THE EFFECTS OF TREATMENT LETHALITY AND TUMOR LETHALITY
ON TESTS OF CARCINOGENICITY
by
Albert John Bailer
Department of Biostatistics
University of North Carolina at Chapel Hill
Institute of Statistics Mimeo Series No. 1815T
December 1986
THE EFFECTS OF TREATMENT LETHALITY AND TUMOR LETHALITY
ON TESTS OF CARCINOGENICITY
by
Albert John Bailer
A Dissertation subuUtted to the faculty of The University
of North Carolina at Chapel Hill in partial fulfillment
of the requi rements for the degree of Doctor of Philosophy
in the Department of Biostatistics.
Chapel Hill
December, 1986
Reader
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..
.
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ABSTRACT
A. JOHN BAILER. The Effects of Treatment Lethality and Tumor
Lethality on Tests of Carcinogenicity (under the direction of
CHRISroPHER J. PORTIER).
ABS'mACT: A simple stochastic model is used to describe the
lifetime experience of an animal exposed to some potentially
tumorigenic compound.
The transitions between states in this model
are governed by hazard functions that correspond to the hazard of
tumor onset, the hazard of tumor-free death, and the hazard of death
for tumor-bearing animals.
Commonly used statistical tests of
carcinogenicity are examined relative to this model under varying
degrees of treatment lethality and tumor lethality.
Treatment
lethality corresponds to the situation when the hazard of tumor-free
death increases as the treatment dose increases, and tumor lethality
corresponds to the situation when the hazard of tumor-bearing death
exceeds the hazard of tumor-free death.
using large sample theory, the squared relative efficacy of the
commonly used statistical tests of carcinogenicity relative to a
theoretical standard were computed for a variety of treatment
lethality-tumor lethality conditions.
The carcinogenicity tests are
shown to have varying degrees of robustness to the effects of
lethality.
The lifetable test and the
Cochran-Armi~age
linear trend
test are seen to be highly sensitive to increases in treatment
lethality. Increases in tumor lethality and treatment lethality
affect the performance of commonly used prevalence tests such as the
logistic regression score test.
using a Monte Carlo simulation of data that might arise from
this stochastic model, the operating characteristics of these tests
were derived for a series of treatment lethality-tumor lethality
conditions.
results.
The small sample results mirrored the large sample
In addition to the commonly used carcinogenicity tests,
two simple, survival-adjusted, quantal response tests were
considered.
be
The operating characteristics of these tests seemed to
more robust to the effects of treatment lethality and tumor
lethality than the operating characteristics of the other procedures
considered.
I ..
'.-
'
. .:
TABLE OF CON'l'EN'l'S
Acknowlegements
• • • •
• • • • • •
List of Tables
• • • • • • • • • •
List of Figures •
iii
iv
• • • • •
v
1. Introduction • • • • • • • • • • • •
1.1 Risk Assessment.
1
• •••
1
...
1.2 Animal Tumorigenicity Studies.
1. 3 Hypothesis Testing
• • • • • •
3
1.3.1 Incidence versus Prevalence •
4
1.3.2 Onset Lifetable Test
5
••••••
1.3.3 Quantal Response Tests
••••
5
1.3.3.1 Cochran-Armdtage Trend Test
5
1.3.3.2 Survival-Adjusted Quantal Response Tests •
6
1.3.4 Survival-Adjusted tests • • • • • • • • • • •
9
1.3.4.1 prevalence Tests •
9
1.3.4.2 Lifetable Test ••
10
1.4 Statement of the Problem and outline
10
2. Test Statistics and a Simple stochastic Model
2.1 Elaboration of Test Statistics
2.1.1 Incidence Test
••••
12
••••••••••••
12
•••••••••••••••••
13
2.1.2 Quanta1 Response Tests
• • • •
2.1.3 Survival-Adjusted Tests •
..
2
2.1.3.1 LifetableTest
2.1.3.2 Prevalence Tests
••••
• •••
14
15
15
15
ii
·...............
2.2 Stochastic Model
2.2.1 Choice of the form of the Hazard Functions
2.2.2 Hypotheses in terms of the Stochastic Model •
3. Asymptotic Results •
...
3.1 Introduction •
...
3.2 Conditions Considered
3.3 Efficacy for the Generic Test Statistic
3.3.1 The Expected Value of T
G
3.3.2 The Variance of TG ••••
3.4 Multinomial Cell Probabilities •
3.5 Squared Relative Efficacies
••
3.5.1 Comments on calculating efficacies ••
3.5. 2
S.~)i'esul
ts .
4. Small Sample Results ~:
·..
· ...... .
"1'"
4.1 Simulation·OonditfOtls.
4.2
Simulation~Results •••
4.2.1 Type I Error Rates
4.2.2 Power Results
5. Discussion •
References
...
Appendices ••
Appendix A: Complete SRE results • •
Appendix B: Complete NTP Simulation Results
Appendix C: Complete NeI Simulation Results
Appendix D: poly-k Simulation Results
• • • •
iii
ACI<NCMLEDGEMENTS
Many individuals have helped me in the course of doing this
research.
First and foremost among these individuals would be my
adviser, Chris Portier.
I consider myself lucky to have worked with
such a fine and insightful statistician.
For his contributions and
encouragement, I will always be grateful.
I can never truly express my gratitude to Larry Kupper for
convincing me to switch programs in order to study Biostatistics. I
have enjoyed interacting with him in his role as my academic adviser
and as a committee member on my dissertation.
In addition, I would
like to thank the other members of my dissertaUoIl ,~orgndttee, Harvey
Checkoway, Ed Davis, and Keith Muller,_for
the~~be.~pful
conments.
I would never have finished this pro;eet witbgut the love and
support of my wife Jennifer.
Her patience and uplifting
encouragement kept me going when the dissertation had me down.
Thank God I am done.
iv
LIST OF TABLES
2.1 Tumor onset Parameters and Associated Lifetime probabilities
of Tumor onset
. . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Tumor-free death parameters and Associated Lifetime probability
of Tumor-free death • • • •
• • • 21
3.1 squared Relative Efficacies for Commonly Used Tests of
Carcinogenicity • • • • • •
4.1
Type
. 47
I Error of Carcinogenicity Tests for varying levels of
Treatment Lethality and Tumor Lethality using a nominal 0.05
test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Power of Carcinogenicity Tests for varying levels of Treatment
Lethality and Tumor Lethality when the Treatment Induces a Tw0-
.•
fold Tumorigenic Effect in the High Dose Group • • • • • ••
54
4.3 Power of Carcinogenicity Tests for varying levels of Treatment
Lethality and Tumor Lethality when the Treatment Induces a Fivefold Tumorigenic Effect in the High Dose Group • • • • • ••
55
4.4 Power of Carcinogenicity Tests for varying levels of Treatment
Lethality and Tumor Lethality when the Treatment Induces a Tenfold Tumorigenic Effect in the High Dose Group • • • • • • • 56
4.5
Type
I Error of the poly-3 test at the 5% nominal level for
varying shapes and background rates under moderate treatment
lethality . . . . . . . . . . . . . . . . . . . .
59
v
LIST OF FIGURES
1:
Three-State stochastic Model for Carcinogenicity Experiments
when Cause-of-death is unobtainable • • • • • • • • • • • • • 18
2:
Survival Probabilities of Tumor-bearing versus Tumor-free Male
Mice when Tumor Presence leads to a 10-fold increase in lifetime
risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3:
Empirical Distribution of the Onset test statistic under varying
levels of Treatment Lethality and Tumor Lethality for Male Mice
Liver Tumors
4:
. . • • . . . • . . . • . . . • • . . . • . • . 61
Empirical Distribution of the Cochran-Armitage Trend test
statistic under varying levels of Treatment Lethality and Tumor
Lethality for Male Mice Liver Tumors
5:
• • • • • • • • • • • • 62
Empirical Distribution of the Truncated Trend test statistic
under varying levels of Treatment Lethality and Tumor Lethality
for Male Mice Liver Tumors
6:
• • • • • • • • • • • • • • • • • 63
Empirical Distribution of the Poly-3 Trend test statistic under
varying levels of Treatment Lethality and Tumor Lethality for
Male Mice Liver Tumors
7:
• • • • • • • • • • • • • • • • 64
Empirical Distribution of the Logistic Score test statistic
under varying levels of Treatment Lethality and Tumor Lethality
for Male Mice Liver Tumors
8:
• • • • • • • • • • • • • • • • • 65
Empirical Distribution of the Hoel-walburg test statistic under
varying levels of Treatment Lethality and Tumor Lethality for
Male Mice Liver Tumors
• • • • • • • • • • • • • • • • • • • 66
vi
9:
Empirical Distribution of the Lifetable test statistic under
varying levels of Treatment Lethality and Tumor Lethality for
Male Mice Liver Tumors
• • • • • • • • • • • • • • • • • • • 67
Chapter 1:
Introduction
Section 1.1: Risk Assessment
Exposure to a variety of man-made compounds is common in
eve~y
life.
New chemicals are being introduced into industrial
processes and into the food industry at a rapid pace. Assessing
the potential risk of these compounds is an important problem that
engages toxicologists, epidemiologists and statisticians (Van
Ryzin,1980). While epidemiologists deal with risk assessment using
observational methods on humans, toxicologists tend to focus on
controlled experimentation on rodents.
The goals of these
controlled experiments can be expressed in terms of the statistical
•
"
concepts of estimation and hypothesis testing.
The estimation
aspect of risk assessment is concerned with the exploration of the
properties of various risk measures.
The basic measure of interest
in risk assessment can be defined in a variety of ways.
The measure
in greatest use for risk assessment is the virtually safe dose or
VSD.
The VSD is the dose level which corresponds to the dose at
which a specified increase in risk above background is attained.
This specified increase represents an arbitrarily selected small
level. Another measure of interest is the administered dose at which
50 percent of the exposed animals die from a tumor.
called the
'l'D
SO
This measure is
of a particular compound. A 'l'D SO is analogous to a
cause-specific LOSO where a LO SO is the adminstered dose at which 50
2
percent of the exposed animals die from any cause.
third measure
A
of interest is the highest dose at which no effect (e.g.
tumorigenesis) is observed.
This measure is known as the No
Observed Effect Level or NOEL.
A small 'I'DSO or NOEL implies that
the compound under study has some health effect and should be
scrutinized in greater detail for possible regulation.
The
estimation of these quantities and the distributional properties of
the estimates of these measures is of interest to many government
agencies such as the Food and Drug Administration (Cornfield, 1977;
Mantel & ScheidenDan,197S) and the National Institutes of Health
(Carter,1979).
The hypothesis testing aspect of this research
addresses the significance of dose-response relationships that may
exist between administered doses of a compound under study and an
outcome of interest (-e'.g. tumorigenesis, teratogenesis, or death).
This paper is devoted to a: study of the hypothesis testing aspects
of animal tumorigenicity studies; hence, the remainder of the
introduction will focus on this problem.
1.2 Animal Tumorigenicity Studies
Fairweather(1985) described the basic study paradigm for
assessing
tumorigenicity as the "lifetilNH!xposure rodent study."
The basic study design involves randomly assigning rodents to K+1
groups, where animals in the
i th group receive the i th dose level
( zi) of the compound under study, and the dose levels are arranged
in ascending order with respect to exposure where the lowest dose
level corresponds to a control group (i-O,l, ••• ,K).
observed until death or terminal sacrifice.
The rodents are
The basic data recorded
3
for each animal are group membership, time to death, and an
indicator of tumor presence.
Many statistical issues are involved
in the design of these studies including sample size, number of dose
groups, allocation of sample to dose groups, and other concerns
(Portier and Hoel, 1984; Ciminera, 1985) • A design conunonly used by
the National Toxicology Program allocates SO animals to each of four
dose groups including a control group.
The rodents are followed for
two years, at which time the surviving animals are sacrificed and
the study is terminated.
1.3 Hypothesis Testing
The null hypothesis in this type of experiment is that there is
no difference in tumor incidence among the K+l dose groups.
Tumor
onset is an unmeasurable event in the case:-.of,ocC\1l1k.(not palpable)
tumors, and this presents difficulties for many,of.;1;he hypothesis
tests proposed for this type of experiment...
••
The te.rm "tumor onset"
is used to mean the presence of the first hi5tOpathologically
detectable tumor of the type being studied.
testing will not be addressed.
Multiple tumor site
The lethality of the tumor and
toxicity of the adDdnistered dose (also known as treatment lethality
or dose-related mortality) are two factors which affect the validity
of proposed hypothesis tests.
These concepts will be discussed
relative to each of the hypothesis tests described below.
one may
test whether an agent is potentially harmful or potentially
beneficial.
•
For the purposes of this paper, attention will be
focused on the alternative of identifying potentially harmful
compounds.
4
1.3.1 Incidence versus Prevalence
Incidence and prevalence are important measures of the presence
of a disease in a POPUlation.
Incidence is a measure of the onset
of new cases over a period of time, and prevalence is a measure of
the number of cases that are present in the population at a given
time.
Thus, incidence is a measure of the rate of change of
disease status over an interval of time and,
proportion measure of disease status.
prevalence is a
For tumorigenicity
experiments, the "disease" of interest. is tumor presence in a
particular tissue.
These experiments are designed to assess whether
a particular compound leads to an increased risk of tumor onset.
Tumor onset is a rate measure.
inference about incid.ence.
Hence, one is interested in
In terms of survival methods, the
instantaneous rate of tumor onset would be described by a hazard
function which implies that the incidence over an interval of time
is essentially the cumulative hazard over that interval.
The
•
•
prevalence at a particular time is the proportion of animals alive
at time t that have the tumor.
As previously mentioned, tumor onset
is an unobservable event in the case of occult tumors.
This fact
has motivated a host of tests based on various assumptions related
to the lethality of the tumor and the treatment lethality of the
compound under study.
If one assumes that tumors are instantly
lethal, then the time of an observed death with tumor present is the
time of tumor onset; therefore, a test of tumor onset can be
constructed.
If tumors are incidental, then animals that die in a
particular interval represent a random sample of the animals alive
at the start of that interval since death represents a random
•
5
sampling mechanism with respect to tumor presence; therefore, an
estimate of tumor prevalence is applicable.
If there is no tumor
lethality and treatment lethality is present or there is no
treatment lethality but tumor lethality is present, then a test of
prevalence will be a valid test of incidence since the prevalence
function at time t will be a function of the hazard of tumor onset
and some constant factor that is the same for all dose groups
(Lagakos,1982).
This will be illustrated in Chapter 2.
1.3.2 onset Lifetable test
If it were possible to observe tumor onset, then an onset
lifetable test would be appropriate.
This test is the same as a
standard lifetable test except that the strata are formed for each
tumor onset time instead of for each death tinHi'~·· This test is a
hypothetical standard since the event of tumor onset is
.
."
unobservable.
However, the onset times are knoWn'in simulation
studies; therefore, this test will provide a useful benchmark.
1.3.3 Quantal Response Tests
The remaining tests can be divided into two broad categories:
binomial based tests which only use the quantal response and tests
which correct for treatment induced survival differences.
1.3.1.1 Cochran-Armdtage Trend Test
Define the probability of tumor onset in an animal in dose group
j before the time of terminal sacrifice as R .
j
A test of
HO:RO••••• ~ versus H1 : there is a linear trend in proportions
6
relative to increasing dose levels was proposed by Armdtage (1955).
This test is a test of linear trend in proportions for a set of
treated groups and will be denoted the Cochran-Armdtage trend test.
This test can be expressed as a test of the hypothesis HO: a-O
versus Hl : ~>O where it is assumed that ~i • «+ ~zi where zi is the
dose administered to animals in the i th group (Chapman and Nam,
1968).
In the Cochran-Armdtage trend test, one compares the
observed proportions of tumor occurences in the study groups; hence
this test measures tumor incidence over the study period and would
not be affected by the lethality of a tumor.
The trend test assumes
that all animals are at equal risk of tumor development.
this test could be grossly affected by treatment lethality.
However,
If the
higher doses were acutely toxic, many animals might not survive long
enough to develop the tumor.
If this occurs, the Cochran-Armdtage
trend test would become very conservative and would have decreased
power for detecting group differences.
Mortality effects on the
.,.
trend test have led some investigators to examine survival
adjustments to the trend test.
1.3.3.2 Survival-Adjusted Quantal Response Tests
Two
testing procedures which adjust for treatment related acute
toxici ty will be described below.
Both adjustment procedures are
based on altering the number of animals at risk of tumor onset.
Recall that the Cochran-Armdtage trend test assumes that all animals
in each dose group are considered to be at equal risk of tumor
onset.
The reason that one may wish to adjust the trend test is
easily illustrated by considering the following case.
Suppose a
..
7
particular compound leads to an increased risk of tumor incidence
and is acutely toxic.
Then it is unlikely that animals in the high
dose group would survive long enough for tumor onset to occur,
whereas in the controls or the low dose groups a few tumors may
occur.
In this situation, the trend test Would not reject a truly
significant result because of acute toxicity.
Thus, if one can
adjust the estimate of tumor incidence in the high dose groups when
a toxic effect is observed, then a valid test of tumor incidence can
be constructed.
The first ad hoc adjustment procedure considers at
risk only those animals that die after the first tumor is observed
in any group.
The idea of adjusting the number at risk when
estimating and testing tumor incidence was suggested by Peto (1974)
and Gart, Chu, and Tarone(1979).
the truncated trend test.
This procedure will be denoted as
A second adjustment procedure operates in
Let t ij represent the surviv~l time of the jth
animal in the i th group. Then the numbe~ at ri~k in group i is
a similar fashion.
defined to be the number of animals that develop tumors in group i
plus I(t ij/tmax )3 where the sum is taken over all non-tumor bearing
animals and t max is the maximum survival time over all groups and
animals within groups.
The maximum survival time is the time until
the death of the animal that lived the longest in any group.
The
term (t ij /t
)3 will be small for t ij much less than t
hence
max
max
animals that do not live long will not contribute greatly to the
number at risk.
..
If treatment lethality is high, this adjustment
will make the number of animals at risk in high dose groups low
which inflates the tumor incidence estimate in this adjusted trend
test relative to the Cochran-Armitage trend test.
This test will be
8
denoted the Poly-3 trend test which reflects the weighting of the
contribution to the number at risk since the (tij/tmax ) ter.m is
raised to the third power. An example is provided below which
illustrates a hypothetical situation where the Cochran-Ar.mitage
trend test does not detect a trend because of treatment lethality
while the adjusted procedures detect a trend.
Consider an
experiment with 10 animals in each of 3 dose groups.
Suppose the
following data were observed:
dose group
z1
dead with tumor
survival times of
non-tumor bearers
4
50,55,60
65,70,75
30,35,40
45,50,55
15,20,25
30,35,40
Suppose the time of the first death with tumor present, tfirst'
occurs at 50
we~ks.
The number considered at risk by the three
trend tests and the value of their respective test statistics are
presented in the table below.
test
Number at risk in dose group
Zo
z1
z2
Trend
Truncated Trend
poly-3
10
10
7.67
10 .
6*
5.22**
10
4
4.38
Test
Statistic***
0.00
2.10
1.47
* 6 • (number of animals that died in group z1 wi th the tumor
present) + (the number of non-tumor bearing animals in
group zl that died after tfirst)
** 5.22 • (number of animals that died in group zl wi th the tumor
present) + (30/75)3 + (35/75)3 + (40/75)3 + (45/75)3 +
(50/75)3 + (55/75)3
*** The calculation of these test statistics is discussed in
Chapter 2.
9
Thus, it is readily apparent that adjusting for treatment lethality
is
important in the trend test.
1.3.4 Survival-Adjusted Tests
1.3.4.1 Prevalence Tests
Two
tests are described for testing the null hypothesis of equal
prevalence in all dose groups.
Prevalence tests will test a
hypothesis of equal tumor incidence in all dose groups when it may
be assumed that the tumors are incidental or that there is no
treatment lethality if the tumors have some degree of lethality.
This implies that any deaths before terminal sacrifice represent
uninformative censoring of observations where the censoring is
uninformative in the sense that animals in every group have the
same risk of being censored.
The first test is based upon combining
prevalence information across strata that have been formed by
stratifying survival times.
For the animals that die in each
stratum, one compares the proportion of animals in each dose group
that are found to possess the tumor.
These
strat~specific
results
are then combined over all stratum to form an overall test of tumor
prevalence.
This procedure was suggested by Hoel and walburg(1972)
and makes use of ideas proposed by Mantel and Haenszel(1959).
Let Yij -l if the jth animal in the i th group is found to possess the
tumor upon death at time t ij and let Yij-O if not. The second test
•
is a logistic regression test which models the probability of tumor
prevalence as a continuous function of dose and survival time1 i.e.
10
The model parameters (a,aO,a1 ) are estimated using Maximum
Likelihood methods and the test of no survival-adjusted differences
in tumor prevalence among groups is a test of HO:
score test or a likelihood ratio test.
~O
based on a
This testing procedure is
advocated by Dinse & Lagakos(1983) and Dinse(1985).
These
testing procedures are sUpPOsedly not affected by treatment
lethality since survival times are incorporated into the tests with
the caveat that prevalence is assumed to be constant within strata
in the Hoel-walburg procedure.
1.3.4.2 Lifetable test
The standard lifetable test is appropriate for fatal tumors
(Tarone,1975; Peto,
analogous to the
et.al.,1980; Lagakos,1982).
Hoel~alburg
This test is
test where each death forms its own
.•
stratum (Haseman, 1984), and the number at risk of tumor onset
differs.
In the lifetable test, the number at risk of dying with
the tumor at a particular time is the number of animals alive
immediately prior to that time.
1.4 Statement of the Problem and Outline
The purpose of this research is to explore the operating
characteristics of the tests described above in the context of a
three state stochastic model.
More specifically, the behavior of
the tests will be examined when group differences in incidence,
treatment lethality and tumor lethality are varied.
Chapter 2 will
T
11
focus on presenting the three state stochastic model and its
accompanying hazard rates that will be used to describe an animal
carcinogenicity experiment, and on an elaboration of the test
statistics commonly used for analyzing the results of these
experiments.
Chapter 3 will focus on the asymptotic properties of
these test statistics.
The efficacy of these tests as functions of
treatment lethality and tumor lethality is of primary concern.
Chapter 4 will present the small sample results of a Monte Carlo
simulation study which explores the level and power of these tests
under standard conditions.
Chapter Swill provide discussion and
conclusions regarding the test statistics examined in this research.
Suggestions for future research will also be provided •
•
Chapter 2:
Test Statistics and a Simple stochastic Model
Section 2.1: Elaboration of Test Statistics
In this section, an elaboration of the fonn and construction of
the test statistics introduced in Chapter 1 will be presented.
Consider a carcinogenicity experiment with K treated groups and a
control group where animals in the i th group receive dose zi'
i-O,l, ••• ,K.
SUpPOse strata have been for.med over S time
intervals, and let nis denote the n~r at risk in the sth stratum
for the i th group, and let dis denote the number of animals with the
response of interest in this same group-stratum combination, and let
cis denote the number of animals censored in this group-stratum
combination. A period in a subscript will be used to denote
,
...
summation over that subscript; hence ni • - tsn is ' die - tsd is ' c i • tsc is ' n. s - tin is ' and d. s - tid is • Let tis denote the expected
number of animals that have the response of interest in the sth
stratum of the i th group.
Using a multinomial model, we find that
tis can be estimated by Eis - nis ( d. sin. s ). Most of the commonly
used tests for carcinogenicity can be formulated as special cases of
a generic test statistic ZG where:
TG
ZG -V
G
with
•
13
k
T - t z. (d. - E. )
G i-O 1
1.
1.
and
z -
(n)
-1
K
t n. z.
. 0 1. 1
1-
The different tests are oriented toward different null hypotheses
depending upon the assumptions used in deriving the test.
However,
in all cases, under the null hypothesis, ZG is asymptotically
distributed as a standard normal variate.
The distinction between
most of the various test statistics is in the, formation of the
stratum and the definition of the number at risk.
2.1.1 Incidence Test
Assuming that tumors are irreversible, then tumor onset can be
treated in the same manner as we treat a death in an ordinary
survival analysis.
If tumor onset were observable, the lifetable
test derived by Tarone (1975) would be applicable to testing the
hypothesis of equal tumor incidence rates in all groups.
The
derivation of a tumor onset time is an intermediate step in a
simulation study and this test is applicable in the framework of
simulation studies.
This "incidence test" corrects for survival and
requires no assumptions concerning tumor lethality, thus it provides
pa useful standard with which to compare the other tests.
In the
14
tumor incidence test, strata are defined by each tumor onset time.
Animals that die prior to getting a tumor are considered as censored
observations. The animals given dose zi which are alive and tumor
free just prior to the sth tumor onset time are denoted by n is and
dis represents the number of animals who subsequently get the tumor
at the sth tumor onset time.
The animals that die tumor-free during
the sth tumor onset time in the i th group are represented by cis.
2.1.2 Quantal Response
The Cochran-Armitage linear trend test (Armitage 1955)
considers the data from the dose groups to be collapsed over the .
entire study period into one stratum( S-l) • All tests of this type
define d il to be the number of animals in group i that are found to
have the tumor. The Cochran-Armitage linear trend test uses nil
equal to the number of animals placed on study and ZG can be
calculated accordingly.
An implicit assumption in the use of this
test is that all animals are at equal risk of getting the tumor over
the duration of the study.
However, because tumors sometimes have
long latency periods and because same treatments decrease survival,
animals may die earlier in some treatment groups and thus be at
decreased risk of tumor onset.
One method of correcting for this
problem would be to modify the value of nil to reflect less-thanwhole-animal contributions for decreased survival.
One way of doing
this would be to define the number-at-risk for these tests as:
*
nil
n' l - t
1
• 1
J-
W••
1J
The weights, w.. , are all equal to 1 for the Cochran-Armitage trend
1J
.•
15
test.
The truncated trend procedure defines the weights as CA>, ,-1 if
1)
the age at death for the jth animal in the i th group, t
ij
, exceeds
the time of the first death with tumor present and CA>. ,-0 if not
1)
(Peto, 1974; and Gart,Chu, & Tarone, 1979).
The second adjustment of this type, the Poly-3 trend test,
defines the weights as CA>ij-1 if the jth animal in the i th group dies
with the tumor present and CA>ij-( tij/tmax )3 if not where t max is the
maxirm.un survival time. This weighting scheme results from the
observation that many tumors seem to appear at the rate of a 3rd to
5th order polynomial in time (see ego Portier, Hedges and Hoel,
1986) .
2.1.3 Survival Adjusted Tests
2.1.3.1 Lifetable Test
The lifetable test is similar to the onset test except that
strata are now formed for each death time with a tumor.
Animals
that die without a tumor are treated as censored observations.
In
terms of the generic test statistic, n is is the number of animals in
group i that are alive just prior to death in the sth stratum and
dis is the number of animals dying with the tumor present in the sth
stratum.
This is a test of treatment related differences in the
hazard of death with the tumor.
2.1.3.2 Prevalence Tests
Hoel and walburg(l972) proposed to test the hypothesis of equal
tumor prevalence in the dosed groups within strata that are chosen
16
external to the observed survival times.
The National Toxicology
Program uses five strata when applying this procedure(Haseman 1984)
where the strata are the time intervals (which are expressed in
weeks): 0-52,53-78,79-92,93-Termina1 Sacrifice, and Terminal
Sacrifice(often 104 weeks).
For this procedure, nis is the number
of animals dying in the interval formed by stratum s in group i and
dis is the number of these animals with the tumor present.
Logistic regression(Oinse and Lagakos 1983) can be used to
model tumor prevalence as a function of dose and survival time.
Unlike the
Hoe1~a1burg
procedure, logistic regression adjusts for
survival times in a continuous manner.
For the simulations that are
discussed in Chapter 4, a logistic model with a linear time effect
and a linear treatment effect is used, and the hypothesis of equal
tumor prevalence is tested with a score test as emploYed by
Oinse(1985).
Note that the generic test statistic ZG has been shown
by Birch (1965) to be equivalent to a logistic regression score test
under a model with a linear treatment effect and a time parameter
for each stratum.
Section 2.2 Stochastic Model
It is convenient to use a three-state stochastic model to
describe the results of a carcinogenicity experiment when cause-ofdeath is unobtainable.
This model is illustrated in Figure 1.
The
transition rates in this model are described by the hazard functions
),1 (t),
ai (t),
and Yi (t,w).
Let E1 be the random variable which
represents the time from initial exposure to the occurence of the
17
first event which is either a tumor onset or a tumor-free death.
