incidence Rates, Example 1
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
259 Note:  T = Incidental Tumors Found at Necropsy.        D = Deaths
260
261
262 If one looks only at the overall tumor incidence rates of the control and the treated groups
263 (70 percent and 50 percent, respectively) without considering the significantly higher
264 early deaths in the treated group caused by the toxicity of this new drug, one can
265 misinterpret the apparent significance (p = 0.002, 1-tailed) as showing a decrease in the
266 treated group in this tumor type.  The one-tailed p-value is 0.5, however, showing no
267 effect of treatment when the survival-adjusted prevalence method is used.
268
269 Example 2 (Gart, Krewski, Lee, Tarone, and Wahrendorf 1986).  Assume that the design
270 used in this experiment is the same as the one used in the experiment in Example 1.
271 Also, assume that the tested new drug in this example induces an incidental tumor that
272 does not directly or indirectly cause animal deaths, in addition to having severe toxicity
273 as in the previous example.  Assume further that the incidental tumor prevalence rates for
274 the control and treated groups are 5 percent and 20 percent, respectively, before 15
275 months of age, and 30 percent and 70 percent, respectively, after 15 months of age; and
276 that the mortality rates at 15 months are 20 percent and 90 percent for the control and the
277 treated groups, respectively.  The results of this experiment are summarized in Table 2.
278
279
280 Table 2: Effects of Differences in Mortality on Tumor Incidence Rates, Example 2
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
282 Note:  T = Incidental Tumors Found at Necropsy.        D = Deaths
283
284
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285 The age-specific tumor incidence rates are significantly higher in the treated group than
286 those in the control group.  The survival-adjusted prevalence method yielded a one-tailed
287 p-value of 0.003, revealing a clear tumorigenic effect of the new drug.  The overall tumor
288 incidence rates, however, are 25 percent for the two groups.  Without adjusting the
289 significantly higher early mortality in the treated group, the positive finding would be
290 missed.
291
292 Peto et al. (1980) recommend that, whether or not survival among treatment groups is
293 significantly different, tumor rates should routinely be adjusted for survival when
294 presenting experimental results.  The Cox test (Cox 1972; Thomas, Breslow, and Gart
295 1977; Gart et al. 1986); the generalized Wilcoxon or Kruskal-Wallis test (Breslow 1970;
296 Gehan 1965; Thomas, Breslow, and Gart 1977); and the Tarone trend tests (Cox 1959;
297 Peto et al. 1980; Tarone 1975) are routinely used to test for heterogeneity in survival
298 distributions and significant dose-response relationships (trends) in survival.
299
300
301 C.  Statistical Analysis of Tumor Data With Information About Cause of Death,
302 Tumor Lethality, but Without Multiple Sacrifices
303
304 1. Role of the Tumor in Animals Death (Contexts of Observation of Tumor
305 Types)
306
307 One way to choose the appropriate survival-adjusted methods in the analysis of
308 tumor data is to base analysis on the role that a tumor plays in causing the
309 animals death.  Tumors can be classified as incidental, fatal, and mortality
310 independent or (observable) according to the contexts of observation described in
311 Peto et al. (1980).  Tumors that are not directly or are indirectly responsible for an
312 animals death, but are merely observed at the autopsy of the animal after it has
313 died of an unrelated cause, are said to have been observed in an incidental
314 context.  Tumors that kill the animal, either directly or indirectly, are said to have
315 been observed in a fatal context.  Tumors, such as skin tumors, for which
316 detection occurs at times other than when the animal dies are said to have been
317 observed in a mortality independent (or observable) context.  To apply a survival-
318 adjusted method correctly based on such information, it is essential that the role of
319 a tumor in an animals death (or the context of observation of a tumor) be
320 determined as accurately as possible.
321
322 Different statistical techniques have been proposed for analyzing data of tumors
323 when information about the role of a tumor in causing death is available.  For
324 example, the prevalence method, the death rate method, and the onset rate method
325 are recommended for analyzing data on tumors observed in incidental, fatal, and
326 mortality independent contexts of observation, respectively  (Peto et al. (1980)).
327 In that paper, Peto et al. demonstrate the possible biases resulting from
328 misclassification of incidental tumors as fatal tumors, or of fatal tumors as
329 incidental tumors.
330
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331 The determination of whether a tumor is incidental, fatal or mortality independent
332 is often difficult, especially for the first two classifications, as it is often hard to
333 tell whether a tumor caused an animals death.  According to Haseman (1999), in
334 practice, a continuum exists between these two extremes: many tumors contribute
335 ultimately to an animals death, but are not instantly (or even rapidly lethal).
336 Such tumors technically are neither incidental nor fatal, and it remains unclear
337 how such tumors should be regarded.  Even if the information on the
338 circumstances of individual animals and tumors is reliable and available, it is
339 overly simplistic to assume that all tumors of a given type are 100 percent fatal or
340 100 percent incidental.  It is likely that there will be a mixture of incidental and
341 fatal tumors.
342
343 As noted above, alternative survival-adjusted statistical procedures that do not
344 need such information have been developed and used for tumor data analysis.
345 Some of the procedures are discussed briefly in the Section IV.C.1 and in detail in
346 Section IV.D.  The alternative procedures should be used to replace the
347 procedures proposed by Peto et al. (1980) in the analysis of tumor data when there
348 is no information available or the information is not accurate enough to perform a
349 meaningful statistical analysis.  
350
351 2. Statistical Analysis of Incidental Tumors
352
353 The prevalence method described in the paper by Peto et al. (1980) should be
354 used in testing for positive trends in prevalence rates of incidental tumors.  The
355 method is described briefly here.
356
357 The method focuses on the age-specific tumor prevalence rates to correct for
358 intercurrent mortality differences among treatment groups in the test for positive
359 trends or differences in incidental tumors.  The experiment period is partitioned
360 into a set of intervals plus interim (if any) and terminal sacrifices.  The incidental
361 tumors are then stratified by those intervals of survival times. The selection of the
362 partitions of the experiment period does not matter very much as long as the
363 intervals are not so short that the prevalence of incidental tumors in the autopsies
364 they contain is unstable, nor yet so large that the real prevalence in the first half of
365 one interval could differ markedly from the real prevalence in the second half
366 (Peto, et al. 1980).
367
368 In each time interval, for each group, the observed and the expected numbers of
369 animals with a particular tumor type found in necropsies are compared.  The
370 expected number is calculated under the null hypothesis that there is no dose-
371 related trend.  Finally, the differences between the observed and the expected
372 numbers of animals found with the tumor type after their deaths are combined
373 across all time intervals to yield an overall test statistic using the method
374 described in a paper by Mantel and Haenszel (1959).
375
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376 The following derivation of the Peto prevalence test statistic uses the notations in
377 Table 3.  Let the experiment period be partitioned into the following m intervals
378 I1, I2, ..., Im.  As mentioned before, interim (if any) and terminal sacrifices should
379 be treated as separate intervals.
380
381 Let Rk be the number of animals that have not died of the tumor type of interest
382 but come to autopsy in time interval k, Pik be the proportion of Rk in group i, and
383 Oik be the observed number of autopsied animals in group i and interval k found
384 to have the incidental tumor type.
385
386 Define O.k = (cid:229) iOik.
387
388 The number of autopsied animals expected to have the particular incidental tumor
389 in group i and interval k, under the null hypothesis that there is no treatment
390 effect, is:
391
392 Eik = O.k Pik.
393
394 The variance-covariance of (Oik  Eik) and (Ojk  Ejk) is:
395
396 Vijk = a k Pik(d  ij  Pjk)
397
398 where
399
400 a k = O.k(Rk  - O.k) / (Rk  1)
401 and
402
403            1    if  i = j,
404 d ij =
405             0   otherwise
406
407 Define
408
409 Oi = (cid:229) k Oik
410
411                   Ei = (cid:229) k Vijk.
412
413 and Vij = (cid:229) k Vijk.
414
415 The test statistic T for the positive trend in the incidental tumor is defined as:
416
417 T = (cid:229) i Di (Oi  Ei)
418
419 with estimated variance
420
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421 V(T) = (cid:229) i(cid:229) j Di Dj Vij
422
423 where Di is the dose level of the ith group.
424
425 Under the null hypothesis of equal prevalence rates among the treatment groups,
426 the statistic
427
428 Z = T / [V(T)]1/2
429
430 is approximately distributed as a standard normal.
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431 Table 3: Notations Used in the Derivation of Peto Prevalence Test Statistics
432
 Interval Group 0 1 .  .  . i .  .  . r Sum
Dose D D .  .  . D .  .  . D
0 1 i r
I R O O .  .  . O .  .  . O O
1 1 01 11 i1 r1 .1
P P .  .  . P .  .  . P P
01 11 i1 r1 .1
I R O O .  .  . O .  .  . O O
2 2 02 12 i2 r2 .2
P P .  .  . P .  .  . P P
02 12 i2 r2 .2
. . . . .  .  . . .  .  . . .
.
. . . . .  .  . . .  .  . . .
.
. . . . .  .  . . .  .  . . .
I R O O .  .  . O .  .  . O O
k k 0k 1k ik rk .k
P P .  .  . P .  .  . P P
0k 1k ik rk .k
. . . . .  .  . . .  .  . . .
.
. . . . .  .  . . .  .  . . .
. . . . .  .  . . .  .  . . .
I R O O .  .  . O .  .  . O O
m m 0m 1m im rm .m
P P .  .  . P .  .  . P P
0m 1m im rm .m
433
434 Notes:
435 R : Number of animals that have not died of the tumor type of interest, but come to autopsy in time interval k.
k
436 P : Proportion of R  in group i.
ik k
437 O : Observed number of autopsied animals in group i and interval k found to have the incidental tumor type.
ik
438 O : 3O .
.k i ik
439
440
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441 As noted above, to use the prevalence method, the experimental period should be
442 partitioned into a set of intervals plus interim (if any) and terminal sacrifices.  The
443 following partitions (in weeks) are used most often by statisticians in CDER in 2-
444 year studies:  (1) 0  50, 51  80, 81  104, interim sacrifice (if any), and terminal
445 sacrifice; (2) 0  52, 53  78, 79  92, 93  104, interim sacrifice (if any), and
446 terminal sacrifice (proposed by National Toxicology Program); and (3) partition
447 determined by the ad hoc runs procedure described in Peto et al. (1980).
448
449 The data for liver hepatocellular adenoma in male mice from a carcinogenicity
450 study are used as an example to explain the prevalence method for testing the
451 positive trend in tumor rates of an incidental tumor.  There were four treatment
452 groups.  The control group had 100 animals, the three treated had 50 animals
453 each.  The dose levels used were 0, 10, 20, and 40 mg/kg/day for the control,
454 low-, medium-, and high-dose groups, respectively.  The study lasted for 106
455 weeks.  In this example, the study period was partitioned into four intervals, 0 
456 50, 51  80, 81  106, and terminal sacrifice.  The numbers of animals died and
457 necropsied, and the numbers of necropsied animals with liver hepatocellular
458 adenoma by treatment group in each interval are included in Table 4.
