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OAR Box 1856 

Prepped by Keeia Richards 

Document Number: 

66) ll-A-03 

Docket Number: 

A-87-11 

Printed 11/24/2008 12:41:50 PM Sheet 66 of 82 
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i t EPA 

United States 

Environment Protection 

Agency 

Research and 

Development 

INTERIM QUANTITATIVE CANCER UNIT RISK 

ESTIMATES DUE TO INHALATION OF BENZENE 

EPA-600/X-85-022 

February 15, 1985 

INTERNAL REPORT 

004200 

Prepared for 

OFFICE OF AIR QUALITY PLANNING AND STANDARDS 

Prepared by 

CARCINOGEN ASSESSMENT GROUP 

Office of Health and 

Environmental Assessment 

Washington DC 20460 
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NOTICE 

ihis document is intended for internal Agency use only. Mention 

of trade names or commercial products does not constitute endorsement 

or recommendation for use. 
P.4 

PREFACE 

This document was prepared for the Office of Air Quality Planning and 

Standards (OAQPS) by the Office of Health and Environmental Assessment (OHEA) 

Dr. Todd Thorslund, Carcinogen Assessment Group, OHEA, is the author. The 

document nas been reviewed within OHEA and OAQPS. 

n 
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':;::::.::: QUANTITATIVE CANCER UNIT RISK ESTIMATES DUE TO INHALATION OF BENZENE 

Ir.f ejection 

In the "Carcinogen Assessment Group's Final Report on Population Risk to 

Ambient Benzene Exposures" dated January 10, 1979, a "unit risk" due to inhaI.*J.» ~£ k, nzen e wa s derived. This unit risk was obtained from the geometric 

mean of estimates of risk from three independent epidemiologic studies. This 

was the first time that the U.S. Environmental Protection Agency (EPA) obtained 

cancer risk estimates due to a chemical exposure based on human epidemiologic 

data. 

Since that original report, extensive new information relating to the carcinogenic potency of benzene has become available. In addition, an improved 

methodology for estimating cancer risk has been developed over time. 

The Carcinogen Assessment Group (CAG) is presently evaluating this new 

information and preparing an extensive report covering each animal toxicologic 

study and epidemiologic study. This report will supply the information from 

which a current, state-of-the-art, quantitative cancer risk assessment for 

benzene will be" derived. 

As new information became available, the CAG was asked on several occasions 

whether or not it would markedly change its unit risk estimate due to the new 

data. On each occasion, upon a preliminary evaluation, it was apparent in our 

judgment that only relatively minor "numerical" alterations would result in the 

joint unit risk estimate from incorporating the new information. With this 

assurance, the EPA program offices continued to base their decisions on the' 

original report. This was done in order to stay on a mandated regulatory 

schedule. Tne schedule would be disrupted if they were forced to wait for a 

current, state-of-the-art risk assessment for benzene to be completed before 

1 
P.6 

proceeding. 

In a petition to the Administrator of the EPA, the Natural Resources 

Defense Council (NRDC) takes exception to this approach. The NRDC makes the 

conjecture that the information found in the following sources indicates that 

EPA has seriously underestimated the unit risk: 

o an epidemiologic study of Ohio rubber workers (Rinksy et al., 1981) 

(updating Infante et al., 1977), 

o an epidemiological study of chemical workers submitted to EPA by 

the Chemical Manufacturers Association (Wong et al., 1983), 

o the animal bioassay conducted by the National Toxicological Program (NTP, 1984), 

o a further update through 1983 of the rubber workers study by Rinsky et al., and 

o a review of the health effects literature and a quantitative risk 

assessment published by the California Department of Health Ser- . 

vices (DHS, 1984). 

The time schedule for answering the NRDC petition does not allow for a completion of EPA's updated risk assessment. Fortunately, a May 1984 report entitled "Quantitative Estimates of Risk of Leukemia from Occupational Exposure to 

Benzene," prepared by Crump and Allen for the Occupational Safety and Health 

Administration, used the information cited by the NRDC to make risk assessments, 

This report uses methodology in obtaining risk estimates that is consistent in 

most respects to that employed by EPA, and it contains much better human exposure estimates in the epidemiologic studies than has been previously available. 

The approach to be taken here is to use this secondary source to make interim quantitative unit risk estimates that will be used until the more extensive estimates are completed. However, it must be realized that the new esti-
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.-nates do not represent the optimum use of the information EPA presently has at 

hand. Even so, due to the structural nature of the type of models used to 

estimate risk, it is not anticipated that the resulting final estimates will 

differ by an appreciable amount from the interim estimate developed here. The 

main advantage of the new estimates will be their scientific credibility. 

I.. tiu.c next two sections, unit risks based upon epidemiologic studies and 

animal studies will be developed using parameters calculated by Crump and 

Allen, The third section discusses these results. The fourth section develops 

and gives CAG recommendations for a single composite unit risk estimate, and 

discusses alternative approaches. The final section summarizes the results and 

conclusions of this investigation. 

Unit Risk Estimates Based on Epidemiologic Studies 

Crump and Allen (1984) estimated the lifetime risk due to different durations and levels of exposure to benzene in the work place. 

The epidemiologic data sets used to estimate these risks were obtained 

from a reorganizing of the data collected by Rinsky et al. (1981), Uong et al. 

(1983), and Ott et al. (1978) in three separate investigations. Other studies, 

most notably those of Askoy et al. (1979) and Askoy (1978), which dealt with 

Turkish shoe workers, indicated an association of leukemia with benzene. 

However, we agree with Crump that the exposure information compared with the 

studies used is so imprecise that they are not suitable for quantitative estimation. 

A computer tape containing follow-up information through 1978, which is 

an updated version of the cohort discussed by Rinsky et al. (1981), was used. 

This is the most recent information presently available on the cohort. 

The NRDC implies that an update through 1983 of the rubber workers studied 

by Rinsky et al. (1981) exists. However, the CAG has not been able to locate 

3 
P.8 

"-:'-1* ? data base, and, given the usual lag time required for epidemiologic 

investigations, a study that current is not very likely. 

The information contained in Wong et al. (1983), which involves the mortality experience of male chemical workers occupationally exposed to benzene, 

was used independently and in conjunction with other studies to estimate unit' 

ri elec 

The study conducted by Ott et al. (1978) was also used in combination with 

the other studies to estimate risk, but less emphasis was placed on it due to a 

lack of a clear dose-response relationship. 

Crump and Allen (1984) were able to relate observed and expected numbers 

of cases of leukemia to groupings of various exposure parameters for the three 

studies. These data are shown in Tables 1-3 and 6-11 of the Crump and Allen 

(1984) report, included here iri Appendix A. 

The exposure categories used were denoted as cumulative dose, weighted 

cumulative dose, and window dose. The "slope" parameter b and its 95% statistical confidence interval were estimated for various assumptions and combinations of data and dose parameters using techniques described by Crump" and Allen 

(1984). These estimated parameters and confidence intervals are shown in 

Tables 12-17 of the Crump and Allen (1984) report, and are also reproduced in 

Appendix A. 

Once an estimate of the slope parameter b is obtained, it can be translated into a unit risk by a straightforward mathematical manipulation. The 

transformation depends upon whether the model is of absolute or relative risk, 

the type of exposure parameter used, and the environmentally exposed population's assumed total and leukemia age-specific death rate. 

Mathematically, the risk due to a constant lifetime exposure of x ppm in 

the air may be expressed as 
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t 

- / [h2(x,v) + hi(v)]dv 

P(x) = / {h2(x,t)e 0 }dt 

0 

where h2(x,t) is the age-specific death rate at age t due to a constant lifetime exposure at level x, and h^(t) is the age-specific death rate for all 

other causes. See Gail (1975) for a derivation of this result. 

In the present situation 

h2(x,t) = $(t)5 r(x,t) 

where 

•1 i f a relative risk model 

6 = 

0 i f an absolute risk model 

*(t) is the background age-specific leukemia death rate of the environmentally 

exposed population and 

0 t < 2.5 

r(x,t) = 

b*x(t-2.5) 2.5 < t 

for the cumulative exposure model, and 

0 t < 5 

r(x,t) = b*x(t-5) 5 <_ t < 10 

5 b*x + bji(t-lO) 10 <_ t < 15 

3 

20 b*x + b_\(t-15) 15 <_ t 

3 6 
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for the weighted cumulative exposure model, and 

0 t < 5 

r(x,t) = b*x(t-5) 5 <_ t < 15 

10 b*x 15 £ t 

for the window exposure model. The term b* = b/(8/24) x (240/365) = 4.56b 

simply translates the 8 hours/day 240 days/year exposure in the industrial 

setting used by Crump and Allen (1984) into a continuous lifetime exposure for 

the U.S. environmental case. 

Since there is no information to suggest that the background leukemia and 

total age-specific death rates for those exposed to benzene in the environment 

would differ from the U.S. norm, the total U.S. rates taken from 1978 (the most 

current year available) are used for *(t). 

Based upon these conventions, the risk due to 1 ppm constant exposure to 

benzene is calculated for each of the b values and their confidence bounds, as 

given in Tables 12-17 of Crump and Allen (1984) reproduced in Appendix A. 