Let E2 represent the time from tumor onset to death. Define &-1 if
the tumor is present and 0 otherwise. Thus for animals receiving
dose zi' the hazard functions at time t can be defined as:
Ai (t) - lim (6)-1 Pr { t S E1 < t + 6, &-1
6+0
e3
(6)-1 Pr
{t ~ E1 < t + 6, &-0
i (t) - lim
6+0
I
El~t,
zi
I E1~t,
zi
}
}
and,
Yi (t,w) _ lim (6)-1 Pr { t ~ E2 < t + 6
6+0
I
E1-w~t,
6-1.
E2~t.
zi }
section 2.2.1 Choice of the form of the Hazard Functions
A
major concern in the modeling of survival data is determining
a reasonable form for the hazard functions described above and
finding logical values for the parameters'of these functions.
This
formulation is required in order to derive efficacy values in
Chapter 3 and is required as a foundation for doing the simulations
that are summarized in Chapter 4.
Portier, Hedges and Hoel (1986)
provide hazard functions that adequately fit a large historical
database of untreated animals.
analyses are· used in this study.
The models suggested by their
A
two-parameter Weibull function
was used to model the tumor onset hazard function for z-O (the
,
control group).
This function was of the following form:
For the hazard of death given the tumor is absent and z-O, a
18
Figure 1:
'Ihree-State Stochastic Model for Carcinogenicity
Experiments when Cause-of-death is unobtainable.
Alive and
Tumor Free
~
Alive and
Tumor Present
Dead
I
19
modified Weibull hazard function provided an adequate fit.
This
model is given by
For the purposes of the efficacy calculations and the simulations,
a( t) will be treated as not varying with tumr type.
The hazard
functions for the other groups will be modelled in a proportional
hazards framework where:
Ai(t) - (1 + nOzi)~(t)
and
Tables 2.1 and 2.2 provide the values for a.1 and n.1
used in the derivations which follow.
(i~l)
which are
The origin of the parameters
is given as the sex-species-tumor site combination from Portier, et
al.
The hazard of death for a tumr bearing animal was modeled by
assuming that this hazard was equal to the hazard of death for a
tumor-free animal plus some treatment-independent continuous
function of the time since tumor onset; i.e. Yi(t,w) - ai(t)+f(t-w).
The portion of the cumulative hazard attributed to f can be written:
t
,
J
f( s-w) ds -
.O~ (t-w) (tmax ) ~-
1
w
This cumulative hazard implies that the lifetime hazard of death for
an animal with early tumor onset is approximately (1 + '0 ) times
the lifetime hazard of death for a tumor-free animal.
Thus, by
20
Table 2.1
Tumor Onset Parameters and Associated Lifetime
Probabilities of Tumor Onset
sex/spec.
si te
Female Mice
Inte~entafY system
Thyroid FollIcular Cell
H~ioma-Hemangiosarcoma
Liver
Leukemia/Lymphoma
Female Rat
L\}l1g
Liver
Thyroid Follicular Cell
LeUkemia/L~phoma
Mamary Glahd Fibroadenoma
Hale Mice
Thyroid Follicular Cell
He~ioma-H~iosarcoma
Leukemia/Lymphoma
Lung
Liver
Male Rat
Lung
Mesothelioma
Liver
Inte~entary system
Leukemia/Lymphoma
l1t
8.06E-13
1. 33E-Q9
2. 38E-12
1.02E-OS
2. 62E-14
3. 62E-04
2.89E-32
5. 25E-OS
6. 51E-07
2.32E-12
4.OSE-04
5.09E-21
1. 13E-12
8. 57E-07
4. llE-07
4. 13E-05
1.60E-15
2.92E-13
7.97E-1O
3.93E-10
tlz
4.9
3.5
5.0
3.4
6.4
0.8
14.7
3.1
2.7
5.4
0.8
9.2
5.4
2.6
2.9
1.4
6.5
5.5
3.9
4.4
Pre tumor before
104 weeks)
0.01
0.02
0.03
0.08
0.27
0.01
0.03
0.09
0.19
0.26
0.01
0.03
0.13
0.18
0.33
0.02
0.03
0.05
0.06
0.31
•
21
Table 2.2
Tumor-free death parameters and Associated lifetime
Probability of Tumor-free Death
s~/s~c.
Female
Female
Male
Hale
Mice
Rats
Mice
Rats
~
2. 87E-04
l.24E-04
6.S8E-04
l.24E-04
~
~
Pr(death)
1. 42E-l4
2. 48E-l6
l.2lE-lS
9.02E-17
6.S
7.4
7.0
7.7
0.26
0.26
0.23
0.3S
22
varying the value for .0' it is possible to model the range of tumor
lethality, from incidental tumors (.0·0) to highly lethal tumors
(.0»0).
Figure 2 illustrates the survival of male mice who get a
tumor that leads to a 10-fold lifetime risk versus male mice who are
tumor-free for their entire lifetime.
In Chapter 3, efficacy values will be derived for 3 treatment
lethality factors (ceo) and 3 tumor lethality factors (.0)' for each of
the 20 sex-species-site combinations given in Table 2.2.
For.the simulation study described in Chapter 4, 4 onset
factors(~O)'
3 treatment lethality factors(ceo), and 3 tumor
lethality factors (.0) were considered.
Hence, 36 onset by treatment
lethality by tumor lethality combinations were studied for each of
the 20 sex-species-tumor site combinations given in Table 2.2
yielding a total of 720 unique simulation conditions.
Section 2.2.1 Hypotheses in terms of the Stochastic Model
An
experimenter is interested in whether increases in
administered dose are related to increases in tumor incidence. As
discussed by MCKnight and Crowley( 1984), the null hypothesis in
carcinogenicity studies should be expressed in terms of tumor
incidence rates since tests in terms of other rates can be biased
when test assumptions are violated.
In the context of the model
above, the null hypothesis test of interest then would be
Ho:Ao(t).~(t)
••••• ~(t). The incidence test addresses this
hypothesis directly since it is based upon the time of tumor onset.
The remaining tests address this hypothesis in special cases as
outlined below.
23
Figure 2:
Survival Probabilities of Tumor-bearing versus Tumor-free
Male Mice when Tumor Presence leads to a lO-fold increase
in lifetime risk •
•
0
~
en
0
,
co
••
0
••
•
••
••
••
••
••,
r--.
0
.....
>-
---
•- : <.0
~o
L)
.•...
.•......•....
2U1
".
0-0
"......
.........
0
>
'S; -or
..... 0
e
'. '" .....
~
Vi ,....,
0
.
.
LEGEND
no turror oresent
onset at 15 weeks
··..······..······..·..····....·7·5·..·..·············..···
onset at
weeks
o'nsefar';rnj"weeks
.................................
('oJ
0
0
.....
.....
......
0
0
0.0
20.0
40.0
60.0
Weeks on Study
80.0
100.0
....
24
The hypothesis tested by the Cochran-Armitage trend test is
whether the probability of developing the tumor in group j before
study termination (TS), nj , is the same in every group. This
probability can be expressed in terms of the hazard functions
defined above as:
TS
Kj
•
J
Aj(U) exp
o
u
{-J
(Aj(X) +
~j(x))dx }
(2.1)
du
0
Under the assumption that Aa(t) ••••• ~(t), the only time we are
assured that nO·n1• •• •• 'i< is when BO(t)·B1 (t)· ••.• ~(t).
cases, it is possible to have nj ~ ni (i~j) even when
In other
Aa(t).A1(t) ••••• ~(t).
(i~j)
Similarly, it is possible to have nj • ni
when the A'S differ.
The hypothesis tested in the lifetable test is that there is no
difference in the event-specific hazard functions for death with
tumor in the K+1 groups (Tarone 1975).
The hazard is "event-
specific" since differences in the time until death with tumor
present are of interest.
Death without the tumor present is treated
as a censoring mechanism.
The hazard of death at time s in group j
and tumor onset before time s will be denoted by h j (s) • The hazard
function, hj(s), can be written in the terms of the stochastic
model as:
25
where
When the assumption of instantly lethal tumors is true (i.e. the
pr(D-t\t-s) is 1 for t.s and is 0 for t>s), the expression for the
hazard function reduces to hj(s) • Aj(S).
The lifetable test rejects the null hyPOthesis of no survival
differences in the .various dose groups when decreased survival with
tumor is associated with increasing dose levels.
If the hazard of
death given the tumor is present is some function of the hazard of
.,
death given the tumor is absent (e.g. Yj(t,U)·l3 j (t)+!(t-u» then
decreased survival with tumor in the higher dose groups can occur
when
130(t)~l3l(t)~
••• ~~(t) even though
Aa(t).~(t) ••••• ~(t) •
Therefore, treatment lethality effects can cause greater than
expected Type I errors and inflated power estimates.
The prevalence tests compare the probabilities of tumor
presence given death within a particular stratum or at a certain
time.
The null hyPOthesis for these procedures can be stated as
HO:KO(S) ••••• ~(S) where Kj(s).pr(tumor presentlanimal dies at time
s ). This probability will equal the prevalence, Pr(tumor
presentlanimal alive at time s), if the tumor is incidental.
In
terms of the stochastic model given above, this probability can be
expressed as:
26
where
Aj (s), the density for death with tumor at time s,
is given by:
Under the incidental tumor assumption,
Yj(W,u)-~j(w),
this
probability reduces to:
.,
where
AjIS) - [
~(u)eX+[~IX)dx } duo
o
0
Hence, the prevalence tests are functions only of the tumor
incidence rate when the incidental tumor assumption is valid.
Chapter 3: Asymptotic Results
section 3.1: Introduction
Asymptotic relative efficiency(ARE) is a fairly simple concept
to define.
The ARE of test S relative to test T is the limit of
the ratio of the sample sizes
~ns
that are required for each test
to have the same power at the same significance level (Randles and
Wolfe, 1979, p. 144).
Thus, if ARE < 1 in the comparison of test S
relative to test T, then test S requires a larger sample size than
test T to attain the same limiting power. AREs can be derived as
the squared ratio of the efficacies of two test statistics where
,
"
"efficacy" is a term used by Randles and Wolfe (1979) • Efficacy
denotes the limiting value of the ratio of the derivative with
respect to the parameter of interest of the mean of a test statistic
to its standard error evaluated at the null value of that parameter.
This result follows from Noether's Theorem which provides a
"computationally useful asymptotic relative efficiency expression
for test procedures when certain conditions are satisfied" (Randles
& Wolfe,1979).
This theorem is relevant for test statistics with
the same continuous limiting distribution and that possess certain
standard error and expected value properties. As mentioned
previously, the derivation of Asymptotic Relative Efficiency is
relevant under the conditions that the test statistics have the same
asymptotic significance level and the same asymptotic power.
28
The problem that one encounters in deriving AREs for the
situation addressed in this manuscript is that not only do
violations of test assumptions alter the power of these tests but
these violations also potentially alter the significance level of
these tests.
Therefore, it is not reasonable to define the ARE of
the test statistics in this situation.
The asymptotic behavior of
these tests is of interest and an alternate index or at least an
alternate interpretation of large sample behavior is required.
efficacy values provide such an index.
The
By their very definition,
they are a standardized measure of the rate of change of the mean of
a test statistic.
Examining efficacy values will lead to insight
into the sensitivity of test statistics to violations in the test's
assumptions.
For example, if a violation leads to an increase in
efficacy relative to a standard situation then the test is more
likely to reject a hypothesis than nominally specified.
section 3.2: Conditions Considered
What follows is the derivation of. the form of the efficacy
values and AREs (if appropriate) for varying conditions of treatment
lethality and tumor lethality.
Treatment lethality refers to the
phenomena where higher doses of a compound are related to greater
mortali ty• In terms of the hazard functions discussed previously,
treatment lethality is represented as
~O(t)<~l(t)<••• <~(t).
The
four distinct situations that are addressed in this chapter are:
1.
The condition of equal treatment lethality
(~O(t).~l(t)•••.• ~(t))
( Yj ( t, x).~j ( t) ) •
and no tumor lethality
29
2.
The condition of increasing treatment lethality
(~O(t)<~l(t)< ••• <~(t»
and no tumor lethality
( Yj ( t, x) -~j ( t) ) •
3.
The condition of equal treatment lethality
(~O(t)-~l(t)-••• -~(t»
and tumor lethality (Yj(t,x»~j(t».
4• The condition of increasing treatment lethality
The condition of "no tumor lethality" is also known as the
"incidental tumor" condition and the phrases will be used
interchangably.
In order to derive the efficacy term, one needs to posit some
structure on the hazard functions used in the three-state stochastic
model considered in the previous chapter.
The same proportional
hazards framework that was discussed in Chapter 2 will be used in
this development.
Recall that this framework uses a simple linear
relationship to relate the hazard of tumor-free death in dose group
zi to the hazard of tumor-free death in the control group(zO).
This
is illustrated below:
As
before, the relationship between dose and the hazard of tumor
onset is also modelled using a simple linear relationship where:
Section 3.3: Efficacy for the Generic Test Statistic
The hypothesis of interest in tumorigenicity studies is that
30
the hazard of tumor onset is the same in all groups.
In terms of
the proportional hazards framework, this is a test of
~A
-
o.
The
efficacy for the generic test statistic, TG, can be defined in the
notation of Randles and Wolfe (1979) as follows:
efficacy (TG ) - eff(TG) -
where
:t
E [ TG
A
1evaluated at t,,-O
and
In the discussion that follows, v' and
Recall that TG can be written as
K
T - t
G i-O
zi' (d.
1.
- E. )
where
d.
1.
and
5
- t d.
s-l
1S
1.
(12
will be derived for TG•
31
K
s
E.1. - E E.
s-l
1S
s
- E n.
s-l
E d.
s
1S
- E
n. s
j-O JS
s-l
n.
1S
K
E n.
j-O JS
The outcome of an animal carcinogenicity study can be viewed as
a multinomial experiment where columns represent strata and rows
represent "+" - the occurence of the response of interest or "_" censoring before the response of interest can be observed.
As
discussed previously, strata represent different quantities in the
different tests.
In general, define the multinomial cell
probabilities as:
~
- •~r ( response of interest occurs in the sth stratum
'I'+is
I
Zl'
and
+.
-lS
Pr
censoring occurs in the sth stratum
I
Zl' )
Denote dis as the count of the number of positive responses in the
sth stratum in the i th group and cis as the number of observations
censored in the sth stratum in the i th group.
These cell counts,
being from a multinomial distribution, possess the following
properties:
- n.1 .
and
These properties generalize to the cells that represent censoring.
Before the mean and variance of TG are derived, certain
relationships between nis ' ni ., and n will be assumed in order to
32
facilitate the derivation of the efficacy values. The first
assumption is that experimental units are assigned to treatment
groups in a known proportion, i.e. the ratio of group sample sizes
to total sample size,
n.1. In • . (i-O,1, ••• ,K) is known.
00 , 1
The
second assumption is that ratio nisin. s can be approximated by
E(nis)/E(n. s ).
This second relationship is derivable from taking
the constant teOD of a Taylor's Series expansion of x/y about E(x)
and E(y).
The adequacy of this assumption can be checked by
examining the external consistency of the efficacy results (i.e. are
the relative efficacy calculations consistent with the small sample
results?) and the internal consistency of the efficacy results.
Since the Cochran-Armitage trend test. efficacy calculations do not
require the second assumption to derive efficacy values (only 1
stratum), internal consistency can be checked by examining whether
calculations from the Cochran-Armitage trend test has the same
efficacy as the onset test and the prevalence tests under the
condition of no treatment lethality and no tumor lethality.
As discussed previously, the term, nis ' represents the number
at risk immediately prior to the start of stratum s for the onset
test and the lifetable test, and it represents the number of animals
that die in the sth stratum in the prevalence tests.
In terms of
the multinomial cell counts, the number at risk in the onset test
and the lifetable test can be written as:
n.
1S
- n.
1.
-
s-1
t (d.
r-1 1r
+ c. )
1r
and the number at risk in the prevalence tests can be written as:
n.1S - d.1S + C.1S
33
The n. s terms represent the sum of the nis terms over all groups
K
n
t n
.s - J'0
js
The expectation of nis and n. s for the onset and lifetable tests
are simply
E(n1,s) - n •• (a),1
and
K
[ 1 - t
s-1
t
j-O r-1
•
OOJ' (++J'r + +-J'r)
]
From the second assumption discussed previously,
-
n. s
K s-1
]
~ OOJ' (++J' r + +-J' r )
[ 1 - t
j-O r-1
Similarly for the prevalence test,
-nis
A
n. s
E(n is )
E(n. s )
-
(a), (
1 ++is + +-is
)
K
t
(a),
j-O J
(
++js + +-js
Thus, from this point onward nis/n. s will be replaced by ooi ~is
where it is understood that the ~is will have different meaning for
the different tests.
34
section 3.3.1 The Expected Value of TG
The derivation of E(TG) follows:
where
(3.1)
S
S
K
S
K
E(E1,.) • J: E(E'r) • J: oo,'t, ,J: E(d)'r) - J: ooi't,
J: n
r-1 1
r-1 1 1r )-0
r-1 1r j-O ••
(0),
++)'r (3.2)
Therefore,
The derivative of the expected value of TG can be found directly:
K
[S, - SJ: 't, K
']
J: 00, + j
r-1 1r _ ) + r
6
v' • --- v
- n
J: z, 00,
J: +,
T
~~A T
··i-O 1 1 s-l +lS
G
G
j 0
where
Section 3.3.2 The Variance of TG
The derivation of Var(TG) now follows.
Recall that TG is a
35
linear combination of variables. Hence, Var(TG) can be written as
the sum of variances minus the sum of covariances. In terms of the
test statistic,
K
2
K
- t z. Var (d 1••
i-O
1
-
E1·.) + 2 t
K 2
K
t ZJ'Zlcov«dJ. -E. ),(d1 -E1 »
• J•
••
1-0 j <l
• t z. Var (d. - E. )
. 0 1
1.
1.
since the groups are independent
1-
-
~ z~1
i-O
(var(di ) + Var(E. ) - 2 Cov(di ,Ei )
•
1.
•
•
J
The form of the two variance terms and the covariance are derived as
follows.
Var(di. ) - Var
S
- t n
s-1
where
PdiS]
s-1
S
S
- t Var(d. s) + t Cov(dis,d ir )
s-1
1
s~r
S
Wi ++is (1-++ is ) + t -n
s~r
wi++is++ir
36
2 2 Var [ .Kt djs
- ooi't
is
)-0
]
since the treatment groups are independent,
(3.4a)
-n
where
K
- n
1 'to1S _t 00.)
j 0
00.
++)S.
2 2
K
K
E(E 1• S )E(E1• r ) - n •• oo.'t.
'to
t
OOj ++js t~. ++kr
1 1S 1r j _0
k-O K
.~ oo~ ++js++jr +
[)-0
j;k"'j"'k ++js++kr· ]
37
Therefore,
K
.~.E(dis)E(djr)
l~J
38
(3.4b)
- -n
Combining (3.4a) and (3.4b) yields
(3.5)
The covariance term, Cov(di. ,Ei.) is derived as follows:
Cov(d.1. ,E.1. ) - E(d.1. E.1. ) - E(d.1. )E(E,1. )
From (3.1) and (3.2), it is easy to show that
+
S
S
- I
I
s-1 r-1
K
w.~.
I E (d1'sd . r )
J
1 1r j-O
Note that for i_j
E(disd jr ) -
E(d is ) E(d jr ) - n .• wiwj++is++jr
39
- -n •• ooi ++is++ir +
and for s-r, j-i •••
n~.oof++is++ir
E(disdis ) - E(drs) - Var(d is ) + E2 (d is )
Therefore, .
E(d . E. ) 1. 1.
S
S
K
n2 ~~
~~ ~'·'i.ir
~ I.' I.' ++l'S ++J'r
~
.:.~l·~j
··s-l r-1
J~l
S
+ E
s;6r
+
't.
00.
1 lr
S
E
00.
1
s-l
[
-n
••
00.
1
't.
lS
Hence,
Cov(d.1. ,E.1. ) - E(d.1. E.1. ) - E(d.1. )E(E.1. )
~
oo~'t.
. +.
Cov(d.1. ,E.1. ) - s¢r n •• 1 1r [- ++lS
+lr ]
(3.7)
At this point, Var(TG) can be derived as
K
2 { S
Var(TG) - n . E zi
• ·1-0
E
s-l
wi ++is
40
+
S 2 2 K
t 00. 't.
t 00
(l-++ jS )
s-l 1 1S j-O j ++js
K
S 2
t 00. 'tis't
t 00.
ir j-O
s;*r 1
) ++js ++jr
S
2
+ 2 t
s;*r
00 ,
1
't
+ +
ir +is +ir
}
(3.8)
section 3.4: Multinomial Cell Probabilities
The discussion that follows presents the multinomial cell
probabilities (++'s and +_'s) for the four most commonly used tests
of carcinogenicity.
The derivatives of these probabilities with
respect to (A will also be presented.
The probability tested by the Cochran-Armitage trend test is
the probability of tumor onset before study termination. This
probability, nj , was expressed in terms of the hazard functions
defined in Chapter 2 as equation (2.1) which is reproduced below:
TS
nj •
u
J~(u)·exp {-J (~(x) + Bj(x»dx }
o
du
0
Since the Cochran-Armitage trend test considers only 1 stratum, the
multinomial framework proposed above reduces to a binomial
experiment.
This implies that ++il-ni and +-il - 1 - ni • The
derivatives of the multinomial probabilities are also required for
41
the efficacy calculations.
The derivatives of the + and + terms
+
-
are presented below:
Let
and
A,(u)
- [A'1 (x)dx
1
B,
1
o
(u) -
[a,o
1
(x)dx.
Then,
TS
-J
Zi Xo(u) (l-'\,(u) I eXP{-'\,(UI-Bi (Ull}
E.A-O
du
0
and
,
+-1'1
,
6
- 6E.A
- - ++1'1
+-1'1
since +-1'1 - 1 - ++1'1·
E.A-O
The multinomial cell probabilities are the same for the
lifetable test and for the two prevalence tests since ++is
represents the probability that a tumor is present in an animal in
group i that dies during stratum s and +-is represents the
probability that a tumor-free animal in group i dies during stratum
s.
The tests differ in the
~is
terms.
These multinomial cell
probabilities corresponding to the non-sacrifice strata and their
derivatives are presented below:
and
42
+-i5 -
1: ~i(u)exp(-Ai(U)-Bi(U))
du dx
s-l
The derivatives are simply,
and
+~iS • _I . zi ai (u)
JS - 1
J\o(u) exp(-J\o(U)-B i (u))dudx
The multinomial probabilities corresponding to the terminal
sacrifice stratum and their associated derivatives are presented
below:
and
These derivatives would be
and
43
Note that the quantal response probability,
over stratum of the ++js terms.
~j'
is simply the sum
Hence, all of the commonly used
tests of carcinogenicity use the same multinomial cell
probabilities.
The onset lifetable test will have multinomial probabilities of
the fOOD ++is-pr( &-1 n E1 t(s-1,s] ) where & is an indicator of
tumor presence and E1 is the random variable that indicates the time
to first event.
The multinomial probabilities and their
accompanying derivatives in terms of the stochastic model are
presented below:
++is -
e
+,
-lS -
L1
L1
Ai(u)exp(-Ai(U)-Bi(U))du
~i(u)exp(-Ai(u)-Bi(u))du
·J
s
Xi Xolul (l-"olul I exp{-"o lul-Bi lUll} du
(A-O
s-l
and
,
+-1'1
&
s
+
- -& ( - 1'1
A
· -J Xi "olu)
(A-O
s-l
Bilu) exp {-"oIUI-BiIUI} du
·44
Section 3.5: Squared Relative Efficacies
Given the derivation of the efficacy of the generic test
statistic, the multinomial cell probabilities and the derivatives,
it is now possible to determine the efficacies of these tests for a
particular choice of hazard functions (A,
~,
and y).
As
discussed
by Randles and Wolfe (p.149,1979), the ratio of squared efficacies
of test S to test T will equal the asymptotic relative efficiency of
test S with respect to test T when these tests have the same
limiting significance level, the same limiting power, and the same
continuous limiting distribution.
These assumptions are not
guaranteed for the prevalence tests if non-incidental tumors are
considered.
These assumptions are not guaranteed for the lifetable
test if non-instantly lethal tumors are considered.
Finally, these
assumptions are not guaranteed for the Cochran-Armitage trend test
if any treatment lethality is present.
Therefore, when considering
the squared relative efficacy results, it is only valid to consider
asymptotic relative efficiency for a small subset of test
conditions.
The squared efficacy of the onset test will be divided
by the squared efficacy of each of the commonly used carcinogenicity
tests in order to obtain a measure of the behavior of these tests
relative to some standard.
If the squared relative efficacy(SRE) of
a test is greater than 1, then that test is less' likely to reject
~ts
null hypothesis than the onset test.
If the SRE is less than 1,
the test is more likely to reject its null hypothesis than the onset
test.
Ryan(1985) examined the efficiency of the Cochran-Armitage test
relative to the
Hoel~alburg
test for incidental tumors and relative
45
to the lifetable test for instantly lethal tumors.
In this
research, Ryan claimed that the Hoel-Walburg test and the lifetable
test should be routinely used over the Cochran-Armitage test because
of asymptotic relative efficiency properties. An initial difficulty
with this claim is the lethality of the tumor is assumed known or
that its lethality may be determined by a pathologist.
If the Hoel-
walburg test and the lifetable test are applied to tumors with
lethality properties that differ from those assumed, then
substantial biases can be introduced (Lagakos, 1982).
Gart and
Tarone( 1986) challenge the results of Ryan and find that the
Cochran-Armitage trend test is very efficient relative to the HoelWalburg procedure and the lifetable test when tumor rates are
moderate «50%) and final survival is "not very poor." Neither
Ryan(1985) nor Gart and Tarone (1986) considered the impact of
treatment lethality and tumor lethality on the large sample behavior
of these tests.
Section 3.5.1 Comments on calculating efficacies
The hazard functions presented in chapter 2 will be used for
the calculations that follow.
The fOnD of these hazard functions
are not amenable to easily calculated integrals when determining the
multinomial cell probabilities hence numerical integration
techniques were required to obtain efficacy values.
A Simpson'S
Composite algorithm (Burden, Faires, and Reynolds,1978,p. 200) was
used to do the numerical integrations.
The efficacies for the onset
test, lifetable test, and logistic regression test were based upon
assuming a 2 year study where stratum are formed at weekly time
46
points.
The efficacies were evaluated for a four group design with
doses 0.0, .25, .50 and 1.0.
National Toxicology program.
computer resources.
This design is cOllIlIOnly used by the
only one design was considered due to
The efficacies were calculated for 9 treatment
lethality-tumor lethality conditions for each of 20 sex-speciestumor site combinations.
Section 3.5.2 SRE results
The SRE's for a subset of sex-species-tumor site combinations
for all 4 cOIlIlIOnly used carcinogenicity tests are presented in Table
3.1.
only a subset of the SRE values are presented in the text
since the results were consistent across all 20 sex-species-tumor
site combinations.
Appendix A.
The complete set of SRE values are presented in
From this table, one can see some clear patterns in the
SRE's emerging.
The SRE for the Cochran-Armitage trend test equals 1 for the no
treatment lethality case and decreases from that point as treatment
lethality increases.
Technically, this implies that the mean of the
Cochran-Armitage trend test statistic changes less rapidly than does
the mean of the onset test statistic as treatment lethality
increases which implies that the Cochran-Armitage trend test is less
likely to reject its null hypothesis than the onset test.
For small
.amples, this may translate into lower than nominally specified Type
I error rates and into lower power.