459
460
461 Table 4: Data of Liver Hepatocellular Adenoma of Male Mice
462
Time Groups
Intervals
(Weeks) Control Low Medium High
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 2 31 6 5 16 31 3 17 18 4 14 29
Sacrifice
Total 7 100 7 8 50 16 8 50 16 12 50 24
463 Notes:   T = Number of necropsies with the above tumor.
464              N = Number of necropsies during a time interval.
465             % = Percent of necropsies with the above tumor.
466
467
468 The observed incidences and the expected incidences of the tumor type calculated
469 under the null hypothesis that there is no trend (or drug induced increase) are
470 shown in Table 5.  The expected tumor rates in each interval were calculated in
471 the following way.  First, the tumor rate for the interval using data of all treatment
472 groups in the interval was estimated.  For example, the estimated tumor rate for
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473 the interval 51  80 weeks was 6/74 = 0.0811.  Second, the expected incidences
474 for individual groups in the interval were calculated by multiplying the numbers
475 of necropsies by the estimated tumor rate.  For the interval 51  80 weeks, the
476 expected tumor rates for the control, low-, medium-, and high-dose groups were
477 26x(6/74)=2.11, 18x(6/74)=1.46, 17x(6/74)=1.38, and 13x(6/74)=1.05,
478 respectively.
479
480 Table 5: Observed and Expected Tumor Incidences Liver
481 Hepatocellular Adenoma of Male Mice
482
Time Observed & Groups
Intervals Expected
(Weeks) Incidences Control Low Medium High
0  50 Observed 0 0 0 0
Expected 0 0 0 0
51  80 Observed 1 1 3 1
Expected 2.11 1.46 1.38 1.05
Observed 4 2 2 7
Expected 6.61 2.50 2.50 3.39
Terminal Observed 2 5 3 4
Sacrifice
Expected 5.56 2.87 3.05 2.51
Total Observed 7 8 8 12
Expected 14.28 6.83 6.93 6.95
483 Note: The expected tumor incidences were calculated under the null hypothesis that
484           there is no trend.
485
486
487 The test statistics Ts and their variances V(T)s for the data of the 5 intervals
488 calculated by the formulas listed above are included in Table 6.  It is noted that
489 the first interval, 0 - 50 weeks, did not contribute anything to the overall test result
490 since none of the 14 animals that died during the first time interval developed
491 liver hepatocellular adenoma.  The overall result shows a statistically significant
492 positive trend in tumor rates of this tumor (with one-sided p-value 0.002).
493
494
495
496
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497 Table 6: Test Statistics, Their Variances, z-values, and P-value of
498  Peto Prevalence Analysis of Incidental Tumors
499
500 Liver Hepatocellular Adenoma of Male Mice
Time T-Stat Variance of T P-Value
Intervals T T-Stat  z = ----------
(Weeks) V(T)      [V(T)]0.5
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
501 Note: The z and p-value columns do not add up to the totals. The z and p-value of
502           overall total row were calculated based on the T and V(T) of the row.
503
504
505 Also as noted above, this method used normal approximation in the test for
506 positive trend or difference in tumor prevalence rates.  The accuracy of the normal
507 approximation depends on the number of tumor occurrences in each group in each
508 interval, the number of intervals used in the partitioning, and the mortality
509 patterns.  The approximation may not be stable and reliable when the numbers of
510 tumor occurrences across treatment groups are small.  In this situation, an exact
511 permutation trend test based on an extension of the hypergeometric distribution
512 (to be discussed in Subsection III.C.6) should be used to test for the positive trend
513 in tumor prevalence rates.
514
515 3. Statistical Analysis of Fatal Tumors
516
517 It is recommended that the death rate method described in Peto et al. (1980) be
518 routinely used to test for the positive trend or difference in incidence of tumors
519 observed in a fatal context.
520
521 The notations of Subsection III.C.2 with some modifications will be used in this
522 section to derive the test statistic of the death rate method.  Now let t1 <t2 < ...<tm
523 be the time points when one or more animals died of the fatal tumor of interest.
524 These time points are used to replace the intervals used in the prevalence method.
525 The notations in Table 3 are redefined as follows:
526
527 Rk:  The number of animals at risk of all groups just before tk.
528
529 Pik:  (The same as in the prevalence method) Proportion of Rk in Group i.
530
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531 Oik:  Observed number of animals in Group i dying of the fatal tumor of
532 interest at time tk.
533
534 O.k = (cid:229) i Oik.
535
536 As in the prevalence method, the test statistic T for the positive trend in the fatal
537 tumor is defined as:
538
539 T = (cid:229) i Di(Oi  Ei)
540
541 with estimated variance
542
543 V(T) = (cid:229) i(cid:229) j Di Dj Vij.
544
545 where Di, Oi, Ei, and Vij are defined similarly as in Subsection III. C.2.
546
547 Under the null hypothesis of equal tumor rates across the treatment groups, the
548 statistic
549
550 Z = T / [V(T)]1/2
551
552 is distributed approximately as standard normal.
553
554 4. Statistical Analysis of Tumors Observed in Both Incidental and Fatal
555 Contexts
556
557 When a tumor is fatal for some animals and is incidental for other animals in the
558 experiment, data for the incidental and fatal tumors should be analyzed separately
559 by the prevalence and the death rate methods.  Results from the different methods
560 can then be combined to yield an overall result.  The combined overall result can
561 be obtained simply by adding together either the separate observed frequencies,
562 the expected frequencies, and the variances, or the separate T statistics and their
563 variances (Peto et al. 1980).
564
565 5. Statistical Analysis of Mortality Independent Tumors
566
567 Tumors that are mortality independent, such as skin tumors and mammary gland
568 tumors, which are visible and/or can be detected by palpation in living animals,
569 are analyzed by CDER statistical reviewers using the onset rate method.  The
570 onset rate method for mortality independent tumors and the death rate method for
571 fatal tumors are essentially the same in principle except that the endpoint in the
572 onset rate method is the occurrence of such a tumor (e.g., skin tumor reaching
573 some prescpecified size) rather than the time or cause of the animals death.
574
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575 In the onset rate method, all those animals that, although still alive, have
576 developed the particular mortality independent tumor and hence are no longer at
577 risk for such a tumor are excluded from the calculation of the numbers of animals
578 at risk.  The Rk, Pik, and Oik described in Section III.C.3 are now redefined as
579 follows for the onset rate method:
580
581 Rk: The number of animals alive and free of the mortality independent
582 tumor of interest in all groups just before tk.
583
584 Pik: (The same as in the death rate method) Proportion of Rk in Group i.
585
586 Oik: Observed number of animals in Group i found to have developed
587 the mortality independent tumor of interest at time tk.
588
589 The test statistic T and its estimated variance V(T) are the same as those defined
590 in the death rate method.
591
592 6. Exact Methods
593
594 As noted in previous sections, the prevalence method, the death rate method, and
595 the onset rate method used normal approximation in the test for the positive trend
596 in tumor incidence rates.  Mortality patterns, the number of intervals used in the
597 partitioning of the study period, and the numbers and patterns of tumor
598 occurrence in each individual interval have effects on the accuracy of the normal
599 approximation.  It is also well known that the approximation results may not be
600 stable and reliable, and tend to underestimate the exact p-values when the total
601 numbers of tumor occurrence across treatment groups are small (Ali 1990).  In
602 this situation, the exact permutation trend test should be used to test for the
603 positive trend (Gart et al. 1986; Goldberg 1985).  The exact permutation trend test
604 is a generalization of the Fishers exact test to a sequence of 2x(r+1) tables.  The
605 exact permutation trend test procedure described below is for tumors observed in
606 an incidental context.  However, the positive trends in incidence rates of tumors
607 observed in a fatal or in a mortality independent context can be tested in a similar
608 way.  In those cases, the number of 2x(r+1) tables will be equal to the number of
609 time points when one or more animals died of a particular fatal tumor, or when
610 one or more animals developed a particular mortality independent tumor.
611 Fairweather et al. (1998) contains a discussion on the limitations of applying
612 exact methods to fatal tumors.
613
614 The exact method is derived by conditioning on the row and column marginal
615 totals of each of the 2x(r+1) tables formed from the partitioned data set of Table
616 3.  Consider the k-th interval Ik (in Table 3) and rewrite it as in Table 7.  Let the
617 column totals C0k, C1k, ..., Crk and the row totals O.k and A.k be fixed.  Define Pik
618 = Cik/Rk.  Then the quantities Eik = O.kPik, Vijk = a k Pik(d ij-Pjk), Ei, and V(T)
619 (defined in Subsection III.C.2) are all known constants.
620
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621
622
623 Table 7: The Data in the k-th Time Interval Ik Is Written as a 2 x  (r + 1) Table
624
         Group        0            1     .  .  .     i      .  .  .     r
         Dose        D           D    .  .  .    D   .  .  .     D             Total
0 l i     r
       # w tumor        O         O     .  .  .   O    .  .  .     O O
0k lk ik rk .k
       # w/o tumor        A          A   .  .  .   A    .  .  .     A A
0k lk    ik rk .k
            Total        C          C     .  .  .   C     .  .  .    C R
0k lk ik rk k
625
626
627
628 Now let y be the observed value of Y = (cid:229) DiOi, where Oi = (cid:229) kOik, the total
629 number of tumor bearing animals of the tumor of interest in treatment group i.
630 Then (under conditioning on the column and row marginal totals in each table)
631 the observed significance level or
632
633 p-value = P[(cid:229) DiOi>=y] = P((cid:229) iDi (cid:229) kOik>=y) = P((cid:229) k(cid:229) iDiOik>=y)
634
635 = P((cid:229) kYk>=(cid:229) yk) = P(Y>=y),
636
637 where Y = (cid:229) Yk = (cid:229) k(cid:229) iDiOik and y = (cid:229) yk, the observed value of Y.
638
639 This p-value (P(Y>=y) is computed from the exact permutational distribution of
640 Y.  Given the observed row and column marginal totals in a 2x(r+1) table, all
641 possible tables having the same marginal totals can be generated.  Let Sk
642 (k=1,2,...,K) be the set of all such tables generated from the k-th observed table.