These results are shown in Tables 1-6. A comparison of these results with 

those derived in the original CAG document and those obtained from animal 

experiments, as well as a discussion of their relevance, will be the subject of 

a subsequent section. 

Unit Risk Estimates Based on Animal Studies 

At the time the CAG originally evaluated the carcinogenic potency of benzene, no animal studies existed demonstrating a carcinogenic response. Benzene 

and arsenic were pointed out to be the only compounds where human evidence was 

positive and animal evidence negative. 

Some individuals argued that this cast serious doubt on the possibility 
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TABLE 1. RESULTS FOR RELATIVE RISK MODEL USING CUMULATIVE DOSE 

Data set 

95% lower 

bound 

Unit risk estimate 

MLE 

95% upper 

bound 

Rinsky -2 et al . 1.65x10 

(fcllow-up from 1950, 

Table 6)a 

II 

Rinsky et al. 1.53x10-2 

(follow-up from 1940, 

Table 2) 

III 

Rinsky et al. (revised 1.78xlO-2 

exposures, Table 7) 

IV 

Rinsky et al. (Table 6) 7.78x10-3 

and Ott et al. (Table 1) 

5.10xl0-2 1.08X10"1 

5.10x10-2 1.13X10-1 

6.43x10-2 1.44X10"1 

2.89x10-2 6.87x10-2 

Same as IV except 

two questionable 

cases added 

4.45X10"3 2.04x10-2 5.10x10-2 

VI 

Wong et al. (Table 3, 8.76xl0"4 

SMR=50 assumed 

for unexposed) 

VII 

Rinsky et al. (Table 6) 2.67xl0"2 

Ott et al. (Table 1) 

and Wong et al. (Table 3) 

VIII 

Same as VII except 1.56xl0"2 

SMR=100 assumed 

for unexposed 

1.04x10*1 2.42X10'1 

7.32x10-2 1.60X10'1 

3.55x10-2 6.43x10-2 

aThe tables referred to are those given in Crump and Allen (1984), and are 

reproduced in Appendix A. 
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TABLE 2. RESULTS FOR ABSOLUTE RISK MODEL USING CUMULATIVE DOSE 

Data set 

Unit risk estimate 

95% lower 

bound MLE 

95% upper 

bound 

I 

Rinsky et al. 1.02x10-2 

(follow-up from 1950, 

Table 6) a 

II 

Rinsky et al. 9.31xl0"3 

(follow-up from 1940, 

Table 2) 

III 

Rinsky et al. 1.22x10-2 

(revised exposures, 

Table 7) 

IV 

Rinsky et al. (Table 6) 7.23xl0"3 

and Ott et al. (Table 1) 

2.45x10-2 4.77x10-2 

2.20x10-2 4.40x10-2 

3.06x10-2 5.99x10-2 

1.96x10-2 3.79x10-2 

Same as IV except 

two questionable 

cases added 

7.11x10-3 2.08x10-2 4.04x10-2 

aThe tables referred to are those given in Crump and Allen (1984), and are 

reproduced in Appendix A. 
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TABLE 3. RESULTS FOR RELATIVE RISK MODEL USING WEIGHTED CUMULATIVE DOSE 

Unit risk estimate 

95% lower 95% upper 

Data set bound MLE bound 

l 

Rinsky et al. 1.30xl0"2 4.10xl0-2 8.79xl0"2 

Table 8) a 

II 

Kinsky et al. 7.29xl0"3 2.49xl0"2 5.59X10"2 

(Table 8) and 

Ott et al. 

(Table 10) 

aThe tables referred to are those given in Crump and Allen (1984), and are 

reproduced in Appendix A. 

TABLE 4. RESULTS FOR ABSOLUTE RISK MODEL USING WEIGHTED CUMULATIVE DOSE 

Unit risk estimate 

95% lower 95% upper 

Data set bound MLE bound 

I 

Rinsky et al. , 7.47x10-3 1.76xl0" 2 3.36xl0" 2 

1940-1970 follow-up 

(Table 8) a 

II 

Rinsky et al . 5.43xl0" 3 1.40xl0" 2 2.71xl0" 2 

(Table 8) and 

Ott et al . " 

(Table 10) 

a

The tables referred to are those given in Crump and Allen (1984), and are 

reproduced in Appendix A. 
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TABLE 5. RESULTS FOR RELATIVE RISK MODEL USING "WINDOW" DOSE 

Unit risk estimate 

95% lower 95% upper 

Data set bound MLE bound 

i 

Rinsky et al. 5.56xl0"3 1.67xl0"2 2.48x10-2 

(Table 9) a 

II 

Rinsky et al. 3.60xl0"3 1.15xl0"2 2.48x10-2 

(Table 9) and 

Ott et al. 

(Table 11) 

aThe tables referred to are those given in Crump and Allen (1984), and are 

reproduced in Appendix A. 

TABLE 6. RESULTS FOR ABSOLUTE RISK MODEL USING "WINDOW" DOSE 

Unit risk estimate 

95% lower 95% upper 

Data set bound MLE bound 

I 

Rinsky et al. 4.34xl0"3 l.lOxlO"2 .-2.17xl0"2 

(Table 9) a 

II 

Rinsky et al. 3.48x10-3 8.98xl0"3 2.52xl0"2. 

(Table 9) and 

Ott et al. • 

(Table 11) 

aThe tables referred to are those given in Crump and Allen (1984), and are 

reproduced in Appendix A. 

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L-nat. uenzene was a carcinogen. Others argued that it simply meant that the 

correct exposure route-animal strain-species model had not been adequately 

tested. Subsequent events have proved the latter view to be correct. 

Goldstein et al. (1980) and Maltoni et al. (1983) have shown benzene to 

be carcinogenic for various strains of rats and mice via the inhalation route. 

I:, u-iiiun, Maltoni et al. (1983) and the National Toxicology Program (NTP) 

(July 1984, unpublished) have demonstrated that benzene is also carcinogenic via 

gavage exposure. 

Crump and Allen (1984) evaluated these studies and selected what they 

considered to be the most relevant end points upon which to base risk extrapolation models. Lacking an independent EPA evaluation of these studies, the 

approach taken here is simply to adopt Crump and Allen's selection of endpoints. This data ba.se is also reproduced and displayed in Appendix A of this 

report. 

Using these 23 selected end points, Crump and Allen (1984) estimated the 

doses corresponding to an increased risk of 10"^ using the multistage model 

and, where time-to-tumor data existed, the multistage-Weibull model. These 

results were summarized in their Tables 23 and 24, which are also included in 

Appendix A. 

The dose corresponding to an increased risk of 10"6 in an animal experiment may be converted to the risk for a human due to a lifetime exposure of 1 

ppm benzene in the air in the following manner. 

Let the dose corresponding to an increased risk of IO"6 be denoted as x. 

Assuming that ppm exposures are equivalent between species, our unit risk in 

inhalation experiments is simply 

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X O D X 

where (10"**) is the slope of a linear model required to give a risk of IO'6 due 

x 

to 8 hours/day of exposure for 5 days/week and (24) t]\ translate the slope 

8 5 

from a 40 hours/week industrial exposure to correspond to a constant exposure. 

Using this formula and the values of x given in Table 23, Appendix A, the 

unit risks based upon animal inhalation studies are obtained. These are reproduced in Table 7. 

To obtain the unit risk estimates for animal gavage experiments, the standard assumption used by EPA of equivalence between species on the basis of 

mg/surface area is used. This is at variance with the Crump and Allen (1984) 

equivalence assumption of mg/kg between species. We take the unit risk estimate 

to be 

<¥H># 'l"' 1^' 

where x is the dose corresponding to a IO"6 risk, L/Le is the fraction of the 

lifespan the animal was exposed, d is the days/week the animal was exposed, Wa 

is the weight of the animal in kg, and 3.19 x 20/70 is the estimated dose in 

mg/kg due to a constant exposure of 1 ppm benzene in the air, assuming 20 m3 

breathed per day, a 70-kg individual, and the weight of 3.19 mg of benzene 

in one m3 of air for each ppm. 

The values for x are obtained from Table 24, Appendix A, and substituted 

into the above formula to obtain the estimates shown in Table 8. 

A comparison of these results with the human estimates, and a discussion 

of their relevance, is the subject of the next section. 

12 
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TABLE 7. UNIT RISK ESTIMATES BASED UPON RODENT INHALATION STUDIES 

Multistage model 

Data sets MLE 95% upper limit 

Goldstein et al. 

(1980) 

Leukemia, male rats — 1.11 x IO- 3 

Leukemia, male mice 2.06 x IO-6 5.41 x IO"4 

Bioassays from 

Maltoni et al. 