The SRE for the lifetable test clearly decreases as treatment
lethality increases and within a given level of treatment lethality,
increases as tumor lethality increases. A possible explanation for
47
Table 3.1: Squared Relative Efficacies for Commonly Used
Tests of Carcinogenicity
Sex-Species/
Tumor Site
Treatment
Lethality
1+au
Hale Mice
Liver
1
2
5
Female Rats
Leuk./Lymphoma
1
2
5
Male Rats
Liver
e
1
2
5
Female Rats
Lung
1
2
5
Tumor
Lethality
1++0
2
2
eff (Zo)/eff (Ztest)
Zt
ZIt
~w
Zlog
1
2
10
1
2
10
1
2
10
1.000
1.000
1.000
1.073
1.073
1.073
1.293
1.293
1.293
1.000
1.000
1.000
0.884
0.889
0.920
0.709
0.720
0.789
1.000
1.000
1.000
1.023
1.049
1.174
1.198
1.260
1.628
1.000
1.000
1.000
1.023
1.049
1.170
1.194
1.256
1.614
1
2
10
1
2
10
1
2
10
1.000
1.000
0.999
1.057
1.057
1.056
1.206
1.206
1.206
1.000
1.000
0.999
0.857
0.866
0.915
0.661
0.678
0.780
1.000
1.000
0.999
1.027
1.069
1.250
1.238
1.345
1.941
1.000
1.000
0.999
1.027
1.068
1.246
1.232
1.341
1.928
1
2
10
1
2
10
1
2
10
1.000
1.000
1.000
1.140
1.140
1.140
1.564
1.564
1.564
1.000
1.000
1.000
0.848
0.856
0.898
0.662
0.675
0.758
1.000
1.000
1.000
1.028
1.065
1.286
1.257
1.350
2.029
1.000
1.000
1.000
1.025
1.062
1.285
1.234
1.328
2.015
1
2
10
1
2
10
1
2
10
0.972
0.953
0.904
0.969
0.955
0.921
0.971
0.968
0.961
0.972
0.953
0.904
0.798
0.805
0.846
0.581
0.608
0.748
0.972
0.953
0.904
0.993
1.068
1.381
1.184
1.415
2.919
0.972
0.953
0.904
0.992
1.068
1.378
1.184
1.419
2.937
48
this phenomena is that increasing treatment lethality is more likely
to cause earlier detection of death with tumor present for
incidental and moderately lethal tumors, hence even if the rate of
tumor onset is the same in all groups, the tumor-bearing animals in
the high dose group are more likely to die earlier than the tumorbearing animals in the lower dosed groups.
This may lead to higher
than nominally specified Type I error rates when applying the
lifetable test to small samples when treatment lethality is present
and the tumor is only moderately lethal.
The increase in SRE toward
1 within a given level of treatment lethality as tumor lethality
increases illustrates that the test is behaving more like the onset
test as tumor lethality increases which is obvious since the time of
tumor onset equals the time to death with tumor present for
instantly lethal tumors.
The SRE's for the prevalence tests reflect the complicated
effects caused by treatment lethality and by tumor lethality • The
SRE of the prevalence tests equals 1 for conditions of no treatment
lethality regardless of the degree of tumor lethality that is
present.
The SREs of the prevalence tests tend to become
increasingly greater than 1 as treatment lethality and tumor
lethality increase.
The effects of treatment lethality and tumor
lethality on the SRE for the prevalence tests seem to be more than
simply additive effects.
Notice that the high treatment lethality-
high tumor lethality case has the highest SRE for the prevalence
tests.
This may reflect an interactive effect of the two
lethalities.
The SRE for the Hoel-Walburg procedure was almost
always greater than the SRE for the logistic regression procedure.
49
This implies that the Hoel-Walburg procedure will be more sensitive
than logistic regression to changes in treatment lethality and tumor
lethality.
From the large sample behavior of these tests, one might
predict that the prevalence tests when applied to small samples will
reject less frequently than nominally specified when treatment
lethality and tumor lethality are present, and this behavior will be
most severe in the conditions of high treatment lethality and high
tumor lethality.
The behavior of the SRE's for female rats with lung tumors is
somewhat problematic. A possible explanation of this erratic
behavior is that for a tumor with such a low background rate (as is
the case for this sex-species-tumor site combination) no test will
do very well - including tests that are conditional on tumor onset
times.
As
a final note, the SRE results are consistent with Gart and
Tarone(l986) in suggesting that the Cochran-Armitage trend test is
very efficient with respect to the
Hoel~alburg
test for incidental
tumors under even a quintupling of treatment lethality • The
condition of instant lethality was not considered so this result
cannot be compared directly.
Chapter 4:
Small Sample Results
Section 4.1 Simulation Conditions
The efficacy results provide useful insights into the behavior
of these test statistics as sample sizes become large.
practically
speaking, toxicology experiments are restricted in terms of the cost
and the logistics of managing large numbers of animals.
Therefore,
it is of interest to assess the operating characteristics of these
tests for sample sizes that one would use in practice. A simulation
study provides a means of assessing the small sample behavior of
these tests.
The protocols used by the National Toxicology program (NTP) and
the National Cancer Institute (NCI) were used to determine the
sample sizes and number of groups that are simulated. A typical NTP
study will have 4 groups including a control group with 50 animals
randomly assigned to each of the groups. A typical NCt study would
have 50 animals assigned to each of 3 groups including a control
group.
The doses were standardized to fall into the interval [0,1]
where zO-O is the dose adDdnistered to the control group and z3-1
(or z2-1) is the dose adDdnistered to the highest dosed group in an
NTP (NCI) study.
The intermediate doses for the NTP study design
were zl-.25 and z2-.50 and for the NCI design, zl-.50.
A consideration in any simulation study is the number of
replications of each study condition that one will perform.
For
51
this study, 1300 replications were used.
When using simulations to
study the operating characteristics of test procedures, each
replication represents a Bernoulli trial with the probability of
success equal to the significance level of the test (or power of the
test for non-null situations).
Hence, one could use the normal
approximation to the binomial distribution to determine the number
of replications to attain a specified coverage probability.
Recall
that a 90% confidence interval for the probability of success of a
binomial random variable would be ( P-1.645 s.e. (f», f>+1.645 s.e. (f»
) where s.e.(f» is the standard error of f> and f> is an estimate of
probability of success.
The variance of the estimated success
probability would equal P(l-P)/n where P is the true probability of
success.
SUpPOse one wished to estimate the P so that the interval
( .04, .06)
contains this true success probability 90% of the time
when P-0.05. One could estimate the sample size (number of
replications) required by setting n-(1.645/.01)2 * .05 *.95
=1286.
In terms of a simulation study of the operating characteristics of
statistical tests, the "success" probability corresponds to the
probability of rejecting a null hypothesis.
This was the strategy
used to decide upon 1300 replications for each condition.
Section 4.2 Simulation Results
The results from the simulations that used the NCI design were
virtuall~
identical to the results from the simulations that used
the NTP design, and the results were reasonably consistent across
sex-species-tumor site combinations.
Therefore, only a subset of
52
the NTP results are presented in the main body of Chapter 4.
The
full set of tabulated simulation results are presented in Appendix B
for the NTP design and in Appendix C for the NCI design.
A subset
of the sex-species-tumor site combinations that were simulated using
the NTP design are presented in Tables 4.1-4.4.
These combinations
correspond to tumors that have background rates that range from 1%
to 33%.
These tables contain information about the Type I Error
Rates and about the power properties of the statistical procedures
examined in this research.
These properties will now be examined in
the next two sections.
Section 4.2.1 Type I Error Rates
The Type I error rates of these tests correspond to the entries
of Table 4.1.
This table corresponds to the "no onset effect"
condition which is represented by YO·O or equivalently 1+yO·1. All
tests were examined at a specified Type I error rate of 0.05.
Hence
any departure of the observed Type I error rate from the specified
error rate represents a potential problem for a test.
If the
observed Type I error rate drops appreciably below the specified
level for a given test, then that test will be called "conservative"
for that particular set of simulation conditions.
If the opposite
situation occurs, then that test will be called "anti-conservative"
or "liberal" for that particular set of conditions.
The
Type
I error of the incidence test, zo' is unaffected by
changes in treatment lethality( «Xo) or by changes in tumor
lethality(.O).
If one examines the significance level of this test
over a series of sex-species-tumor site combinations as «Xo and .0
,.,..
1Il
Table 4.1
Type I Error of Carcinogenicity Tests for varying levels of Treatment Lethality
and Tumor Lethality using a nominal 0.05 level.
Tumor
Treatllellt
Tumor
Sex-Species
Lethality
Lethality
/TUmor rate Site
Z
Z0
1++0
1+«ro
Zt
Ztt
ZIt
P
4.2
Female Rats
Lung
1
4.2
4.2
4.3
1
4.3*
1.2%
3.8
3.7
1
2
3.7
3.7
3.9
4.5
4.3
4.3
4.3
1
10
4.3
5.7
6.7
2
4.1
3.9
1
3.8
2,.,
4.0
5.5
6.4
2
3.9
3.9
2
3.5
3.5
3.9
4.4
10
3.2
5
1
5.2
4.3
9.8
11.2
14.3
8.1
11.8
5
2
3.7
3.2
8.0
9.0
5.2
6.5
5
10
3.5
3.3
Hale Rats
Liver
4.9
5.2
5.0
5.5
1
1
5.1
4.6%
4.7
1
2
4.6
4.9
4.5
4.3
4.8
4.7
4.9
4.3
1
10
4.8
4.5 ' 5.7
8.7
2
6.5
5.8
1
4.6
5.0
5.8
8.8
5.7
2
2
2
10
4.5
3.9
3.8
6.0
3.3
5.8
3.9
6.1
18.2
5
1
1.5
5.2
17.7
5
2
5.8
1.7
3.8
4.2
12.2
10
5.8
4.2
5
1.8
Female Rats
Leuk./Lymphoma 1
5.3
5.7
5.2
5.5
5.5
1
19.1%
4.2
4.2
1
2
4.0
4.2
3.8
1
10
6.0
5.8
5.9
5.9
6.1
5.1
4.9
4.3
11.2
2
1
3.3
10.2
2
2
5.1
3.7
4.9
4.0
7.8
10
4.6
4.4
3.5
2
3.5
5.7
2.5
43.2
5
1
1.2
5.0
5
2
5.5
1.2
5.5
1.9
38.3
5.5
2.2
20.5
5
10
1.9
5.6
Hale Hice
Liver
5.7
5.2
1
6.1
5.8
5.7
1
32.5%
1
5.8
6.7
6.5
2
7.2
6.1
5.5
5.7
1
10
5.5
5.8
5.5
2
5.7
2.4
4.8
13.1
1
5.6
2
3.7
2
5.0
2.5
4.6
10.8
2
10
4.9
4.7
2.8
8.2
1.9
5
4.9
47.7
0.3
3.4
1
1.0
5
2
3.9
0.5
3.4
39.8
1.5
5
5.6
0.5
4.1
24.7
10
0.8
* entries are given in percentages
e
,. e ..
~w
4.3
4.0
4.8
5.5
5.0
3.2
6.5
4.4
2.0
5.1
4.8
4.6
5.5
5.6
2.4
4.9
5.0
2.5
5.5
4.2
5.3
4.8
4.2
1.8
5.0
3.2
0.5
5.5
6.5
5.5
5.8
4.2
1.2
4.6
3.4
0.3
Zlog
4.1
3.6
4.7
5.6
5.1
3.7
10.6
7.4
4.5
5.2
4.4
4.8
6.1
5.9
3.1
6.6
6.0
3.6
5.4
4.0
4.8
5.1
4.2
2.7
6.2
3.5
0.8
5.7
6.5
5.8
6.3
4.5
2.2
5.4
4.2
1.2
e
·. e
e
~
1Il
e
Table 4.2
Power of CarcinQgel1icity Tests for varyi~ levels of Treatment Lethali~ and Tumor Lethality
when the Treatment Induces a Two-fo d Tumorigenic Effect in the HIgh Dose Group.
Treatllent
Tumor
Sex-Species
Tumor .
Lethality
Lethality
!TUmor rate Site
Z0
Z
1++0
1+«0
Ztt
ZIt
Zt
~w
P
Female Rats
1.2%
Hale Rats
4.6%
Female Rats
19.1%
Hale Mice
32.5%
* entries are given
Lung
1
1
1
2
2 '.
2
5
5
5
Liver
1
1
1
2
2
2
5
5
5
Leuk./Lymphoma 1
1
1
2
2
2
5
5
5
Liver
1
1
1
2
2
2
5
5
5
in percentages
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
13.5*
12.2
11.2
10.6
12.2
10.0
11.0
12.9
12.8
23.8
20.5
22.8
21.0
19.8
21.0
15.4
18.8
20.5
55.6
54.3
56.0
56.7
53.4
54.1
51.2
48.5
49.4
73.9
74.8
71.4
69.2
68.8
72.7
66.8
64.9
63.8
13.4
12.2
11.1
10.2
12.0
9.8
9.4
11.2
11.2
23.8
20.6
22.4
14.8
15.1
15.9
6.3
7.1
7.5
54.6
54.1
55.1
48.0
44.1
44.9
25.2
24.5
25.0
70.9
71.0
67.8
51.5
SO.8
54.9
14.8
14.5
15.4
13.5
12.0
11.2
11.2
12.8
10.4
16.3
17.5
18.3
23.9
20.2
22.5
18.5
18.1
18.5
11.4
13.9
15.0
55.1
53.5
55.7
55.4
52.8
52.2
49.8
46.5
47.0
71.5
72.2
68.5
65.5
65.8
69.5
57.8
57.7
57.3
13.6
12.4
11.1
12.9
13.8
10.3
16.7
16.8
13.3
23.6
20.8
22.8
20.2
18.9
17.4
13.4
14.8
12.2
55.3
54.2
55.5
51.8
46.2
45.4
33.8
27.9
25.8
71.8
72.3
68.8
60.6
58.8
58.6
33.5
31.5
26.5
13.1
11.9
11.1
15.2
16.1
11.3
27.0
25.8
17.3
23.6
20.5
22.7
28.7
25.9
25.7
42.2
41.8
36.0
53.6
53.8
54.2
73.8
68.5
65.1
92.9
91.9
79.8
69.7
70.8
68.7
80.9
81.3
80.7
97.8
97.2
91.8
13.2
11.8
10.6
11.8
11.8
6.8
10.3
10.4
4.0
24.0
20.3
22.1
20.2
17.8
13.6
14.5
15.5
8.3
55.2
53.9
47.5
54.5
47.6
26.9
45.9
33.9
8.7
71.8
71.8
63.4
67.2
63.5
45.1
57.7
51.2
14.8
Zlog
13.5
12.0
12.2
12.8
12.7
8.7
14.8
14.1
7.7
23.2
20.7
22.5
21.0
19.1
16.2
16.2
17 .9
11.5
55.6
54.0
49.8
56.8
48.8
32.9
51.4
37.7
14.1
72.3
73.1
67.2
69.6
65.9
55.6
65.8
59.4
30.0
an
an
Table 4.3
Power of Carcinggenicity Tests for varying levels of. Treatment Lethalitl and Tumor Lethality
when the Treatment Induces a Five-fold Tumorigenic Effect in the igh Dose Group.
TreatllE!llt
Tumor
Sex-Species
Tumor
Lethality
Lethality
!TUmor rate Site
Z0
Z
1++0
Ztt
Zit
1m,
Zt
P
Female Rats
Lung
38.1
1
38.9
39.0
38.0
1
38.7* 39.1
42.5
1.2%
42.8
43.1
42.4
42.0
40.4
1
2
38.2
38.4
37.9
38.2
38.1
1
10
30.8
40.8
2
1
38.8
37.9
41.8
48.1
37.8
41.2
40.1
42.4
42.5
2
48.5
36.4
2.
2····
10
36.7
35.8
38.5
36.2
39.7
20.5
35.8
44.2
42.2
5
1
32.9
64.3
32.6
2
36.8
34.5
43.5
39.2
57.6
28.1
5
39.6
47.5
5
10
35.9
37.4
SO.3
13.2
Male Rats
Liver
1
1
80.5
79.5
80.2
80.2
78.8
79.6
4.6%
79.5
78.5
79.3
79.5
1
2
78.2
79.1
77.6
10
1
76.8
77.0
77.4
76.8
75.2
1
76.8
64.8
73.8
75.1
2
73.2
86.0
76.5
2
2
65.5
73.3
12.5
84.8
12.5
2
75.7
71.5
67.5
60.2
10
64.8
81.5
1
5
63.6
35.7
55.2
53.4
89.8
58.5
2
68.7
34.8
57.3
89.0
55.5
5
51.3
64.7
54.8
5
10
33.9
41.1
82.6
33.0
Female Rats
Leuk./Lymphoma 1
99.9
1
99.8
99.9
99.8
99.8
99.9
19.1%
1
2
100.0
99.9
99.9 100.0
99.9
99.9
10
99.8
99.4
1
99.9
99.8
99.8
99.8
99.8
2
1
99.8
99.7
99.8
99.8
99.9
2
2
99.9
99.7
99.7
99.6
99.8
99.8
97.6
2
10
100.0
99.6
99.9
99.6 100.0
99.5
1
99.8
97.2
99.8
99.1 100.0
5
99.8
99.5
97.8
5
2
96.4
97.9 100.0
79.2
10
99.8
97.5
99.8
97.8 100.0
5
Male Mice
Liver
1
100.0 100.0 100.0 100.0 100.0 100.0
1
32.5%
1
2
100.0 100.0 100.0 100.0
99.9 100.0
10
100.0 100.0 100.0 100.0 100.0 100.0
1
2
1
100.0
99.9 100.0 100.0 100.0 100.0
2
100.0 100.0 100.0 100.0 100.0 100.0
2
99.7
2
10
100.0
99.9 100.0
99.9 100.0
5
1
100.0
92.7
98.9 100.0
99.9
99.9
2
99.8
5
100.0
92.4 100.0
98.5 100.0
10
100.0
92.7
97.9 100.0
93.8
5
99.9
* entries are given in percentages
hero
e
e'
e ..
Zlog
38.8
42.6
33.2
40.0
38.3
24.0
38.2
32.8
16.7
79.9
79.3
76.4
76.7
74.8
65.2
64.0
62.3
42.1
99.9
99.9
99.6
99.8
99.7
98.5
99.8
99.0
89.5
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
99.0
e
e
\0
til
,
e"
Table 4.4
Power of Carcinggenicity Tests for varyi~ levels of Treatment
when the Treatment Induces a Ten-fo d Tumorigenic Effect
Treatllellt
Tumor
1'mIor
Lethality
Lethality
Sex-Species
!TUmor rate Site
1++0
1+00
Zo
Zt
1
FR
Lung
1
75.7* 75.8
1.2%
2
76.5
1
76.3
10
74.9
75.1
1
2
1
73.9
12.5
2
74.8
2
73.0
10
74.2
12.7
2'"
1
73.0
68.2
5
2
12.6
68.6
5
10
73.1
70.1
5
Liver
1
99.5
99.2
Male Rats
1
2
99.5
99.2
4.6%
1
10
99.5
99.5
1
98.8
97.1
2
1
2
98.6
97.5
2
99.0
97.4
2
10
96.2
78.5
5
1
96.8
76.2
2
5
76.2
97.8
5
10
FR
Leuk. /Lymphoma 1
1
100.0 100.0
19.1%
100.0 100.0
1
2
1
10
100.0 100.0
100.0 100.0
2
1
2
2
100.0 100.0
10
100.0 100.0
2
100.0 100.0
5
1
5
2
100.0 100.0
100.0 100.0
5
10
Male Mice
Liver
1
100.0 100.0
1
32.5%
1
100.0 100.0
2
1
100.0 100.0
10
2
1
100.0 100.0
2
100.0 100.0
2
2
10
100.0 100.0
5
1
100.0
99.9
5
100.0
99.8
2
5
100.0
99.8
10
* entries are given in percentages
e
Lethality and Tumor Lethality
in the HIgh Dose Group.
Zp
76.1
76.0
74.9
75.8
76.6
76.3
79.9
79.1
80.4
99.3
99.5
99.5
98.2
98.4
98.8
92.8
93.0
94.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Ztt
76.0
75.9
74.8
75.5
74.2
73.0
75.8
71.8
70.5
99.2
99.3
99.4
97.8
98.0
97.8
89.6
85.4
82.3
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
ZIt
75.7
75.8
75.1
81.3
80.6
77.7
92.2
90.8
81.7
99.2
99.3
99.4
99.6
99.6
99.3
99.6
99.8
99.6
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
~y
74.3
73.1
60.8
71.2
68.5
43.7
65.8
55.5
26.6
99.6
99.5
99.1
98.5
98.0
94.4
92.9
90.7
12.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.6
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Zlog
76.0
74.3
63.8
74.4
70.2
SO.l
12.8
61.5
32.0
99.4
99.5
99.3
98.7
98.4
97.3
95.8
94.2
83.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
57
change then it appears that there is no apparent change in the Type
I error rate for Zoo
Furthermore, most of the observed Type I error
rates fall into the 90% confidence interval (.4,.6).
The results
for Female Rat Lung tumors may provide an exception.
These tumors
are vary rare; hence it is likely that simulation of such a tumor
may result in many data sets where no tumors were observed.
This
phenomena was also observed by Portier and Hoel (1984) who noted that
low background tumor rates caused Type I error problems in tests of
trends in proportions.
This may be due to the data being discrete
for low background tumor rates.
Therefore, a test that is
conditional upon tumor occurence may be conservative for such a rare
tumor.
The Cochran-AIBdtage trend test, Zt' the poly-3 trend test, Zp'
..
and the truncated trend test, Ztt' have smaller Type I error rates
with increasing treatment lethality for almost all conditions
considered.
This result confirms the statements in the previous
section where the
aj(x).
when
j were seen to be a function of both >"j (x) and
In fact, rt j is a decreasing function of aj(x). Therefore,
>..a(t).~(t)
rto~ ••• ~~'
specified.
rt
••••• ~(t) and
aO(t)~~(t)~ ••• ~~(t),
we see that
and the test will be less likely to reject than nominally
TUmor lethality seems to have no effect on the
significance levels of these tests.
This is an expected result
since rt j is not a function of Yj. Generally, both·of the modified
trend tests (Zp and Ztt) show superior robustness to treatment
lethality over that of the Cochran-Armitage trend test. The modified
trend procedures tend to have larger Type I error than the true
significance level for the smallest background tumor rate, and the
58
effect of treatment lethality on the level of the quantal response
trend tests appears to increase as the background tumor rate
increases.
The Poly-3 test appears to be superior to the truncated
trend test in this regard.
The anti-conservative nature of Zp for
the low background case described in the previous section is because
the shape of the tumor incidence function for this case is much
smaller than 3.
A small simulation experiment was done to assess
the effect of changes in the shape parameter of the tumor incidence
function (112 ) on the Type I error rate of the Poly-3 test. The
results of the simulations for the case of moderate treatment
lethality (1 + cxa - 2) are summarized in Table 4.5.
Except for the
case of a rare tumor, this test does very well at maintaining the
proper Type I error.
For higher treatment
I error dropped off dramatically.
As
lethalitY(cxa~4),
the Type
the true shape of the tumor
onset distribution increased to 5, the Type I error dropped to about
2% for all background rates and very high treatment lethality
(cxa~10).
In addition to the simulation results presented in Table
4.5, the operating characteristics
o~
an obvious modification of the
Poly-3 test, the Poly-k test(i.e. set 112-k) was considered.
It was
found that, except for extremely small backgrounds, the true Type I
error rate was not "significantly" different from the nominal level.
Thus, when some knowledge of the shape of the tumor incidence
funtion over time is available, the Poly-3 test can be improved.
Power tables for the simulations of the poly-k procedure are given
in Appendix o.
The Type I error of the lifetable test, ZIt' increases as the
level of treatment lethality increases. Within a given degree of
..
59
Table 4.5
Type I error rate of the Poly-3 test at the 5% nominal level for varying
shapes and background rates under moderate treatment lethality.
True Shape (~)
Background Rate
0.01
0.05
0.20
*
1.0
2.5*
6.4
6.5
Entries are given as percentages
3.0
3.1
4.7
6.0
5.0
2.5
3.8
4.5
7.0
1.8
5.5
4.0
60
treatment lethality, increasing tumor lethality leads to rejection
probabilities which are closer to the nominal levels.
This is
expected since, as .0 increases, the age at death from the tumor
converges to the age at tumor onset.
The empirical behavior of this
test matches its predicted behavior based on a consideration of the
event-specific hazard functions, hj(S), given earlier.
It is worth
noting that this test is valid only for instantantly lethal tumors.
TUmors which led to only a 10-fold increase in lifetime risk were
considered in this study.
From Figure 2, one can see that this
study examines the behavior of the lifetable test for moderately
lethal tumors which should provide a situation for the lifetable
test to do well.
The rejection probabilities of the
the logistic regression test,
Hoel~alburg
test, Zhw' and
Zlog' were affected in a complex
fashion by treatment lethality and tumor lethality. Wi thin a
particular level of tumor lethality, the Type I error rate tended to
decrease with increasing levels of treatment lethality as predicted
by Lagakos(1982).
Dinse(1985) illustrated similar effects of
treatment lethality on the prevalence tests Zhw and Zlog.
Figures 3 through 9 illustrate the effects of treatment
lethality and tumor lethality on the distributions of the test
statistics considered in this study for the male mice liver tumors.
Each figure depicts the distribution of a test statistic under a
particular treatment lethality and tumor lethality condition.
The
top left graph illustrates the distribution of the test statistic
under conditions of no treatment lethality and incidental tumors (no
tumor lethality).
Treatment mortality increases along the
61
Figure 3:
Empirical Distribution of the onset test statistic under
varying levels of Treatment Lethality and Tumor Lethality
for Male Mice Liver Tumors~
Nonl
*
Tr..tmlnt Llth.lity
Low
High
62
Figure 4:
Empirical Distribution of the Cochran-Armitage Trend test
statistic under varying levels of Treatment Lethality and
Tumor Lethality for Male Mice Liver Tumors.
Non.
:.,=
••
.....
....
... "
~­
00
e2
~
...._
. .i.IoIoIi.IoIoIl"I"I"Il"I"I"I~....
Tr.ltm.nt LlthlUty
Low
63
Figure 5:
.i
Empirical Distribution of the Truncated Trend test
statistic under varying levels of Treatment Lethality and
Tumor Lethality for Male Mice Liver Tumors.
Trlltmlnt Llth,lIt.,
Low
Non.
I:
u
S
,.
...._1IIIIIIII.
...
.
••
-.
.':
-'=o ..
..e2"
~
CI CI
t! ..._.-01.............................- '
High
64
Figure 6:
Empirical Distribution of the Poly-3 Trend test statistic
\Ulder varying levels of Treatment Lethality and Tumor
Lethality for Male Mice Liver Tumors.
Non.
•c:
3
'13
.s
=.:
....
.
~
.
••
~;~
.. "
e2
~
00
~
......~I.1.1.1'""...",Ia_. .....
Tr••tm.nt L.th.llty
Low
High
65
Figure 7:
Empirical Distribution of the Logistic Score test
statistic under varying levels of Treatment Lethality and
Tumor Lethality for Male Mice Liver TUmors.
None
Tr••tm.nt L.th.lity
Low
High
66
Figure 8:
Empirical Distribution of the Hoel~alburg test statistic
under varying levels of Treatment Lethality and Tumor
Lethality for Male Mice Liver Tumors.
Tr.ltmlnt LlthlUty
Low
Non.
-.
:.
,,=
4.
i~
~.
a"
00
e2 '-_.-1...",.,.................._
~
4
CI
f
..
67
Figure 9:
Empirical Distribution of the Lifetable test statistic
under varying levels of Treatment Lethality and Tumor
Lethality for Male Mice Liver Tumors.
T,..tment Leth'lity
Low
None
_
c:
~u
S
-..-.
w.w........_ _..
......
~1IIIiW,j
:.-
.':
..
Ai:_
..e2"
~
00
.,!
....u.................IooIoIiiI. . ._
CI::
•
....
I
68
horizontal axis where the middle column illustrates a3(t) - 2aO(t)
and the third column, a3(t) • SaO(t). Tumor lethality increases as
one moves vertically down each column where the second row
represents a 2-fold increase in tumor lethality and the third row
represents a lO-fold increase in tumor lethality.
Under the null
hyPOthesis of no treatment effect on tumor incidence and when each
test's assumptions are satisfied, all test statistics should be
distributed as N(O,l); hence a standard normal distribution has been
superimposed over the empirical distributions of the test statistics
to act as a visual aid.
If the distribution of the test statistic
shifts to the right relative to the standard normal curve, the
statistic has rejected more frequently than nominally specified.
If
the distribution shifts to the left, then the statistic has rejected
less frequently than nominally specified.
From Figure 3, it is apparent that neither treatment lethality
nor tumor lethality cause severe changes to the distribution of Zoo
The remaining tests all show some sensitivity to changes in tumor
lethality or treatment lethality.
The quantal response tests are displayed in Figures 4-6.
The
Cochran-ArDdtage test statistic (Figure 4) is very sensitive to
changes in treatment lethality but not affected by changes in tumor
lethality.
The distribution of this test statistic shifts to the
left (an apparent location change) as treatment lethality increases;
however, the distribution of this statistic is not shifted when
tumor lethality increases.
one can easily see from Figure 5 that
the results for the truncated trend statistic are very similar to
the results for the Cochran-ArDdtage trend test though the location
•
69
shift for Ztt appears to be less extreme than that for Zt when
treatment lethality increases.
the Zp statistic.
Figure 6 illustrates the behavior of
This statistic does not appear to be affected by
lethality increases, i.e. no major shift in the distribution of Zp
is apparent.