643 From a set of K tables taking one from each Sk and assuming independence
644 between the K tables, the above expression for the p-value can now be written as
645
646 p-value = (cid:229) [P(Y1 = yi) ... P(Yk = yk)]
647
648 where yk =(cid:229) iDiOik (k=1,2,...,K), the sum is over all sets of K tables such that
649 yi+y2+...+yk >=y, the observed value of Y, and P(Yk=yk) is the conditional
650 probability given the marginal totals in the k-th table, i.e.,
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651
 (cid:230) C (cid:246) (cid:230) C (cid:246) (cid:230) C (cid:246)  (cid:230) R (cid:246)
0k 1k rk k
652                                     P(Yk=yk) =  o (cid:231) O0k(cid:247) (cid:231) O1k(cid:247) . . . (cid:231) Ork(cid:247)    (cid:231) Ok(cid:247)
653
654
655 Example (Lin and Ali 1994).  Consider an experiment with 3 treatment groups
656 (control, low-, and high-dose) with dose levels D0=0, D1=1, and D2=2,
657 respectively.  Suppose the study period is partitioned into the intervals 0-50, 51-
658 80, 81-104 weeks, and the terminal sacrifice week.  Consider a tumor type
659 (classified as incidental) with data in Table 8.
660
661
662
663 Table 8: Hypothetical Tumor Data for Exact Permutation Trend Test
664
                 Dose levels
Time intv.         0               1             2 Total
 0  -  50 O         0                0             0            0
C         1                3             3            7
51 - 80 O         0                0             0            0
C         4                5             7          16
81 - 104 O         0                0             2             2
C       10               12          15           37
Term. Sacr. O         0                1            0             1
C       35              30           25           90
665      O = observed tumor count,   C = number of animals necropsied
666
667
668
669 Since all the observed tumor counts (i.e., Os) in the first two time intervals are
670 zeros, the data for these intervals will not contribute anything to the test statistic,
671 and these intervals may be ignored.  The observed subtables formed from the last
672 two intervals are given in Table 9.
673
674 Now, generate all possible tables from observed subtable 1.  Since the marginal
675 totals are fixed, these tables may be generated by distributing the total tumor
676 frequency O.1(=2) among the three treatment groups.  Thus, each table will
677 correspond to a configuration of this distribution of O.1.  The configurations, the
678 values of Y1, and the P(Y1=y1) are shown in Table 10.
679
680
681
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682 Table 9: Observed Subtables From the Above Hypothetical Tumor Data
Observed subtable 1 Observed subtable 2
Dose   0   1   2 Total Dose   0   1   2 Total
O   0   0   2 2=O O   0   1   0 1=O
.1 .2
A 10 12 13 35=A A 35 29 25 89=A
.1 .2
C 10 12 15 37=R C 35 30 25 90=R
1 2
683
684
685
686 Table 10: All Possible Configurations of o.1 and the
687 Corresponding Hypergeometric Probabilities
Configurations y P(Y=y )
1 1 1
0,  0,  2 4 .15766
0,  2,  0 2 .09910
2,  0,  0 0 .06757
0,  1,  1 3 .27027
1,  0,  1 2 .22523
1,  1,  0 1 .18018
688
689
690 To illustrate the computation of y1 and P(Y1=y1) consider the last row.  Here y1=
691 D0x1 + D1x1 + D2x0 = 0x1 + 1x1 + 2x0 = 1, and
692
 (cid:230) 10(cid:246) (cid:230) 12(cid:246) (cid:230) 15(cid:246)  (cid:230) 37(cid:246)
693                                  P(Y1=1) =  o (cid:231)  1(cid:247) (cid:231)  1(cid:247) . . . (cid:231)  0(cid:247)     (cid:231)  2(cid:247)  =  0.18018
694
695 The configurations and probabilities obtained from observed subtable 2 are given
696 in Table 11.
697
698 Note that the first configuration (0,0,2) in Table 8 corresponds to the observed
699 subtable 1 with a value of y1= (0x0)+(2x2)=4 and a probability of .15766, and the
700 second configuration (0,1,0) in Table 8 corresponds to the observed subtable 2
701 with a value of y2= (0x0)+(1x1)+(0x0)=1 and a probability of .33333.  Thus, the
702 observed value of y = y1+y2 = 4+1=5.  Now the exact p-value (right-tailed) is
703 calculated as follows:
704
705
706 P(Y = Y1+Y2 >=5) = P(Y1=4,Y2=1)+P(Y1=4, Y2=2)+P(Y1=3, Y2=2)
707
708 = .15766 x .33333 + .15766 x .27778 + .27027 x .27778
709
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710 = .17142
711
712
713
714 Table 11: All Possible Configurations of O.2 and the
715 Corresponding Hypergeometric Probabilities
Configurations y P(Y=y )
1 1 1
0,  0,  1 2 .27778
0,  1,  0 1 .33333
1,  0,  0 0 .38889
716
717
718 For the purpose of comparison, it should be noted that the normal approximated
719 p-value for the data set in the above example is .0927.
720
721
722 D.  Statistical Analysis of Data Without Information About Cause of Death and
723 Without Multiple Sacrifices
724
725 As noted previously, in the analysis of tumor data, it is essential to identify and adjust for
726 possible differences in intercurrent mortality among treatment groups to eliminate or
727 reduce biases caused by these differences.  It is also necessary for the analysis to
728 appropriately account for tumor lethality.  The widely used prevalence method, the death
729 rate method, and the onset rate methods for analyzing incidental, fatal, and mortality
730 independent tumors, respectively, described in previous sections rely on good
731 information on tumor lethality and cause of death.  There are situations in which sponsors
732 have not included tumor lethality and cause of death information in their statistical
733 analyses and electronic data sets.  Under those situations, statistical reviewers in CDER
734 either treated all tumors as incidental or relied on cause of death assessments by the
735 reviewing pharmacologists and toxicologists in the Center.  There are consequences in
736 misclassifying tumors as lethal or not in survival adjusted statistical tests.  The prevalence
737 method will reject the null hypothesis of no positive trend less frequently than it should
738 as the lethality of a tumor increases (Peto et al. 1980; Dinse 1994).  This will increase the
739 probability of failing to detect true carcinogens.
740
741 The Bailer-Portier poly-3, and poly-6 (in general poly-k) tests (Bailer and Portier 1988;
742 Dinse 1994) have been proposed for testing linear trends in tumor rates.  These tests are
743 basically modifications of the survival unadjusted Cochran-Armitage test (Cochran 1954;
744 Armitage 1955, 1971) for linear trend in tumor rate.  If the entire study period is
745 considered as one interval, the data for a particular tumor type will be in the form of
746 Table 12.  The notations in Table 12 to be used to explain these tests are the same as
747 those in Table 7 except that the k-th interval now is the entire study period.  The second
748 subscript, k, for the k-th interval was dropped from the notations.
749
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750
751 Table 12: The Data Using the Entire Study Period as an Interval
752
          Group         0          1       .  .  .     i      .  .  .      r
          Dose        D          D      .  .  .    D  .  .  .     D            Total
0 l i      r
      # w. tumor        O         O  .  .  .     O  .  .  .     O O
0  l         i      r
      # w/o tumor        A          A     .  .  .     A     .  .  .     A A
0 l i  r
          Total        C          C     .  .  .     C  .  .  .     C R
0 l i        r
753
754
755
756
757 The Cochran-Armitage test statistic for linear tend in tumor rate is defined as (Armitage
758 1955):
759
760 R { R (cid:229)  OiDi  O (cid:229)  Ci Di } 2
761 c CA2 = ---------------------------------------------------------  or
762       O (R  O) { R (cid:229)  Ci Di2  { (cid:229)  Ci Di) 2 }
763
764
765 { (cid:229)  Di (Oi  Ei) }
766                       =  ---------------------------------------
767       (cid:229)  Ei Di2  ( (cid:229)  Ei Di) 2 / O
768
769 Where O = (cid:229)  Oi,   A = (cid:229)  Ai,  R= (cid:229)  Ci, Ei = O Ci / R.
770
771 The test statistic c CA2 is distributed approximately as  c 2 on one degree of freedom.
772
773 The Cochran-Armitage linear trend test is based on a binomial assumption that all
774 animals in the same treatment group have the same risk of developing the tumor over the
775 duration of the study.  However, as noted previously, the animals risk of developing the
776 tumor increases as study time increases.  The assumption is thus no longer valid if some
777 animals die earlier than others.  It has been shown that as long as the mortality patterns
778 are similar across treatment groups, the Cochran-Armitage test is still valid, although it
779 may be slightly less efficient than a survival adjusted test (Dinse 1994).  However, if the
780 mortality patterns are different across treatment groups, the Cochran-Armitage test can
781 give very misleading results.
782
783 The Bailer-Portier poly-3 test adjusts for differences in mortality among treatment groups
784 by modifying the number of animals at risk in the denominators in the calculations of
785 overall tumor rates in the Cochran-Armitage test to reflect less-than-whole-animal
786 contributions for decreased survival (Bailer and Portier 1988).  The modification is
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787 made by defining a new number of animals at risk for each treatment group.  The number
788 of animals at risk for the i-th treatment group C*i is defined as
789
790 C* i = (cid:229)  W ij
791
792 where w ij the weight for the j-th animal in the i-th treatment group, and the sum is over
793 all animals in the group.
794
795 Bailer and Portier (1988) proposed the weight  w ij as follows:
796
797 w ij = 1  to animals dying with the tumor, and
798
799 w ij = ( tij / tsacr )3 to animals dying without the tumor
800
801 where tij is the time of death of the j-th animal in the i-th treatment group, and tsacr is the
802 time of terminal sacrifice.
803
804 The power of 3 used in the weighting is from the observation that tumor incidence can be
805 modeled as a polynomial of order 3.  Similarly the poly-6 test (or the general poly-k test)
806 assigns the weight  w ij = (tij / t sacr  )6  (or w ij = ( tij  / tsacr )k ) to animals dying without
807 the tumor when the tumor incidence is close to a polynomial of order 6 (or order k).
808
809 The class of Bailer-Portier poly-k tests are carried out by replacing the Cis by the new
810 numbers of animals at risk C*is in the calculation of the above Cochran-Armitage test
811 statistic.
812
813 The class of Bailer-Portier poly-k tests adjust differences in survival, do not need the
814 information about cause of death, and call for only a (the terminal) sacrifice.  Results of
815 simulation studies by Bailer and Portier (1988), and Dinse (1994) show that the tests
816 performed very well under many conditions simulated.  They are also relatively robust to
817 (not affected greatly by) tumor lethality.
818
819 Bieler and Williams (1993)  pointed out that, since animal survival time is generally not a
820 fixed quantity, the numerators and denominators of the adjusted quantal response
821 estimates
822
823 p*i = Oi / C*i
824
825 are both subject to random variation.
826
827 Bieler and Williams (1993) proposed a test called the ratio trend test (also called Bieler-
828 Williams poly-3 test), which is another modification to the Cochran-Armitage linear
829 trend test.  The ratio trend test employs the adjusted quantal response rates calculated in
830 Bailer and Portier (1988) and the delta method (Woodruff 1971) in the estimation of the
831 variance of the adjusted quantal response rates p*i = Oi / C*i.