(1983) 

Leukemia, both 

sexes, rats 1.34 x IO"4 4.40 x IO"4 

Zymbal gland or 

nasal cavity 

carcinoma or 

leukemia, 

both sexes, rats 1.12 x IO"3 1.80 x IO"3 

13 
TABLE 8. UNIT RISK ESTIMATES BASED UPON RODENT GAVAGE STUDIES 

Data sets 

Model 

Multistage 

MLE 95% upper limit 

Multistage-Weibull 

MLE 95% upper limit 

NTP bioassays 

Zymbal gland carcinoma, 

male rats 

All squamous cell 

carcinomas, male rats 

Zymbal gland carcinoma, 

female rats 

All squamous cell 

carcinomas, female rats 

Squamous cell carcinoma of 

preputial gland, male mice 

All squamous cell 

carcinomas, male mice 

Alveolar/bronchiolar 

carcinoma, male mice 

Lymphoma, NOS, male mice 

All squamous cell 

carcinoma., female mice 

1.33 

1.73 

2.20 

9.61 

5.19 

1.61 

3.61 

2.08 

8.18 

x 

X 

X 

X 

X 

X 

X 

X 

X 

IO"2 

IO"2 

IO"2 

10-3 

10-2 

IO"2 

10-2 

10-2 

10-6 

2.00 

2.26 

3.22 

1.60 

1.25 

1.1.9 

6.48 

4.32 

1.17 

X 

X 

X 

X 

X 

X 

X 

X 

X 

10-2 

10-2 

10-2 

10-2 

10-1 

io-i 

10-2 

10-2 

10-2 

1.38 

1.94 

2.30 

9.53 

1.36 

2.33 

4.56 

2.92 

8.98 

X 

X 

X 

X 

X 

X 

X 

X 

X 

10-2 

10-2 

10-2 

IO"3 

10-2 

10~4 

10-2 

10-2 

IO"6 

2.25 x 

2.55 x 

3.55 x 

1.78 x 

1.61 x 

1.50 x 

8.29 x 

6.79 x 

1.44 x 

IO"2 

10-2 

10-2 

IO"2 

io-i 

io-i 

10-2 

10-2 

IO-2 

14 
TABLE 8. (continued) 

Data sets 

Model 

Multistage 

MLE 95% upper limit 

Multistage-Weibull 

MLE 95% upper limit 

NTP bioassays (continued) 

Mammary gland carcinoma, 

female mice 

Alveolar/bronchiolar 

carcinoma, female mice 

Lymphoma, female mice 

3.49 x IO'2 

2.83 x IO"2 

9.23 x IO"3 

Bioassays from Maltoni et al. (1983) 

Leukemia, male rats 

All tumors, male rats 

Zymbal gland carcinoma, 

female rats 

Leukemia, female rats 

All tumors, female rats 

Leukemia, both sexes, r.ts 

All tumoi ., both sexes, rats 

2.40 x IO"5 

3.20 x 10~5 

2.02 x IO"2 

5.76 x IO'2 

4.26 x IO"3 

1.88 x IO"2 

5.71 x IO"2 

4.21 x IO"2 

5.69 x IO"2 

1.33 x IO"2 

2.31 x IO"2 

3.28 x IO"2 

6.32 x IO"3 

8.95 x IO"2 

9.55 x IO"3 

4.40 x IO"2 

4.55 x IO"2 

4.63 x IO"2 

6.79 x IO"2 

7.24 x IO"2 

3.84 x IO"2 

15 Tl 

CO 
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uiacussion of Results 

Employing the six models and various combinations of data sets and assumptions, a total of 21 unit risk estimates, with their 95% statistical confidence 

bounds, was obtained using epidemiologic data. These estimates are shown in 

Tables 1 through 6. The MLEs range from 8.98 x IO- 3 to 1.04 x 10- 1 , or slightly 

liwi c u.ian one order of magnitude. The effects of the model assumptions on the 

unit risk estimates are illustrated by the results shown in Table 9. All of 

the six models have been fitted to the Rinsky et al. cohort that was followed 

from 1940 to 1978, and unit risk estimates have been obtained. For the sake of 

comparison, the risks calculated by Crump and Allen (1984) for a white male 

exposed 8 hours per working day from age 20 to age 60 are also given. We note 

a drop in risk going from cumulative to weighted cumulative to window dose, as 

well as from relative to absolute, with the ratio of i:he maximum to the minimum 

risk estimate being less than a factor of five. 

All of the models are statistically consistent with the observed data, so 

that a selection of one model over another is a matter of judgment. The use of 

information concerning leukemia responses in other studies might suggest.the 

appropriate model. With regard to the dose parameters, Crump and Allen (1984) 

argue that the weighted cumulative dose is to be preferred, since the temporal 

leukemia response is based upon that observed in the survivors exposed to the 

atomic bomb in Hiroshima and Nagasaki. They also argue that the cumulative 

dose is acceptable but that the window dose has a considerably smaller credibility. With regard to the structural form of the model, little information 

exists. If all leukemia results from the same mechanism, and benzene affects 

a stage in this mechanism, then the relative risk model would hold. Crump and 

Allen (1984) have a slight preference for this form of the model, although no 

rationale is given. On the other hand, if the action of benzene is different 

16 
P.21 

TABLE 9. RISKS DUE TO 1 PPM BENZENE EXPOSURE 

BASED UPON RINSKY ET AL. COHORT, FOLLOW-UP FROM 1940 TO 1978 

Exposure 

parameter 

Cumulative 

Weighted 

cumulative 

Window 

Exposure 

duration 

Lifetime 

40 working 

years3 

Lifetime 

40 working 

years 

Lifetime 

40 working 

years 

Model form 

Relative Absolute 

5.10 x IO"2 

6.62 x IO"3 

4.40 x IO"2 

4.94 x 10~3 

1.67 x IO"2 

1.75 x IO"3 

2.20 x IO"2 

2.21 x IO"3 

1.76 x IO'2 

1.90 x IO"3 

1.10 x 10-2 

1.35 x IO"3 

a 8 hours/day 5 days/week exposure to 1 ppm from age 20 to age 60. 

17 
P.22 

from other factors producing leukemia, an absolute risk model may be more 

?nnrnr.r-iate. In principle, we would prefer to base our estimate on the most 

extensive and inclusive body of data available that is of acceptable quality. 

This argues for making use of all three epidemiologic studies, but requires 

some adaptation since, due to the availability of information, the Wong et al. 

study can only be analyzed in one form. 

In general, the studies in which the species and route of exposure most 

closely correspond to the environmentally exposed population are given the most 

weight in developing unit risk estimates. Also, the route of exposure in the 

epidemiologic studies and the environment are both by inhalation. As a result, 

we would place most of our emphasis on the unit risk estimates developed from 

the epidemiologic studies. Even so, animal studies can supply valuable confirmatory information. However, a number of factors strongly suggest that animal 

studies are less reliable than those based upon human response. 

Among the more important factors for benzene are the following: 

• Equivalent exposures were higher in the animal than in the epidemiologic studies, resulting in a greater extrapolation distance to 

the unit risk. 

• The possibility always exists that some unknown qualitative difference between man and rodent could result in a major difference 

in sensitivity to benzene. 

§ The risk estimates are upper-bound in nature, and could be considerably above the true risks. 

When estimating inhalation risks from gavage studies, the following important considerations also arise: 

• An implicit assumption is made that the fraction of benzene 

delivered to the target organ via gavage in rodents is equal 

18 
P.23 

co the fraction of the benzene delivered to the target organ 

from the tidal volume of air by man. Such an assumption is 

highly speculative. 

• The approximate surface area correction is employed—a usage 

which, although standard, is somewhat controversial. 

i\tCh.i"9 these factors in mind, we look at the animal results: 

In Table 10, all of the animal responses related to leukemia are presented. We note that, with the exception of the NTP gavage study for male mice, 

these responses are all below the human estimates—which is reassuring. In 

general, the largest estimates of the unit risk are associated with the gavage 

studies. 

In Table 11, the effects of varying some of the assumptions in the unit 

risk estimate are explored for the most sensitive end point preputial gland 

carcinomas in B6C3F1 male mice obtained in a gavage study. We note a change of 

one order of magnitude due to the difference between the surface area and 

weight equivalence assumptions. Another change of one order of magnitude 

results from using a 95% upper-bound rather than a non-zero maximum likelihood 

point estimate of the linear term. Thus, these two sources of uncertainty, 

taken together, change the estimate by more than two orders of magnitude. 

Also, it should be noted that the Zymbal gland and preputial gland are 

found only in rodents and not in man. While tumors in these organs are a 

definite indication of carcinogenicity, they involve an additional extrapolation assumption when attempting to link them quantitatively to tumors in 

humans. 

Considering the points raised and the general guidelines previously discussed, a "best judgment" single unit risk number will be developed by the CAG 

as requested by OAQPS in the next section. 

19 
P.24 

TABLE 10. ANIMAL-DERIVED ESTIMATES OF UNIT RISK 

BASED UPON LEUKEMIA OR LYMPHOMA RESPONSE 

Investigator 

Goldstein et al . 

Goldstein et al . 

Maitoni et al . 

Maltoni et al . 

Maltoni et al . 