The empirical distribution of the prevalence test statistics,
Zlog and Zhw' are presented in Figures 7 and 8, respectively.
From
Figure 7, it appears that logistic regression is not severely
affected by treatment lethality but is shifted slightly to the left
as tumor lethality increases.
The most dramatic shift appears in
the bottom right graph which may suggest a interactive effect of
high tumor lethality and high treatment lethality on the
distribution of ZlogO
The Hoel-Walburg test statistic with NTP
intervals, Zhw' is seen in Figure 8 to behave in a similar manner to
Zlog relative to increases in treatment lethality and tumor
lethality.
High tumor lethality and high treatment lethality appear
to lead to an even greater leftward shift in the distribution of Zhw
than was seen in the distribution of Zlog.
The lifetable test statistic, Zlt' is seen to be very sensitive
to increases in treatment lethality for tumors that are not
instantly lethal.
It appears that an interaction between treatment
and tumor lethality is present in these results, and the interaction
•
..
is opposite to the one for the prevalence tests.
Figure 9
demonstrates the rightward shift of the distribution of this
statistic under conditions of increasing treatment lethality.
The
rightward shift due to high treatment lethality is moderated by
higher levels of tumor lethality.
This is not surprising since Zlt
70
converges to Zo for instantaneously lethal tumors.
Section 4.2.2 PoWer Results
Table 4.2 presents the probability of rejection for the test
statistics considered in this study for the situation where the
compound induces a doubling in tumor onset in the high dose group
over the control group.
For conditions of no treatment lethality
and no tumor lethality, all tests have essentially the same power,
and
all tests show an increase in power as the background tumor rate
increases. Within a given level of background tumor rate, the power
of these tests will vary according to the Type I error rate given
previously.
For example, since quantal response tests become
conservative with increasing levels of dose-related toxicity, it is
expected (and is observed) that these tests are less powerful with
the introduction of dose-related toxicity, and therefore these tests
have a decreased capability of detecting true differences in tumor
incidence between the groups.
The inflated Type I error for the
lifetable test leads to a corresponding inflation in power; hence,
many compounds may be incorrectly flagged as tumorigenic when using
this test.
Tumor lethality, which leads to conservative Type I
error rates in the prevalence tests is translated into reduced power
for detecting true tumorigenic differences between the groups.
From Tables 4.3 and 4.4, it appears that essentially all of the
tests have a power of 1 for tumor sites with a background tumor rate
exceeding 19% and a five- or ten-fold increase in tumor incidence in
the high dose group relative to the control group.
For a 5%
background tumor rate, no treatment lethality, and no tumor
•
71
lethality, the power of the tests are approximately 0.8 for the 5fold increase in tumor incidence and nearly 1.0 for the 10-fold
increase in tumor incidence.
For a 1% background tumor rate, no
treatment lethality, and no tumor lethality, the power of the tests
range from 0.4 for the 5-fold increase in tumor incidence to 0.75
for the lO-fold increase in tumor incidence. With regard to
increases in tumor lethality and increases in treatment lethality,
the tests behave in a similar fashion to the results found in Table
4.2.
Chapter 5. Discussion
The large sample behavior of the commonly used tests of
carcinogenicity and the results from this simulation study indicate
the sensitivity of many standard tests for carcinogenicity to
treatment lethality and tumor lethality.
Thus, treatment lethality
and tumor lethality clearly play important roles in the analysis of
bioassay experiments.
Quantal response trend tests are robust to tumor lethality
assumptions which is not surprising since these tests depend only on
the presence of the tumor and not on the time of tumor occurence.
However, treatment lethality has dramatic effects on the quantal
response tests.
This is related to the fact that even if a dose-
response exists, treatment lethality can kill off animals prior to
the occurence of a tumor.
Since most carcinogenicity studies show
some evidence of treatment lethality, a survival-adjusted quantal
response trend test is a necessity.
The utility of the lifetable test is questionable since it is
extremely sensitive to treatment lethality.
The prevalence tests
are proposed as tests which correct for treatment lethality;
however, it was surprising to find the degree of the effect that
extreme treatment lethality can'have on the Type I error of these
tests.
The magnitude of the effect of treatment lethality on the
lifetable test and on the prevalence tests was seen to depend on
73
tumor lethality.
Since many studies will have moderate treatment
lethality and unknown tumor lethality, the tests should be used with
care.
As with any analysis of the operating characteristics of test
statistics, the results of the simulation study and the large sample
study are only applicable to the cases considered.
However, the
cases considered here cover a broad range of possibilities and
should be applicable to most carcinogenicity experiments. one case
not considered was when the effect of treatment on tumor incidence
was non-linear.
Since all of the tests studied here assume a linear
trend as the alternative hypothesis, consideration of only the
linear case is justified. As further research, it would be of
interest to consider the power of the more robust linear trend tests
when the data arises from a non-linear treatment effect.
Finally,
the logistic regression model used in this analysis controlled for
survival differences by using a linear time effect.
It may be
possible to improve the operating characteristics of this test
statistic by using a cubic time effect similar to that used by the
Poly-3 test.
The research discussed above considered the basic bioassay
study which included only one sacrifice - that being done at study
termination.
It is worth noting that study designs are now being
implemented which include interim sacrifices. When interim
sacrifices are used, information is available for estimating the
tumor incidence function, and thus better tests of tumor incidence
can be constructed.
MCKnight and Crowley( 1984) propose a parametric
test that makes use of interim sacrifice information which allows
74
the tumor incidence function to be estimated and subsequently
tested.
oewanji and Kalbfleisch (1985) develop a nonparametric
alternative of such a test, and Portier and Dinse (1986) have
proposed a semi-parametric version of this test.
In summary, when no information is available on tumor lethality
and differences in treatment lethality exist, the poly-3 procedure
appears to be the most robust test.
If information is available
about tumor lethality, a survival-adjusted test can be used.
If the
shape of the tumor incidence function is expected to folow time to
some power k, the poly-3 test can be modified to become a Poly-k
test which should have superior operating characteristics to the
poly-3 test.
75
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carter, L. (1979) How to Assess Cancer Risks. Science,204,811-816.
Chapman, D.
&
Nam, J. (1968) Asymptotic Power of Chi-Square Tests
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Ciminera, J. (1985) Some Issues in the design, evaluation, &
interpretation of tumorigenicity studies in animals.
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Cornfield, J. (1977) Carcinogenic Risk Assessment. Science,198,693699.
oewanji, A. & Kalbfleisch, J. (1985) Non-parametric methods for
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Dinse, G. & Lagakos, S. (1983) Regression Analysis of Tumor
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Dinse, G. (1985) Testing for a Trend in Tumor prevalence Rates: I
Nonlethal Tumors. Biometrics, 41,751-770.
Fairweather, W. (1985) CUrrent Issues in the Interpretation of
Animal Tumorigenicity Studies. proceedings of the
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Gart, J.,Chu, K., & Tarone, R. (1979) Statistical Issues in
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Carcinogenicity. Journal of the National Cancer
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Gart, J., & Tarone, R. (1986) Efficiency of Age-Adjusted Tests in
Animal Carcinogenicity Experiments: A Personal View.
Unpublished manuscript.
Haseman, J. (1984) Statistical Issues in the design, analysis, and
interpretation of animal carcinogenicity studies.
Environmental Health perspectives,58,385-392.
76
Hoel, D. & walburg, H. (1972) Statistical Analysis of survival
experiments. Journal of the National Cancer
Institute, 49, 361-372.
Lagakos, S. (1982) An evaluation of some two-sample tests used to
analyze animal carcinogenicity experiments. Utilitas
Mathematicas,218,239-260.
Mantel, N.
&
Haenszel, W. (1959) Statistical Aspects of the analysis
of data from retrospective studies of disease.
Journal of the National Cancer Institute,22,719-748.
Mantel, N.
&
Scheiderman, M. (1975) Estimating "Safe" Levels, a
Hazardous Undertaking. Cancer Research,35,1379-1386.
McKnight, B. & Crowley, J. (1984) Tests for differences in tumor
incidence based on animal carcinogenesis
experiments. Journal of the American Statistical
Association,79,639-648.
Peto, R. (1974) Guidelines on the analysis of tumor rates and death
rates in experimental animals. British Journal of
Cancer, 29,101-105.
Peto, R.,Pike, M.,oay, N.,Gray, R.,Lee, P.,Parish, S.,Peto,
J.,Richard, 5., and Wahrendorf, J. (1980) Gudielines
for simple, sensitive significance tests for
carcinogenic effects in long-term
animal experiments. In Annex to Long-Term and ShortTerm Screening Assays for Carcinogens: A Critical
Appraisal,International Agency for Research on
Cancer Monographs, Supplement 3,331-426,Lyon:IARC.
Portier, C. and Dinse, G. (1986) Semi-Parametric Analysis of Tumor
onset in Survival/Sacrifice Experiments, unpublished
Manuscript.
Portier, C.,Hedges, J., & Hoel, D. (1986) Age-Specific Model of
Mortality and TUmor onset For Historical Control
Animals in the National Toxicology Program's
Carcinogenicity Experiments, Cancer
Research, 46, 4372-4378.
Portier, C. & Hoel, D. (1984) Type I error of trend tests in
proportions and the design of cancer screens.
Commun. Statist.-Theor. Meth.,13,1-14.
Randles, R. & Wolfe, D. (1979) Introduction to the Theory of
Nonparametric Statistics.Wiley,New York.
Ryan, L. (1985) Efficiency of age-adjusted tests in animal
carcinogenicity experiments. Biometrics,41,525-531.
Tarone, R. (1975) Tests for trend in life table analysis.
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77
Van Ryzin, J. (1980) Quantitative Risk Assessment. Journal of
Occupational Medicine,22,321-326.
78
Table A.1: ~red ~lative Efficacies for CcJmDnly used
Tests of carcinogenicity for Female Mice
'I\JnDr
Site
Treatment
Lethality
l+cro
Hemangiana1
Hemafigiosarcana
2
5
Liver
1
2
5
~oid
ollicular
cell
1
2
5
leukemia;
Lynpma
1
2
5
I~tary
1
2
5
'I\JnDr
Lethality
1+'0
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
eff2(Zo)/ef~(Ztest)
Zt
ZIt
~
Zlog
1.000
1.000
1.000
1.114
1.114
1.114
1.486
1.486
1.486
1.000
1.000
1.000
1.087
1.087
1.087
1.345
1.345
1.345
1.000
1.000
1.000
1.092
1.092
1.092
1.371
1.371
1.371
1.000
1.000
1.000
1.117
1.117
1.117
1.505
1.505
1.505
1.000
1.000
1.000
1.114
1.114
1.114
1.490
1.490
1.490
1.000
1.000
1.000
0.891
0.895
0.919
0.720
0.729
0.784
1.000
1.000
1.000
0.877
0.883
0.917
0.694
0.706
0.781
1.000
1.000
1.000
0.879
0.885
0.917
0.698
0.710
0.781
1.000
1.000
1.000
0.893
0.897
0.919
0.728
0.736
0.785
1.000
1.000
1.000
0.891
0.895
0.919
0.721
0.729
0.784
1.000
1.000
1.000
1.018
1.045
1.219
1.174
1.239
1.740
1.000
1.000
1.000
1.022
1.057
1.263
1.200
1.287
1.922
1.000
1.000
1.000
1.021
1.056
1.276
1.193
1.280
1.949
1.000
1.000
1.000
1.020
1.040
1.157
1.179
1.227
1.550
1.000
1.000
1.000
1.018
1.045
1.224
1.173
1.239
1.753
1.000
1.000
1.000
1.017
1.043
1.218
1.164
1.229
1.729
1.000
1.000
1.000
1.021
1.056
1.262
1.193
1.280
1.917
1.000
1.000
1.000
1.020
1.055
1.276
1.185
1.272
1.946
1.000
1.000
1.000
1.018
1.038
1.155
1.168
1.216
1.538
1.000
1.000
1.000
1.017
1.044
1.223
1.162
1.228
1.742
e
79
Table A.2: ?quared Relative Efficacies for CCJma1ly Used
Tests of carcinogenicity for Female Mice
2
TLmDr
Site
Liver
Treatment
Lethality
l+orc
1
2
5
~oid
ollic:ular
cell
1
2
5
leukemia,!
Lynpnria
1
2
e
5
Man'mary Glani
Fibroadenana
1
2
5
1
2
5
TLmDr
Lethality
1+'0
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
2
eff (Zo)/eff (Ztest)
Zt
ZIt
~
Zlog
1.000
1.000
1.000
1.182
1.182
1.182
1.952
1.952
1.952
1.000
1.000
1.000
1.068
1.068
1.068
1.254
1.254
1.254
1.000
1.000
0.999
1.057
1.057
1.056
1.206
1.206
1.206
1.000
1.000
1.000
1.093
1.093
1.093
1.372
1.372
1.372
0.972
0.953
0.904
0.969
0.955
0.921
0.971
0.968
0.961
1.000
1.000
1.000
0.923
0.925
0.933
0.791
0.794
0.816
1.000
1.000
1.000
0.863
0.871
0.913
0.669
0.685
0.775
1.000
1.000
0.999
0.857
0.866
0.915
0.661
0.678
0.780
1.000
1.000
1.000
0.877
0.881
0.911
0.696
0.706
0.770
0.972
0.953
0.904
0.798
0.805
0.846
0.581
0.608
0.748
1.000
1.000
1.000
1.011
1.022
1.104
1.121
1.148
1.358
1.000
1.000
1.000
1.025
1.066
1.286
1.222
1.326
2.043
1.000
1.000
0.999
1.027
1.069
1.250
1.238
1.345
1.941
1.000
1.000
1.000
1.023
1.049
1.186
1.210
1.271
1.672
0.972
0.953
0.904
0.993
1.068
1.381
1.184
1.415
2.919
1.000
1.000
1.000
1.008
1.019
1.099
1.097
1.123
1.321
1.000
1.000
1.000
1.024
1.065
1.284
1.215
1.320
2.040
1.000
1.000
0.999
1.027
1.068
1.246
1.232
1.341
1.928
1.000
1.000
1.000
1.022
1.047
1.185
1.198
1.260
1.665
0.972
0.953
0.904
0.992
1.068
1.378
1.184
1.419
2.937
80
Table A.3: ~red Relative Efficacies for carrral1.y Used
Tes s of carcinogenicity for Male Mice
'l\m)r
Site
Treatment
Lethality
1+ao
Hemangiana. 1
Hemafigiosarcana
2
5
Liver
1
2
5
~oid
ollicular
cell
1
2
5
Leukemia;
Lynpnna
1
2
5
Lung .
1
2
5
'l\m)r
lA:!thality
1++0
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
. ef~(Zo)/eff2(Ztest)
Zt
1.000
1.000
1.000
1.152
1.152
1.152
1.755
1.755
1.755
1.000
1.000
1.000
1.073
1.073
1.073
1.293
1.293
1.293
0.974
0.960
0.909
0.985
0.974
0.936
1.021
1.018
1.006
1.000
1.000
1.000
1.117
1.117
1.117
1.522
1.522
1.522
1.000
1.000
0.999
1.076.
1.075
1.075
1.305
1.305
1.305
ZIt
~
Zlog
1.000
1.000
1.000
0.930
0.931
0.939
0.804
0.807
0.828
1.000
1.000
1.000
0.884
0.889
0.920
0.709
0.720
0.789
0.974
0.960
0.909
0.823
0.824
0.840
0.613
0.629
0.720
1.000
1.000
1.000
0.909
0.911
0.927
0.758
0.763
0.801
1.000
1.000
8·99~
.88
0.890
0.921
0.710
0.721
0.789
1.000
1.000
1.000
1.010
1.022
1.106
1.108
1.135
1.347
1.000
1.000
1.000
1.023
1.049
1.174
1.198
1.260
1.628
0.974
0.960
0.909
0.990
1.042
1.330
1.153
1.303
2.469
1.000
1.000
1.000
1.016
1.033
1.148
1.146
1.188
1.498
1.000
1.000
0.999
1.021
1.0~1
1.2 3
1.189
1.262
1.751
1.000
1.000
1.000
1.009
1.021
1.104
1.098
1.125
1.332·
1.008
1.00
1.000
1.023
1.049
1.170
1.194
1.256
1.614
0.974
8:~gB
0.990
1.041
1.330
1.151
1.301
2.476
00
1'800
1.
1.000
1.015
1.032
1.147
1.139
1.180
1.489
1.000
1.000
0.99~
1.02
1.051
1.20~
1.18
1.258
1.738
e
•
81
Table A.4: ~red Relative Efficacies for CCIlI'la'l1y Used
Tes s of carcinogenicity for Male Rats
2
'l\Jm:)r
Site
Liver
Treatment
Lethality
1+eto
1
2
5
Isukemia/
LYJlP'1atB
1
2
5
Int:ntary
Sysem
1
2
e
5
Lung
1
2
5
Mesotheliana
1
2
5
'l\Jm:)r
Lethality
1++0
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
2
eff (Zo)/eff (Ztest)
Zt
ZIt
Zm.r
Zlog
1.000
1.000
1.000
1.140
1.140
1.140
1.564
1.564
1.564
1.000
1.000
1.000
1.096
1.096
1.096
1.352
1.352
1.352
1.000
1.000
1.000
1.106
1.106
1.106
1.393
1.393
1.393
0.993
0.988
0.981
1.031
1.029
1.025
1.119
1.119
1.120
1.000
1.000
1.000
1.158
1.158
1.158
1.673
1.673
1.673
1.000
1.000
1.000
0.848
0.856
0.898
0.662
0.675
0.758
1.000
1.000
1.000
0.831
0.842
0.900
0.640
0.659
0.766
1.000
1.000
1.000
0.834
0.845
0.901
0.640
0.659
0.765
0.993
0.988
0.981
0.799
0.819
0.907
0.593
0.629
0.802
1.000
1.000
1.000
0.856
0.862
0.899
0.674
0.686
0.758
1.000
1.000
1.000
1.028
1.065
1.286
1.257
1.350
2.029
1.000
1.000
1.000
1.037
1.076
1.248
1.299
1.397
1.931
1.000
1.000
1.000
1.032
1.080
1.345
1.277
1.402
2.275
0.993
0.988
0.981
1.028
1.119
1.481
1.289
1.548
3.071
1.000
1.000
1.000
1.026
1.058
1.261
1.245
1.326
1.931
1.000
1.000
1.000
1.025
1.062
1.285
1.234
1.328
2.015
1.000
1.000
1.000
1.034
1.074
1.246
1.286
1.386
1.928
1.000
1.000
1.000
1.029
1.078
1.345
1.262
1.389
2.281
0.993
0.988
0.981
1.027
1.119
1.477
1.287
1.552
3.099
1.000
1.000
1.000
1.022
1.055
1.259
1.218
1.299
1.905
82
Table B.1: Probabili~ of Rejectial for carci~nici~ Tests for varying
levels of Treatment Lethality and 'l\m:)r ~thal~ for emale Mice
Hemagianas-Hemangiosarcanas using the
design.
Q1set Treatment 'l\.m:)r
Factor ~thality Lethality
1++0
l+yO
1+0r0
Zt
Zp
Zlog Zm.,
Zo
Ztt
ZIt
1
1
1
1
1
I
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.7
6.8
5.8
5.2
4.7
4.9
2.4
2.3
3.7
17.7
18.4
16.9
13.8
13.5
12.8
7.4
7.3
6.5
59.9
62.8
62.4
53.5
54.3
50.2
32.2
30.5
32.0
95.5
96.5
96.0
91.9
91.2
91.2
71.1
70.4
71.2
entries are percentages.
6.3
6.5
5.5
5.4
5.0
5.2
3.5
4.0
4.8
17.0
17.8
16.1
15.2
14.8
14.0
12.5
12.1
11.7
60.5
62.6
61.6
59.8
60.4
55.9
49.4
47.9
49.8
95.8
96.8
96.2
94.7
94.0
94.8
1
88K·.0
88.8
6.0
6.4
5.2
6.2
5.5
5.4
5.1
5.5
6.8
16.5
17.4
16.0
16.5
15.9
14.3
16.8
15.7
12.7
60.3
62.1
62.0
61.9
61.5
55.2
51.7
49.7
44.3
95.8
97.1
96.2
95.0
93.8
93.2
86.8
85.4
81.0
5.9
6.5
5.4
6.1
5.3
5.3
5.2
5.2
6.2
16.5
17.5
16.9
16.2
16.1
13.5
16.8
15.2
11.5
60.2
62.4
61.5
62.2
61.2
52.5
55.5
52.7
44.3
95.7
97.0
96.1
95.5
94.3
92.8
91.4
89.8
83.2
5.8
5.8
5.3
5.8
5.1
3.9
5.0
5.0
5.1
16.5
17.5
15.7
15.0
13.9
11.2
15.2
14.0
8.2
59.5
61.7
59.7
61.2
59.6
46.5
50.0
45.1
33.4
95.5
96.5
95.5
95.0
93.4
89.0
87.0
85.5
70.7
6.1
6.0
5.2
7.5
6.7
6.4
9.1
9.8
10.6
16.4
17.5
15.8
19.0
19.3
18.2
29.0
26.9
22.9
60.0
61.5
61.5
68.2
67.2
63.5
78.0
75.5
72.7
95.6
96.9
96.2
97.6
96.8
96.8
98.8
97.1
97.3
6.3
6.5
5.2
5.5
5.2
5.4
4.5
4.9
6.7
16.6
17.8
15.9
16.0
15.8
15.2
15.5
14.5
14.0
60.4
62.5
61.9
61.8
61.5
58.2
55.1
53.5
54.9
95.9
97.1
96.1
95.5
94.9
95.4
91.5
91.~
92.
e
83
Table B.2: Probabi1i~ of Rejection for carci~niCi~ Tests for varying
levels of Treabnent r.sthalit;y arxi 'l\m:)r Iethali for emal.e Mice
Integumentar:y System bJnDrs using the
design.
cnset Treatment 'l\.m:)r
Factor lethality lethality
1++0
l+yO
Zt
l+cro
Zp
Zloq ~
Zo
Ztt
ZIt
e
.
-
...
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
*3.2
1
2
3.3
1
10
5.2
1
1
2.1
2
2
2.0
2
1.3
10
2
1
0.8
5
1.5
2
5
10
1.4
5
9.1
1
1
2
8.8
1
10
9.0
1
1
7.7
2
2
8.4
2
10
7.9
2
1
4.4
5
2
4.0
5
10
4.6
5
1
1
29.8
2
32.2
1
28.2
10
1
1
25.4
2
2
23.5
2
10
26.1
2
1
16.0
5
2
15.0
5
10
15.5
5
63.4
1
1
1
2
60.8
60.3
1
10
1
50.8
2
2
52.8
2
10
50.4
2
1
32.2
5
2
35.2
5
10
32.9
5
entries are percentages•
3.2
3.3
5.2
2.4
2.2
1.5
7.3
6.6
7.7
9.2
9.0
9.0
8.5
9.0
8.5
11.5
12.5
13.2
29.9
32.2
28.9
28.3
25.9
29.1
27.2
26.1
27.3
62.6
60.7
59.2
55.0
56.8
53.9
45.7
49.3
46.9
3.5
3.5
5.0
5.0
4.8
3.7
9.3
7.8
8.8
9.2
8.9
9.2
12.3
11.7
11.2
14.4
14.6
14.2
30.2
31.9
29.5
30.8
28.5
30.7
33.2
31.5
28.9
62.6
60.2
59.5
57.2
59.0
54.0
51.4
53.8
45.4
3.5
3.5
5.1
5.0
4.8
3.6
9.1
7.8
8.7
9.2
9.0
9.1
12.2
11.7
10.7
14.1
14.4
14.0
30.2
31.9
29.0
30.3
28.2
28.9
32.9
31.0
26.8
62.9
60.2
59.3
56.9
58.5
52.4
51.8
53.2
42.6
3.6
3.8
5.8
5.3
4.9
3.5
5.2
5.5
4.5
9.1
9.2
10.1
12.7
12.2
8.8
9.6
9.2
7.8
29.9
31.5
28.9
29.4
27.2
25.3
26.1
24.5
19.3
62.2
59.4
58.3
55.9
56.2
47.2
45.8
45.8
32.7
3.3
3.6
5.1
6.3
5.4
4.1
10.5
9.2
10.3
9.2
8.9
9.3
14.0
13.8
12.3
18.0
17.9
17.2
30.0
31.5
28.9
~3.7
1.9
33.8
42.9
41.2
39.2
62.4
60.4
59.4
62.1
64.0
59.9
69.0
70.1
63.2
3.2
3.3
5.2
3.6
3.2
3.2
6.2
6.2
7.2
9.3
9.0
9.1
9.8
10.1
10.4
11.1
11.2
11.4
29.8
31.9
29.0
29.5
27.3
30.8
28.2
26.9
28.5
62.5
60.4
59.7
56.3
58.4
56.0
49.4
53.2
49.8
84
Table B.3: Probabili!:y of Rejectioo for carci~nici~ Tests for varying
levels of Treat:nent IBthaliq; and 'l\m)r lethali for emale Mice
Liver 'l\m)rs using the NIP design.
Q1set Treat:nent 'l\m)r
Factor lethality lethality
1++0
l+yO
l+cr.o
Zt
Zp
Zloq ~
Zo
Ztt
ZIt
1
1
*5.0
1
2
4.2
10
1
5.2
4.2
2
1
2
2
4.5
2
10
3.5
1.5
5
1
5
1.4
2
10
1.8
5
1
29.3
1
1
31.5
2
1
32.1
10
2
25.2
1
2
22.8
2
2
10
23.2
5
1
10.9
10.5
5
2
5
10
10.~
1
1
95.
1
2
95.0
1
10
95.3
2
1
90.2
2
2
90.2
2
10
91.2
5
1
67.1
5
2
68.7
10
67.3
5
1
1
100.0
1
2
100.0
1
10
100.0
2
1
99.9
2
2
100.0
2
10
99.9
5
1
98.2
5
2
98.2
is
98.2
5
10
* table entries are percentages.
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
5.0
4.6
~.5
.8
5.9
4.8
4.8
3.8
4.8
30.5
32.2
32.8
31.6
29.8
29.5
25.7
24.6
23.3
95.6
95.3
95.2
93.4
93.5
94.0
88.8
88.5
88.3
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
100.0
5.2
4.7
5.5
6.2
5.8
4.1
5.0
3.6
2.4
30.8
31.8
33.2
31.0
28.3
25.4
23.6
18.5
15.3
95.5
95.2
95.0
92.8
92.1
92.3
81.7
80.6
73.3
100.0
100.0
100.0
100.0
100.0
99.9
99.5
99.1
99.0
5.1
4.6
5.4
6.1
6.0
3.4
6.5
4.1
2.3
30.2
32.2
33.6
32.9
29.8
22.4
29.0
23.3
12.2
95.9
95.2
94.0
94.3
92.9
88.0
89.8
86.8
68.8
100.0
100.0
100.0
100.0
100.0
99.9
100.0
99.8
98.2
5.2
4.6
5.7
6.2
5.5
2.2
5.6
3.4
1.1
30.3
31.8
32.0
32.5
28.3
18.9
25.0
21.3
7.4
95.5
94.8
92.9
93.7
92.2
81.9
85.9
82.6
52.9
100.0
100.0
99.9
100.0
100.0
99.8
100.0
99.~
93.
5.2
5.2
5.2
9.9
8.4
7.3
19.1
17.2
13.1
30.4
32.2
32.8
42.4
41.1
37.2
60.0
58.5
47.8
95.5
94.8
95.4
97.2
96.9
96.6
98.8
99.3
97.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.2
4.6
5.4
6.0
5.8
5.2
5.6
4.3
5.2
30.9
32.6
33.5
32.8
~1.4
9.8
27.0
26.~
25.
9~.1
9 .4
95.5
93.9
94.3
94.6
90.0
90.4
90.5
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
99.9
e
85
Table 8.4: Probabili~ of Rejection for carci~nici~ Tests for varying
levels of Treatment lethalitY am '!\mOr lethali for emale Mice
Ieukemia;Lyn¢anas using the NI'P deSlgn.
Qlset Treatment '!\mOr
Factor lethality lethality
1++0
l+yO
1+<;>
Zt
Zp
Zlog Zrnt
Zo
Ztt
ZIt
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*3.4
4.5
4.7
3.1
2.2
2.4
0.1
0.2
0.2
62.2
64.5
61.5
40.1
39.9
38.7
6.5
5.8
6.7
100.0
100.0
99.9
99.2
99.3
99.3
75.2
71.6
72.0
100.0
100.0
100.0
100.0
100.0
100.0
98.5
98.5
98.8
entries are percentages.