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832
833 The computational formula for Bieler-Williams ratio trend (modified C-A) test statistic is
834 given as follows:
835
836
837        (cid:229)  mi p*i Di  ((cid:229)  miDi) ((cid:229) mi p*i) / (cid:229) mi
c 2
838 BW   =  ----------------------------------------------------
839                      {c [(cid:229)  mi Di 2 -  ((cid:229)  mi Di )2 / (cid:229)  mi]}1/2
840
841 where
842
843 c = (cid:229)(cid:229)  (rij  ri.)2 / [R  (r + 1)]
844
845 mi = (CI*)2 / Ci
846
847 rij = yij - p* wij
848
849 ri. = (cid:229)  rij / Ci
850
851 yij = tumor response indicator (0 = absent at death, 1 =  present at death) for the jth
852 animal in the ith group.
853
854 Bieler and Williams (1993) showed that the Bailer-Portier poly-3 trend test is anti-
855 conservative when tumor incidence rates are low and treatment toxicity is high.  Their
856 study also showed that for tumors with low background rates, the ratio trend test (Bieler-
857 Williams poly-3 test) yielded actual Type I errors close to the nominal levels used and
858 was observed to be less sensitive than the Bailer-Portier poly-3 trend test to
859 misspecification of the shape of tumor incidence function and the magnitude of treatment
860 toxicity.
861
862 A more recent simulation study by Chen, Lin, Juque, and Arani (2000) showed the
863 following additional results about the characteristics of the Bailer-Portier poly-3 and the
864 ratio trend tests (Bieler-William poly-3 test).  For individual tumor types, the two tests for
865 trend yield attained Type I errors around the nominal levels (5 percent and 1 percent) for
866 tumors with spontaneous rates in the range between 2 percent to 20 percent.  When
867 spontaneous rates are below the range, the two tests become conservative (i.e., less likely
868 to show  statistically significant results).  For tumors with spontaneous rates above 20
869 percent to 60 percent (the upper rate used in the simulation), the ratio trend test still
870 maintains the attained Type I error rates close to the nominal levels, but the Bailer-Portier
871 poly-3 test becomes more and more conservative as the rates go up.  The introduction of
872 the compound symmetric correlation structure (although a not very realistic structure)
873 among tumors corrects the problem of conservativeness somewhat in the Bailer-Portier
874 poly-3 test, but the patterns of conservativeness continue to exist.
875
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876 The ratio trend test (Bieler-William poly-3 test), like the Bailer-Portier poly-3 test,
877 adjusts differences in survival, does not need the information about cause of death, and
878 results only in a (the terminal) sacrifice.  Results of simulation studies (Bieler and
879 Williams 1993; Chen, Lin, Huque, and Arani 2000) show that the tests performed very
880 well under many simulated conditions.  It is also shown to be relatively robust to (not
881 affected greatly by) tumor lethality, misspecification of the shape of tumor incidence
882 function, and the magnitude of treatment toxicity.  The ratio trend test (Bieler-William
883 poly-3 test) should be used to replace the asymptotic tests that depend on the information
884 of tumor lethality and cause of death when the information is unavailable.
885
886 Theoretically, exact versions of the class of tests can be developed for testing data of
887 studies with small numbers of tumor bearing animals by applying the test procedures to
888 all possible permuted configurations of the outcome.  However, because these tests use
889 risk sets based on all animals in each treatment group, the computations involved in the
890 exact tests will be extensive.  Therefore, for studies with small numbers of tumor bearing
891 animals, the current practice of treating them as incidental tumors and applying the exact
892 permutation trend test should continue.
893
894 E.  Statistical Analysis of Data From Studies With Dual Controls
895
896 There are two categories of studies with dual control groups.  The first category usually
897 consists of studies using an untreated control group and a vehicle control group (Category
898 A).  Other variations of nonidentically treated, nondrug treatment controls groups are also
899 occasionally used and are included in Category A for statistical purposes.  The second
900 category (Category B) includes studies that use two identical control groups (Society for
901 Toxicology 1982; Haseman, Winbush, and ODonnell 1986).
902
903 The main reasons for using two differently treated controls, generally an untreated
904 control and a vehicle control in a study in Category A are to determine whether the
905 vehicle has effects on tumor incidence and pattern, body weight, and food consumption
906 (in dietary studies) on the test animals, and to make sure that the control animals are
907 subjected to the same influences (e.g., gavage or injection) as the drug treated animals, so
908 that all animals will be subject to equal physiological response and stress (i.e., to isolate
909 the treatment effect from other possible effects) (Gart et al. 1986; Dayan 1988).
910
911 There are arguments for and against using two identical control groups in a study
912 (Category B).  The arguments for this design are that the results from the two identical
913 controls can be used as a mechanism for identifying the extent of control variability (Gart
914 et al. 1986) and the results can be used to help evaluate the biological significance of
915 increases in tumor incidence in the treated groups (i.e., true increases versus noise).
916 From the biological perspective, the dual control data can be viewed as equivalent to
917 having contemporary historical data.  In this case, consideration of other appropriate
918 historical control data is essential if the results with the two contemporary controls are
919 different.  As described below, however, there may be difficulties in statistical analysis of
920 data from a study using this design.
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921 Statisticians and pharmacologists/toxicologists should decide collaboratively which of the
922 two control groups is appropriate for the analysis of data from a study in Category A.
923 Ordinarily, analyses of data of the vehicle control and the treated groups are the most
924 meaningful assessment of drug effect.  Even in this case, however, the untreated control
925 can give information about spontaneous variability.  There are other situations in which
926 three analyses  control 1 versus treated groups, control 2 versus treated groups, and
927 control 1 plus control 2 versus treated groups  are performed.  Because concerns about
928 the possible effects of the vehicle substance on the test animals are the reason for using
929 the vehicle control in addition to the untreated control, it is also of interest to compare the
930 mortality, tumor rates, body weight, and food consumption (in dietary studies) between
931 the two control groups.
932
933 Data from dual identical control groups may or may not be combined for statistical
934 analysis of data.  If comparisons of the controls for Category B studies show no large
935 differences in mortality and tumor rate, the data from the two control groups are usually
936 combined to form a single control group in subsequent analyses (Haseman et al. 1990).
937 If the data show evidence of differences in mortality or tumor incidence between the
938 identical controls, three tests  control 1 versus treated groups, control 2 versus treated
939 groups, and control 1 plus control 2 versus treated groups  for each tumor/organ
940 combination should be carried out.
941
942 In the second case, the question of how to interpret the results of a study in Category B
943 can be approached from two perspectives.  First, a trend or a difference in tumor rate
944 could be considered significant only if it is significant for both of the controls.  The basis
945 for this conclusion would be that a real finding should be reproducible.  Alternatively, the
946 trend or the difference in tumor rate between groups could be considered significant as
947 long as any one of the three tests (i.e., drug vs. control 1, drug vs. control 2, and drug vs.
948 pooled control) either control and pooled control shows a significant result, assuming that
949 most carcinogenicity studies are relatively under powered.  The first approach is
950 conservative in the sense that the null hypothesis will be rejected less often.  The second
951 approach, on the other hand, will result in an increased false positive rate.
952
953 Currently, no good information exists about how to appropriately adjust the significance
954 levels for the above two approaches to maintain the 10 percent overall false positive rate
955 used by the Center.  In general, the test result could be regarded as providing only
956 equivocal evidence of a positive finding unless all the three tests yield consistent results
957 (i.e., all statistically significant or all not statistically significant) (Haseman et al. 1990).
958 In such instances, from a biological prospective it is particularly important to evaluate the
959 control response relative to a historical control.
960
961
962 V.  INTERPRETATION OF STUDY RESULTS
963
964 Interpreting results of carcinogenicity experiments is a complex process, and there are risks of
965 both false negative and false positive results.  The relatively small number of animals used and
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966 low tumor incidence rates can result in the failure to detect the carcinogenicity of a drug (i.e., a
967 false negative).  Because of the large number of comparisons involved (usually 2 species, 2
968 sexes, and 30 or more tissues examined), a great potential exists for finding statistically
969 significant positive trends or treatment-placebo differences due to chance alone (i.e., a false
970 positive).  Therefore, it is important that an overall evaluation of the carcinogenic potential of a
971 drug take into account the multiplicity of statistical tests of significance for both trends and
972 pairwise comparisons.  The evaluation should also make use of historical information and other
973 information related to biological relevance (e.g., positive findings at the same site in the other
974 sex and/or in the other species, and evidence of increased preneoplastic lesions at the target
975 organs/tissues).
976
977 A.  Adjustment for the Effect of Multiple Tests (Control Over False Positive
978 Error)
979
980 It is well known that, for a multi-group study (e.g., 3 doses and placebo), trend tests are
981 more powerful (i.e., more likely to detect an effect) than pairwise comparisons.  Tests for
982 trend instead of pairwise comparison tests between control and high-dose groups are
983 therefore the primary tests in the evaluation of drug related increases in tumor rate.
984
985 Statistical and nonstatistical procedures have been proposed for controlling the overall
986 false positive rate.  Surveys of some of those procedures can be found in Lin and Ali
987 (1994), and Fairweather et al. (1998).  In this guidance document, only the statistical
988 decision rules for controlling the overall false positive rates associated with trend tests
989 and pairwise comparisons used by the Center in interpreting the final results of
990 carcinogenicity studies are discussed.  The decision rules were developed based on
991 historical control data of CD rats and CD mice (strains that are most widely used in
992 studies of pharmaceuticals) to achieve an overall false positive rate of around 10 percent
993 for the standard two-species, two-sex in-vivo studies and the alternative ICH one-species,
994 two-sex in-vivo studies.
995
996 In the past, statisticians in CDER used the statistical decision rule described in Haseman
997 (1983) in tests for significance of trends in tumor incidence.  The decision rule was
998 originally developed for pairwise comparison tests in tumor incidence between the
999 control and the high-dose groups and was derived from results of carcinogenicity studies
1000 conducted at National Toxicology Program (NTP).  Strains of Fischer 344 rats and
1001 B6C3F1 mice were used in the NTP studies.  Like most studies of pharmaceuticals, four
1002 treatment/sex groups with 50 animals in each group were used in the NTP studies.  All of
1003 the NTP studies lasted for 2 years.  The decision rule tests the significant differences in
1004 tumor incidence between the control and the dose groups at 0.05 level for rare tumors and
1005 at 0.01 level for common tumors.  A tumor type with a background rate of 1 percent or
1006 less is classified as rare by Haseman; more frequent tumors are classified as common.
1007 Hasemans original study and a second study using more recent data with higher tumor
1008 rates show that the use of this decision rule in the control-high pairwise comparison tests
1009 would results in an overall false positive rate between 7 to 8 percent and between 10 to
1010 11 percent, respectively (Haseman 1983, 1984a, 1991).