NTP 

Exposure route 

Inhalation 

Inhalation 

Inhalation 

Gavage 

Gavage 

Gavage 

Species-sex 

Male rats 

Male mice 

Male and female 

rats 

Male rats 

Female rats 

Female mice 

Unit risk 

estimate 

1.11 x IO"3 

5.48 x IO"4 

4.41 x IO"4 

1.33 x 10-2 

6.32 x 10~3 

5.69 x IO"2 

20 
TABLE 11. UNIT RISK ESTIMATES USING THE MOST SENSITIVE END POINT--PREPUTUL GLAND RESPOr E 

IN B6C3F1 MALE MICE UNDER VARIOUS ASSUMPTIONS 

Model and statistic used 

Case 

number 

Multistage 

MLE 95% upper bound 

Mortalit y corrected 

Multistage-Weibul l 

MLE 95% upper bound 

Exposure 

equivalance 

mg/kg mg/m' 

Unit risk 

estimate 

1 

2 

3 

4 

5 

6 

7 

8 

X 

X 

X 

X 

X 

X 

X 

X X 

X 

X 

X 

X 

X 

X 

X 

1.61 

1.36 

1.25 

3.02 

1.34 

1.13 

1.04 

2.51 

x 10-1 

x IO"2 

x 10-1 

x IO"2 

x IO'2 

x IO"3 

x IO"2 

x IO"3 

21 
P.26. 

Composite Unit Risk Estimate 

Considering the information presented, we feel quite confident that if 

low-dose linearity holds, the true unit risk lies somewhere between 1 x 10~2 

and 1 x 10*1. Producing a single number from the various estimates presented 

is a highly subjective undertaking that is open to criticism, no matter what 

approach is taken. 

Applying our best judgment, we believe that the joint unit risk estimate 

should: 

t be based upon epidemiologic studies only; 

• use the most extensive data base available; 

t give equal weight to the cumulative dose and weighted cumulative dose, 

as well as relative and absolute forms; and 

• use the ML point estimates. 

In Table 12, the MLE of unit risk is given for each of the four model 

types, based on the most complete data set that is common to all models. Not 

having any rationale for preferring one model over another, we take the geometric mean to obtain a pooled model average. This results in the estimate 

2.11 x 10*2. This estimate, unfortunately, does not take into account the 

results of the Wong et al. study. A somewhat ad-hoc but reasonable adjustment 

would be to assume that the ratio of the Rinsky-Ott-Wong studies to Rinsky-Ott 

for the relative risk cumulative dose model was the same as for other models. 

Under this assumption, the computed ratio would be multiplied by the pooled 

model average to obtain a single composite estimate. 

Taking the SMR = 100 for the unexposed group, and using the pooled information in the Rinsky-Ott-Wong studies is a reasonable approach to obtaining a 

joint estimate for cumulative doses. This gives a result of 3.55 x 10~2, which 

is ootained from data set VIII and is shown in Table 1. Using this approach, 

22 
P.27 

TABLE 12. RISKS DUE TO LIFETIME 1 PPM BENZENE EXPOSURE 

BASED UPON COMBINED OTT ET AL. AND RINSKY ET AL. COHORTS, 

FOLLOWED FROM 1940 TO 1978 

Model form 

Exposure parameter Relative Absolute 

Cumulative 

Weighted cumulative 

2.89 x IO"2 

2.49 x IO'2. 

1.96 x IO"2 

1.40 x IO"2 

Geometric mean = (2.89 x 2.49 x 1.96 x 1.4)1/4 x IO"2 = 2.11 x IO"2. 

our correction ratio is estimated to be 

R = 3.55 x IO"2 T 2.89 x IO"2 = 1.23 

The "corrected" joint unit risk estimate is thus 

u = 2.11 x IO"2 x 1.23 = 2.60 x IO"2 

which we recommend as our single best judgment unit risk estimate. 

However, a number of other approaches are possible. 

One approach might be to take the geometric mean, 2.66 x IO"2, of the 21 

estimates. However, since the estimates are not random samples from some welldefined population, the rationale for such an approach is not clear. 

Another approach that is regarded as "safe" is to take the highest estimate, regardless of the quality of the information on which it is based. 

As seen in Table 1, the Wong et al. study gives the highest estimate of 

risk, 1.04 x 10"1, with a 95% upper bound of 2.42 x 10-1. However, much of the 

23 
potency associated with this estimate can be attributed to the fact that the 

non-exposed group had no cases of leukemia. As a result, the increase of risk 

over controls may be due to an artifact in the data rather than to a true 

carcinogenic response. 

Another approach that has been suggested is to use as an estimate the sin-

^ e d?ta. set model that has the most credibility associated with it. In cur 

opinion, this would be the estimate taken from data set I, Table 3, which is 

the Rinsky et al. study - weighted cumulative dose relative risk model. This 

gives a result of 4.10 x IO"2. 

It is apparent that regardless of the method used to obtain the joint unit 

risk, the resulting answers are relatively consistent, and are close to the 

original estimate of 2.41 x IO"2. 

Summa ry 

From the slope parameters estimated by Crump and Allen, the unit risk for 

leukemia due to a lifetime exposure of 1 ppm benzene in the air has been estimated. Using various models and combinations of assumptions and epidemiologic 

studies, 21 unit risk estimates, ranging from 0.9 x 10"2 to 1. x 10"1 , were 

obtained. Based upon the criteria of using the data from all epidemiologic 

studies with reasonable exposure information and an average value over all the 

mathematical models believed to be plausible, a combined unit risk estimate of 

2.6 x 10~2 was derived. This is taken to be the CAG's best-judgment unit risk, 

and is only slightly larger than the original estimate of 2.4 x 10^2, which is 

based upon far less reliable data. 

Unit risks were also obtained from animal studies. However, they are 

considered to be confirmatory in nature and intrinsically less reliable than 

those based upon the human response. The inhalation studies that would be 

preferred due to route similarity tend to give estimates that are an order of 

24 
P.29 

ma-anitude lower. Gavage studies, although tending to give higher estimates 

than human, up to about five times in the extreme, are dependent upon a large 

series OT unverifiable assumptions. Thus, while they may be a valid upper 

bound, they are judged to be overly conservative, based upon the human data. 

A more detailed and direct comparison of the human and animal data will be 

possible in the CAG's final report. 

25 
P.30 

REFERENCES 

Aksoy, M.; Erdem, S.; Dincol, G. (1974) Leukemia in shoe-workers exposed 

chronically to benzene. Blood 44(6):837-841. 

Aksoy, M. (1978) Benzene and leukemia. Lancet i:441. 

California Department of Health Services. (1984, September) Report to the 

Scientific Review Panel on benzene. Prepared by the staffs of the Air 

Resources Board and the Department of Health Services. 

Carcinogen Assessment Group, U.S. Environmental Protection Agency. (1979, 

January 10) Final report on population risk to ambient benzene exposures. Available from: NTIS, Springfield, VA. PB82-227372. 

Crump, K.S.; Allen, B.C. (1984, May) Quantitative estimates of risk of 

leukemia from occupational exposure to benzene. Prepared for the 

Occupational Safety and Health Administration. 

Gail, M. (1975) Measuring the benefit of reduced exposure to environmental 

carcinogens. J. Chronic Dis. 28:135-147. 

Goldstein, B.D.; Snyder, C.A.; Laskin, S.; Bromberg, I.; Albert, R.E.; 

Nelson, N. (1980) Myelogenous leukemia in rodents inhaling benzene. 

Unpublished data. 

Infante, P.F.; Rinsky, R.A.; Wagoner, J.K.; Young, R.J. (1977) Leukemia • 

in benzene workers. Lancet July 19:76-78. 

Maltoni, C ; Conti, B.; Cotti, G. (1983) Benzene: a multipotential carcinogen. Am. J. Ind. Med. 4:589-630. 

National Toxicology Program (NTP). (1984, July) NTP technical report on 

the toxicology and carcinogenesis studies of benzene (CAS No. 71-43-2) 

in F344/N rats and B6C3F1 mice (gavage studies). NIH Publication No. 

84-2545, NTP-84-072. Unpublished. 

Ott, M.G.; Townsend, J.C ; Fishbeck, W.A.; Langner, R.A. (1978) Mortality 

among individuals occupationally exposed to benzene. Arch. Environ. 

Health 33:3-10. 

Rinsky, R.A.; Young, R.J.; Smith, A.B. (1981) Leukemia in benzene workers. 

Am. J. Ind. Med. 2:217-245. 

Wong, 0.; Morgan, R.W.; Whorton, M.D. (1983, August 31) Comments on the 

NIOSH study of leukemia in benzene workers. Technical report submitted 

to Gulf Canada, Ltd. by Environmental Health Associates. 