3.3
4.8
4.6
4.6
3.8
3.8
1.5
0.8
1.5
63.8
64.4
62.8
54.1
53.9
50.9
28.5
24.3
28.4
100.0
100.0
100.0
100.0
99.8
99.9
98.0
98.1
97.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
3.2
4.5
4.6
4.8
3.9
3.1
1.2
0.7
0.8
63.2
64.3
62.6
51.4
50.4
44.0
20.5
17.7
14.1
100.0
100.0
-100.0
99.7
99.7
99.8
93.0
90.7
85.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.7
3.4
4.8
4.7
6.7
4.9
3.4
5.5
4.3
1.5
64.5
66.5
62.5
63.7
59.9
48.0
54.4
44.2
28.2
100.0
100.0
100.0
100.0
99.8
99.9
100.0
100.0
98.1
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
3.5
4.8
4.5
6.1
4.8
2.5
5.5
3.6
0.6
63.2
65.0
60.8
62.5
58.5
41.8
48.8
40.1
19.2
99.9
100.0
99.9
100.0
99.8
99.a
99.8
99.7
93.4
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
3.7
4.8
4.5
12.1
10.5
8.8
32.2
29.0
21.2
63.4
63.7
63.2
76.4
75.8
70.8
92.8
90.0
82.9
100.0
100.0
100.0
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
3.6
5.2
4.5
6.6
5.9
5.4
5.2
3.9
5.5
65.2
67.0
65.1
63.9
63.5
61.4
53.5
50.7
53.8
100.0
100.0
100.0
100.0
99.9
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
86
Table B.5: Probabili~ of Rejectim for carc~ci~ Tests for varying
levels of Treatment ~thaliiY arxi 'I\Jrl[)r lethali for emale Mice
'lhyroid Follicular eel 'I\Jrl[)rs using the
design.
Q'lset Treatment 'I\Jrl[)r
Factor lethality lethality
1++0
l+yO
l+cxa
Zt
Zp
Zo
Zlog ilW
Ztt
Zlt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
~
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*5.1
5.5
6.5
4.2
4.7
4.6
2.9
2.1
2.8
14.5
15.0
15.9
13.3
13.5
11.7
7.5
7.0
8.5
51.5
52.6
52.0
46.2
46.7
45.2
29.3
30.1
31.0
87.4
88.8
88.5
82.2
82.1
83.0
63.7
64.8
65.5
entries are percentages.
4.9
5.7
6.5
4.9
5.4
5.5
6.5
6.4
5.9
14.9
15.3
16.2
14.7
15.2
13.8
14.0
13.7
15.2
51.1
52.2
52.2
50.8
51.4
49.0
44.0
46.1
46.2
88.9
89.2
89.5
86.8
86.2
87.5
81.8
82.2
82.7 .
5.0
5.7
6.8
6.2
6.1
5.8
8.5
8.7
6.8
14.6
14.9
16.0
15.9
16.8
13.2
16.2
15.8
13.0
50.5
51.8
52.4
51.6
52.3
47.3
46.2
44.7
39.2
88.3
89.1
89.2
86.8
85.8
84.9
78.8
77.7
72.8
4.9
5.6
6.9
6.1
6.0
5.2
8.0
8.4
6.2
14.6
14.7
15.8
15.4
16.4
11.6
15.8
14.9
11.0
50.1
51.8
52.5
51.8
51.3
43.0
46.6
45.4
34.0
88.4
89.2
88.5
87.2
85.8
81.5
82.8
80.2
68.3
4.9
5.9
6.4
5.5
6.0
4.5
6.2
5.3
3.2
14.7
14.8
15.6
15.3
15.3
9.1
13.5
12.4
7.9
50.1
51.8
49.5
50.7
49.2
38.8
41.5
38.9
25.7
88.0
89.0
86.7
86.6
84.4
76.~
77.
74.9
55.5
4.~
5.
6.4
6.8
7.2
7.0
12.7
12.6
10.8
15.2
14.5
16.2
19.2
18.7
16.2
28.2
27.8
24.2
50.0
52.7
52.0
58.4
57.9
54.2
68.2
68.1
62.1
88.8
89.1
89.2
91.8
90.4
9g.5
9 .4
95.4
92.6
5.0
5.5
6.6
5.3
5.7
5.7
6.3
5.4
5.7
14.8
15.2
16.2
14.6
15.~
14.
14.5
13.5
15.4
51.5
52.7
52.3
51.4
51.8
49.8
44.8
46.4
47.2
88.9
89.5
89.4
87.5
86.5
87.6
83.4
82.5
83.7
e
87
Table B.6: Probabili~ of Rejectioo for carci~icit~ Tests for varying
levels of Treat:nent r.ethali tY atxi '1\1IrOr lethali y for emale Rats
Liver 'I\I1Drs using the NrP design.
Q1set Treat:nent 'I\I1Dr
Factor lethality lethality
1++0
l+yo
Zt
l+oro
Zp
Zlog Zm.t
Zo
Ztt
Zlt
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*4.7
6.2
5.5
3.9
3.8
4.2
2.0
1.5
2.0
18.2
20.8
16.5
12.8
12.6
13.3
4.4
4.5
4.2
60.5
63.3
64.3
50.7
50.7
45.8
17.6
16.8
19.2
96.1
94.9
95.3
87.2
85.2
86.0
48.5
42.5
45.0
entries are percentages.
4.5
6.3
5.5
4.5
4.3
4.5
4.4
3.3
3.7
18.3
20.8
16.5
14.5
13.5
14.7
7.4
7.4
7.4
61.5
64.2
65.3
56.4
56.3
52.4
28.1
27.1
31.2
96.5
95.6
96.0
90.9
89.2
90.2
67.9
63.2
66.0
4.0
6.5
5.5
6.2
5.6
5.8
7.5
6.0
5.9
17.8
20.8
16.5
17.7
16.3
16.3
14.8
14.6
12.5
62.3
65.6
65.8
61.8
61.4
57.8
44.2
42.0
43.5
96.6
95.5
96.2
93.4
92.3
91.6
79.5
77.1
74.4
4.1
6.5
5.4
6.1
5.6
5.6
7.5
6.2
5.4
17.8
20.7
16.5
17.5
16.2
16.2
15.4
15.2
12.8
62.2
65.3
65.4
62.1
61.5
57.7
47.8
45.2
46.8
96.8
95.4
96.0
94.5
93.2
92.7
86.8
83.5
82.1
4.2
6.6
5.2
6.4
5.6
5.3
7.5
5.8
4.8
17.5
20.4
16.0
17.7
15.8
15.0
15.1
14.7
11.8
62.2
64.2
65.5
62.6
60.7
55.8
46.9
43.0
41.7
96.5
95.7
95.7
94.6
93.1
91.3
84.9
81.1
75.8
3.9
6.3
5.2
7.4
6.5
6.7
11.3
9.5
9.5
17.8
20.5
16.2
20.3
18.4
19.9
23.7
24.5
21.9
62.~
63.
64.8
66.6
66.1
64.2
63.4
62.2
62.5
96.5
95.4
95.6
96.2
95.1
94.9
94.8
93.8
93.8
4.1
6.2
5.2
6.3
5.6
5.4
7.9
6.7
6.5
17.9
20.9
16.4
17.8
16.5
17.2
16.1
15.6
15.1
62.1
65.1
65.4
63.3
62.1
60.5
50.3
47.9
52.9
96.8
95.6
96.2
95.0
93.7
93.8
87.6
85.~
87.
88
Table B. 7: Probabili~ of Rejectioo for carci~nici~ 'n!sts for varying
levels of Treatment lethalitY am 'l\mor IA!thali y for emale Pats
Ieukemia;Lyupnnas using the Nl'P deSlgn.
Q1set Treatment 'l\mor
Factor U!thality U!thality
1++0
l+yO
Zt
1+«0
Zp
Zlt
Zo
Zlog ~
Ztt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*5.7
2
4.2
1
1
10
5.8
3.3
2
1
3.7
2
2
2
10
3.5
1.2
5
1
2
1.2
5
5
10
1.9
1
1
54.6
2
54.1
1
55.1
1
10
48.0
2
1
44.1
2
2
44.9
2
10
1
25.2
5
24.5
2
5
10
25.0
5
1
1
99.8
1
2
99.9
10
1
99.8
99.7
2
1
2
99.6
2
10
99.6
2
1
97.2
5
2
96.4
5
10
5
97.5
100.0
1
1
1
2
100.0
1
10
100.0
1
100.0
2
2
2
100.0
10
100.0
2
1
100.0
5
2
10 0
5
10
10 .0
5
entries are percentages.
8.
5.2
3.8
5.9
4.9
4.9
4.4
5.0
5.5
5.6
55.1
53.5
55.7
55.4
52.8
52.2
49.8
46.5
47.0
99.9
99.9
99.8
99.8
99.8
99.9
99.8
99.5
99.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.5
4.2
5.9
4.3
4.0
3.5
2.5
1.9
2.2
55.3
54.2
55.5
51.8
46.2
45.4
33.8
27.9
25.8
99.8
99.9
99.8
99.8
99.7
99.6
99.1
97.9
97.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.4
4.0
4.8
5.1
4.2
2.7
6.2
3.5
0.8
55.6
54.0
49.8
56.8
48.8
32.9
51.4
37.7
14.1
99.9
99.9
99.6
99.8
99.7
98.5
99.8
99.0
89.5
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.5
4.2
5.3
4.8
4.2
1.8
5.0
3.2
0.5
55.2
53.9
47.5
54.5
47.6
26.9
45.9
33.9
8.7
99.9
99.9
99.4
99.8
99.7
97.~
99.
97.8
79.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.6
5.5
4.2
6.1
11.2
10.2
7.8
43.2
38.3
20.5
53.6
53.8
54.2
73.8
68.5
65.1
92.9
91.9
79.8
99.8
100.0
99.8
99.9
99.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.3
4.0
6.0
5.1
5.1
4.6
5.7
5.5
5.5
55.6
54.3
56.0
56.7
53.4
54.1
51.2
48.5
49.4
9 •9
1 0.0
99.9
99.8
99.9
100.0
99.8
99.8
ag.8
1 .0
100.0
100.0
100.0
100.0
10 0
10 .0
100.0
100.0
8
8.
e
89
Table B.8: Probabili ~ of Rejection for carci~nici~ts for varying
levels of Treatnent IBthali tY and 'I\.m)r lethali for
e Rats
Lung 'I\.m)rs using the NI'P design.
Q1set Treatnent 'I\.m)r
Factor lethality lethality
1++0
1+yO
1+ao
Zt
Zp
Zo
Zloq Zm.,
Ztt
ZIt
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*4.2
2
1
3.7
10
4.3
1
1
2
3.8
2
2
3.9
10
3.2
2
1
5
4.3
2
5
3.2
10
3.3
5
1
1
13.4
2
12.2
1
10
11.1
1
2
1
10.2
2
2
12.0
10
2
9.8
1
9.4
5
2
5
11.2
10
11.2
5
1
1
39.1
2
43.1
1
10
38.4
1
1
2
37.9
2
40.1
2
10
35.8
2
1
32.9
5
5
2
34.5
10
35.9
5
1
75.8
1
1
2
76.3
10
75.1
1
1
2
72.5
2
2
73.0
10
2
72.7
1
68.2
5
2
5
68.6
10
5
70.1
entries are percentages.
4.2
3.8
4.3
3.9
3.9
3.5
9.8
8.0
9.0
13.5
12.0
11.2
11.2
12.8
10.4
16.3
17.5
18.3
38.9
42.5
37.9
40.8
42.4
38.5
44.2
43.5
47.5
76.1
76.0
74.9
75.8
76.6
76.3
79.9
79.1
80.4
4.2
3.7
4.3
5.7
5.5
3.9
11.2
8.1
5.2
13.6
12.4
11.1
12.9
13.8
10.3
16.7
16.8
1~.3
3 .0
42.4
38.2
41.8
42.5
36.2
42.2
39.2
37.4
76.0
75.9
74.8
75.5
74.2
73.0
75.8
71.8
70.5
4.1
3.6
4.7
5.6
5.1
3.7
10.6
7.4
4.5
13.5
12.0
12.2
12.8
12.7
8.7
14.8
14.1
7.7
38.8
42.6
33.2
40.0
38.3
24.0
38.2
32.8
16.7
76.0
74.3
63.8
74.4
70.2
50.1
72.8
62.5
32.0
4.3
4.0
4.8
5.5
5.0
3.2
6.5
4.4
2.0
13.2
11.8
10.6
11.8
11.8
6.8
10.3
10.4
4.0
38.1
40.4
30.8
37.8
36.4
20.5
32.6
28.1
13.2
74.3
73.1
60.8
71.2
68.5
43.7
65.8
55.5
26.6
4.3
3.9
4.5
6.7
6.4
4.4
14.3
11.8
6.5
13.1
11.9
11.1
15.2
16.1
11.3
27.0
25.8
17.3
38.0
42.0
38.1
48.1
48.5
39.7
64.3
57.6
50.3
75.7
75.8
75.1
81.3
80.6
77.7
92.2
90.8
81.7
4.3
3.7
4.3
4.1
4.0
3.5
5.2
3.7
3.5
13.5
12.2
11.2
10.6
12.2
10.0
11.0
12.9
12.8
38.7
42.8
38.2
38.8
41.2
36.7
35.8
36.8
39.6
75.7
76.5
74.9
73.9
74.8
74.2
73.0
72.6
73.1
90
Table B.9: probabili!-yof Rejection for carci~nicitte:fts for varying
levels of Treatment I.ethal~and 'l\mor Lethali for
e Rats
Mamnary Gland Fibr
nanas using the
design.
Q1set Treatment Tumor
Factor rsthali ty' rsthality
l+yO
1+«0
1++0
Zt
Zp
Zo
Ztt
Zloq Zm,
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*4.5
6.1
6.2
2.6
2.5
2.7
0.2
0.3
0.2
61.8
64.8
62.5
43.4
45.8
44.8
12.8
12.5
11.6
100.0
99.9
100.0
99.6
99.7
99.8
89.5
87.7
89.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.8
.. table entries are percentages.
4.2
6.1
5.3
3.2
4.0
3.7
1.9
1.3
1.5
62.0
65.9
62.8
54.0
54.9
52.1
33.2
32.5
33.8
100.0
100.0
100.0
99.9
99.9
100.0
98.9
99.0
99.4
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.2
6.2
5.6
3.1
3.6
2.9
0.9
1.0
0.2
62.9
66.5
62.9
51.5
50.8
46.4
24.5
21.2
14.9
100.0
99.9
'100.0
99.8
99.8
99.9
96.2
93.3
93.3
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
4.3
6.2
6.0
4.9
4.8
2.6
5.8
3.3
0.8
62.8
67.1
61.4
61.2
5~.5
4 .7
53.8
47.1
21.4
100.0
100.0
100.0
100.0
99.9
99.9
99.9
99.9
96.5
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.1
6.0
5.5
4.8
4.5
2.0
4.7
3.5
0.5
62.1
66.1
58.8
58.9
58.8
40.6
49.9
42.4
14.8
100.0
99.9
100.0
99.9
99.9
99.5
99.8
99.6
92.3
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
4.0
6.2
5.1
11.7
10.8
8.7
38.5
35.2
24.2
61.4
63.2
62.7
74.7
76.5
70.2
93.8
93.2
85.8
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.4
5.8
5.6
5.1
5.1
4.7
5.1
3.9
4.7
63.3
67.1
65.2
61.2
62.9
60.2
53.7
54.3
55.0
100.0
100.0
100.0
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
e
91
Table B.10: probabili~ Rejection for carci~nici~ Tests for varying
levels of Treat:nent I.e
iff am 'l.'\.uror I.ethali~for emale Rats
design.
'Ihyroid Follicular eel 'l.'\.urors using the
()lset Treat:nent 'l.'\.uror
Factor I.ethality I.ethality
Z
1++0
l+yO
l+eto
Zt
Zloq ~
Zo
Ztt
ZIt
P
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.0
4.8
5.1
2.9
3.1
3.3
2.8
1.5
2.2
32.7
33.5
32.6
26.3
27.6
25.5
14.4
13.8
14.5
96.5
96.8
97.1
93.2
93.9
93.3
78.8
81.2
80.4
100.0
100.0
100.0
100.0
99.9
100.0
99.8
99.6
99.6
entries are percentages.
6.4
5.2
5.3
4.5
5.1
4.9
5.7
4.8
4.8
33.2
33.6
33.6
32.5
34.5
33.0
28.4
28.9
29.8
96.2
97.0
97.1
95.0
96.0
95.3
92.5
92.4
92.4
100.0
100.0
100.0
100.0
99.9
100.0
99.9
100.0
100.0
6.4
4.8
5.2
4.5
4.4
3.9
5.1
3.6
2.5
33.8
33.8
33.2
31.3
32.0
27.2
24.0
21.6
17.5
96.4
96.8
97.2
94.5
94.4
93.5
86.2
85.1
82.2
100.0
100.0
100.0
100.0
99.9
100.0
99.9
99.9
99.7
6.2
4.9
5.5
4.3
4.7
2.7
6.4
4.2
1.6
33.4
33.6
32.9
33.2
33.3
20.8
31.5
25.4
11.4
96.3
96.6
95.5
95.4
95.1
89.3
92.4
89.2
68.2
100.0
100.0
100.0
100.0
99.9
99.9
99.9
100.0
98.6
6.2
5.0
5.2
4.7
4.5
2.2
5.4
4.2
1.3
32.6
33.5
31.5
31.9
30.9
17.4
27.0
22.7
8.3
96.0
96.7
94.5
95.3
94.5
85.1
89.2
86.4
55.3
100.0
100.0
100.0
100.0
99.9
99.8
99.9
100.0
95.7
5.9
5.6
5.5
8.5
8.7
6.6
22.8
20.8
13.9
32.3
34.1
33.4
43.8
46.1
40.7
67.8
67.5
53.7
95.2
96.5
96.4
98.2
98.2
97.3
99.9
99.5
99.3
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
6.4
5.4
5.5
4.5
4.8
4.8
6.5
5.1
4.9
33.8
33.8
33.9
33.3
34.8
33.8
30.2
31.3
31.4
96.4
97.1
96.8
95.2
96.0
95.8
93.0
92.6
93.1
100.0
100.0
100.0
100.0
99.9
100.0
99.9
100.0
100.0
92
Table B.11: Probabili!:y of Rejection for carciKci ~'n!sts for varying
e Mice
levels of Treatrlent ~thality and 'I\.Dn:)r Lethali for
Hemagiana-Hemangiosarcanas using the NI'P sign.
cnset Treatment 'I\mDr
Factor Lethality Lethality
1++0
1+0;,
1+ YO
Zp
Zt
Zo
Zlog Zm.r
Ztt
Zlt
1
1
1
5.8
5.7
*5.8
5.7
5.8
5.8
5.8
1
1
2
6.1
6.1
5.9
5.9
6.1
6.1
6.1
6.4
1
10
6.2
6.3
6.4
1
6.2
6.3
6.5
2
4.8
1
1
5.5
6.8
6.8
6.8
6.6
7.6
1
2
4.0
5.2
2
6.6
6.2
7.5
6.7
~.5
4.1
4.9
1
2
10
.5
5.4
4.8
6.1
5.5
1
1.4
3.8
6.8
5
1
6.5
6.5
9.9
5.8
5
2.2
4.8
7.1
1
2
7.5
6.2 10.6
7.2
1
3.0
5.1
5
10
1.2
4.6
4.2
8.2
5.5
2
1
1
18.9 18.5 18.2 18.2 18.2 18.2 18.2
2
1
19.1 18.9 18.8 18.8 19.2 18.9 18.8
2
2
1
10
18.4 17.9 18.2 18.2 17.8 18.1 18.2
2
2
1
14.5 17.8 19.6 19.5 19.3 21.9 19.5
2
2
2
15.7 16.9 18.7 18.8 19.2 21.6 18.7
2
2
10
14.1 16.9 17.4 17.2 15.9 20.6 18.5
2
1
6.5 11.2 17.5 17.7 16.8 26.1 17.9
5
2
6.1 11.3 17.2 17.4 15.8 26.8 17.8
2
5
2
5
10
6.0 10.8 15.9 15.5 13.5 23.8 17.4
66.5 67.7 67.3 67.1 67.~ 66.5 67.4
5
1
1
1
65.7 66.6 66.6 66.6 66.
5
2
66.2 66.5
5
1
10
66.3 67.8 67.9 67.7 66.6 67.5 68.2
5
2
1
53.2 60.0 63.5 63.8 63.0 67.8 64.4
5
2
2
52.3 59.2 62.0 61.8 61.7 68.5 63.3
2
10
55.8 62.3 63.0 63.5 60.2 68.5 64.9
5
5
5
1
23.2 41.6 51.3 55.1 51.8 68.8 54.3
22.5 42.8 52.5 54.9 51.8 69.9 57.0
5
2
5
22.2 42.5 47.8 50.2 43.2 69.3 56.9
5
10
5
1
96.5 96.7 96.6 96.6 96.5 96.6 96.6
10
1
10
1
2
96.5 97.1 96.9 97.0 96.6 96.8 96.9
10
1
10
95.7 96.5 96.3 96.3 95.9 96.2 9~.3
90.7 94.4 95.5 95.8 95.7 97.4 9 .9
10
2
1
10
2
2
91.2 94.5 95.3 95.8 95.6 96.8 95.8
10
2
10
91.1 94.2 94.3 94.8 93.7 97.0 96.0
1
55.5 80.8 87.2 90.7 89.2 96.6 91.3
10
5
10
55.7 80.3 85.3 89.9 86.3 9~.0 90.0
5
2
10
54.8 81.3 82.4 87.4 81.2 9 .9 91.2
5
10
* table entries are percentages.
e
93
Table B.12: Probabili!:y of aejection for carC~nici~Tests for varying
levels of Treatment lethalitY and 'I\.DrOr Lethali for Ie Mice
Liver 'I\.DrOrs using the NI'P design.
Q'lset Treatment 'I\.DrOr
Factor Lethality Lethality
1++0
l+yO
l+aa
Zt
Zp
Zo
Ztt
Zloq Zm.t
ZIt
e
.
'
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*5.8
7.2
5.8
2.4
2.5
1.9
0.3
0.5
0.5
70.9
71.0
67.8
51.5
50.8
54.9
14.8
14.5
15.4
100.0
100.0
100.0
99.9
100.0
99.9
92.7
92.4
92.7
100.0
100.0
100.0
100.0
100.0
100.0
99.9
99.8
99.8
5
entries are percentages•
5.7
6.1
5.5
5.6
4.6
4.7
3.4
3.4
4.1
71.5
72.2
68.5
65.5
65.8
69.5
57.8
57.7
57.3
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.7
6.7
5.5
4.8
3.7
2.8
1.0
1.5
0.8
71.8
72.3
68.8
60.6
58.8
58.6
33.5
31.5
26.5
100.0
0•0
1180.0
100.0
100.0
99.9
98.9
98.5
97.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
5.7
6.5
5.8
6.3
4.5
2.2
5.4
4.2
1.2
72.3
73.1
67.2
69.6
65.9
55.6
65.8
59.4
30.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
99.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.5
6.5
5.5
5.8
4.2
1.2
4.6
3.4
0.3
71.8
71.8
63.4
67.2
63.5
45.1
57.7
51.2
14.8
100.0
100.0
100.0
100.0
100.0
99.7
99.9
99.8
93.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.2
6.5
5.7
13.1
10.8
8.2
47.7
39.8
24.7
69.7
70.8
68.7
80.9
81.3
80.7
97.8
97.2
91.8
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
6.1
5.8
5.5
5.7
5.0
4.9
4.9
3.9
5.6
73.9
74.8
71.4
69.2
68.8
72.7
66.8
64.9
63.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
94
Table B.13: Probability of Rejection for
levels of Treatment IAthalitY arxi 'l\m:)r
Ieukemia/LyrrP'latas using the
cnset Treatment 'l\m:)r
Factor ~thality ~thality
1++0
l+yO
l+CXO
Zt
Zp
1
*5.2
2
5.5
10
4.1
1
3.0
2
2.8
10
3.0
1
0.8
2
0.5
10
0.5
~1
1
40.8
41.7
1
2
1
10
43.2
2
1
31.9
2
27.5
2
10
28.2
2
1
5.8
5
7.8
5
2
10
7.5
5
1
98.5
1
~
1
2
99.2
10
99.0
5
1
1
96.2
5
2
2
96.1
5
2
10
5
2
96.6
5
1
63.5
5
2
66.5
5
5
10
63.5
5
5
1
100.0
10
1
10
1
2
100.0
10
10
100.0
1
1
100.0
10
2
10
2
100.0
2
10
2
10
99.9
1
95.7
10
5
10
2
97.5
5
10
10
96.5
5
* table entries are percentages.
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
1
1
1
2
2
2
5
5.3
5.5
4.5
5.2
3.8
4.2
3.6
2.4
2.8
41.6
42.5
42.9
40.1
34.7
37.2
23.7
27.2
25.9
99.0
99.2
99.3
98.8
98.6
98.8
93.2
93.4
92.6
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
carci~nicivsts
for
design.
~thali
Nl'P
Ztt
5.6
5.4
4.5
5.6
4.1
3.7
4.4
3.3
2.2
41.8
43.1
43.0
41.2
34.3
32.6
23.3
25.0
17.8
98.6
99.0
98.9
98.1
98.2
97.8
89.2
89.2
83.4
100.0
100.0
100.0
100.0
100.0
100.0
99.6
100.0
99.8
for varying
e Mice
Zlog Zm.,
5.7
5.5
5.6
5.8
4.4
4.5
6.2
5.5
4.2
4.2
3.8
2.6
6.7
6.2
5.0
3.5
2.9
1.8
42.1 41.4
43.4 42.7
43.5 41.3
44.2 43.2
37.9 36.1
34.4 28.5
36.8 32.4
36.4 33.0
23.8 16.1
99.0 99.0
99.1 99.0
99.1 98.8
99.2 98.9
99.1 98.6
98.4 96.8
96.1 94.9
96.7 94.7
91.2 83.7
100.0 100.0
100.0 100.0
100.0 100.0
100.0 100.0
100.0 100.0
100.0 100.0
100.0 99.9
100.0 100.0
100.0 99.5
ZIt
4.8
5.5
4.5
8.5
6.2
5.9
17.8
15.4
13.1
41.8
42.2
42.9
52.3
48.2
47.9
67.2
65.8
60.3
98.8
98.6
99.2
99.8
99.6
99.6
99.6
99.7
99.5
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Zo
5.5
5.5
4.8
6.2
4.7
4.5
5.6
4.4
5.2
42.5
43.8
43.0
44.2
39.1
41.5
36.2
37.1
36.8
99.2
99.0
99.4
99.1
99.1
99.0
96.4
97.4
96.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
It
95
Table B.14: Probabili~ of Rejection for carci~nici~Tests for varying
levels of Treatment IAthali tY ani 'I\m)r Lethali for
e Mice
Lung 'I\m)rs using the Nl'P design.
Qlset Treatment 'I\m)r
Factor Lethality Lethality
1+.0
l+yO
l+cxa
Zt
Zp
Zloq Zm.,
Zo
Ztt
Zlt
e
..
..
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*4.8
4.7
4.3
3.8
3.6
3.8
0.7
0.8
0.8
52.9
53.8
52.8
38.0
39.2
38.2
15.8
14.8
16.4
99.8
99.8
99.9
99.3
99.3
99.5
90.5
90.1
90.0
100.0
100.0
100.0
100.0
100.0
100.0
99.8
99.9
99.9
entries are percentages•
5.2
4.1
4.4
5.2
5.2
4.9
4.6
4.6
6.2
52.3
53.7
52.2
47.7
50.8
49.5
45.6
46.8
46.5
99.9
99.8
100.0
99.8
99.7
99.8
99.4
99.2
99.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.1
4.2
4.4
4.6
4.2
4.0
2.7
2.2
2.2
52.6
54.2
52.8
45.6
44.2
42.2
30.8
29.5
23.6
99.8
99.8
. 99.9
99.6
99.5
99.6
97.3
96.0
94.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.0
4.2
4.5
5.8
4.9
3.5
5.8
4.8
2.0
53.0
54.3
51.5
49.4
48.5
37.2
49.0
43.5
22.3
99.9
99.8
99.8
99.8
99.7
99.3
99.3
98.6
94.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.8
3.9
4.5
5.5
4.5
2.7
3.9
3.6
0.8
51.8
53.2
49.2
48.0
45.7
28.3
42.0
36.9
12.6
99.9
99.8
99.5
99.8
99.5
97.8
99.2
97.8
85.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.8
5.2
3.7
4.7
9.6
9.7
8.1
28.4
28.3
17.7
51.3
53.2
51.6
63.4
64.4
59.8
86.8
87.2
73.2
99.8
99.7
99.9
100.0
99.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.9
4.0
4.8
5.3
5.4
5.2
4.8
4.7
5.8
53.5
54.5
53.2
50.0
51.8
51.2
46.6
47.8
47.0
99.9
99.8
100.0
100.0
99.7
99.8
99.4
99.4
99.7
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
96
Table B.15: Prababili~ of Rejection for carci~nici~'n!sts for varying
levels of Treatment tethaliw and 'I\mcr Lethali for
e Mice
'Ihyroid Follicular Cell 'I\mcrs using the
design.