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1011
1012 Concerns have been raised that applying the rule described by Haseman (1983) to
1013 analyses of trend tests would lead to an excessive overall false positive error rate as data
1014 from all treatment groups are used in the tests and considerably lower tumor rates can
1015 yield a wrongly significant result.  Results from recent studies within and outside FDA
1016 show that this concern is valid.  Based on studies conducted by CDER and NTP, the
1017 overall false positive error resulting from interpreting trend tests by use of the above
1018 decision rule is about twice as large as that associated with control-high pairwise
1019 comparison tests.
1020
1021 Based on recent studies using real historical control data of CD mice and CD rats from
1022 Charles River Laboratory and simulation studies conducted internally and in
1023 collaboration with NTP, a new statistical decision rule for tests for a positive trend in
1024 tumor incidence has been developed.  This new decision rule tests the positive trend in
1025 incidence rates in rare and common tumors at 0.025 and 0.005 levels of significance,
1026 respectively.  The new decision rule achieves an overall false positive rate of around 10
1027 percent in a standard two-species and two-sex study (Lin 1995, 1997; Lin and Rahman
1028 1998a, 1998b).  The 10 percent overall false positive rate is seen by CDER statisticians as
1029 appropriate in a new drug regulatory setting.
1030
1031 Regulatory statistical literature emphasizes methods for testing for positive trends in
1032 tumor rate (Lin 1988, 2000); Lin and Ali 1994; Chen and Gaylor 1986; Dinse and
1033 Haseman 1986; and Dinse and Lagokos 1983). There are situations, however, in which
1034 pairwise comparisons between control and individual treated groups may be more
1035 appropriate than trend tests because trend tests assume that a carcinogenic effect is
1036 related to doses or systemic exposure weights, or ranks.  The assumption may be true for
1037 simple direct acting carcinogens in studies not complicated by excessive toxicity.
1038 However, there are many cases in which the response is to a drug metabolite, is mediated
1039 through a receptor (or enzyme) that may be saturated even at the low dose, is
1040 compounded by dose-related toxicity, or is complicated by other nonlinear effects.  Under
1041 those situations, pairwise comparisons may be appropriate and the decision rule described
1042 in Haseman (1983) should be used in interpreting the results of the pairwise comparison
1043 tests.
1044
1045 Sponsors should conduct both trend tests and pairwise comparison tests and present the
1046 results of these two types of tests in the formats used in Table 15.  A recent complication
1047 to the use of the trend test is the choice by a sponsor not to do histopathologic evaluation
1048 of all treatment groups.  Although studies conducted using this design have been
1049 evaluated by CDER, such an approach is not usually recommended.
1050
1051 The high cost (between 1 and 2 million dollars) and long time (a minimum of 3 years) it
1052 takes to conduct a standard long-term, in-vivo carcinogenicity study and the increased
1053 insight into the mechanisms of carcinogenicity provided by advances in molecular
1054 biology have led to alternative in-vivo approaches to the assessment of carcinogenicity.
1055 The International Conference on Harmonization (ICH) has developed guidance for use in
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1056 the United States and in other regions entitled  S1B Testing for Carcinogenicity of
1057 Pharmaceuticals (1998).  This guidance outlines experimental approaches to the
1058 evaluation of carcinogenic potential that may obviate the need for the routine use of two
1059 long-term rodent carcinogenicity studies and allows for the alternative approach of
1060 conducting one long-term rodent carcinogenicity study together with a short- or medium-
1061 term rodent test.  The short- or medium-term rodent test systems include such studies as
1062 initiation-promotion in rodents, transgenic rodents, or newborn rodents, which provide
1063 rapid observation of carcinogenic endpoints in-vivo.  In general, these studies do not
1064 produce false positive results because tumor background rates are very low.  False
1065 positives therefore arise primarily from the 2-year rodent study.  Results from an agency
1066 study using historical control data of CD rats and CD mice (Lin 1997; Lin and Rahman
1067 1998b) showed that the use of significance levels of 0.05 and 0.01 in tests for positive
1068 trend in incidence rates of rare tumors and common tumors, respectively, will result in an
1069 overall false positive rate around 10 percent in a study in which only one 2-year rodent
1070 bioassay (plus the shorter rodent study) is conducted.
1071
1072 The decision rules for testing positive trend or differences between control and individual
1073 treated groups in incidence rates for standard studies using two species and two sexes as
1074 well as studies following ICH guidance and using only one 2-year rodent bioassay are
1075 summarized in Table 13.
1076
1077 The developed decision rules for tests for positive trend and for difference in pairwise
1078 comparisons are based on the proposition that the carcinogenic effect of a drug is
1079 considered positive if one or more tumor types tested in any of the four experiments (or
1080 two experiments under an alternative ICH study) of species/sex combination show a
1081 significant positive trend in tumor incidence rates (or one or more tumor types show a
1082 significant difference in tumor incidence rates when the results of the control-high
1083 pairwise comparisons are used in the final interpretation).  The decision rules were
1084 developed assuming the use of the two-species-and-two-sex (or one-species-and-two-sex)
1085 standard design of a two-year study with 50 animals in each of the four treatment/sex
1086 groups.
1087
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1088 Table 13: Statistical Decision Rules for Controlling the Overall False
1089 Positive Rates Associated With Tests for Positive Trend or With
1090 Control-High Pairwise Comparisons in Tumor Incidences to
1091 Around 10 Percent in Carcinogenicity Studies of Pharmaceuticals
1092
1093
Tests for Positive Trend Control-High Pairwise
Comparisons
Standard 2-Year Studies Common and rare tumors Common and rare tumors
with 2 Species and 2 Sexes are tested at 0.005 and  0.025 are tested at 0.01 and  0.05
significance levels, significance levels, respectively.
respectively.
Alternative ICH Studies Common and rare tumors Under development and not yet
(One Two-Year Study in are tested at 0.01 and  0.05 available.
One Species and One Short- significance levels,
or Medium-Term Study, respectively.
Two Sexes)
1094
1095
1096
1097 B.  Control Over False Negative Error
1098
1099 To make sure that the false negative rate is not excessive, reviewing pharmacologists,
1100 pathologists, and medical officers evaluate the adequacy of the gross and histological
1101 examination of both control and treated groups, the adequacy of the dose selection, the
1102 duration of the experiment in relation to the normal life span of the tested animals, and
1103 the survival of animals in the study.
1104
1105 C.  The Use of Historical Control Data
1106
1107 The concurrent control group is always the most appropriate and important in testing
1108 drug related increases in tumor rates in a carcinogenicity experiment.  However, if used
1109 appropriately, historical control data can be very valuable in the final interpretation of the
1110 study results.  Large differences between studies can result from differences in
1111 nomenclature, pathologists reading slides, the specific animal strain used and laboratory
1112 conditions.  It is therefore extremely important that the historical control data chosen be
1113 from studies comparable to the current study, generally recent studies from the same
1114 laboratory using the same strain of rodent.
1115
1116 Historical control data are particularly useful in classifying tumors as rare or common.  A
1117 statistically significant increase in a rare tumor is unlikely as a chance occurrence so that
1118 it is critical to decide whether a tumor is rare or not.  Rare tumors are generally tested
1119 with less stringent statistical decision rules (see Table 13).  Historical control data can
1120 also be used as a quality control mechanism for a carcinogenicity experiment by
1121 assessing the reasonableness of the spontaneous tumor rates in the concurrent control
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1122 group (Haseman 1984b; Haseman, Huff, and Boorman 1984), and for evaluation of
1123 disparate findings in dual concurrent controls.
1124
1125 For common tumors, in cases of marginally significant trends or differences, historical
1126 control data can help investigators determine whether the findings are real or false
1127 positives.  Historical control data can also help investigators determine whether
1128 nonsignificant findings in rare tumors are true negative or false negative results due to the
1129 lack of power in the statistical tests used.  A widely used informal method is to determine
1130 whether the tumor rates in the treated groups in the experiment are within the range of
1131 reliable historical control data.  If they are, a marginally significant finding for a common
1132 tumor may be discounted as resulting from a random occurrence of a low concurrent
1133 control rate.  Similarly, a nonsignificant increase for a rare tumor can be considered truly
1134 negative if the treated tumor rates are within the historical range.
1135
1136 The above informal method of using historical control data in the interpretation of
1137 statistical test results is not very satisfactory because the range of historical control rates
1138 is usually too wide.  This is especially true in situations in which the historical tumor
1139 rates of most studies used are clustered together, but a few other studies give rates far
1140 away from the cluster.  When the range of historical control data is simply calculated as
1141 the difference between the maximum and the minimum of the historical control rates.
1142 The range does not consider the shape of the distribution of the rates.  The upper
1143 confidence intervals for binomial proportions constructed by the methods described in
1144 Louis (1981), Blyth (1986), Vollset (1993), Jovanovic and Viana (1996), and Jovanovic
1145 and Levy (1997) should probably replace the historical range in the above informal
1146 method.
1147
1148 In addition to the informal use of historical control data in the interpretation of the
1149 statistical testing results mentioned above, more formal statistical procedures have been
1150 proposed that allow the incorporation of appropriate historical control data in tests for
1151 trend in tumor rate.  For example, Tarone (1982), Hoel (1983), Hoel and Yanagawa
1152 (1986), Tamura and Young (1986, 1987), and Prentice et al. (1992) proposed some
1153 empirical procedures using the beta-binomial distribution to model historical control
1154 tumor rates and to derive approximate and exact tests for trend.  The results from those
1155 studies show that the incorporation of the historical control data improves the power of
1156 the tests.  The greatest improvement of power is shown in the tests of rare tumors.
1157 Dempster et al (1983) proposed a Bayesian procedure to incorporate historical control
1158 data into statistical analysis.  The procedure uses the assumption that the logits of the
1159 historical control tumor rates were normally distributed.
1160
1161 These formal statistical procedures work well in situations in which historical data from a
1162 large number of studies with relatively large control groups are available to provide
1163 reliable estimations of the parameters of the prior distributions.  However, the maximum
1164 likelihood estimators (MLEs) of the prior parameters were shown to be unstable, and the
1165 distributions of the MLEs were skewed to the right (i.e., with bunching above the mean
1166 and a long tail below the mean).  The skewness was severe in cases in which only
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1167 historical data of a few small control groups were available.  The skewness of the MLEs
1168 inflated the Type I error of the tests.  Also, these procedures were developed to
1169 incorporate historical control data into the Cochran-Armitage test for linear trend in
1170 tumor incidence.  Since the Cochran-Armitage test is a survival-unadjusted procedure,
1171 these procedures cannot be applied to studies with significant differences in survival
1172 among treatment groups.  Recently, Ibrahim and Ryan (1996) developed a method for
1173 incorporating historical control information into survival-adjusted tests for trend in tumor
1174 incidence.  When using this method, the study period should be partitioned into intervals.
1175 In each interval, the multinomial distribution should be used to model the observed
1176 numbers of animals dying with the tumor, and Dirichlet distribution should be used as the
1177 prior distribution for the historical control tumor rates.  This method applies only to fatal
1178 tumors.