26 
P.31 

APPENDIX A 

NOTE: Tables referred to in Crump and Allen (1984) 

have been reproduced exactly. Tables 4, 5, 

18, 19, 20, 21, and 22 are not included herein, 
Table 1 

Observed and Expected Number of Deaths in 

Ott et al_. Cohort by Cumulative Dose 

Cause 

0-5 ppm-yr 

(1.48)* 

3533 p-y 

WE SMR 

5-20 ppm-yr 

(10.9) 

2961 p-y 

0/E m 

20-80 ppm-yr 80-200 ppm-yr 200+ ppm-yr 

(44.8) (125.9) (352.9) 

3758 p-y 1790 p-y 1229 p-y 

0/E SMR 0/E SMR 0/E SMR 

Total 

(160.04) 

13271 p-y 

0/E SMR 

All Causes 11/22 50 19/27 70 34/39.8 85 21/19 111 17/19 89 102/127 80 

All Malignant 

Neoplasms 2/3.5 57 9/4.6 196 10/7.4 135 7/3.6 194 3/3.4 88 31/22.5 138 

Malignant Neoplasms 

of Digestive Organs 

and Peritoneum 0/1.04 3/1.4 214 3/2.2 136 3/1.03 291 0/.98 0 9/6.7 134 

Malignant Neoplasms 

of Respiratory 

System i/1.07 93 2/1.3 154 4/2.4 167 3/1.2 250 1/1.2 83 11/7.2 153 

Leukemia l/r18 556 0/.202 1/.31 323 0/.14 0/.13 0 2/.96 208 

Other Neoplasms of 

Lymphatic and 

Hematopoietic 

Tissues 0/.28 1/.304 329 1/.47 213 0/.23 0 O/.202 0 2/1.5 133 

Avenge exposure In ppm-years 
P.33 

Table 6 

Observed and Expected Leukemlas 

1n Rinsky et al. Cohort by 

Cumulative Exposure;~T950-1978 Followup 

UWJUfrve 

Exposure 

1n ppm-years 

(average) 

0-5 

(1.29) 

5-20 

(U.O) 

20-80 

(42.2) 

80-200 

(129.0) 

200-1000 

(421) 

1000+ 

(1489) 

Observed 

2 

0" 

0 

0 

5 * 

1 

Expected 

1.11 

0.52 

0.50 

0.31 

0.32 

0.049 

SMR 

180 

0 

0 

0 

1560 

2040 

person-years 

' 16890 

7092 

6591 

3557 

3075 

396 

s 
P.34 

• Table 7 

Observed and Expected leukemlas 

1n Rinsky et a K Cohort by Cumulative 

Exposure Using Revised^xposure Estimates* 1950-1978 Followup 

Curylatlve 

Exposure 

1n ppm-years 

(average) 

0-5 

(1.32) 

5-20 

(11.2) 

20-80 

(42.3) 

80-200 

(129) , 

200-1000 

(393) 

1000+ 

(1142) 

Observed 

2 

0 

0 

1 

• 4 

1 

Expected 

1.13 

0.54 

0.51 

0.30 

0.34 

0.015 

SMR 

177 

0 

0 

333 

1180 

6670 

person-years 

17170 

7667 

•6732 

3335 

3087 

120 
P.35 

Table 8 

Observed and Expected Leukemias 

1n Rinsky et al_. Cohort by Weighted 

CumulativeTJose; 1940-1978 Followup 

We1 anted 

Cumulative 

Exposure 

In ppm-years 

(averaqe) 

0-3 

(0.54) 

3-10 

(5.9) 

10-30 

(17.7) 

30-100 

(56.6) 

100-300 

(163.5) 

300+ 

(554.8) 

Observed 

2 

0 

0 

1 

3 

2 

Expected 

1.55 

0.46 

0.36 

0.33 

0.204 

0.047 

SMR 

129 

0 

0 

305 

1470 

4250 

person-years 

24633 

5843 

4544 

3947 

2286 

633 
P.36 

Table 9 

Observed and Expected Leukemias 

In Rinsky et al. Cohort by Exposure in 

Ten-YearUimlow; 1940-1978 Followup 

ppm-years 

xmrmulated 

12.5 to 2.5 years 

prior to age 

category 

(average) 

0-2 

(0.15) 

2-5 

(3.2) 

5-10 

(7.3) 

10-50 

(23.6) 

50-200 

(104.5) 

200+ 

(471.1) 

• 

Observed 

3 

0 

0 

0 

1 

4 

Expected 

2.025 

0.145 

0.131 

0.309 

0.249 

0.103 

SMR 

148 

0 

0 

0 

401 

3880 

person-years 

27106 

2474 

2178 

4939 

3671 

1518 
P.37 

Table 10 

Observeo *nd Expected Leukemias 1n 

Ott et a h Cohort by Weighted Cumulative Exposure 

Wlighted 

Exposure 

1n ppm-years 

(average) 

0-3 

(.635) 

3-10 

(5.94) 

10-30 

(18.8) 

30-100 

(51.8) 

100+ 

(153) 

Observed 

1 

0 

1 

0 

0 

Expected SMR person-years 

.31 321 5416 

.199 0 2218 

.19 518 2533 

.17 0 2056 

.089 0 1054 
P.38 

Table 11 

Observed and Expected Leukemias 1n 

Ott e_t a_L Cohort by Exposure 1n Ten-Year Window 

oom-years 

accumulated 

12.5 to 2.5 years 

prior to age 

category 

(averaqe) 

0-2 

(.115) 

2-5 

(3.42) -

5-10 

(7.18) 

10-50 

(25.3) 

50-200 

(101) 

200+ 

(263) 

Observed 

1 

0 

0 

1 

0 

0 

Expected 

.44 

.052 

.066 

.21 

.17 

.032 

SMR 

229 

0 

0 

488 

0 

0 

person-years 

6192 

800 

882 

2903 

2105 

395 
Table 12 

Results of Fitting Relative Risk Model 

Using Cumulative Dose 

P.39 

Data Set 

I 

Rinsky et al. 

(followup 7rom 1950 

Table 6) 

Parameter Estimates 

i b 

[back- (Slope of Oose Response) 

[ground) (ppm-years) 

95% 95T" 

.87 

6oodness of Fit 

MLE Lower MLE Upper Ch1-sq. o*.^ p-value 

.0074 .023 .051 5.0 4 .29 

II 

Rinsky et al., 

(followup 7rom 1940, 

Table 2) .82 

III 

Rinsky et al_. 

(reYlseH'exposures, 

Table 7) .88 

IV 

Rinsky et al. 

(Table BT and 

Ott et al. 

(TabTe TJ 1.2 

.0069 .023 .051 

.0080 .029 .065 

.0035 .013 .031 

5.0 4 

3.3 4 

4.8 4 

.29 

.50 

.31 

Same as IV except 

two questionable 

cases added 1.7 .0020 .0092 .023 2.6 4 .63 

VI 

Uong 

(Table 3 

SMR»50 assumed 

for unexposed) 

VII 

Rinsky et al. 

(Table FT ~~ 

Ott et al. 

(TabTI TJ 

and Wong 

(Table 3) 

0.5 

.57 

.00039 .047 .11 

.012 .033 .072 

2.4 2 

11.7 8 

,30 

.16 

VII! 

same as VII except 

SMR-100 assumed 

for unexposed 1.0 .0070 .016 .029 9.5 9 .49 
P.40 

Table 13 

Results of Fitting Absolute Risk Model 

Using Cumulative Dose 

Parameter Estimates 

a b 

(back- (Slope of Dose Response) 

ground) (ppm-years)" 6oodness of Fit 

951 9TS~ 

Data Set MLE Lower MLE Upper Ch1-sq. d.f. p-value 

I 

Rinsky et al. 

(followup from 1950, , 7 - , 

Table 6) 5.9x10*° 8.3x10"' 2.0x10"° 3.9x10"° 5.2 4 .27 

II 

Rinsky et al. 

(followup 7rom 1940, fi inc . 

Table 2) 7.9x10"° 7.6x10"' 1.8x10"° 3.6x10"° 5.1 4 .28 

III 

Rinsky e*: al_. 

(revisecTexposures, fi - - , 

Table 7) 6.0x10"° 1.0x10"° 2.5x10"° 4.9x10"° 4.0 4 .41 

IV 

Rinsky et al. 

(Table 6j "~ 

and 

Ott et al. c 7 fi c 

(TabTe TJ 1.4x10'° 5.9x10" '.^io"° 3.1x10"° 5.1 4 .28 

V 

Same as IV except 

two questionable c 7 « * 

cases added 4.5x10"° 5.8x10'"' 1.7x10"° 3.3x10"° 2.8 4 .59 
P.41 

Table 14 

Results of Fitting Relative Risk Model 

Using Weighted Cumulative Dose 

Parameter Estimates 

a b 

(back- (Slope of Dose Response) 

ground) (ppm-years)" 6oodness of Fit 

95* 9TT 

Data Set MLE Lower MLE Upper Ch1-sq. d.f. p-value 

I 

Rinsky et al. 

(Table tT ~~ .180 .025 .079 .17 2.0 4 .74 

II 

Rinsky et al. 

(Table fT "~ 

and 

Ott et al. 

(TabTe TC) 1.05 .014 .048 - .108 6.3 9 .71 
Table 15 

Results of Fitting Absolute Risk Model 

Using Weighted Cumulative Dose 

P.42 

Data Set 

I 

Rinsky et al. 

1940-1973 ~ 

followup 

(Table 8) 

a 

(background) 

MLE 

Parameter Estimates 

9.0x10 

(Slope of Dose Response) 

(ppm-years)" 

IF? — 55T 

Lower 

2.2x10 

Goodnesu of Fit 

MLE Upper Ch1-sq. d.f. p-value 

5.2xl0'6 9.9xl0"6 2.1 .72 

II 

Rinsky et al . 

(Table BJ 

and 

Ott et al. 

(Table TU) 9.1x10 1.6x10 4.1x10 8.0x10 6.0 .74 
P.43 

Table 16 

ResuUs of Fitting Relative Risk Model 

Using "Window" Dose 

Data Set 

I 

Rinsky et 

(Table 9j 

ila 

(background) 

MLE 

1.11 

Parameter Estimates 

b 

(Slope of Dose Resgi 

(ppm-years) ' 

95% 

Lower MLE 

.017 .051 

jnse) 

95i' 

Upper 

.107 

Goodness of Fit 

Chi-sq. d.f. p-value 

2.2 4 .70 

II 

Rinsky et al. 