Qlset Treatment 'I\mcr
Factor Lethality Lethality
1++0
l+yO
1+a.a
Zt
Zp
Zo
Zloq ~
Ztt
Zlt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*4.5
4.4
3.6
4.4
4.9
4.7
3.7
3.9
3.3
12.5
13.4
12.2
13.7
11.3
11.2
8.7
9.8
10.4'
44.0
41.1
40.9
38.8
39.5
41.8
32.7
36.0
34.6
80.4
77.4
76.0
72.5
73.3
75.3
67.2
63.8
69.1
4.5
4.5
3.8
4.9
5.6
5.4
9.8
10.2
10.3
12.5
13.3
12.4
14.9
13.8
12.0
17.2
17.5
18.8
43.9
40.9
41.0
42.8
44.0
45.8
46.2
51.2
49.2
81.0
77.6
75.4
76.9
77.6
79.7
83.9
80.2
83.5 .
4.6
4.4
3.8
6.3
6.6
5.3
9.8
10.2
7.0
12.5
13.4
11.9
15.8
14.1
11.7
17.2
16.1
13.5
43.6
41.2
40.6
43.0
42.5
42.7
42.2
44.6
37.6
80.8
78.1
75.8
76.9
75.3
76.2
76.5
71.4
72.2
4.5
4.4
4.2
6.2
6.5
4.7
9.3
9.3
5.8
12.5
13.6
12.8
15.4
13.0
10.1
15.8
14.2
9.~
43.
40.8
39.5
41.4
39.8
32.6
40.3
39.8
21.5
80.7
77.5
72.5
75.8
73.~
64.
75.g
67.
47.6
4.6
4.5
4.3
5.8
6.1
3.3
6.0
5.3
2.7
12.6
13.1
12.5
13.9
12.1
8.2
12.0
10.0
4.8
42.8
41.0
37.8
38.7
36.9
25.8
34.2
33.0
15.2
80.2
77.2
69.5
73.8
70.2
55.7
68.7
59.8
34.4
4.5
4.5
4.0
7.2
7.4
5.8
12.9
13.2
8.4
12.3
13.2
12.3
18.0
1~.8
1 .6
25.1
22.3
19.2
43.5
41.2
41.2
47.1
48.5
47.2
61.5
62.4
50.9
80.1
77.8
75.8
82.0
80.9
80.7
92.8
90.0
85.5
4.5
4.5
3.8
4.8
5.5
5.1
5.4
5.4
4.8
12.5
13.5
12.3
14.0
12.8
11.4
11.3
11.6
12.9
44.2
41.4
41.1
40.2
41.4
43.2
38.2
42.4
40.3
80.6
77.6
75.9
75.7
75.4
77.5
75.2
71.6
76.1
e
entries are percentages.
•
97
Table B.16: Probabili~ of Rejectioo for carci~nici~Tests for varying
levels of Treatnent Ii!thali t~ 'I\mcr lethali for
e Rats
Integumentary System
rs using the Nl'P design.
Q1set Treatment 'I\mcr
Factor lethality lethality
1++0
l+yO
l+OU
Zp
Zt
Zloq Zm.,
Zo
Ztt
Zlt
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*5.1
2
1
5.5
10
1
5.8
1
4.1
2
2
2
4.2
10
2
3.8
1
1.6
5
2
2.3
5
10
1.8
5
22.1
1
1
2
1
25.7
10
24.1
1
1
19.1
2
2
16.7
2
18.7
10
2
1
8.4
5
2
10.2
5
10
10.2
5
1
86.1
1
2
85.1
1
10
85.2
1
1
75.6
2
2
75.5
2
75.8
10
2
1
50.4
5
2
50.5
5
10
48.7
5
1
99.7
1
2
1
99.8
10
99.8
1
2
1
99.5
2
2
99.2
10
99.3
2
1
92.2
5
2
92.7
5
10
91.4
5
entries are percentages.
5.2
5.5
5.9
4.8
5.4
4.6
4.2
4.6
4.5
22.8
26.3
24.4
24.2
21.8
22.1
17.0
20.1
19.1
86.5
86.0
85.0
83.3
82.1
82.9
74.3
74.5
73.4
99.8
99.9
99.8
99.7
99.8
99.8
98.6
98.5
98.5
5.1
5.8
5.6
5.2
5.7
3.8
5.1
5.0
2.6
23.5
26.8
24.5
24.5
20.8
19.8
16.5
18.0
12.5
86.2
85.8
85.2
81.5
80.0
76.8
64.6
62.4
52.8
99.7
99.9
99.8
99.5
99.4
99.4
96.5
95.0
93.1
4.9
5.5
6.2
5.0
5.5
3.0
6.3
5.2
2.1
23.5
26.2
24.9
25.4
21.4
16.2
21.9
21.6
9.4
86.3
85.8
83.8
84.5
82.0
70.3
76.1
71.8
44.8
99.8
99.9
99.4
99.8
99.5
97.8
98.8
98.2
86.5
5.2
5.4
6.0
5.5
4.9
2.8
4.9
4.6
1.9
23.4
26.2
22.8
24.5
20.3
12.8
18.4
18.9
7.0
86.2
85.7
82.2
81.8
80.6
64.570.8
63.7
34.5
99.8
99.9
99.5
99.8
99.2
96.5
97.3
95.9
76.7
5.2
5.9
5.8
8.8
8.9
7.3
21.1
21.2
12.2
23.6
26.2
24.7
34.1
31.8
27.9
52.6
51.2
38.8
85.6
84.5
84.8
92.3
90.6
89.2
96.7
96.3
90.9
99.9
99.8
99.8
100.0
99.9
99.8
100.0
100.0
100.0
4.9
5.6
5.8
5.2
5.6
5.2
5.1
5.5
4.9
23.5
26.6
24.6
25.2
23.2
23.4
19.8
23.3
20.6
86.6
86.1
85.5
84.5
83.6
85.2
77.5
78.1
75.9
99.8
99.9
99.8
99.7
99.8
99.8
99.0
99.2
99.3
98
Table B.17: Probabili!:y of ~jection for carci~nicivsts for varying
levels of Treatment rethali ty and 'l\mor U!thali for
e Pats
Liver 'l\mors using the NI'P design.
Q'lset Treatment 'l\m)r
Factor U!thality U!thality
1++0
l+yO
1+aa
Zt
Zo
Zp
Ztt
Zlog ~
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
*
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
~
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*5.0
4.9
4.8
4.5
4.6
3.3
1.5
1.7
1.8
23.8
20.6
22.4
14.8
15.1
15.9
6.3
7.1
7.5
79.5
78.5
76.8
64.8
65.5
64.8
35.7
34.8
33.9
99.2
99.2
99.5
97.1
97.5
97.4
78.5
76.2
76.2
4.9
4.7
4.7
5.7
5.0
3.9
3.9
3.8
4.2
23.9
20.2
22.5
18.5
18.1
18.5
11.4
13.9
15.0
80.2
79.3
77.0
73.2
73.3
71.5
55.2
57.3
54.8
99.3
99.5
99.5
98.2
98.4
98.8
92.8
93.0
94.9
5.2
4.5
4.9
5.8
5.8
3.8
6.1
5.2
4.2
23.6
20.8
22.8
20.2
18.9
17.4
13.4
14.8
12.2
80.2
79.5
77.4
73.8
72.5
67.5
53.4
51.3
41.1
99.2
99.3
99.4
97.8
98.0
97.8
89.6
85.4
82.3
5.2
4.4
4.8
6.1
5.9
3.1
6.6
6.0
3.6
23.2
20.7
22.5
21.0
19.1
16.2
16.2
17.9
11.5
79.9
79.3
76.4
76.7
74.8
65.2
64.0
62.3
42.1
99.4
99.5
99.3
98.7
98.4
97.3
95.8
94.2
83.2
5.1
4.8
4.6
5.5
5.6
2.4
4.9
5.0
2.5
24.0
20.3
22.1
20.2
17.8
13.6
14.5
15.5
8.3
79.6
79.1
75.2
75.1
72.5
60.2
58.~
55.
33.0
99.g
99.
99.1
98.5
98.0
94.4
92.9
90.7
72.9
5.5
4.3
4.3
8.7
8.8
6.0
18.2
17.7
12.2
23.6
20.5
22.7
28.7
25.9
25.7
42.2
41.8
36.0
78.8
78.2
76.8
86.0
84.8
81.5
89.8
89.0
82.6
99.2
99.3
99.4
99.6
99.6
99.3
99.6
99.8
99.6
5.1
4.6
4.8
6.5
5.7
4.5
5.8
5.8
5.8
23.8
20.5
22.8
21.0
1~.8
2 .0
15.4
18.8
20.5
80.5
79.5
77.6
8
71.
7 .5
7 .7
63.6
68.7
64.7
99.5
99.5
99.5
98.8
98.6
99.0
96.2
96.8
97.8
e
table entries are percentages.
•
99
e
TableS.18: Probabili!:y of ReJection'for carci~nici~Tests for varying
e Rats
levels of Treatment Lethality arx:i 'I\.1m:)r U!thali y for
Luekemia/Lynpxnas using the NI'P design.
Q'lset Treatment 'I\.1m:)r
Factor U!thality U!thality
1++0
l+yO
1+e;,
Zt
Zp
Zo
Zlog ~
Ztt
ZIt
1
5.7
6.2
6.0
1
*5.5
5.8
5.7
6.2
1
2
4.7
4.8
5.1
5.0
4.8
4.8
4.8
1
1
10
4.4
4.8
5.1
4.9
5.0
5.0
4.8
1
1
1
1.5
3.0
2.7
4.5
4.2 15.5
4.5
2
1
2
3.1
4.0
3.5
4.7
4.8 17.3
2
5.6
1
10
3.7
2.2
1.5
1.9
1.0 10.3
5.0
2
1
1
0.1
1.8
0.8
5.7
4.2 62.8
4.5
5
1
2
3.5
0.3
1.9
0.5
2.8 59.4
1
5
5.3
10
0.4
2.5
0.5
0.4
0.5 28.1
5.4
1
5
1
1
65.9 66.2 67.0 67.4 67.2 64.1 69.4
2
2
67.0 67.2 67.9 68.1 66.8 66.0 69.4
1
2
10
69.2 69.0 69.2 65.1 63.2 68.8 71.6
1
2
2
1
46.2 59.1 52.4 67.2 65.8 87.3 68.3
2
2
45.8 59.2 50.5 60.8 59.2 86.6 70.5
2
2
49.2 60.4 49.8 44.0 37.3 80.2 69.0
10
2
2
1
10.9 38.2 19.8 59.1 51.8 98.9 61.1
2
5
43.6 38.2 98.5 57.5
2
11.2 36.6
5
2
12.8 39.1 16·f
14.
12.5
8.4 93.4 60.7
10
2
5
1
100.0 100.0 100.0 100.0 100.0 100.0 100.0
1
5
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
1
5
10
100.0 100.0 100.0 100.0 100.0 100.0 100.0
1
5
2
1
99.4 99.9 99.5 99.9 99.9 100.0 100.0
5
2
99.8 100.0 99.9 100.0 100.0 100.0 100.0
2
5
99.8 100.0 99.8 99.5 98.7 100.0 100.0
10
5
2
1
92.7 99.2 96.8 99.8 99.5 100.0 100.0
5
5
2
91.8 99.8 95.5 99.8 99.7 100.0 100.0
5
5
10
91.0 99.5 93.2 91.5 82.9 100.0 99.9
5
5
1
100.0 100.0 100.0 100.0 100.0 100.0 100.0
1
10
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
1
10
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
1
1
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
2
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
2
10
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
1
10
5
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
5
10
10
5
99.9 100.0 100.0 99.9 99.2 100.0 100.0
'" table entries are percentages.
100
Table B.19: Probabili~ of Rejection for carCilmnici~Tests for varying
e Rats
levels of Treatment Ii!thali ty and 'l\m)r I.A!thali for
Lung 'l\m)rs using the NI'P design.
cnset Treatment 'l\m)r
Factor I.A!thali ty I.A!thali ty
1++0
l+yO
1+a.a
Zp
Zt
Zo
Zlog Zm..r
Ztt
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*5.5
1
2
6.8
10
1
5.5
2
1
5.4
2
2
4.8
10
5.2
2
5
1
4.0
2
3.5
5
10
3.9
5
1
1
31.2
2
31.7
1
10
1
33.5
1
29.9
2
2
28.2
2
10
30.7
2
1
26.2
5
2
24.7
5
10
23.5
5
1
70.7
1
1
2
68.5
1
10
68.6
1
67.9
2
2
2
64.8
10
68.2
2
1
56.6
5
2
56.0
5
10
5
56.8
1
1
95.8
1
2
95.0
1
10
96.3
2
1
94.2
94.1
2
2
10
93.2
2
1
87.8
5
87.8
2
5
10
89.4
5
entries are percentages.
5.6
5.7
6.7
6.5
5.6
5.6
7.2
6.1
5.5
6.1
6.6
5.7
9.4
8.7
7.4
8.2
8.1
5.0
31.2 30.5
31.2 31.0
33.5 33.2
33.1 33.0
31.7 30.2
34.4 30.4
37.3 33.8
34.7 28.5
34.9 23.9
70.5 70.8
68.9 68.5
68.5 . 68.5
12.8 71.2
71.2 66.7
72.7 68.2
73.6 65.1
73.6 60.9
74.4 57.8
95.9 95.8
95.3 95.0
96.2 96.3
96.3 95.6
96.0 94.9
96.3 93.3
96.1 31.8
96.5
9.0
97.2 89.9
5.8
6.8
6.5
6.7
5.5
4.2
8.6
6.6
2.8
31.1
31.1
30.0
32.3
27.7
19.2
32.1
23.9
10.4
70.8
68.7
60.5
71.1
63.2
49.2
66.8
52.9
24.6
95.9
95.0
90.4
95.9
93.1
74.9
91.8
85.
53.6
5.8
6.4
5.9
6.4
5.3
3.3
6.0
4.2
1.8
30.6
29.8
26.7
31.1
26.6
16.1
27.5
20.3
7.9
70.8
67.8
59.2
70.0
62.2
42.2
58.8
48.3
20.2
95.2
94.6
88.8
95.2
92.5
69.5
87.7
80'8
42.
5.5
6.9
5.5
9.4
8.7
7.5
19.3
15.9
9.3
31.1
30.3
33.8
42.1
40.0
37.2
~.8
.2
41.8
70.2
68.4
68.6
81.8
78.3
74.1
92.8
90.2
77.9
95.7
95.2
96.0
98.9
97.7
96.7
99.8
99.8
97.9
5.8
6.8
5.5
5.5
5.2
6.0
6.1
4.7
5.5
31.5
31.2
33.7
32.1
29.9
32.9
31.5
29.7
28.9
71.2
69.0
69.2
71.1
68.9
70.9
66.5
66.3
66.5
95.9
95.6
96.2
95.8
95.5
95.4
93.5
93.4
94.7
e
101
Table B.20: probabi1i~ of Rejection for carci~nici~Tests for varying
levels of Treatment U!thalitY am 'I\m:>r Lethali for
e Rats
Mesothelianas using the NI'P design.
Q1set Treatment 'l\.m)r
Factor Lethality Lethality
Z0
1++0
l+yO
l+aa
Zp
Zt
Zlog ~
Ztt
Zlt
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*4.9
4.3
4.9
2.8
3.4
4.6
1.8
1.0
1.5
31.5
31.3
33.5
23.0
23.2
24.4
9.9
9.4
11.4
66.5
66.6
69.4
53.0
54.7
55.1
29.5
26.1
29.4
93.5
92.8
92.8
85.2
86.5
86.8
56.8
53.0
56.7
entries are percentages.
4.9
4.5
4.9
3.3
4.4
5.3
4.8
4.5
4.6
31.2
31.0
33.2
26.1
26.4
27.4
18.0
17.1
17.2
66.3
68.2
70.0
59.5
61.1
61.9
44.4
41.0
43.6
94.2
93.8
93.2
90.9
91.7
90.5
76.4
74.0
76.8 .
4.8
4.4
5.1
5.2
5.6
6.5
7.8
6.5
6.2
31.2
31.3
33.2
28.6
29.2
27.1
24.4
22.4
19.0
66.2
67.7
69.5
62.2
62.8
60.5
48.4
44.2
39.0
93.8
93.7
93.3
91.3
90.7
88.5
75.4
72.0
66.7
4.8
4.3
4.8
5.0
5.2
6.2
8.0
6.9
5.8
31.4
31.2
33.9
28.7
28.7
25.7
25.0
23.5
18.1
66.7
68.0
69.4
63.9
63.4
57.6
56.9
50.4
39.8
94.0
94.0
92.8
93.5
92.5
87.7
85.8
80.9
68.9
5.1
4.8
5.4
5.1
4.9
5.4
6.5
5.5
3.5
31.0
30.3
32.9
27.8
26.7
22.8
21.6
20.1
14.5
66.7
67.2
67.9
62.5
61.5
52.1
52.1
44.7
33.2
94.0
93.4
93.2
92.6
91.7
84.3
80.2
75.6
59.0
4.8
4.5
5.0
6.8
7.3
7.6
13.8
13.2
11.6
31.2
30.3
33.5
35.4
35.1
34.0
46.7
45.0
39.2
66.7
68.5
69.2
72.2
72.3
70.2
81.9
77.0
71.5
94.0
93.6
92.9
96.3
95.9
95.4
96.6
9~.2
9 .2
4.9
4.5
5.1
4.7
4.9
6.3
6.7
6.2
6.5
31.5
31.0
33.2
28.9
29.2
29.8
25.0
23.8
24.4
66.3
68.6
70.2
64.0
64.8
65.2
55.6
54.2
55.6
94.1
94.2
93.5
92.9
93.2
92.4
85.9
85.5
86.2
102
Table C.1: Probabili!-y of Rejection for carci~nici~ Tests for varying
levels of Treat:nent rsthali ty and 'l\mDr IJatllallij for emale Mice
Herlagiaoas-Hemangiosarcaoas using the
design.
Q'lset Treat:nent 'l\mDr
Factor IJathality IJathality
1++0
l+yO
l+ac
Zt
Zp
Zo
Zloq ~
Ztt
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
§
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.7
6.8
5.8
5.2
4.7
4.9
2.4
. 2.3
3.7
17.7
18.4
16.9
13.8
13.5
12.8
7.4
7.3
6.5
59.9
62.8
g2.4
3.5
54.3
50.2
32.2
30.5
32.0
95.5
96.5
96.0
91.9
91.2
91.2
71.1
70.4
71.2
entries are percentages.
6.3
6.5
5.5
5.4
5.0
5.2
3.5
4.0
4.8
17.0
17.8
16.1
15.2
14.8
14.0
12.5
12.1
11.7
60.5
62.6
61.6
59.8
60.4
55.9
49.4
47.9
49.8
95.8
96.8
96.2
94.7
94.0
94.8
89.1
88.0
88.8
6.0
6.4
5.2
6.2
5.5
5.4
5.1
5.5
6.8
16.5
17.4
16.0
16.5
15.9
14.3
16.8
15.7
12.7
60.3
62.1
62.0
61.9
61.5
55.2
51.7
49.7
44.3
95.8
97.1
96.2
95.0
93.8
93.2
86.8
85.4
81.0
5.9
6.5
5.4
6.1
5.3
5.3
5.2
5.2
6.2
16.5
17.5
16.9
16.2
16.1
13.5
16.8
15.2
11.5
60.2
62.4
61.5
62.2
61.2
52.5
55.5
52.7
44.3
95.7
97.0
96.1
95.5
94.3
92.8
91.4
89.8
83.2
5.8
5.8
5.3
5.8
5.1
3.9
5.0
5.0
5.1
16.5
17.5
15.7
15.0
13.9
11.2
15.2
14.0
8.2
59.5
61.7
59.7
61.2
59.6
46.5
50.0
45.1
3g.4
9 .5
96.5
95.5
95.0
93.4
89.0
87.0
85.5
70.7
6.1
6.0
5.2
7.5
6.7
6.4
9.1
9.8
10.6
16.4
17.5
15.8
19.0
19.3
18.2
29.0
26.9
22.9
60.0
61.5
61.5
68.2
67.2
63.5
78.0
75.5
72.7
95.6
96.9
96.2
97.6
~6.8
6.8
98.8
97.1
97.3
6.3
6.5
5.2
5.5
5.2
5.4
4.5
4.9
6.7
16.6
17.8
15.9
16.0
15.8
15.2
15.5
14.5
14.0
60.4
62.5
61.9
61.8
61.5
58.2
§5.1
3.5
54.9
95.9
97.1
96.1
95.5
94.9
95.4
91.5
91.9
92.5
e
103
Table C.2: Probabili!:y of Re:jecticn for carci~nici~ Tests for varying
levels of Treatment Lethality am 'I\m)r Lethali for emal.e Mice
Integumentary System 'I\m)rs using the
design.
cnset Treatment 'I\m)r
Factor Lethality Lethality
1++0
1+yO
1+ao
Zt
Zp
Zo
Ztt
Zlt
Zloq ~
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*2.9
2
2.7
1
10
2.8
1
1
3.5
2
2
2
1.7
10
2.7
2
5
1
1.2
2
5
0.9
10
1.0
5
1
8.3
1
1
2
8.8
10
1
8.6
2
1
7.1
2
2
8.5
10
7.2
2
1
4.5
5
2
5
3.6
10
4.4
5
1
1
26.5
1
2
27.7
10
28.5
1
2
1
23.0
2
2
23.5
10
23.5
2
5
1
13.5
2
14.4
5
10
14.5
5
1
1
56.2
1
2
57.6
1
10
56.6
2
1
46.4
2
48.4
2
50.2
2
10
5
1
34.0
5
2
31.8
34.2
5
10
entries are percentages.
2.9
2.6
2.8
3.5
1.7
2.7
1.5
1.2
1.3
8.2
8.6
8.5
7.1
8.5
7.2
5.1
4.3
5.3
25.1
26.5
27.8
23.2
24.0
23.8
18.4
19.8
20.1
54.9
56.8
55.1
48.8
50.8
53.0
44.7
42.9
45.5
2.8
2.6
2.6
3.5
1.8
.2.8
4.8
3.8
3.5
7.8
8.5
8.5
7.5
9.2
7.6
10.0
7.7
8.4
24.9
25.8
28.2
24.7
25.2
24.2
24.6
25.7
21.7
55.7
55.7
55.2
52.5
53.0
52.2
51.8
48.8
45.8
2.8
2.6
2.7
3.5
1.8
2.8
4.8
3.8
3.5
7.9
8.5
8.6
7.5
9.1
7.5
9.6
7.5
8.3
25.1
25.9
28.4
24.6
24.8
23.4
23.6
25.0
20.1
55.6
56.0
55.2
51.9
52.0
50.8
51.2
48.1
43.7
2.8
2.2
2.2
2.5
1.5
2.0
4.5
4.7
3.6
7.1
7.5
7.8
5.6
7.5
6.0
9.3
8.2
7.8
24.0
25.1
24.5
21.8
23.4
19.5.
22.8
21.8
16.4
54.5
55.5
52.8
49.8
49.3
44.8
44.8
41.7
33.6
2.7
2.4
2.5
3.7
1.9
2.9
6.4
6.7
6.0
7.2
8.1
8.1
7.8
9.7
7.9
15.7
12.8
12.4
24.8
25.6
27.5
26.7
27.4
27.0
34.5
36.5
32.8
55.2
54.8
54.5
56.5
57.5
58.4
66.8
64.3
62.3
2.8
2.5
2.8
3.5
1.8
2.8
2.6
2.5
3.2
8.2
8.5
8.2
7.2
8.7
7.5
7.2
5.5
7.0
24.8
26.2
27.6
23.8
24.6
24.5
21.6
23.5
22.6
54.8
55.8
54.7
50.8
52.2
53.9
50.2
48.4
50.8
104
Table C.3: Probabili~ of Rejectioo for carci~nici~ts for varying
levels of Treatment r.ethality am 'l\m)r lethali y for
e Mice
Liver 'l\m)rs using the OCI design.
Q'lset Treatment 'l\m)r
Factor lethality lethality
1++0
l+yO
l+CU
Zt
Zp
Zo
Ztt
Zloq ~
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
*4.3
2
4.2
10
5.2
1
4.1
2
5.2
10
3.8
1
2.2
2
2.5
10
2.0
1
29.1
27.2
2
10
29.8
22.5
1
2
21.6
10
22.5
1
10.8
2
9.9
10
11.8
1
93.9
2
94.5
10
93.5
1
89.4
2
89.2
10
88.5
1
68.7
2
66.2
10
66.2
1
100.0
2
99.9
10
100.0
1
100.0
2
99.9
100.0
10
1
99.0
2
98.1
10
98.5
entries are percentages.
4.1
4.0
5.0
5.2
6.0
4.8
5.9
4.7
4.5
29.2
27.2
29.5
27.5
27.3
27.7
22.3
22.7
23.1
94.5
94.7
93.5
93.5
92.7
92.7
88.9
86.3
88.9
100.0
100.0
100.0
100.0
100.0
100.0
99.9
99.9
99.8
4.7
4.3
5.2
5.5
6.2
4.3
5.7
4.9
3.2
29.1
27.0
29.2
28.5
26.6
24.5
19.8
17.8
16.1
94.5
94.8
93.7
92.5
91.6
89.8
81.6
77.0
73.2
100.0
99.9
100.0
100.0
100.0
100.0
99.7
99.3
99.2
4.7
4.6
5.5
5.4
6.3
3.6
7.3
5.3
2.5
29.1
27.1
29.g
29.
27.0
21.5
25.2
22.3
14.2
94.6
94.7
92.9
93.9
92.4
87.2
90.7
85.3
70.4
100.0
99.9
100.0
100.0
100.0
99.8
99.8
99.8
98.8
4.3
3.9
5.5
5.5
5.7
2.9
5.5
4.0
2.2
28.6
26.5
27.4
27.6
26.4
18.1
23.2
19.1
9.5
94.2
94.3
92.2
92.7
91.5
81.4
85.5
78.6
55.2
100.0
100.0
100.0
100.0
99.9
99.5
99.8
99.4
94.3
4.2
4.6
4.9
8.1
7.9
6.2
19.9
16.7
12.5
28.7
27.6
28.4
36.2
37.6
34.1
58.2
54.2
45.8
93.8
93.0
92.8
96.8
96.8
95.7
99.2
98.4
98.1
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.1
4.0
5.2
5.5
6.2
4.8
6.5
4.8
4.8
29.0
27.8
29.8
28.1
27.9
28.2
24.8
24.3
26.0
94.5
94.6
93.5
93.8
93.2
93.5
90.4
87.8
90.5
100.0
100.0
100.0
100.0
100.0
100.0
99.9
99.9
99.9
e
...
105
Table C. 4: Probabili ~ of Rejettioo for carci~nici~ Tests for varying
levels of Treat:nent LethalitY arrl 'l\.m:)r Lethali y for enale Mice
Luekemia/Lyq:ilanas using the N:I deSlgn.
cnset Treatment 'l\.m:)r
Factor Lethality Lethality
1++0
l+yO
Zt
1+oco
Zp
Zo
Ztt
Zlog Zm.r
Zlt
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.0
4.8
5.2
1.9
2.1
2.2
0.2
0.2
0.1
59.5
61.3
62.2
39.3
37.6
38.9
5.6
7.9
6.2
100.0
99.8
100.0
99.2
98.6
99.0
75.2
75.5
74.9
100.0
100.0
100.0
100.0
100.0
100.0
99.1
99.3
98.6
entries are percentages.