1179
1180 D.  Evaluation of Validity of Designs of Negative Studies
1181
1182 In negative or equivocal studies, that is, studies for which either the sponsors or FDAs
1183 statisticians detected no statistically significant positive trend or difference in tumor rate,
1184 the statistical reviewers will perform a further evaluation of the validity of the design of
1185 the experiment to see if there were sufficient numbers of animals living long enough to
1186 provide adequate exposure to the chemical and to be at risk of forming late-developing
1187 tumors.  The reviewers also want to see if the doses used were adequate to present a
1188 reasonable tumor challenge to the tested animals (Haseman 1985).
1189
1190 As a rule of thumb, a 50 percent survival rate of the 50 initial animals in any treatment
1191 group between weeks 80 to 90 of a 2-year study would be considered to yield a sufficient
1192 number of animals with adequate exposure.  The percentage can be lower or higher if the
1193 number of animals used in each treatment/sex group is larger or smaller than 50, but
1194 between 20 to 30 animals should be still alive during these weeks.
1195
1196 The adequacy of doses selected and of the animal tumor challenge in long-term
1197 carcinogenicity experiments is evaluated by pharmacologists and the CDER
1198 Carcinogenicity Assessment Committee (CAC) based on the previously described ICH
1199 approaches as well as on the results of the long-term carcinogenicity experiments.  To
1200 assist the evaluation, CDER statistical reviewers are often asked to provide analyses of
1201 body weight and mortality differences and, occasionally, other differences between
1202 treated and control groups.
1203
1204
1205 VI.  PRESENTATION OF RESULTS AND DATA SUBMISSION
1206
1207 To facilitate the statistical reviews, sponsors should present study results and data in such a way
1208 that FDA statistical reviewers are able to verify the sponsors calculations, to validate their
1209 statistical methods, and to trace back the sponsors conclusions through their summaries and
1210 analyses of the raw data (FDA 1987).
1211
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1212 In the sponsors report, in addition to the volumes containing study data of individual animals, a
1213 statistical analysis section should be included containing summary statistics of the study data,
1214 results of statistical analyses of the data, results and findings, and main conclusions of the study.
1215 In the statistical analysis section, the sponsor should include descriptions of the statistical
1216 procedures used and pertinent literature references.  The descriptions of statistical methodology
1217 and references are particularly important if the sponsor decides to use designs and methods of
1218 analysis and interpretation other than those recommended in this guidance document.
1219
1220 Tables 14, 15, and 16 include examples of formats for presenting summaries and results of
1221 analyses of survival and tumor data.  Presentations of data summaries and analyses results should
1222 be made for each species/sex combination.  Descriptive statistics such as mean, standard
1223 deviation, and range, which are important in characterizing the distinctive and essential features
1224 of a study, should also be reported by species/sex combination.  Graphics that are useful and
1225 informative in presenting study results should be used to display summary data, especially
1226 summary statistics over time.
1227
1228 Two sets of formats and specifications were previously used regularly by the Divisions of
1229 Biometrics, Office of Biostatistics.  They were (a) the Divisions of Biometric Formats and
1230 Specifications for Submission of Animal Carcinogenicity Study Data, and (b) the Submitters
1231 Toxicological Uniform Data Information Exchange Standard (STUDIES).  Because mistakes
1232 have often been made by sponsors in data sets using the STUDIES formats, the Office of
1233 Biostatistics now recommends that sponsors submit the data sets in the simpler divisions of
1234 biometrics formats and specifications described in Lin (1998).  Discussions of the statistical
1235 analyses on which the formats were developed can be found in Lin (1998).
1236
1237 Data sets described in the above Divisions of Biometrics formats and specifications document
1238 are divided into two groups, Group A and Group B, depending on whether the data will be used
1239 immediately in the statistical review and evaluation of the carcinogenicity studies.  Group A
1240 includes data sets that are always used by statisticians performing a statistical review and
1241 evaluation of the carcinogenicity studies.  Group B includes data sets that may be used by
1242 medical officers, pharmacologists, toxicologists, and statisticians in their final interpretations of
1243 the study results.  Sponsors are urged to submit the two groups of data sets together with their
1244 original, initial submissions of the hardcopy NDA or IND.  However, if a sponsor under some
1245 special circumstances cannot submit the two groups of data sets together, the Group A data sets
1246 should be submitted first.
1247
1248 The FDA has issued a guidance document (1999) to encourage and assist drug applicants in
1249 submitting an electronic archival copy of a new drug applications (NDAs), including
1250 amendments and supplements.  The Agencys effort to encourage applicants to submit
1251 applications electronically is an integrated part of the Agencys Electronic Records; Electronic
1252 Signatures regulation (Electronic Records; Electronic Signatures, Office Federal Register, March
1253 20, 1997).  The above submission of data from carcinogenicity studies to statisticians should be a
1254 part of an electronic NDA.  The information in the formats and specifications, discussed above,
1255 have been incorporated into the Agencys guidance on regulatory submission of electronic
1256 applications (FDA 1999).  Drug sponsors should follow the guidance and recommendations
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1257 included in the nonclinical pharmacology and toxicology section of the guidance in their
1258 preparation and submission of electronic carcinogenicity study data.
1259
1260 Table 14: Example Format for Showing Summary of Deaths and Sacrifices of Male Mice
1261
1262
1263                               Control                       Low                        Medium                       High    
1264     Week       E    D   S   N  NP       E   D   S   N  NP        E   D   S   N  NP        E   D   S   N  NP
1265
1266   34         70   --  --  -- --       70  --  -- --  --       70  --  --  -- --       70 --  --  -- --
1267
1268   35         70  1   1   1  1  70  --  -- --  --  70  --  --  -- --       70 --  --  -- --
1269   36         68  --  --  -- --  70   1  -- --  1  70  --  --  -- --       70 --  --  --  --
1270
1271   39         68  --  --  -- --  69  --  --  --  --  70  --  --  -- --       70 1   --  1  --
1272
1273   41         68  --  --  -- --  69  --  --  -- --  70   1  --  --  1       69  --  --  --  --
1274
1275   43         68  --  --  -- --  69  --  --  -- --  69   1 --  1  --       69  --  --  -- --
1276
1277   49         68  --  --  -- --  69  --  -- --  --  68  --  --  -- --       69    1  --  --  --
1278
1279   52*       68  --  10 10 --  69  --  10 10 --  68  --  10 10 --       68  --  10 10 --
1280
1281   53         58    1  --  1  --  59  --  -- --  --  58  --  --  --  --       58  --  --  --  --
1282
1283   58         57  --  --  -- --  59  --  -- --  --  58   3  --  3  --       58  --  --  --  --
1284
1285   62         57    1  --  1  --  59  --  --  --  --  55  --  --  --  --       58     1  --   1  --
1286
1287   65         56  --  --  --  --  59  --  --  --  --  55  --  --  --  --      57     1  --  1  --
1288
1289   70         56  -- --  --  --  59  --  --  --  --  55   3  --  3  --       56     1  --  1  --
1290
1291   71         56  --  1   1  --  59  1   1  2  --  52   1  --  1  --       55  --  --   --  --
1292
1293 (Continue to the end of the study)
1294
1295   Term*       41     2  39 41 --  40  --  40 40 --  36  --  36 --  --       38     1  37 36  2
1296
1297 Mean
1298 survival      668              680             650             632
1299
1300 Notes: E = Number of animals entering the period;  D = Deaths;  S = Sacrificed moribund;
1301 N = At least one tissue was examined microscopically;  NP = No tissues were examined
1302 microscopically;  * = Scheduled and terminal sacrifices.
1303
1304
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1305 Table 15: Example Format for Showing Summary of Incidences and Results of
1306 Statistical Tests (P-values) of Neoplastic Lesions (in Male Mice)
1307
1308
1309      Organ/Tissue                                                             Control        Low       Medium       High
1310       And Tumor
1311
1312
1313 Number of animals at the beginning                                  50              50             50               50
1314
1315 Liver                                     (40)    (45)    (50)   (43)
1316
1317    Hepatocellular adenoma                      4          5          7     10
1318    (Context of obser. of the tumor)#
1319
1320      Unadjusted P-values##:
1321        Exact test                          P=      P=      P=    P=
1322        Asymptotic test                     P=      P=      P=     P=
1323    Hepatocellular carcinoma                 2        2            5       3
1324    (Context of obser. of the tumor)#
1325
1326      Unadjusted P-values##:
1327        Exact test                          P=      P=      P=     P=
1328        Asymptotic test                     P=      P=      P=     P=       
1329    Hemangioma                               0       0        2       3
1330    (Context of obser. of the tumor)#
1331
1332      Unadjusted P-values##:
1333        Exact test                          P=      P=      P=     P=
1334        Asymptotic test                     P=      P=      P=     P=
1335    Hepatoma                                  0        1        1       2
1336    (Context of obser. of the tumor)#
1337
1338      Unadjusted P-values##:
1339        Exact test                          P=      P=      P=     P=
1340        Asymptotic test                     P=      P=      P=     P=
1341
1342
1343 See the footnotes on next page.
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1344 Table 15 (Continued): Example Format for Showing Summary of Incidences and
1345 Results of Statistical Tests (P-values) of Neoplastic Lesions (in Male Mice)
1346
1347
1348      Organ/Tissue                                                             Control        Low       Medium       High
1349       And Tumor
1350
1351
1352 Lung                                      (45)    (47)    (49)   (45)
1353
1354    Bronchiolar/alveolar adenoma              2        1       4     8
1355    (Context of obser. of the tumor)#
1356
1357      Unadjusted P-values##:
1358        Exact test                          P=      P=      P=     P=
1359        Asymptotic test                     P=      P=      P=     P=
1360
1361    Bronchiolar/alveolar carcinoma           2      2       5      4
1362    (Context of obser. of the tumor)#
1363
1364      Unadjusted P-values##:
1365        Exact test                          P=      P=      P=     P=
1366        Asymptotic test                     P=      P=      P=     P=
1367
1368
1369 (List the numbers of animals with the tissues examined,
1370 overall tumor incidences, and the p-values of trend
1371 tests and pairwise comparisons for all organs/tissues and tumors.)
1372
1373
1374 Notes: Numbers in parentheses are numbers of animals with the tissues examined
1375              microscopically.
1376             The p-values under the control group are from trend tests.
1377             The p-values under each dosed group are from pairwise comparisons between that dosed
1378              group and the control group.
1379             #Contexts of observation of the tumor, if information is available, should be one of the 
1380 four possibilities: fatal, incidental, mortality independent, and mixture of fatal and 
1381 incidental. Use N.A. to indicate that the information is not available.
1382 ##Unadjusted P-values are the p-values unadjusted for effect of multiple tests.