(Table 57 ~" 

and 

Ott et al. 

(TabTe TT) 1.3 .011 .035 .076 5.1 10 .88 
P.44 

Table 17 

Results of Fitting Absolute Risk Model 

Using "Window" Dose 

Parameter Estimates 

a b 

(back- (Slope of Dose Response) 

ground) (ppm-years)" Goodness of Fit 

55? 55?" 

Data Set MLE Lower MLE Upper Ch1-sq. d.f. p-value 

I 

Rinsky et al. - * , ,. 

(Table 97 ~ 4.5x10"° 1.5x10"° 3.8x10"° 7.5x10'° 2.3 4 .68 

II 

Rinsky et al. 

' (Table fj "" 

and _ 

Ott et ah c c c c 

(Table 11) 1.7x10

 D 1.2x10"° 3.1x10"° 8.7x10"° 5.0 10 .89 
P.45 

Table 23 

Doses Corresponding to Increased Risk of 10" 

In Rodent Inhalation Studies 

Multistage Model 

Data Sets • MLE 95S Lower LlmTT 

Bioassays from Goldstein et a1_. (1980) (Dose units • ppm/8 hr day) 

Leukemia, male rats Inf. .379E-2* 

Leukemia, male mice 2.041 .776E-2 

Bioassays from Maltoni et aj_. (1983) (Dose units • ppm/8 hr day) 

Leukemia, both sexes, rats .314E-1 .955E-2 

Zymbal gland or nasal cavity 

carcinoma or leukemia, both sexes, rats .375E-2 .233E-2 

a .379E-2 means .379 x 10"Z 
P.46 

Table 24 

Doses Corresponding to Increased Risk 

of 10 in Rodent Gavage Studies 

____^ Model 

Multistage Multistage-Weibull" 

95i 55X 

_ Data Sets MLE Lower Limit MLE Lower Limit 

NTP Bioassays (Dose units • mg/kg body wt.) 

Zymbal gland carcinoma, 

•ale rats 

All squamous cell 

carcinomas, male rats 

Zymbal gland card noma, 

female rats 

All squamous cell 

carcinomas, female rats 

Squamous cell carcinoma 

of preputial gland, 

male mice 

All squamous cell 

carcinomas, male mice 

Alveolar/bronchiolar 

carcinoma, male mice 

Lymphoma, NOS, male mice 

All squamous cell 

carcinomas, female mice 

Mammary gl::.o carcinoma, 

NOSr fen ', i. ice 

Alveolar/bronch1olar 

carcinoma, female mice 

Lymphoma, female mice 

.576E-3* 

.444E-3 

.348E-3 

.797E-3 

.297E-3 

.690E-3 

.427E-3 

.742E-3 

1.883 

.442E-3 

.545E-3 

.167E-2 

.383E-3 

.339E-3 

.238E-3 

.479E-3 

.123E-3 

d29E-3 

•238E-3 

.357E-3 

.132E-2 

.270E-3 

.366E-3 

.271E-3 

.555E-3 

.394E-3 

.333E-3 

.804E-3 

.113E-2 

.660E-1 

.338E-3 

.527E-3 

1.716 

•329E-3 

.333E-3 

INF. 

.341E-? 

.300E-3 

-216E-3 

.430E-3 

.955E-4 

.103E-3 

.186E-3 

-227E-3 

.107E-2 

.227E-3 

•.213E-3 

.401E-3 

Bioassays from Maltoni et al_ 

Leukemia, male rats 

All tumors, male rats 

Zymbal gland carcinoma. 

female rats 

Leukemia, female rats 

All tumors, female rats 

Leukemia, both sexes, rats 

All tumors, both sexes. 

rats 

(1983) 

.708 

.532 

.840E-3 

INF. 

.295E-3 

.399E-2 

.905E-3 

(Dose units 

.128E-2 

.736E-3 

.519E-3 

.269E-2 

.190E-3 

.178E-2 

.386E-3 

• mg/kg body wt.) 

" 

K7r>r_-) MMXIC C7A « in'3 
P.47 

CRIM3 - APPENDIX A' 

DATA ANO MODEL PARAMETERS FOR ANIMAL STUDIES 

This appendix summarizes the data and models used to estimate 

cancer risks from three long-term rodent bioassays: Goldstein et a h 

(1980), Maltoni et a h (1983), and NTP (1983). For the time-to-response 

r.^t^tcge-Weibull model applied to the NTP data (pages A24-A35), time 

1s measured 1n weeks and the tumor Indicator variable has the followirj 

Interpretation: 

1: Death without carcinogenic response of interest; 

2: Death with carcinogenic response of Interest. 

AO 
P.48 

Data from Goldstein e_t a h (1980) 

Spedes and Sex: Sprague-Dawley rats, male 

Endpoint: Leukemia 

Exposure Route: Inhalation 

Doses 0 75 225 

(ppm/8 hr day) 

# affected 0 1 0 

# at risk 67 40 45 

Multistage Model -

Chi-square Goodness-of-Fit Statistic: 2.819 

Degrees of Freedom: 2 

p-value: .2419 

Maximum Likelihood Parameter Estimates: 

qQ • .660E-2 

Linear term corresponding to 955 upper limit 

on risk, (q/) ; .264E-3 

Al 
P.49 

Data from Goldstein et o h (1980) 

Spedes and Sex: AKR, C57BL, and CD-I mice, male 

Endpoint: Leukemia 

Exoonre Route: Inhalation 

Doses 0 

(ppm/8 hr day) 

# affected 0 

# at risk 210 

75 

0 

50 

225 

2 

160 

/ 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: .699E-1 

Degrees of Freedom: 2 

p-value: .9661 

Maximum Likelihood Parameter Estimates: 

Q0"°

 1 

q: - 0 

q2 » .240E-6 

L1r._r.; '.srm corresponding to 95S upper limit 

on risk (q^) : .129E-3 

A2 
P.50 

Data from Maltoni et a_h (1983) 

Spedes and Sex: Sprague-Dawley rats, male and female 

Endpoint: Leukemia 

Exposure Route: Inhalation 

Doses 0 241 

(ppm/8 hr day) 

# affected 1 2 

# at risk 365 193 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: -

Degrees of Freedom: * 

p-value: -

Maximum Likelihood Parameter Estimates: 

q0 ' -274E-2 , 

qx - .318E-4 

Linear term corresponding to 951 upper limit 

on risk In*): .I05E-3 

\ 

A3 
P.51 

uata from Maltoni et a_h (1983) 

Spedes and Sex: Sprague-Dawley rats, male and female 

Endpdnt: Zymbal gland or nasal cavity carcinomas or leukemia 

Exposure Route: Inhalation 

Doses 0 . 241 

(ppm/8 hr day) 

# affected 4 14 

# at risk 365 193 

Multistage Model -

Ch1-square Goodness-of-Fit Statistic: -

Degrees of Freedom: -

p-value: -

Maximum Likelihood Parameter Estimates: 

q0 - .110E-1 

qx • .267E-3 

Linear term corresponding to 95X upper limit 

. on risk (o^*). .42EE-3 

K4 
Data from Maltoni et a h (1983) 

Spedes and Sex: Sprague-Dawley rats, male 

Endpoint: Leukemia 

Exposure Route: Gavage 

Doses 0 

(mg/kg body wt) 

I affected 0 

# at risk 28 

50 

0 

28 

250 

4 

33 

Multistage Model -

Ch1-square Goodness-of-Fit Statistic: .145 

Degrees of Freedom: 2 

p-value: .9304 

Maximum Likelihood Parameter Estimates: 

q 0 " ° 

qx • 0 

q2 » .200E-5 

io• erm corresponding 

on risk (q. ): .783E-3 

to 95X upper 1 imit 

A5 
P.53 

uata fr&n Maltoni et a h (1983) 

Spedes and Sex: Sprague-Dawley rats, male 

Endpoint: All tumors 

Exposure Route: Gavage 

Doses 0 

(mg/kg body wt) 

# affected 2 

# at risk 28 

50 

1 

28 

250 

8 

33 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: .519 

Degrees of Freedom: 1 

p-value: .4713 

Maximum Likelihood Parameter Estimates: 

q0 - .529E-1 

qx • 0 

q2 - .353E-5 

L1n<«r terra corresponding to %% upw?. limit 

on risk (t\*): .136E-2 • 

A6 
P.54 

Data from Maltoni et a_h (1983) 

Spedes and Sex: Sprague-Dawley rats, female 

Endpoint: Leukemia 

Exposure Route: Gavage 

Doses 0 

(mg/kg body wt) 

# affected 1 

# at risk 30 

50 

2 

30 

250 

1 

32 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: .577 

Degrees of Freedom: 2 

p-value: .7484 

Maximum Likelihood Parameter Estimates: 

q0 • .445E-1 

Linear term corresponding to 955 upper limit 

on risk (q,*): .372E-3 

A7 
P.55 

Data from Maltoni et a h (1983) 

Spedes and Sex: Sprague-Dawley rats, female 

Endpolnt: Zymbal gland carcinoma 

Exposure Route: Gavage 

Doses 0 

(mg/kg body wt) 

# affected 0 

# at risk 30 

50 

2 

30 

250 

8 

32 

Multistage Model -

Ch1-square Goodriess-of-F1t Statistic: .527E-1 

Degrees of Freedom: 2 

p-value: .9739 

Maximum Likelihood Parameter Estimates: 