6.0
4.8
5.7
3.5
3.8
3.4
1.6
1.5
1.2
59.2
60.3
62.0
50.3
49.5
52.5
26.7
29.1
24.8
100.0
100.0
100.0
99.9
99.7
99.9
98.9
98.4
98.4
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
6.0
5.2
5.5
3.7
3.7
2.7
1.6
1.5
0.7
59.7
61.3
61.2
48.9
46.5
44.2
22.0
21.3
13.2
100.0
100.0
'100.0
99.8
99.2
99.5
94.4
92.5
88.5
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
99.9
6.2
4.8
5.5
5.8
4.5
3.0
5.2
4.5
1.5
60.5
61.2
62.2
59.7
56.7
49.4
52.8
49.8
27.5
100.0
100.0
100.0
99.9
99.9
99.8
100.0
99.5
98.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.8
5.1
5.5
5.2
4.5
2.5
4.3
4.1
0.9
g9.a
0.8
59.0
57.6
54.3
42.1
47.8
42.0
18.3
100.0
100.0
100.0
99.8
99.8
99.6
99.6
98.8
94.6
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
5.9
5.0
4.8
11.1
9.2
8.4
32.8
27.6
23.1
5~.3
5 .0
62.0
73.1
71.0
71.2
91.6
89.~
83.
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
6.2
5.3
5.2
5.2
5.3
5.0
4.4
5.5
5.4
60.6
62.1
63.5
59.7
59.2
62.3
51.8
53.2
52.6
100.0
100.0
100.0
99.9
100.0
100.0
99.9
99.8
99.6
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
106
Table C.5: Probabili!-yof Rejectioo for carci~niCi~ 'n!sts for varying
levels of Treatment U!thalitr arxl 'I\Jm:)r lethali for emale Mice
'lhyroid Follicular eel 'I\Jm:)rs using the I design.
Q'1set Treatment 'I\Jm:)r
Factor lethality lethality
1++0
l+yO
l+e:to
Zt
Zp
Zo
Zloq ~
Ztt
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*5.5
6.3
5.0
4.4
5.4
4.8
2.5
2.8
2.8
13.8
14.1
14.5
13.8
11.8
13.7
8.1
8.1
8.2
51.5
48.3
49.6
41.2
44.6
41.6
29.7
29.8
27.5
87.6
86.5
88.1
82.5
82.2
84.0
63.4
63.2
62.6
entries are percentages.
5.5
5.9
4.8
4.4
5.4
4.8
3.5
4.1
3.7
12.8
13.1
13.8
14.2
12.8
14.2
12.5
12.0
12.6
50.5
47.4
48.7
45.1
47.8
45.2
43.5
42.8
40.4
87.7
85.8
88.4
86.5
86.8
87.~
82.
82.5
80.5 .
5.5
5.8
4.8
4.9
5.9
5.0
6.0
6.5
4.8
13.1
12.7
13.6
14.7
14.3
14.3
14.8
14.9
12.2
50.7
48.1
48.5
47.2
47.3
43.8
44.7
43.2
35.2
87.7
85.9
88.5
86.6
86.0
85.6
80.1
78.1
70.3
5.5
5.8
4.9
4.9
5.8
4.9
5.6
6.0
4.6
13.5
12.8
13.9
15.0
13.9
12.8
14.4
14.3
11.5
50.9
48.4
48.5
47.2
47.5
40.2
46.1
42.9
31.7
87.8
86.1
87.5
87.2
85.9
82.8
81.8
79.8
65.9
5.1
5.8
4.7
4.5
5.2
3.7
4.9
5.3
3.9
12.4
12.5
12.0
13.2
11.8
9.~
13.
12.0
7.4
50.1
47.3
46.6
45.7
45.3
35.5
39.2
37.2
23.5
87.5
85.4
85.4
85.5
84.5
76·8
74.
72.9
54.5
5.4
5.5
6.2,
5.4
4.5
4.8
5.6
4.5
6.6
5.5
5.5
4.8
10.6
4.5
10.3
4.8
4.3
8.8
12.9 12.8
12.6 13.2
13.1 13.7
17.2 14.3
16.2 13.5
16.4 14.4
23.8 13.1
23.5 12.5
21.0 13.2
49.7 50.6
46.7 47.2
48.1 48.8
53.3 45.5
55.3 47.6
50.5 45.6
66.4 44.0
65.2 43.3
59.4 42.5
87.2 87.5
85.3 85.3
87.8 88.8
90.5 86.8
90.4 86.9
90.5 . 87.2
95.1 82.3
95.1 82.2
92.0 81.8
e
107
Table C.6: Probabili!y of Rejectioo 'for carci~ci~ Tests for varying
levels of Treatment Ii!thali tY and 'l\.mOr Lethali for emal.e Rats
Liver 'l\.mOrs using the ocr design.
Qlset Treatment 'l\.mOr
Factor Lethality Lethality
1++0
l+yO
l+CU
Zp
Zt
Zlog ~
Zo
Ztt
ZIt
•
e
•
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*4.9
2
7.2
1
10
5.3
1
1
4.3
2
2
4.5
2
10
4.4
2
1
1.6
5
2
1.4
5
10
1.8
5
1
16.3
1
2
18.3
1
10
18.0
1
12.8
2
1
10.4
2
2
10
14.0
2
1
5.1
5
2
4.3
5
10
4.9
5
1
1
59.9
2
57.8
1
10
59.4
1
1
46.1
2
2
45.9
2
10
43.2
2
1
17.8
5
2
16.8
5
10
16.7
5
1
94.9
1
2
96.0
1
10
1
95.7
1
86.6
2
2
2
86.8
85.8
10
2
47.5
1
5
2
48.7
5
45.9
10
5
entries are percentages •
4.8
6.8
5.2
4.5
4.5
4.5
2.2
1.7
2.2
16.0
17.5
17.0
13.5
10.9
14.8
6.9
6.0
6.8
59.5
58.0
59.0
50.4
50.6
47.8
26.8
26.5
26.2
94.9
96.0
95.9
90.5
90.6
89.8
67.5
66.7
64.7
4.7
6.8
4.9
4.8
5.2
5.4
5.1
4.4
4.0
15.6
17.4
17.2
15.5
13.1
16.8
13.8
12.4
12.0
59.9
58.1
60.0
56.0
55.8
51.2
42.8
42.1
40.0
94.8
96.1
96.2
92.2
93.0·
91.3
80.8
80.5
74.0
4.8
6.8
4.8
4.8
5.2
5.1
4.9
4.3
4.2
15.7
17.3
17.4
15.5
13.0
16.8
13.6
12.5
12.2
59.9
58.2
59.5
56.8
56.2
51.8
45.4
44.5
41.5
95.2
96.1
96.0
93.3
93.5
91.6
86.2
85.4
81.4
4.5
6.3
4.8
5.3
5.4
4.7
6.5
5.8
5.1
14.8
17.8
16.6
15.3
13.5
15.5
15.5
15.1
11.1
59.6
57.5
59.0
57.6
57.5
48.3
45.8
44.1
37.2
95.2
96.2
95.7
92.9
93.7
90.8
84.2
83.1
75.3
4.5
6.5
4.8
6.4
6.1
6.2
9.1
8.5
8.4
15.2
17.0
16.5
17.8
15.7
19.5
22.1
22.8
20.0
59.5
58.2
59.8
62.8
61.2
57.7
62.2
61.9
59.7
95.4
96.3
96.0
94.6
95.3
93.8
93.5
93.1
93.6
4.7
6.6
5.0
5.3
5.4
5.3
5.2
4.8
4.6
15.2
17.2
16.7
15.6
13.7
17.3
14.4
14.5
13.8
59.7
58.1
59.8
58.3
57.8
54.8
48.1
47.1
47.5
94.8
96.2
96.2
93.8
93.9
92.4
87.5
86.7
86.7
108
Table C.7: probabili!:y of ~jectia1 for carci~nici~ Tests for varying
levels of Treatment rsthality arxi 'l\.m)r lethali for emale Rats
Luekemia;L~ using the tel deSlgn.
Q1set Treatment 'l\.m)r
Factor lethality lethality
1++0
l+yO
l+ao
Zt
Zp
Zo
Zlog ~
Ztt
ZIt
1
5.0
5.5
1
1
*5.3
5.4
5.2
5.2
5.2
2
1
1
5.2
5.3
5.0
5.1
5.2
4.8
5.4
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
4.5
3.2
3.2
3.5
1.2
1.5
1.7
53.2
52.2
50.g
41.
42.7
41.0
25.2
22.6
21.9
100.0
99.9
99.8
99.6
99.3
99.7
96.6
97.4
97.2
100.0
100.0
100.0
100.0
100.0
100.0
190.0
1 0.0
100.0
entries are percentages.
4.5
5.1
4.5
5.1
4.3
5.9
4.5
53.2
51.8
50.7
50.5
49.8
48.8
47.7
46.1
45.9
100.0
100.0
99.8
99.8
99.8
99.8
99.5
99.6
99.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.8
4.5
4.1
3.7
2.8
2.5
1.9
52.7
52.8
50.0
47.0
45.2
41.8
33.5
28.4
23.2
100.0
99.9
99.8
99.8
99.4
99.7
98.2
98.3
97.6
100.0
100.0
100.0
100.0
10g.0
10 .0
10g.0
10 .0
100.0
5.2
5.3
3.9
2.1
5.8
3.8
0.8
53.8
52.8
47.2
51.2
46.9
30.2
49.2
36.8
12.8
100.0
100.0
99.8
99.9
99.6
98.2
99.6
99.3
89.5
100.0
100.0
100.0
100.0
100.0
100.0
10g.0
10 .0
100.0
5.0
4.5
3.9
1.2
4.6
3.5
0.5
53.3
51.6
45.9
49.6
44.7
26.8
42.2
32.3
8.3
100.0
100.0
99.6
99.8
99.5
96.9
98.8
97.8
77.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.8
4.3
10.8
9.3
7.9
37.8
34.1
18.2
51.0
50.2
50.5
67.2
66.5
60.2
92.4
91.5
78.2
99.8
99.8
99.7
100.0
100.0
99.9
100.0
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.3
5.2
4.5
4.8
4.7
6.0
4.3
54.4
51.8
51.2
50.7
50.5
49.8
47.8
46.5
46.5
100.0
99.9
99.9
100.0
99.9
99.8
99.6
99.8
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
•
e
109
'<.
'l-
Table C.8: probabili~ of Rejectioo for carci~ci~ Tests for varying
levels of Treatment lethality an::1 'l\JlOOr lethali for emale Rats
Llmg 'l\JlOOrs using the r«:I design.
Q'lset Treatment 'l\JlOOr
Factor lethality lethality
1++0
l+yO
1+e;,
Zt
Zp
Zo
Ztt
Zloq Zm.r
ZIt
•
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*4.5
1
2
5.2
10
1
5.2
1
2
3.3
2
2
4.3
10
2
4.5
1
5
3.2
2
3.1
5
10
4.8
5
1
1
12.3
2
10.5
1
1
10
11.5
2
1
10.3
2
2
11.1
10
2
9.6
1
5
9.8
2
5
9.7
10
5
9.9
1
1
36.9
2
37.4
1
10
38.5
1
2
1
34.2
2
2
37.8
2
10
35.8
1
33.8
5
2
33.1
5
10
30.1
5
1
1
69.6
2
1
71.8
1
10
71.2
1
2
69.2
2
2
69.4
2
10
70.3
5
1
63.2
2
64.2
5
10
5
64.6
entries are percentages.
4.5
5.1
5.2
3.4
4.3
4.5
4.1
3.7
5.8
12.0
10.4
11.1
10.4
11.2
9.5
12.2
11.5
11.9
35.8
36.3
37.5
35.6
39.1
37.7
42.8
42.1
39.2
69.5
70.8
70.8
72.8
72.8
73.5
75.5
77.2
76.8
4.3
4.8
5.2
3.7
4.5
4.5
5.8
5.0
5.3
11.9
10.1
11.5
10.5
11.5
9.6
13.7
12.8
10.5
35.6
36.5
38.4
36.0
38.5
35.5
41.4
36.7
30.5
68.2
71.2
71.2
72.4
70.6
70.4
70.2
68.3
65.2
4.3
3.6
4.8
4.3
5.5
2.5
3.6
2.6
4.4
3.0
4.3
1.4
5.5
4.5
4.6
3.9
4.4
1.4
12.1 10.6
10.2
9.4
11.0
7.1
10.2
8.8
10.8
8.2
8.0
3.7
12.5 10.1
10.8
7.9
7.8
3.2
35.8 34.7
37.0' 33.1
31.2 27.3
34.8 32.0
33.7 ·30.7
23.3 16.7.
37.1 29.3
29.8 23.7
8.3
12.9
68.5 67.7
70.3 69.4
56.2 54.6
70.1 68.2
64.5 63.8
46.5 40.8
67.0 57.6
59.8 53.5
30.9 24.2
4.0
4.5
4.8
5.1
5.2
5.2
3.8
3.3
4.8
4.3
4.6
4.5
10.1
3.4
8.9
3.2
6.3
5.2
11.5 12.2
10.1 10.4
11.2 11.4
12.0 10.3
12.6 11.1
9.9
9.5
22.0 10.4
20.5 10.3
13.8 10.4
34.8 ·36.1
35.2 36.9
37.2 37.9
40.4 34.4
43.5 37.9
38.7 36.0
61.4 35.2
57.9 35.0
40.6 31.9
67.5 69.2
69.9 70.9
70.5 70.7
77.6 70.1
77.5 70.2
74.1 70.8
90.1 65.9
88.5 68.5
77.8 67.5
110
Table C.9: Probabi1i~ of Rejectim for carci~nici~ Tests for varying
levels of Treatnent Iethal~am 'I\.mor I.ethali for emale Rats
MalmIary Glarxi Fibr
nanas using the
design.
Q'1set Treatnent . 'I\.mor
Factor I.ethali ty I.ethali ty
l+yO
l+cxa
1++0
Zt
Zp
Zo
Zloq ~
Ztt
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*5.1
4.8
5.3
2.0
2.8
2.4
0.5
0.2
0.3
62.0
61.2
57.5
44.3
39.5
41.8
12.3
11.3
11.2
100.0
100.0
99.9
99.9
99.5
99.7
90.2
89.8
89.2
100.0
100.0
100.0
100.0
100.0
100.0
99.9
99.9
100.0
5
5
entries are percentages.
4.8
5.1
5.3
2.8
4.3
3.6
2.0
1.6
2.2
60.6
61.8
57.8
54.0
48.6
51.7
33.2
33.1
32.9
100.0
100.0
100.0
99.9
99.9
99.9
99.1
99.3
99.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.7
4.8
4.9
3.2
4.2
2.8
1.9
0.8
0.5
61.2
61.0
57.5
51.4
45.6
44.4
25.6
22.6
15.5
99.9
100.0
100.0
100.0
99.7
99.8
96.2
95.1
92.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.7
4.9
5.4
4.5
5.3
2.7
4.8
4.7
1.2
62.1
62.7
56.8
61.2
52.7
43.5
52.4
47.5
22.1
100.0
100.0
99.9
100.0
99.9
99.8
99.6
99.8
96.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.2
5.2
4.6
4.2
4.8
2.6
4.3
l.9
0.9
61.2
61.7
54.8
58.9
50.2
38.0
46.0
40.4
15.0
100.0
100.0
99.9
100.0
99.8
99.4
99.5
99.2
91.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.8
4.5
5.2
5.2
9.7
10.3
8.0
36.1
34.1
21.9
59.8
59.5
56.1
74.5
70.5
68.6
93.3
92.3
86.2
99.9
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.4
~.2
.5
3.8
5.5
5.3
4.2
4.8
5.4
61.1
62.2
58.9
60.8
55.7
~.4
3.9
51.8
53.9
100.0
100.0
100.0
100.0
99.9
0 •0
18
1 0.0
99.9
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
•
e
~
111
rr
Table C.10: probabili~ ReJection for carci~ci~ Tests for varying
levels of Treatment I.e
i arrl 'l\m)r I.ethali}l for emale Rats
'Ihyroid Follicular eel 'l\m)rs using the I design.
Q1set Treatment 'l\m)r
Factor I.ethality I.ethality
1++0
l+yO
l+cxa
Zt
Zp
Zo
Ztt
Zlog ~
Zlt
e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*6.0
2
5.6
1
10
4.4
1
2
1
3.8
3.8
2
2
10
3.6
2
1
5
2.2
2.1
2
5
10
2.7
5
1
1
30.9
1
2
27.7
10
31.8
1
1
26.8
2
26.7
2
2
10
25.1
2
1
13.8
5
2
5
13.9
10
14.2
5
1
1
94.8
2
94.8
1
10
96.2
1
1
91.8
2
2
2
92.0
2
10
93.6
1
79.5
5
2
78.5
5
10
79.2
5
1
100.0
1
2
100.0
1
1
10
100.0
2
1
99.9
2
2
100.0
10
2
99.9
99.8
1
5
2
99.8
5
10
5
99.6
entries are percentages.
5.7
5.9
4.2
4.7
4.9
4.5
5.4
4.8
5.3
31.0
27.4
31.7
31.4
31.1
28.9
25.4
26.9
26.5
94.8
95.0
96.3
94.3
95.0
96.4
91.9
93.4
93.7
100.0
100.0
100.0
99.9
100.0
99.9
100.0
100.0
100.0
5.5
6.3
4.3
5.2
4.9
3.8
5.2
3.7
3.7
31.3
28.2
31.8
30.2
28.9
25.4
22.0
20.3
16.5
94.5
94.6
96.3
93.9
94.0
93.7
85.8
84.7
82.0
100.0
100.0
100.0
99.9
100.0
99.9
100.0
99.9
. 99.7
5.4
6.1
4.6
5.2
5.1
2.9
5.8
4.7
2.8
31.2
28.0
29.7
31.8
29.8
20.4
27.2
24.5
11.9
94.5
95.1
94.8
94.5
94.2
87.9
91.8
89.5
71.2
100.0
100.0
100.0
99.9
100.0
99.8
100.0
99.9
99.3
5.8
6.2
5.4
5.0
4.5
2.5
5.7
4.2
2.5
30.4
27.5
27.9
30.0
28.2
16.8
23.7
21.8
9.8
94.2
94.8
93.7
93.9
92.8
85.3
87.5
85.1
57.2
100.0
100.0
100.0
99.9
100.0
99.8
99.8
99.8
95.7
5.8
5.9
4.4
9.4
7.8
6.5
21.8
21.0
13.5
30.9
27.0
31.6
42.5
40.8
35.8
64.8
64.9
50.0
93.9
94.5
96.0
97.1
97.7
97.8
99.6
99.8
98.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.5
6.0
4.4
4.8
5.2
4.3
5.7
4.8
5.2
31.4
27.5
31.6
31.3
31.5
29.3
26.5
28.4
28.1
94.7
94.9
96.2
94.2
95.2
96.5
92.8
92.9
93.8
100.0
100.0
100.0
99.9
100.0
99.9
100.0
100.0
100.0
112
Table C.11: Prc:babili ~ of RejectiCll for carciKci ~Tests for varying
levels of Treatment I.l!thaliq; and 'l\m)r I.ethali for
e Mice
Hemagiana-Hemangiosarcanas using the OCI sign.
Cklset Treatnent 'l\m)r
Factor I.ethali ty I.ethali ty
l+yO
l+aa
1++0
Zt
Zp
Zo
Zloq ~
Ztt
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
~
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.1
5.8
4.5
4.1
4.2
4.2
2.2
1.8
1.8
17.6
17.8
19.5
12.9
13.0
12.8
6.6
5.1
6.1
60.5
61.6
g3.7
2.6
49.6
51.6
23.5
21.9
22.4
96.5
96.2
96.7
89.9
89.1
91.3
~.5
7.4
57.1
5
5
5
5
5
10
10
10
10
10
10
10
10
10
~
* table entries are percentages.
5.9
5.7
4.2
4.2
4.5
4.4
3.4
2.9
3.5
17.0
17.2
18.2
14.3
13.8
13.7
11.0
9.2
9.6
60.6
62.2
63.5
59.4
57.0
57.8
41.2
40.3
41.1
96.7
96.4
96.5
94.8
93.6
95.1
82.4
82.7
82.2
5.6
5.5
4.2
4.5
5.1
4.9
5.4
5.0
4.8
16.7
16.6
17.8
16.1
15.5
14.8
16.3
14.7
15.5
61.3
62.2
63.9
62.9
60.5
60.9
51.9
49.9
47.2
96.5
96.2
96.8
95.3
95.0
94.8
87.7
88.0
84.7
5.6
5.5
4.2
4.5
5.0
4.8
5.4
4.9
5.1
16.5
16.8
18.2
16.2
15.3
14.8
16.4
14.6
14.6
61.5
62.4
63.9
63.2
60.2
60.2
54.2
51.9
48.9
96.5
96.3
96.8
95.8
95.1
95.5
90.9
91.2
88.5
5.9
5.3
4.2
4.5
5.2
4.2
6.7
5.1
4.9
16.1
,16.8
17.3
15.8
15.7
13.3
14.9
13.9
14.2
61.0
61.9
62.6
61.9
60.2
56.4
51.4
47.9
43.2
96.6
96.6
96.2
95.5
94.6
93.8
88.6
87.6
80.9
6.1
5.3
4.2
5.6
5.8
5.7
9.5
7.6
8.5
16.2
17.0
17.8
18.3
16.9
17.g
23.
22.4
24.3
61.2
62.5
63.5
66.2
64.7
65.5
69.5
66.2
64.8
96.7
96.8
96.8
96.6
96.5
96.8
96.5
96.4
96.1
5.7
5.5
4.2
4.4
4.9
4.6
5.2
4.7
5.2
16.7
16.7
18.1
16.2
15.5
14.8
15.6
14.5
16.9
60.8
61.8
63.6
62.6
60.5
g2.1
5.5
51.8
54.6
96.7
96.3
96.8
9~.9
9 .2
96.5
90.7
91.8
91.8
.,
e
,
113
Table C.12: probabili~ of Rejection for carci~ci~Tests for varying
levels of Treatment Lethality and 'I\mDr lethali for
e Mice
Liver 'I\mDrs using the tel design.
Qlset Treat:nent 'I\mDr
Factor lethality Iethality
Zp
1++0
l+yO
1+0r0
Zt
Zo
Ztt
Zlgg ~
Zlt
-e
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
*4.8
2
4.5
1
10
5.5
1
2
1
1.9
2
2
3.3
10
2.9
2
1
0.2
5
2
5
0.5
10
0.4
5
1
1
67.0
2
1
65.7
64.5
10
1
2
1
50.8
2
48.4
2
10
48.7
2
1
17.2
5
5
2
15.1
10
14.2
5
1
1
100.0
2
1
100.0
10
100.0
1
2
1
100.0
2
99.8
2
10
99.9
2
5
1
93.8
2
92.4
5
10
92.2
5
1
1
100.0
1
2
100.0
1
10
100.0
2
1
100.0
2
2
100.0
2
10
100.0
1
99.7
5
2
5
99.8
5
10
100.0
entries are percentages.
4.8
4.4
5.1
4.2
5.2
4.9
3.3
4.4
4.8
68.7
68.1
66.5
67.2
64.6
64.2
55.6
56.0
55.5
100.0
100.0
100.0
100.0
100.0
100.0
99.9
99.9
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.8
4.3
. 5.3
3.7
4.5
3.5
1.5
1.4
0.8
68.5
68.2
66.0
62.2
56.8
53.4
34.9
33.0
24.5
100.0
100.0
100.0
100.0
100.0
99.9
99.1
99.0
97.7
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.8
4.4
5.7
4.6
5.2
3.3
4.5
4.8
1.2
69.1
69.2
64.5
69.5
63.9
50.3
63.4
57.7
30.8
100.0
100.0
100.0
100.0
100.0
99.9
100.0
99.9
98.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.4
4.4
5.8
4.4
4.8
2.2
3.7
3.3
0.4
67.3
68.1
62.9
66.8
60.1
41.7
55.6
47.6
14.1
100.0
100.0
100.0
100.0
100.0
99.8
99.7
99.9
93.3
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.8
4.4
5.8
10.5
10.4
8.7
42.1
41.3
24.3
64.3
65.2
66.2
82.0
80.2
74.9
97.5
96.5
89.8
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
4.9
4.4
5.4
4.5
5.5
5.7
4.5
5.3
6.2
69.9
69.3
68.2
69.3
66.8
66.6
61.5
62.8
61.1
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
114
Table C.B: Prababili!¥ of Rejection for carci~nici~Tests for varying
levels of Treatmant lethalitY arx:l 'I\m:)r IA!thali for
e Mice
Luekemia/Lynpnnas using the N:I design.
Q'1set Treatment 'I\m)r
Factor IA!thality IA!thality
l+yO
l+or.a
1+'0
Zt
Zp
Zloq ~
Zo
Ztt
Zlt
5.2
1
5.2
4.6
5.2
1
5.2
*5.4
1
5.1
1
2
4.3
4.0
4.3
4.2
1
4.2
4.3
4.1
1
5.9
5.8
1
10
5.9
6.1
5.7
5.5
6.0
4.3
2
1
2.8
1
5.0
5.5
5.2
7.5
5.3
2
4.3
4.9
1
2
3.3
5.1
4.8
7.1
5.0
5.2
2
10
3.5
4.8
7.4
4.9
3.9
1
5.8
3.1
5
1
0.6
4.3
4.8 16.2
1
6.1
5.3
2.5
1
5
2
0.6
3.8
4.9
3.9 17.0
4.8
2.8
1
5
10
0.8
2.4
3.2
2.0 12.5
4.8
1
40.5 40.1 40.4 40.2 39.2 39.3 40.2
2
1
1
38.6 39.1 38.7 39.2 39.1 38.6 39.0
2
2
1
2
10
39.1 39.0 38.8 39.3 36.5 37.9 38.8
2
1
27.3 34.6 36.3 39.2 37.7 47.1 38.4
2
2
2
26.8 34.7 35.2 38.2 35.4 46.2 38.5
2
2
2
10
26.9 35.2 33.0 33.5 28.8 45.~ 38.3
5
1
7.2 23.2 24.1 33.8 30.5 64.
2
32.5
2
7.8 24.3 24.2 34.9 29.7 63.4 34.6
2
5
10
7.4 24.8 18.6 24.6 17.6 56.4 34.6
2
5
1
1
98.7 98.8 99.0 98.8 98.9 98.4 98.7
5
1
2
98.6 98.4 98.5 98.5 98.4 98.5 98.7
5
1
10
98.5 98.6 98.5 98.5 98.4 98.5 98.7
5
2
5
1
94.0 97.8 98.0 99.0 98.7 99.3 98.7
2
2
95.6 98.5 98.0 98.8 98.5 99.6 98.9
5
2
10
94.6 97.5 96.8 97.1 95.6 98.7 98.3
5
5
1
63.6 90.9 87.0 96.3 94.2 99.6 96.5
5
2
62.4 93.3 88.3 97.0 94.3 99.9 97.3
5
5
10
64.9 93.8 83.9 91.8 84.5 99.5 97.0
5
5
10
1
1
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
1
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
1
10
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
2
1
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
2
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
10
10
5
97.3 100.0 100.0 100.0 100.0 100.0 100.0
1
10
10
5
2
98.3 180 •0 99.9 100.0 99.~ 100.0 108. 0
10
5
10
97.6 1 0.0 99.6 100.0 99. 100.0 10 .0
* table entries are percentages.
e
115
Table C.14: Probabili~ of Rejection for carci~nicivsts for varying
levels of Treatnent Lethality arxl '1'lJIror IBthali for
e Mice
.
Lung 'I\m)rs using the OCI design.
cnset TreatDent '1'lJIror
Factor IBthali ty IBthali ty
•
e
l+yO
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
l+cro·
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
1++0
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
Zt
Zp
*3.8
5.2
5.3
2.8
3.0
2.6
0.8
0.9
1.0
47.8
49.6
50.4
39.8
38.7
35.5
16.0
15.1
14.6
99.8
99.9
99.7
99.0
99.5
99.1
88.9
91.2
89.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
3.5
5.2
4.9
5.5
5.3
4.1
4.5
4.2
4.5
49.0
50.0
50.4
51.5
48.6
46.2
47.0
44.5
45.1
100.0
100.0
99.7
99.6
100.0
99.8
99.2
99.8
99.5
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5
5
entries are percentages.