1383  
1384
1385
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1386 Table 16: Example Format for Showing Historical Control Data (in Male Rats)
1387
1388 The historical control data are based on the carcinogenicity studies conducted at XYZ
1389 Laboratory between 1995 and 2000.
1390
1391 Species: Mouse, Sex: Male, Strain: Crl:CD-1 Mice
1392
1393
1394                                                                           Historical Control Incidences
1395         Studies                              Tumor type 1         Tumor type 2       . . .       Tumor type T
1396
1397
1398 Study #1 (1992)                                 1/49                       4/49              . . .               8/50
1399
1400 Study #2 (1992)       1/50          3/50        . . .         4/50
1401
1402    .                    .             .        . . .           .
1403    .                    .             .         . . .           .
1404    .                    .             .         . . .           .
1405
1406 Study #n (1996)       0/50          2/50        . . .         5/50
1407
1408 Total                 2/347         23/417      . . .         34/417
1409
1410 Standard
1411 Deviation             1.0%          3,2%        . . .         4.0%
1412
1413 Range                 0%-2%         0%-10%      . . .         3%-17%
1414
1415
1416
1417
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1418
1419
1420 REFERENCES
1421
1422 Ahn, H., and R.L. Kodell (1995), Estimation and Testing of Tumor Incidence Rates in
1423 Experiments Lacking Cause-of-Death Data, Biometrical Journal, 37, 745-763.
1424
1425 Ahn, H., and R.L. Kodell, and H. Moon (2000), "Attribution of Tumor Lethality and Estimation
1426 of Time to Onset of Occult Tumors in the Absence of Cause-of-Death Information," Applied
1427 Statistics, 49, 157-169.
1428
1429 Ali, M.W. (1990) "Exact Versus Asymptotic Tests of Trend of Tumor Prevalence in
1430 Tumorigenicity Experiments: A Comparison of P-values for Small Frequency of Tumors," Drug
1431 Information Journal, 24, 727-737.
1432
1433 Armitage, P. (1955), Tests for Linear Trends in Proportions and Frequencies,  Biometrics, 11,
1434 375-386.
1435
1436 Armitage, P. (1971), Statistical Methods in Medical Research, John Wiley, New  York.
1437
1438 Bailer, A., and C. Portier (1988), Effects of Treatment-Induced Mortality on Tests for
1439 Carcinogenicity in Small Samples, Biometrics, 44, 417-431.
1440
1441 Bannasch, P., R.A. Griesemer, F. Anders, B. Becker, J.R. Cabral, G.D. Porta, V.J. Feron, D.
1442 Henschler, N. Ito, R. Kroes, P.N. Magee, B. McKnight, U. Mohr, R. Montesano, N.P. Napalkov,
1443 S. Nesnow, A.E. Pegg, G.N. Rao, V.S. Turusov, J. Wahrdrendorf, and J. Wilbourn (1986),
1444 Long-Term Assays for Carcinogenicity in Animals, in Long-Term and Short-Term Assays for
1445 Carcinogens: A Critical Appraisal, Editors, R. Montesano, H. Bartsch, H. Vainio, J. Wilbourn,
1446 and H. Yamasaki, IARC Scientific Publications No. 83, Lyon, France.
1447
1448 Berlin, B., J. Brodsky, and P. Clifford (1979), "Testing Disease Dependence in Survival
1449 Experiments with Serial Sacrifice,"  Journal of American Statistical Association, 74, 5-14.
1450
1451 Bieler, G.S., and R.L. Williams (1993), Ratio Estimates, the Delta Method, and Quantal
1452 Response Tests for Increased Carcinogenicity, Biometrics, 49, 793-801.
1453
1454 Blyth, C.R. (1986), "Approximate Binomial Confidence Limits," Journal of American Statistical
1455 Association, 81,  843-855.
1456
1457 Breslow, N.  (1970), "A Generalized Kruskal-Wallis Test for Comparing K Samples Subject to
1458 Unequal Patterns of Censorship,"   Biometrics, 57, 579-594.
1459
1460 Chen, J.J., K.K. Lin, M.F. Huque, and R.B. Arani (2000), "Weighted P-Value for Animal
1461 Carcinogenicity Trend Test," Biometrics, 56, 586-592.
1462
G:\815dft.doc 38
04/23/01 Draft  Not for Implementation
1463 Chen, J.J., and D.W. Gaylor (1986), "The Upper Percentiles of the Distribution of the Logrank
1464 Statistics for Small Numbers of Tumors," Communications in Statistics - Simulation and
1465 Computation, 15, 991-1002.
1466
1467 Chu, K.C., C. Cueto, and J.M. Ward (1981), "Factors in the Evaluation of 200 National Cancer
1468 Institute Carcinogen Bioassays," Journal of Toxicology and Environmental Health, 8, 251-280.
1469
1470 Cochran, W. (1954), Some Methods for Strengthening the Common c 2 Tests, Biometrics, 10,
1471 417-451.
1472
1473 Cox, D.R.  (1959), "The Analysis of Exponentially Distributed Life-times with Two Types of
1474 Failures," Journal of Royal Statistical Society, Series B, 21, 4121-421.
1475
1476 Cox, D.R.  (1972), "Regression Models and Life Tables (with discussion)," Journal of Royal
1477 Statistical Society, Series B, 34, 187-220.
1478
1479 Dayan, A.D. (1988), Biological Assumptions in Analysis of the Bioassay, in Carcinogenicity,
1480 The Design, Analysis and Interpretation of Long-Term Animal Studies, an International Life
1481 Sciences Institute (ILSI) monograph, edited by H,C. Grice and J.L. Ciminera, Springer-Verlag,
1482 New York.
1483
1484 Dempster, A.P., M.R. Selwyn, and B.J. Weeks (1983), Combining Historical and Randomized
1485 Controls for Assessing Trends in Proportions, Journal of the American Statistical Association,
1486 78, 221-227.
1487
1488 Dewanji, Anup and J.D. Kalbfleisch (1986), "Nonparametric Methods for Survival/Sacrifice
1489 Experiments," Biometrics, 42, 325-341.
1490
1491 Dinse. G.E. (1988), "Estimating Tumor Incidence Rates in Animal Carcinogenicity
1492 Experiments," Biometrics, 44, 405-415.
1493
1494 Dinse, G.E. (1991), "Constant Risk Differences in the Analysis of Animal Tumorigenicity Data,"
1495 Biometrics, 47, 681-700.
1496
1497 Dinse, G.E.  (1994), "A Comparison of Tumor Incidence Analyses Applicable in Single-
1498 Sacrifice Animal Experiments," Statistics in Medicine, 13, 689-708.
1499
1500 Dinse, G.E., and J.K. Haseman (1986), "Logistic Regression Analysis of Incidental-Tumor Data
1501 from Animal Carcinogenicity Experiments," Fundamental and Applied Toxicology, 6, 751-770.
1502
1503 Dinse, G.E., and S.W. Lagokos (1983), "Regression Analysis of Tumor Prevalence Data," The
1504 Journal of the Royal Statistical Society, Series C, 32, 236-248.
1505
1506 Fairweather, W.R., A. Bhattacharyya, P.P. Ceuppens, G. Heimann, L.A. Hothorn, R.L. Kodell,
1507 K.K. Lin, H. Mager, B.J. Middleton, W. Slob, K.A. Soper, N. Stallard, J. Ventre, and J. Wright
G:\815dft.doc 39
04/23/01 Draft  Not for Implementation
1508 (1998), Biostatistical Methodology in Carcinogenicity Studies, Drug Information Journal, 32,
1509 401-421.
1510
1511 Food and Drug Administration (FDA), (1987), Guideline for the Format and Content of the
1512 Nonclinical/Pharmacology/Toxicology Section of An Application.
1513
1514 FDA (1997), Formats and Specifications for Submission of Animal Carcinogenicity Study Data,
1515 Divisions of Biometrics I, II, III, and IV, Center for Drug Evaluation and Research. Rockville,
1516 Maryland; March 12, 1997.
1517
1518 FDA (1999), Guidance for Industry, Providing Regulatory Submissions in Electronic Formats ---
1519 NDAs, Center for Drug Evaluation and Research.
1520
1521 Gart, J.J., D. Krewski, P.N. Lee, R.E. Tarone, and J. Wahrendorf (1986), Statistical Methods in
1522 Cancer Research, Volume III - The Design and Analysis of Long-Term Animal Experiments,
1523 International Agency for Research on Cancer, World Health Organization.
1524
1525 Gehan, E.A. (1965), "A Generalized Wilcoxon Test for Comparing K Samples Subject to
1526 Unequal Patterns of Censorship," Biometrika, 52, 203-223.
1527
1528 Goldberg, K.M. (1985), "An Algorithm for Computing An Exact Trend Test for Multiple 2 x K
1529 Contingency Tables," a paper presented at Symposium On Long-Term Animal Carcinogenicity
1530 Studies.
1531
1532 Haseman, J.K.  (1983), "A Reexamination of False-Positive Rates for Carcinogenesis Studies,"
1533 Fundamental and Applied Toxicology, 3, 334-339.
1534
1535 Haseman, J.K. (1984a), "Statistical Issues in the Design, Analysis and Interpretation of Animal
1536 Carcinogenicity Studies," Environmental Health Perspective, 58, 385-392.
1537
1538 Haseman, J.K.  (1984b), Use of Historical Control Data in Carcinogenicity Studies in Rodents,
1539 Toxicologic Pathology, 12, 126-135.
1540
1541 Haseman, J.K. (1985), "Issues in Carcinogenicity Testing: Dose Selection," Fundamental and
1542 Applied Toxicology, 5, 66-78.
1543
1544 Haseman, J.K. (1991), a personal communication to Robert Temple, M.D., CDER, FDA.
1545
1546 Haseman, J.K., J. Huff, and G.A. Boorman (1984), "Use of Historical Control Data in
1547 Carcinogenicity Studies in Rodents," Toxicologic Pathology, 12, 126-135.
1548
1549 Haseman, J.K., J.S. Winbush, and M.W. ODonnell (1986), Use of Dual Control Groups to
1550 Estimate False Positive Rates in Laboratory Animal Carcinogenicity Studies, Fundamental and
1551 Applied Toxicology, 7, 573-584.
1552
G:\815dft.doc 40
04/23/01 Draft  Not for Implementation
1553 Haseman, J.K., G. Hajian, K.S. Crump, M.R. Selwyn, and K.E. Peace (1990),  Dual Control
1554 Groups in Rodent Carcinogenicity Studies, in   Statistical Issues in Drug Research and
1555 Development,  K. E. Peace, Editor, Marcel Dekker, New York.
1556
1557 Haseman, J.K. (1999), personal communication to the author.
1558
1559 Hoel, D.G. (1983), Conditional Two Sample Tests with Historical Controls, (cid:31) in  Contributions
1560 to Statistics, P.K. Sen, Editor, North-Holland Publishing Company.