% " ° ' 

qx - .119E-2 

..ear term corresponding to 951 upper limit 

ii risk (q^) : .192E-2 

AS 
P.56 

Data from Maltoni et aj. (1983) 

Spedes and Sex: Sprague-Dawley rats, female 

Endpoint: All tumors 

Exposure Route: Gavage 

Doses 0 

(mg/kg body wt) 

# affected 6 

# at risk 30 

50 

10 

30 

250 

21 

32 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: .741E-2 

Degrees of Freedom: 1 

p-value: .9315 

Maximum Likelihood Parameter Estimates: 

q 0 - .227 

q1 » .339E-2 

Linear term corresponding to 951 upper limit 

on risk (qx *): .526E-2 

A9 
P.57 

uata from Maltoni et a h (1983) 

Spedes and Sex: Sprague-Dawley rats, male and female 

Endpolnt: Leukemia 

Exposure Route: Gavage 

Doses 0 

(mg/kg body wt) 

# affected 1 

# at risk 58 

50 

2 

58 

250 

5 

65 

Multistage Model -

Ch1-square Goodness-of-Fit Statistic: .326E-1 

Degrees of Freedom: 1 

p-value: .8562 

Maximum Likelihood Parameter Estimates: 

q0 - .191E-1 

qx - .251E-3 

Linear term corresponding to 955 upper limit 

on risk (tjj*): .561E-3 

A10 
P.58 

Data from Maltoni et a h (1983) 

Spedes and Sex: Sprague-Dawley rats, male and female 

Endpoint: All tumors 

Exposure Route: Gavage 

Doses 0 50 

(mg/kg body wt) 

# affected 8 11 

# at risk 58 58 

Multistage Model -

Chl-square Goodness-ofDegrees of Freedom: -

p-value: -

250 

29 

65 

Fit Statistic: -

Maximum Likelihood Parameter Estimates: 

q0 " -148 

qx - .110E-2 

q2 - .266E-5 

Lljier 'inn corresponding to 955 upper limit 

on risk {q*): .259E-2 

All 
P.59 

Data from NTP (1983) 

Spedes and Sex: F344/N rats, male 

Endpoint: Zymbal gland carcinoma 

Exposure Route: Gavage 

Doses 

# affected 

# at risk 

0 

2 

50 

50 

6 

50 

100 

10 

50 

200 

17 

50 

Multistage Model -

Ch1-square Goodness-of-Fit Statistic: .144E-2 

Degrees of Freedom: 1 

p-value: .9706 

Maximum Likelihood Parameter Estimates: 

q0 - .407E-1 

q2 » .174E-2 

q2 - .712E-6 

Linear term corresponding tc 955 upper limit 

on risk (g^) : .261 E-2 

A12 
P.60 

**•» from NTP (1983) 

Spedes and Sex: F344/N rats, male 

Endpoint: All squamous cell carcinomas 

Exposure Route: Gavage 

Doses 

# affected 

# at risk 

0 

0 

50 

50 

10 

50 

100 

8 

50 

200 

16 

50 

Multistage Model -

Chi-square Goodness-of-F1t Statistic: 5.530 

Degrees of Freedom: 3 

p-value: .1493 

Maximum Likelihood Parameter Estimates: 

q0 ' 0 

qx - .225E-2 

Linear term corresponding to 955 upper limit 

on rU k {q*): .295E-2 

A13 
P.61 

Data from NTP (1983) 

Spedes and Sex: F344/N rats, female 

Endpoint: Zymbal gland carcinoma 

Exoosure Route: Gavage 

Doses 0 25 50 100 

# affected 0 5 5 14 

# at risk 50 50 50 50 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: 1.302 

Degrees of Freedom: 2 

p-value: .5220 

Maximum Likelihood Parameter Estimates: 

%' ° 

q: - .287E-2 

q2 * o 

^ q 3 - .310E-7 

Linear term corresponding to 955 upper limit 

on risk (q^) : .421E-2 

A14 
P.62 

Data from NTP (1983) 

Spedes and Sex: F344/N rats, female 

Endpoint: All squamous cell carcinomas 

Exposure Route: Gavage 

Doses 

# affected 

# at risk 

0 

0 

50 

25 

1 

50 

50 

4 

50 

100 

6 

50 

Multistage Model -

Chi-square'Goodness-of-Fit Statistic: .478 

Degrees of Freedom: 1 

p-value: .4890 

Maximum Likelihood Parameter Estimates: 

q0 • .444E-25 

qx • ,125Er2 

q2 - .P93E-6 

Linear term corresponding to 955 upper limit 

on risk {q^): .209E-2 • 

A15 
P.63 

Data from NTP (1983) 

Species and Sex: B6C3F, mice, male 

Endpoint: Squamous cell carcinoma of the preputial gland 

exposure Route: Gavage 

Doses 0 25 50 100 

# affected 0 3 18 28 

# at risk 50 50 50 50 

Multistage Model -

Chi-square Goodness-of-Fit Statistic: 3.874 

Degrees of Freedom: 2 

p-value: .1446 

Maximum Likelihood Parameter Estimates: 

q: - .337E-2 

q = .567E-4 

Linear: tenii . .responding to 955 upper limit 

on risk {q^): .811E-2 

A16 
P.64 

Data from NTP (1983) 

Spedes and Sex: B6C3F. mice, male 

Endpoint: All squamous cell carcinomas 

Exposure Route: Gavage 

Doses 

# affected 

# at risk 

0 

0 

50 

25 

4 

50 

50 

20 

50 

100 

37 

50 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: 1.814 

Degrees of Freedom: 2 

p-value: .4046 

Maximum Likelihood Parameter Estimates: 

q0 » 0 

qx - .145E-2 

q2 • .131E-3 

Linear term corresponding to 955 upper limit 

on risk (q^) : .773E-2 

A17 
P.65 

Oata from NTP (19.83) 

Spedes and Sex: B6C3F, mice, male 

tnopoint: Alveolar/Bronchiolar carcinoma 

Exposure Route: Gavage 

Doses 

# affected 

# at risk 

0 

5 

50 

25 

11 

50 

50 

12 

50 

100 

w 

50 

Multistage Model -

Ch1-square Goodness-of-Fit Statistic: 1.250 

Degrees of Freedom: 2 

p-value: .5354 

Maximum Likelihood Parameter Estimates: 

q0 - .137 

qx • .234E-2 

Linear term corresponding to 955 upper limit 

on risk (qx * ): .421E-2 

A18 
P.66 

Data from NTP (1983) 

Spedes and Sex: B6C3F} mice, male 

Endpoint: Lymphoma, NOS 

Exposure Route: Gavage 

Doses 0 25 50 100 

I affected 3 5 6 10 

# at risk 50 50 50 50 

Multistage Model -

Ch1-square Goodness-of-Fit Statistic: .440E-1 

Degrees of Freedom: 1 

p-value: .8341 

Maximum Likelihood Parameter Estimates: 

q0 - .639E-1 

....q, 135E-2 

q2 • o 

q3 • .234E-7 

Linear term corresponding to 955 upper limit 

on risk {q*)\ .280E-2 

A19 
P.67 

Data, from NTP (1983) 

Spedes and Sex: B6C3F, mice, female 

r

.

m

±-z*.?.ii All squamous cell carcinomas 

Exposure Route: Gavage 

Doses 0 25 50 100 

# affected 0 0 1 7 

# at risk 50 50 50 50 ' 

Multistage Model -

Chi-square 6oodness-of-F1t Statistic: .123 

Degrees of Freedom: 3 

p-value: .9890 

Maximum Likelihood Parameter Estimates: 

q0 • 0 

•qx- 0 

q2 • 0 

q3 » .150E-6 

Linear term corresponding to 955 upper limit 

on risk (qj*): .760E-3 

A20 
P.68 

Data from NTP (1983) 

Swedes and Sex: B6C3F. mice, female 

tndpolnt: Mammary gland carcinoma, NOS 

Exposure Route: Gavage 

Doses 

# affected 

# at risk 

0 

0 

42 

25 

2 

31 

50 

5 

48 

100 

8 

34 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: .730E-1 

Degrees of Freedom: 2 

p-value: .9642 

Maximum Likelihood Parameter Estimates: 

q0 » 0 

q1 « .226E-2 

q2 - 0 

q3 - .391E-7 

Linear term corresponding to 955 upper limit 

on risk {q^): .370E-2 

A21 
P.69 

Data from NTP (1983) 

Spedes and Sex: B6C3F, mice, female 

Endpoint: Alveolar/Bronchiolar carcinoma 

Exposure Route: Gavage 

Doses 0 25 50 100 

# affected 0 3 6 6 

I at risk 50 47 50 50 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: 1.863 

Degrees of Freedom: 3 

p-value: .6020 

Maximum Likelihood Parameter Estimates: 

q0 • 0 

q'j - Jclv -2 

Linear terra com::podding to 955 upper limit 

on risk (q*): .273E-2 

A22 
P.70 

Data from NTP (1983) 