Ztt
3.9
5.5
5.2
4.9
4.5
2.9
2.8
2.8
1.7
48.8
50.0
50.9
47.6
43.9
39.5
33.7
29.4
24.1
100.0
100.0
. 99.7
99.6
99.8
99.3
97.4
96.8
94.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Zloq
4.0
5.2
5.1
5.7
4.9
2.7
5.7
4.4
1.4
49.3
50.4
48.8
52.5
47.5
35.1
49.8
42.5
23.1
100.0
100.0
99.7
99.6
100.0
99.2
99.4
99.6
95.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Zrn.t
3.5
4.5
4.8
5.5
4.5
1.7
4.4
3.6
0.8
48.8
48.6
46.5
49.8
45.0
27.5
42.9
33.6
12.3
99.9
99.9
99.6
99.5
99.7
97.7
98.5
98.1
82.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0·
99.9
Zlt
3.5
5.8
5.2
10.2
9.3
7.0
27.6
26.5
16.4
47.7
50.0
49.6
64.6
61.0
54.5
86.3
83.8
73.2
99.8
99.7
99.5
99.8
99.9
99.8
100.0
100.0
99.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Zo
3.5
5.3
5.2
5.5
4.9
4.3
4.6
4.5
5.0
49.6
50.1
50.8
52.5
49.3
46.8
46.5
45.4
44.9
100.0
100.0
99.8
99.7
100.0
99.8
99.2
99.6
99.3
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
116
Table C.15: Probabili!:Y of Rejection for carci~nici~'n!sts for varying
levels of Treatment IBthality am 'l\IrOr IBthali for
e Mice
'Ihyroid Follicular cell 'l\IrOrs using the
design.
Qlset Treatment 'l\IrOr
Factor IBthality IBthality
1++0
l+yO
l+aa
Zt
Zp
Zo
Zlog Zm.t
Ztt
Zlt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
~
5
5
~
5
5
10
10
i8
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.1
4.2
4.5
3.8
4.2
3.7
3.7
3.0
4.7
12.5
12.8
12.4
11.5
10.8
12.6
10.4
9.5
10.0
35.4
39.2
37.2
36.8
36.0
37.5
31.0
29.8
31.1
77.0
74.~
77.
71.9
70.8
72.3
62.4
65.8
64.1
10
10
10
10
10
* table entries are percentages.
5.9
4.1
4.5
3.8
4.1
3.7
4.9
4.3
6.4
12.2
12.2
12.1
12.2
11.2
13.2
15.8
13.8
13.7
34.4
37.5
35.8
40.2
37.8
40.3
44.5
43.4
44.7
76.1
74.4
76.8
76.4
74.8
75.3
79.8
81.2
81.4 .
5.8
4.1
4.5
4.0
4.2
3.8
6.4
4.7
5.5
12.~
12.
12.3
12.5
11.7
12.4
15.7
12.9
11.4
34.8
37.7
36.3
40.0
37.5
37.3
41.4
37.8
33.7
76.0
74.8
77.2
76.2
73.0
72.5
73.4
72.3
66.7
5.8
4.0
4.8
4.0
4.2
3.7
6.2
4.4
5.2
12.1
12.8
12.2
11.9
11.3
10.8
14.6
12.3
9.1
34.8
38.0
36.8
39.1
35.2
28.7
37.8
34.0
21.7
76.1
74.8
73.3
75.1
70.g
61.
71.3
69.2
44.4
5.5
3.3
2.7
3.1
3.0
2.2
5.4
4.2
2.9
10.9
11.7
9.5
10.2
9.~
7.
12.1
10.5
4.3
33.g
35.
30.5
34.3
31.8
23.5
30.9
27.~
14.
75.0
73.5
69.1
72.1
67.7
53.9
63.4
60.0
31.2
5.5
3.8
4.4
4.7
4.6
3.8
9.5
7.6
7.8
11.9
11.8
12.0
13.8
13.1
13.2
24.1
21.1
15.4
33.8
36.5
35.4
43.3
42.2
40.2
59.5
58.0
47.5
75.4
74.2
76.4
81.6
77.7
76.3
90.5
89.~
83.
6.0
4.2
4.5
3.8
4.2
3.7
3.8
3.2
5.0
12.3
12.2
12.2
11.7
10.8
12.7
11.5
10.5
10.~
34.
38.2
36.1
37.5
36.3
37.9
34.5
34.1
36.1
76.3
73.9
76.7
73.9
71.7
73.6
70.2
72.2
70.5
e
117
•
Ia
•
e
Table C.16: Probabili~ of Rejectioo for carci~nicivsts for varying
levels of Treatment Ii!thali ~ 'l\.m:)r lethali for
e Rats
rs using the l'l:I design.
Integumentary System
Q1set Treatment 'I\Jm:)r
Factor lethality lethality
1++0
l+yO
1+010
Zt
Zp
Zo
Zlog Zrn.t
Ztt
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
.
1
1
*5.5
2
1
4.7
10
5.1
1
1
3.8
2
2
4.5
2
10
4.0
2
1
5
2.2
2
2.0
5
10
2.0
5
1
23.4
1
2
1
23.0
10
22.5
1
2
1
15.8
2
17.1
2
10
16.5
2
1
5
8.0
2
8.5
5
10
8.6
5
1
1
81.5
2
83.5
1
10
81.7
1
2
1
75.0
2
73.9
2
2
10
73.0
1
47.8
5
2
5
50.6
10
48.1
5
1
1
99.7
2
1
99.8
1
10
99.7
2
1
99.0
2
2
99.2
2
10
98.9
1
5
92.9
2
92.0
5
10
92.0
5
entnes are percentages.
.
5.0
4.5
4.7
4.2
4.9
4.8
4.2
4.2
3.5
23.2
22.3
22.5
19.2
20.2
20.2
17.2
17.8
18.6
81.6
83.8
81.8
82.1
79.2
79.2
70.2
71.8
70.3
99.7
99.9
99.7
99.6
99.7
99.4
98.8
98.5
98.8
4.9
4.5
5.1
5.6
5.4
4.4
5.1
4.5
3.1
23.2
22.1
22.5
19.5
19.8
17.0
16.8
14.9
11.4
82.8
83.8
81.8
80.8
76.9
74.4
62.8
61.5
52.1
99.8
99.8
99.8
99.4
99.5
98.9
96.5
95.4
93.3
4.8
4.7
5.0
5.5
5.3
3.2
5.2
4.9
2.2
23.2
23.2
21.0
20.9
20.1
14.3
21.3
18.2
9.2
82.1
83.6
80.2
82.9
78.5
66.7
74.1
68.0
44.2
99.8
99.9
99.6
99.6
99.6
97.5
98.8
97.5
87.2
4.9
4.8
4.9
4.5
3.4
4.9
5.0
8.3
5.0
7.8
2.8
6.2
4.3 18.2
3.8 19.3
1.8 11.4
22.5 22.4
22.1 22.4
20.5 22.4
20.3 30.1
18.5 30.2
11.3 27.0
18.3 53.8
16.0 48.1
7.1 38.5
81.8 81.3
83.4 83.0
78.0 81.4
81.1 90.4
76.8 88.8
59.8 85.8
64.4 96.4
61.5 94.8
32.5 90.1
99.8 99.8
99.7 99.8
99.5 99.8
99.5 99.9
99.5 99.9
95.7 99.8
97.4 100.0
94.0 100.0
76.5 100.0
4.9
4.4
4.7
4.8
5.2
4.8
5.2
4.5
4.1
22.8
22.3
22.3
19.6
21.6
21.1
19.5
19.8
20.8
81.8
83.7
82.2
83.0
80.6
80.5
74.8
75.0
74.0
99.8
99.9
99.8
99.7
99.6
99.5
99.0
98.8
99.1
118
Table C.17: Probabili ~ of Rejecticn for carci~ici~sts for varying
levels of Treatment tethalitY arxl 'I\m:)r lethali for
e Rats
Liver 'I\m:)rs using the OCI design.
cmet Treatment 'l\m)r
Factor lethality lethality
1++0
l+yO
1+ao
Zt
Zp
Zo
Ztt
Zloq ~
ZIt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
~
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.2
5.8
4.8
4.5
4.2
4.5
2.5
1.8
1.2
18.8
23.2
20.7
12.8
14.7
14.7
6.8
6.5
7.2
75.9
73.9
75.1
61.7
61.0
60.9
33.5
35.6
32.3
99.2
99.1
98.7
96.7
96.2
96.8
78.8
78.1
79.0
entries are percentages.
5.8
5.4
4.4
4.8
4.2
5.2
4.3
3.4
3.0
18.5
22.7
20.8
15.9
17.1
17.3
12.5
12.1
13.9
76.5
74.2
75.2
69.5
68.7
68.0
53.6
55.7
53.1
99.2
99.2
98.7
98.4
97.6
98.7
94.3
92.8
94.1
6.0
5.4
4.5
5.8
5.2
5.2
6.8
5.8
3.7
18.7
23.3
20.7
18.1
18.2
16.8
15.5
14.0
12.1
76.6
74.0
75.2
70.5
68.0
63.6
52.7
52.0
40.8
99.2
99.3
98.6
98.2
97.7
97.2
91.1
88.2
84.6
6.0
5.4
4.5
5.7
5.2
4.4
7.2
6.0
3.5
18.8
23.4
20.3
18.3
19.1
14.~
17.
16.7
12.5
76.2
74.4
74.8
74.2
70.2
61.2
64.2
62.5
41.9
99.2
99.3
98.6
98.9
98.3
96.3
96.2
93.7
84.7
5.8
5.9
4.8
5.2
4.9
4.4
5.2
7.5
5.2
7.8
3.5
7.8
5.3 16.7
5.2 16.9
2.7 11.5
18.4 18.5
22.8 22.9
20.g . 21.3
17.
24.8
18.1 26.1
12.5 23.9
14.5 39.5
13.4 40.9
9.1 35.0
76.7 75.6
74.0 74.1
73.9 74.8
71.7 82.2
67.1 80.8
55.5 78.8
56.8 89.7
53.5 89.6
83.1
31.~
99.
99.0
99.2 99.0
98.4 98.7
98.7 99.~
97.6 99.
93.4 99.4
92.3 99.9
89.3 99.8
12.8 99.5
5.7
5.3
4.5
5.4
5.0
6.2
6.0
5.2
4.8
18.2
22.7
21.2
17.4
19.2
19.2
16.2
16.5
18.7
76.5
74.2
75.5
73.2
71.7
71.6
62.8
65.0
64.5
99.2
99.3
98.7
~8.8
8.2
98.7
97.3
96.8
96.9
.
e
.
1-
•
119
Table C.18: Probabili~ of Rejection for carci~nici~sts for varying
levels of Treatment Lethality and 'l\.m:)r lethali for
e Rats
Luekemia;LYJ1tilanas using the N:I design.
CDset Treatment 'l\.m:)r
Factor lethality lethality
1++0
l+yO
Zt
1+ao
Zp
Zloq ~
Zo
Ztt
ZIt
•
e
l-
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
S
5
5
5
10
10
10
10
10
10
10
10
10
*
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*4.8
5.2
5.2
1.2
2.2
1.6
0.2
0.0
0.2
66.5
65.3
63.2
45.3
44.2
43.8
10.6
10.9
11.9
100.0
100.0
100.0
99.8
99.7
99.6
90.9
91.5
91.7
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
table entries are percentages.
5.2
5.1
5.3
2.4
3.9
3.3
1.4
1.8
1.8
67.2
65.1
63.8
57.2
55.8
54.2
36.8
38.8
37.5
100.0
100.0
100.0
100.0
99.8
100.0
99.7
99.8
99.7
100.0
.100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.0
5.1
5.5
2.4
3.0
2.0
0.5
0.4
0.3
67.2
65.0
63.0
50.8
47.0
44.2
21.8
18.3
14.0
100.0
100.0
100.0
100.0
99.8
99.8
96.8
95.5
94.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.5
5.1
5.7
4.6
4.0
1.5
4.8
3.7
0.4
68.2
65.4
59.5
64.6
56.8
39.1
56.2
45.6
13.3
100.0
100.0
100.0
100.0
99.8
99.5
100.0
99.9
93.8
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.6
5.2
5.6
3.9
4.0
0.9
3.6
3.5
0.4
66.5
64.8
58.4
62.4
55.2
32.8
48.3
40.7
7.6
100.0
100.0
100.0
100.0
99.8
99.2
99.6
99.6
81.5
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.8
4.5
5.2
5.3
14.8
15.3
9.3
62.3
55.5
27.8
62.5
61.5
63.9
84.8
80.8
73.1
99.2
98.4
91.2
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
5.3
5.1
5.3
4.2
5.9
5.0
4.2
4.5
4.6
68.2
67.4
66.4
65.3
62.8
61.2
57.9
59.2
59.1
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
99.9
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
120
Table C.19: Probabili!¥ of Rejectioo for carci~niciVsts for varying
levels of Treatment ISthali tY and 'l\mDr Lethali for
e Rats
Lung 'l\mDrs using the reI design.
Q1set Treatment 'I\ltDr
Factor Lethality Lethality
1++0
l+yo
1+ao
Zt
Zp
Zlog Zrtw
Zo
Ztt
Zlt
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
* table
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*5.9
5.9
4.8
5.8
5.0
6.1
4.5
4.0
4.0
28.2
28.8
29.1
24.9
25.1
26.7
20.8
22.1
20.9
67.8
66.7
66.9
63.6
63.0
62.0
53.2
55.4
53.8
95.4
95.3
96.5
93.6
93.2
94.1
87.7
89.5
88.8
entries are percentages.
5.8
5.5
5.6
5.7
4.5
4.6
6.0
6.3
5.1
5.5
6.5
6.1
6.8
7.5
6.0
6.6
6.4
5.0
27.7 27.8
27.8 28.2
27.8 28.9
28.1 27.8
27.4 26.3
29.2 26.5
32.5 30.2
34.4 27.4
32.4 21.5
66.9 67.3
66.4 . 66.6
66.5 66.9
69.2 68.2
67.7 64.9
66.8 62.2
71.0 ~3.4
71.6
9.6
70.5 54.5
94.9 95.3
95.5 • 95.4
96.1 . 96.5
95.8 95.0
95.2 93.4
95.8 94.0
96.1 91.2
96.2 90.9
96.7 89.8
5.3
5.7
5.8
6.0
5.1
5.4
7.1
6.0
3.7
28.1
28.2
26.6
26.7
23.6
16'8
28.
23.5
9.2
67.1
65.9
57.2
67.8
60.7
41.7
63.4
52.0
22.3
95.3
95.2
87.8
95.0
91.2
74.4
90.~
85.
53.8
4.5
5.1
4.6
S.l
3.7
2.8
4.3
3.8
1.7
27.0
26.2
22.2
25.1
21.9
14.5
21.7
1~.2
.2
65.5
64.7
54.5
~.8
.8
36.9
52.2
43.9
18.2
95.2
94.9
87.8
94.0
89.6
70.2
84.~
76.
43.3
5.5
5.7
4.5
7.6
6.5
6.9
14.8
15.7
8.4
27.9
27.3
27.8
35.7
34.2
31.6
58.7
57.0
38.4
64.6
66.7
66.5
78.2
75.8
69.3
90.2
88.5
75.5
94.5
94.3
96.0
98.2
97.3
96.6
99.7
99.3
97.7
5.8
5.6
4.4
5.8
5.0
6.2
~.2
.0
5.5
27.7
28.3
27.8
25.8
26.2
27.7
25.8
26.8
26.5
67.2
66.4
67.1
7
61.
6 .6
6 .0
62.5
63.3
62.2
95.1
95.5
9~.2
9 .0
93.8
95.2
92.5
93.~
93.
e
...
121
..
Table C. 20: Probabili ~ of Rejection for carci~ci~Tests for varying
levels of Treatment r.ethali tY arrl 'l\.1Ioor IBthali for
e Rats
Mesothelianas using the 1'CI design.
Q1set Treatment 'l\.1Ioor
Factor IBthality IBthality
1++0
l+yo
1+cr.a
Zt
Zp
Zlog Zrn.,
Zo
Ztt
ZIt
1
.
e
~
•
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
5
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
10
10
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
1
1
2
2
2
5
5
5
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
1
2
10
*6.6
5.4
5.5
5.0
3.7
3.7
2.5
1.5
2.6
25.7
27.4
27.9
20.1
20.7
21.6
11.4
10.4
10.5
62.8
62.5
65.2
52.8
50.9
51.5
29.0
26.9
27.5
93.4
94.3
93.5
85.5
85.9
85.2
57.5
56.9
55.2
'" table entries are percentages.
6.4
5.3
5.3
5.0
3.7
3.7
3.4
2.7
3.6
25.1
26.4
26.5
21.8
22.6
23.5
17.5
16.2
16.2
62.5
62.6
64.8
57.6
56.0
56.1
42.8
40.8
43.5
93.6
94.3
93.8
90.1
90.8
89.8
77.5
75.8
74.1
6.0
5.2
5.2
5.9
4.3
4.0
8.5
5.8
5.7
25.2
25.7
26.8
23.8
25.2
23.5
24.1
23.2
20.5
62.2
62.5
64.7
60.1
58.1
55.5
49.3
45.3
39.0
93.7
94.2
93.6
91.2
91.5
87.3
76.4
·~tH
6.2
5.2
5.5
5.8
4.3
4.0
8.2
5.8
5.9
25.2
25.~
27.
24.0
25.2
21.9
25.8
23.6
19.2
62.3
63.2
64.5
61.3
60.5
53.1
54.8
50.0
39.5
93.8
94.1
93.5
92.2
92.7
87.1
84.6
83.8
67.6
6.0
4.6
4.6
5.7
3.2
2.9
5.9
4.1
3.8
24.8
25.8
24.8
23.1
23.1
18.2
21.5
18.1
13.3
61.4
62.5
63.6
60.2
58.9
46.8'
46.5
41.5
31.1
93.7
94.1
92.6
91.5
90.9
83.8
77.1
75.9
55.1
5.8
5.1
4.9
7.0
5.8
4.8
13.5
11.2
9.6
25.0
26.4
26.5
30.8
30.6
29.5
46.2
41.3
36.9
60.7
62.0
64.5
67.8
69.5
65.4
79.5
74.1
70.2
93.0
93.1
93.8
95.3
96.2
94.0
97.8
96.6
94.6
6.2
5.2
5.2
5.7
4.3
3.9
5.9
4.6
5.8
24.8
26.2
26.5
23.8
25.2
25.9
23.6
23.5
22.9
62.0
62.7
65.3
61.6
60.9
59.2
54.5
52.4
52.4
93.5
93.8
94.0
92.0
93.2
91.5
85.4
84.9
83.2
122
Table 0.1: ~ Error of carcinpgeni.ci~Sts for ~ng levels
Backgroun:i
r Rate,
True
of Trea
t Iethali
cnset Distr tions Shape Parameter
Treatment Bkcp. cnset
Test
Iethality 'I\JliDr Shape
Statistics
Rate(%) no
l+aa
Zt
Zp1* Zp3* ZP5* Zp7* Ztt
1
1
3.7+ 3.7
3.7
1
3.7
3.7
3.7
1
3.1
3.1
3.1
1
3
3.1
3.1
3.0
2.8
1
2.8
2.8
1
5
2.8
2.8
2.7
3.0
3.0
1
7
3.0
3.0
3.0
1
3.0
1
1
5.5
5.5
5
5.7
5.5
5.4
5.3
1
3
5.6
5.5
5.5
5.5
5
5.7
5.6
4.8
4.6
4.7
5
5.2
4.6
4.6
1
5
6.5
6.0
1
5
7
6.6
6.1
6.1
~.O
20
1
5.4
5.2
.1
5.2
5.5
1
5.3
5.1
5.7
5.7
5.6
20
3
5.5
5.4
1
5.2
5.2
5.3
5.0
5.4
1
20
5
5.1
4.3
1
20
4.5
4.6
4.5
4.5
4.5
7
1
2.5
2.5
2.5
2.6
2
1
2.7
2.7
3.1
3.1
2
1
3
3.1
3.2
3.2
3.5
2.5
2.5
2.5
2.5
2
1
5
2.5
2.5
1
1.8
1.8
1.8
1.8
2.1
2
7
1.9
2
1
5.5
5.8
6.4
6.9
7.2
6.7
5
4.2
4.2
4.7
5.2
2
5
3
5.3
5.3
3.1
3.2
3.8
4.0
4.5
4.7
2
5
5
2
4.9
5.2
5.5
5.5
5.8
5
7
5.~
2
1
4.1
5.0
6.5
7.2
7.
20
5.2
3.8
5.2
6.0
6.5
7.1
5.7
2
20
3
3.8
4.5
2
20
5
3.0
5.8
5.9
4.9
3.5
4.5
4.8
2
20
7
2.5
4.5
4.g
1
2.2
2.
2.6
3.2
4.4
5
1
2.2
1.8
2.3
2.5
2.8
3.9
5
1
3
1.8
1.5
1.8
5
1
5
1.4
1.4
2.4
4.6
1.3
1.4
4.2
5
1
7
0.9
1.0
1.5
3.8
5.7
8.8 10.5 12.4
7.4
5
1
7.6
6.5
5
~
3.1
3.5
5.2
6.5
1.9
2.5
3.4
4.5
5.5
4.6
~
5
5
2.3
3.4
4.2
5.6
5
7
1.8
4.9
5
3.1
20
1
1.6
3.9
8.5 12.0 16.1
5
2.8
1.8
4.4
7.5
9.6
5
20
3
0.6
1.0
3.3
5.3
6.5
3.9
5
20
5
0.3
2.6
5
0.5
0.8
1.6
2.7
3.9
20
7
+ table entries are p!!rcen~,•
." Zpk tests are Poly:.k tests Wlth k as the expaJeI1t for (tijltmax ).
t.r&
Zloq
3.7
3.0
2.7
3.0
5.2
5.5
4.5
6.0
6.0
5.4
5.2
4.5
2.~
3.
2.
2.1
5.~
5.
4.6
5.8
5.8
7.0
5.6
5.0
4.2
3.8
4.5
4.1
6.6
6.4
4.4
5.7
4.8
6.3
6.3
5.2
.
.
e "'
•
123
..,
e
Table 0.2: Power of CarcinpgeniCi~Sts for ~ng levels of
Treatment IBthality, BackgrOl.lIXi
r Rate,
TrUe Qlset
Distrib1tioos ShaPl! Parameter when the treatment irduces
a ~fold 'lUIOrigenic Effect in the High Dose Group
Test
Treatment Bkep. Q1Set
statistics
IBthality 'l\ItOr Shape
Rate(%) "'0
Zp1* Zp3* Z 5* Zp7* Ztt
l+aa
Zt
Zlog
P
1
1
1
10.5+ 10.3 10.2 10.1 10.0
9.9
9.9
3
10.2 10.0 10.0 10.0 10.0
1
1
9.7
9.7
5
9.2
9.2
1
1
8.9
8.9
8.8
8.5
8.5
2.5
1
7
2.5
2.5
2.5
1
2.5
2.5
2.5
1
22.5 22.4 22.2 21.9 21.9 22.2 22.1
1
3
20.7 20.4 20.6 20.7 20.7 21.1 20.9
~
1
5
21.1 20.6 20.6 20.7 20.8 21.3 20.9
1
5
6.2
1
7
6.3
6.2
6.2
6.2
6.1
5
6.0
1
1
53.0 ~2.5 52.5 52.4 52.1 52.7 53.1
20
51.7
2.8 53.1 53.2 52.9 54.2 54.0
1
20
3
51.4 52.7 52.8 52.5 52.7 52.6 53.0
1
20
5
4.8
5.6
5.6
1
20
7
5.3
5.2
5.3
5.3
8.4
1
8.3
8.5
8.7
8.4
2
1
8.8
8.5
6.2
3
6.1
6.1
6.3
6.8
2
1
6.5
6.8
7.5
7.5
5
7.6
7.9
8.1
8.4
8.4
2
1
7
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2
1
1
19.0 20.4 22.0 23.8 24.5 21.8 21.4
2
5
3
18.3 19.5 21.2 22.0 22.6 22.4 21.9
2
5
18.5 19.5 21.0 21.6 22.5 22.6 22.6
5
2
5
7
4.5
4.7
4.9
5.2
5.5
2
5.3
5.5
5
48.3 54.4 57.2 59.4 60.8 54.7 56.2
20
1
2
38.7 45.5 50.5 54.0 55.9 48.1 52.3
2
20
3
20
33.1 39.5 45.4 48.9 51.5 45.3 50.9
5
2
2.9
4.3
4.8
4.4
5.4
20
7
2.0
3.5
2
1
7.2
7.3
9.5 10.8 11.7 11.6 10.8
1
5
7.2
7.7
8.4
9.1
5.1
5.2
9.3
1
3
5
4.2
4.4
5.6
6.4
8.7
8.7
5
6.9
5
1
0.8
1.2
1.2
1.3
3.2
3.2
7
0.8
5
1
1
14.9 20.5 29.0 33.9 36.8 23.1 24.0
5
5
9.8 13.9 19.2 22.8 26.5 19.8 21.7
3
5
5
5
6.5 10.2 15.4 19.3 22.2 20.2 21.0
5
5
2.1
3.2
4.1
5.2
5.2
5.1
7
1.8
5
5
20
1
28.0 46.8 65.1 74.2 79.0 40.2 52.8
5
14.8 ' 27.3 43.0 52.5 59.5 31.1 48.0
20
3
5
6.5 16.8 30.3 39.4 45.2 26.5 43.5
20
5
5
4.5
2.5
3.4
2.7
1.8
0.3
0.8
20
7
5
+ table entries a~ p!!rcentages.
* Zpk tests are Po y-k tests with k as the exponent for (ti rtmax) •
124
Table 0.3: Power of carcinpgenici~sts for ~ng levels of
Treatment Lethality, Background
r Rate,
True Qlset
Distributioos ~ Paraneter when the treatment irrluces
a Five-fo1d 'l\J'fOrigenic Effect in the High Dose Group
Test
Treatment Bkep. Qlset
Lethality nmr Shape
Statistics
Rate(%) ~
l+ora
Zt
Zp1* Zp3 * ZP5* Zp7* Ztt
Z10q
1
1
28.8+ 27.4 27.1 27.0 26.9 26.8 26.8
1
1
1
29.9 29.2 29.1 28.8 28.8 28.7 29.0
1
28.3 28.5 28.5 28.2 28.2
~ 29.7 28.7
1
1
7
29.5 28.5 27.9 28.0 28.0 27.8 ·27.8
1
1
1
5
83.0 82.8 82.5 82.8 82.7 82.5 82.8
3
79.7 80.0 80.5 80.5 80.4 80.5 80.7
1
5
78.2 77.8 78.8 78.4 78.4 78.3 78.5
~
1
7
1
5
79.0 79.5 80.1 80.3 80.1 79.8 80.1
20
1 100.0 100.0 100.0 100.0 100.0 180 •0 108. 0
1
20
99.9 100.0 100.0 100.0
1
0 1 0.0 10 .0
20
1
~ 99.7 99.8 99.8 99.8 1BO.
9.8 99.8 99.8
20
7
1
99.8 99.9 100.0 100.0 100.0 100.0 100.0
1
1
30.4 30.5 31.5 32.4 33.2 32.5 31.9
2
2
1
25.5 25.7 26.5 27.0 27.3 28.2 28.2
1
~ 24.8 25.3 26.2 26.8 27.1 27.9 27.8
2
2
1
7
24.5 24.6 24.9 25.9 26.6 27.4 27.2
1
77.2 81.2 83.2 84.4 84.8 81.1 81.4
2
5
71.4 75.3 78.5 79.9 80.8 78.4 79.0
2
5
3
2
5
5
68.4 72.9 75.6 77.3 78.7 78.1 78.3
2
5
7
66.5 70.2 73.4 76.0 77.5 77.6 77.9
20
1
2
99.9 100.0 100.0 100.0 100.0 100.0 100.0
2
20
3
99.2 99.8 99.9 99.9 100.0 99.8 99.9
2
20
5
98.6 99.4 99.8 99.8 99.8 99.6 99.8
20
2
7
98.6 99.5 99.8 99.8 99.8 99.7 99.9
5
1
1
22.9 26.1 32.3 37.2 40.2 32.8 30.6
1
3
18.4 20.3 27.5 31.7 33.4 30.7 2~.0
5
5
1
5
15.5 16.8 22.0 25.3 26.8 26.2 2 .4
7
14.0 14.8 20.1 22.8 23.8 24.6 24.5
5
1
1
5
5
66.2 78.5 86.5 89.5 91.6 77.1 79.2
3
47.0 61.0 71.5 77.8 81.2 68.3 74.3
5
5
5
5
5
37.5 52.2 64.7 71.8 75.4 65.5 72.0
5
7
31.4 44.7 55.8 62.7 67.5 61.7 68.4
5
1
5
20
98.7 99.9 100.0 100.0 100.0 99.5 100.0
20
3
89.2 97.8 99.6 99.8 99.8 97.4 99.7
5
4 99.9 94.5 99.5
5
5
20
75.6 93.2 98.6
5
20
7
62.5 86.2 96.4 93.
9 .6 99.2 93.7 99.2
+ table entries are p!!rcen~s.
*, Zpk tests are Po1y-k tests with k as the expooent for (tiftmax).
~e
e
•
"