1561
1562 Hoel, D.G., and T. Yanagawa (1986), Incorporating Historical Controls in Testing for a Trend
1563 in Proportions, Journal of the American Statistical Association, 81, 1095-1099.
1564
1565 Hoel, D., and H. Walburg (1972), Statistical Analysis of Survival Experiments, Journal of the
1566 National Cancer Institute, 49, 361-372.
1567
1568 Iatropoulos, M.J. (1988), Society of Toxicologic Pathologists Position Paper: Blinded
1569 Microscopic Examination of Tissues from Toxicologic or Oncogenic Studies, in
1570 Carcinogenicity, The Design, Analysis, and Interpretation of Tong-Term Animal  Studies, edited
1571 by H.C. Grice and J.L. Ciminera, ILSI Monographs, Spring-Verlag, New York.
1572
1573 ICH (1995), S1C Dose Selection for Carcinogenicity Studies of Pharmaceuticals, ICH - S1C.
1574
1575 ICH (1998), S1B Testing for Carcinogenicity of Pharmaceuticals, ICH - S1B, Federal Register,
1576 vol. 63, 8983-8986, 1998.
1577
1578 Ibrahim, J.G., and L.M. Ryan (1996), "Use of Historical Controls in Time-Adjusted Trend Tests
1579 for Carcinogenicity," Biometrics, 52, 1478-1485.
1580
1581 Jovanovic, B.D. and M.A.G. Viana (1996), Upper Confidence Bounds for Binomial Probability
1582 in Safety Evaluation, American Statistical Association 1996 Proceedings of the
1583 Biopharmaceutical Section, 140-144.
1584
1585 Jovanovic, B.D. and P.S. Levy (1997), "A Look at the Rule of Three," The American
1586 Statistician, 51, No.2, 137-139.
1587
1588 Kodell, R.L., and H. Ahn (1996), "Nonparametric Trend Test for the Cumulative Tumor
1589 Incidence Rates," Communications in Statistics - Theory and Methods, 25, 1677- 1692.
1590
1591 Kodell, R.L., and H. Ahn (1997), "An Age-Adjusted Trend Test for the Tumor Incidence Rate,"
1592 Biometrics, 53, 1467-1474.
1593
1594 Kodell, R.L., B.A. Pearce, A. Turturro, and H. Ahn (1997), "An Age-Adjusted Trend Test for the
1595 Tumor Incidence Rate for Single-Sacrifice Experiments," Drug Information Journal, 31, 471-
1596 487.
1597
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1598 Kodell, R.L., K.K. Lin, B.T. Thorn, and J.J. Chen (2000), Bioassays of Shortened Duration for
1599 Drugs: Statistical Implications, Toxicological Sciences, 55, 415-432.
1600
1601 Lin, K.K. (1988), "Peto Prevalence Method Versus Regression Methods in Analyzing Incidental
1602 Tumor Data from Animal Carcinogenicity Experiments: An Empirical Study," in the 1988
1603 American Statistical Association Annual Meeting Proceedings (Biopharmaceutical Section),
1604 New Orleans, Louisiana.
1605
1606 Lin, K.K. (1995), A Regulatory Perspective on Statistical Methods for Analyzing New  Drug
1607 Carcinogenicity Study Data, Bio/Pharam Quarterly, Vol. 1, Issue 2, 18-20.
1608
1609 Lin, K.K. (1997), Control of Overall False Positive Rates in Animal Carcinogenicity Studies of
1610 Pharmaceuticals, presented at 1997 FDA Forum on Regulatory Sciences, December 8-9, 1997,
1611 Bethesda, Maryland.
1612
1613 Lin, K.K. (2000), Carcinogenicity Studies of Pharmaceuticals, in Encyclopedia of
1614 Biopharmaceutical Statistics, edited by S.C. Chow, Marcel Dekker, New York, 88-103.
1615
1616 Lin, K.K., and M.W. Ali (1994), "Statistical Review and Evaluation of Animal Tumorigenicity
1617 Studies," in Statistics in the Pharmaceutical Industry, Second Edition, Revised and Expanded,
1618 edited by C.R. Buncher and J.Y.  Tsay, Marcel Dekker, Inc., New York.
1619
1620 Lin, K. K. and M. A. Rahman (1998a), Overall False Positive Rates in Tests for Linear Trend in
1621 Tumor Incidence in Animal Carcinogenicity Studies of New Drugs, Journal of Pharmaceutical
1622 Statistics, with discussions, 8(1), 1-22.
1623
1624 Lin, K. K. and M. A. Rahman (1998b), False Positive Rates in Tests for Trend and Differences
1625 in Tumor incidence in Animal Carcinogenicity Studies of Pharmaceuticals under ICH Guidance
1626 S1B, unpublished report, Division of Biometrics 2, Center for Drug Evaluation and Research,
1627 Food and Drug Administration.
1628
1629 Lin, K.K. (1998), CDER/FDA Formats for Submission of Animal Carcinogenicity  Study
1630 Data, Drug Information Journal, 32, 43-52.
1631
1632 Lindsey, J., and L. Ryan (1993), "A Three-State Multiplicative Model for Rodent
1633 Tumorigenicity Experiments,"  Journal of Royal Statistical Society, Series C, 42, 283-300.
1634
1635 Lindsey, J., and L. Ryan (1994), "A Comparison of Continuous- and Discrete-Time Three-State
1636 Models for Rodent Tumorigenicity Experiments," Environmental Health Perspectives, 102
1637 (Suppl. 1), 9-17.
1638
1639 Louis, T.A. (1981), "Confidence Intervals for a Binomial Parameter After Observing No
1640 Success," The American Statistician, 35, No. 3, 154-154.
1641
1642 Malani,  H.M., and J. Van Ryzin (1988), "Comparison of Two Treatments in Animal
1643 Carcinogenicity Experiments,"  Journal of American Statistical Association, 83, 1171-1177.
G:\815dft.doc 42
04/23/01 Draft  Not for Implementation
1644
1645 Mantel, N., and W. Haenszel (1959), "Statistical Aspects of the Analysis of  Data from
1646 Retrospective Studies of Disease,"  Journal of National Cancer Research, 22, 719-748.
1647
1648 Malani,  H.M., and Y. Lu (1993), "Animal Carcinogenicity Experiments with and without Series
1649 Sacrifices," Communications in Statistics - Theory and Methods,  22, 1557-1584.
1650
1651 McKnight, B., and J. Crowley (1984), "Tests for Differences in Tumor Incidence Based on
1652 Animal Carcinogenesis Experiments," Journal of American Statistical Association, 79, 639-648.
1653
1654 Moon, H., H. Ahn, and R.L. Kodell (2000), "Testing Incidence of Occult Tumors by Attributing
1655 Tumor Lethality in the Absence of Cause-of-Death Information," submitted to Biometrics.
1656
1657 OFR (Office of the Federal Register), (1985), "Chemical Carcinogens; A Review of the Science
1658 and Its Associated Principles," in Part II, Office of Science and Technology Policy, Federal
1659 Register, March 14, 1985, 47-58.
1660
1661 OFR, (1995), Dose Selection for Carcinogenicity Studies of Pharmaceuticals, in Part III,
1662 Department of Health and Human Services, Food and Drug Administration, Federal Register,
1663 March 1, 1995, Vol. 60, No. 40, 11278-11281.
1664
1665 OFR, (1997), Electronic Records; Electronic Signatures, Federal Register, March 20, 1997.
1666
1667 Peto, R., M.C. Pike, N.E. Day, R.G. Gray, P.N. Lee, S. Parish, J. Peto, S. Richards, and J.
1668 Wahrendorf (1980), "Guidelines for Simple, Sensitive Significance Tests for Carcinogenic
1669 Effects in Long-term Animal Experiments,"  in Long-term and Short-term Screening Assays for
1670 Carcinogens: An Critical Appraisal, World Health Organization.
1671
1672 Portier, C.J., and G.E. Dinse (1987), "Semiparametric Analysis of Tumor Incidence Rates in
1673 Survival/Sacrifice Experiments," Biometrics, 43, 107-114.
1674
1675 Prasse, K. (1986), Letter to the Editor (on blinded microscopic evaluation of slides from
1676 toxicity and carcinogenicity studies), Toxicology and Applied Pharmacology, 83, 184-185.
1677
1678 Prentice, R.L., R.T. Smythe, D.Krewski, and M.Mason (1992), "On the Use of Historical Control
1679 Data to Estimate Dose Response Trends in Quantal Bioassay," Biometrics, 48, 459-478.
1680
1681 Society for Toxicology (1982), Animal Data in Harzard Evaluation: Paths and Pitfalls,
1682 Fundamental and Applied Toxicology, 2,101-107.
1683
1684 Sontag, J.A., N.P. Page, and U. Saffiotti (1976), Guidelines for Carcinogen Bioassay in Small
1685 Rodents, Carcinogenesis Technical Report, DHEW Publication (NIH), 76-801.
1686
1687 Tamura, R.N, and S.S. Young (1986),  The Incorporation of Historical Information in Tests of
1688 Proportions: Simulation Study of Tarones Procedure, Biometrics, 42, 343-349.
1689
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1690 Tamura, R.N, and S.S. Young (1987), A Stabilized Moment Estimator for the Beta-Binomial
1691 Distribution, Biometrics, 43, 813-824.
1692
1693 Tarone, R.E.  (1975), "Tests for Trend in Life Table Analysis,"   Biometrika, 62, 679-682.
1694
1695 Tarone, R.E.  (1982), The Use of Historical Control Information in Testing for a Trend in
1696 Proportions. Biometrics, 38, 215-220.
1697
1698 Temple, R.T., W.R. Fairweather, V.C. Glocklin, and R.T. O'Neill (1988) The Case for
1699 Blinded Slide Reading, Comments on Toxicology, 2:99-109.
1700
1701 Thomas, D.G., N. Breslow, and J.J. Gart (1977), "Trend and Homogeneity Analyses of
1702 Proportions and Life Table Data," Computer and Biomedical Research, 10, 373-381.
1703
1704 U.S. Interagency Staff Group on Carcinogens (1986), "Chemical Carcinogens; A Review of the
1705 Science and Its Associated Principles," Environmental  Health Perspectives, 67, 201-282.
1706
1707 Vollset, S.E. (1993), "Confidence Intervals for Binomial Proportion," Statistics in Medicine, 12,
1708 809-824.
1709
1710 Williams, P.L., and C.J. Portier (1992), "Analytic Expressions for Maximum Likelihood
1711 Estimation in a Nonparametric Model of Tumor Incidence and Death," Communications in
1712 Statistics - Theory and Methods, 21, 711-732.
1713
1714 Woodruff, R.S. (1971), A Simple Method for Approximating the Variance of a Complicated
1715 Estimate, Journal of the American Statistical Association, 66, 411-414.
1716
1717
1718
1719
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