Spedes and Sex: B6C3F. mice, female 

Endpoint: Malignant lymphoma 

Exposure Route: Gavage 

Doses 0 25 50 100 

# affected 15 24 24 19 

# at ris'. 49 45 50 49 

Multistage Model -

Ch1-square Goodness-of-F1t Statistic: 5.81 

Degrees of Freedom: 2 

p-value: .0548 

Maximum Likelihood Parameter Estimates: 

qQ - .527 

q2 - .H:3E-3 

Linear term corresponding to 955 upper limit 

on risk (qx * ): .369E-2 

A23 
P.71 

Data from NTP (1983) 

Species and Fex: F344/N rats, male 

r--?o1nt: Zymbal gland carcinoma 

Exposure Route: Gavage 

THE 17 rBSFRVATICNi AT LEVEL t WfTH A OCSF rr 0.000QC0CO0 

tTI«C t riJMQr. INJICATCR (NUMBER ») 

12.0 

35.0 

tl J • VJ 

104.0 

11 

11 

4 1 

l( 

1) 

1) 

At 1 

31) 

25.0 

41.0 

87.0 

104.0 

It 

l( 

l( 

21 

1) 

11 

ll 

t) 

29.0 

59.0 

83.0 

tt 

1( 

21 

• 

1) 

2) 

1) 

31.0 

68.0 

96.0 

l( 

It 

1( 

1) 

1) 

I) 

32.0 It 

74.0 It 

101.0 U 

1) 

I) 

2) 

THE 20 OBSERVATIONS AT LEVEL 2 WITH A OPSE CF 50.0000 

ITI*E,TUMP» INTICATCR tNUM^ER)) 

35. 0 

63. 0 

89.0 

100.3 

THE 

51. 0 

J3.0 

83.0 

93. 0 

98. 0 

THE 

51. 0 

83.0 

87.J 

91. 0 

95. 0 

102.0 

11 

I t 

I t 

I t 

24 

I t 

H 

2( 

I t 

2t 

28 

l l 

2( 

l l 

I t 

I t 

I t 

11 

1) 

1) 

1) 

49.0 l l 

65. 0 I t 

*n.o ll 

101.0 11 

OBSFRVATIOMS *T 

I ) 

1! 

I I 

1) 

ITMC,TV*fV> 

57. 0 l l 

77.0 I t 

116.0 11 

°1. 0 ?i 

100.0 l l 

OBSERVATIONj AT 

1) 

I ) 

I ) 

I ) 

3) 

2) 

ITIHL,TUMOR 

64. 0 I t 

*4.0 It 

8 7.0 t'A 

91.0 ?i 

97. 0 ?( 

104. 0 l( 

I ) 50. 0 I t 

l l 71.0 21 

" t ) 9«.0 21 

n u;.o it 

LEVTL 3 WITH A 

1) 

11 

11 

2) 

OCSF 

INTICATPR INUMRERJJ 

l l 69. 0 2t 

1 ) 80.0 21 

I ) 87.0 l l 

I ) 94. 0 I t 

1) 104.0 I t 

LEVFL 4 WITH A 

I ) 

I ) 

I ) 

n 

23) 

onse 

INJICATCR INUMQERU 

l l 7P.T l l 

I ) "S.3 l l 

-') 3B.0 ?i 

"!» «?.J 1( 

I )

 ,JB.0 U 

in J l.K. O 21 

i ) • 

2) 

1 1 

I ) 

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r

0 

55. 0 21 

80. 0 I t 

96. 0 I t 

104.0 I t 

cr 100.000 

70. 0 l l 

Rl. O l l 

88. 0 11 

94. 0 21 

104.0 21 

TF 200.000 

• 

7«5.0 11 

H6.0 11 

fW.O l l 

94. 0 l l 

99.0 21 

I ) 

1) 

1) 

27) 

1) 

I ) 

2) 

1) 

2) 

I ) 

I ) 

I ) 

1) 

2) 

59. 0 

80. 0 

99. 0 

104.0 

72. 0 

83. 0 

92. 0 

97. 0 

* 83. 0 

86. 0 

90. 0 

94. 0 

100. 0 

2( 

I t 

I t 

2< 

i l 

11 

2( 

It 

I t 

21 

11 

21 

H 

1) 

1) 

1) 

2) 

2) 

1) 

2) 

1) 

• HE MAXI^fM L IKSLlHnn) EST'^ATIQ.,' )F JOSE COEFFICItN" 

OC 0!«.4591678931740-03 

Q( I)-.17337191*2280-04 

01 2J«.1656627949150-07 

01 3)>.0C000OO0OO0OD»00 

THE MAXIKJM LIKELIHOOD ESTIMATION OF TIME FUNCTION 

CT-.oo&oconoonooo-rOo I «*i . oo ooooooooo 

A24 
P.72 

Data from NTP (1983) 

Spedes and Sex: F344/N rats, male 

. .. Endpoint: All squamous cell carcinomas 

Exposure Route: Gavage 

TKE 16 CPSERViTIONS »T LEVEL I WITH A OCSE CF C.CCCCCCOCC 

UtKEiTU^CR INClC«rCR UUMEERII 

JL2JL0_U _ 

35.0 I t 

83.0 It 

104.0 I I 

'THE 22 

35.0 It 

63.0 21 

89.0 21 

100 .0 I t 

L04-_0„l.t . 

m 22 

51.0 I t 

72.0 21 

83.0 It 

.93. 0 I t 

104.0 it 

THE 26 

51. 0 21 

14.0 It 

89.0 2 H 

"9*. 0 lt ~ 

98.C It 

t04oC 2<"" 

.11 

11 

2) 

32) 

25.0 It 

41. 0 I t 

€7.0 It 

DBSERVAMONS AT 

I ) 

I ) 

1) 

2) 

.26) 

tUME.TUWCR 

47.0 It 

65.0 I t 

' C C l( 

ico.o 2t 

104.0 2( 

CeSERV'TIONS *T 

I ) 

1) 

2) 

2) 

ITlfE.TUMCP 

57.0 tt 

73.0 I t 

66.0 2t 

94. 0 If 

23) IC4.0 2( 

CBSERVATtCNS IT 

t ) 

11 

n 

" l i 

11 

6 ) 

f TIME, TUTJR 

64.0 I t 

(5. 0 It 

90 rO 21 

94.0 2 1 

99..0 li; 

1) 

1) 

11 

LEVEL 

29.0 l l 

59.0 i t 

CE.O it 

2 WI TH A 

11 

2) 

I) 

CC!E 

INCICITCR (NUMBER )l 

tl !C.Q 21 l l 

1) 

I) 

1) 

3) 

LEVEL 

71.0 1( 

95.0 I t 

ICJ.O l l 

3 WITH a 

1) 

I ) 

1) 

OCSE 

INCICITCR IMJMBERII 

n 

i) 

n 

2) 

2) • 

LEVEL 

69.0 it 

77.0 I t 

C7.0 2( 

57.0 21 

4 WIT»- a 

n 

i i 

n 

i i 

COSE' 

INDICATCR INLMBER)) 

1) 79.0 I 1 I ) 

2) 

l l 

\ 

86.n i i 

91.0 l l 

9 5.0 I t 

iCf.O l-; 

21 

2) 

I ) 

w 

3 1 . C 11 

6f.O it 

96.C i t 

CF 50.COCO 

55.0 I t 

80.0 It 

96.0 I t 

1C2.C If 

CF iCC.CCC 

7C.0 if 

89.0 It 

et.o i t 

se.o it 

OF 2CC.C00 

?!.C 11 

87.0 l l 

51.C 2( 

95.0 2t 

102.0 2 

I) 

1) 

I ) 

1} 

1) 

1) 

1) 

I) 

1) 

2) 

1) 

1) 

3) 

I) 

2) 

i) 

32.0 

7«.0 

101.0 

59.0 

8C.0 

99.0 

IC2.0 

72.0 

81.0 

92.0 

1C0.0 

(3. 0 

88.0 

92.0 

97.0 

104.0 

I t 

it 

If 

If 

2( 

21 

21 

I t 

21 

if 

2( 

it 

It 

I t 

11 

l l 

1 

l; 

2 

1 

11 

I 

1 

_.. 

1] 

ii 

2 

IJ 

2] 

1 

11 

I. 

9 

T KE •'AXtniM LlKELfHOOO ESTIMATION OF DOSE COEFFICIENT! 

QI o>-.oceccccccoooo»cc 

01 11*.2443073818240-04 

01 2)-.C(fCCCCCCCC0DrCC 

Qt 31-.0000000000000 i00 

THE rfcXllHJM LIKELIMOOO ESTIMATION OF 11 P»e FI.KTIC * 

{r-.oooococoooooo*ooM*i.eeccccaccae 
P.73 

Data from NTP (1983) . 

«•-"••»•£ and Sex: F344/N rats , female 

Endpoint: Zymbal gland ca cinoma 

Exposure Route: Gavage 

THE 5 OnSCRVlTICNS AT LEVEL 1 WITH A PCSF. PF O.0000O0C*00 

tTlMF,TU»«po INTICATQP t NUMBER)) 

33.0 i t 1) 93.0 I t 1) 97.0 I t 1) 103.0 it i ) 104.0 i t 46) 

THE 13 OBSERVATION", AT LEVEL ?. WITH A DOSE nr 25.0000 

ITIMEtTUMrjF INOICATflR tNUMPEP)) 

48. 0 

*8. 0 

103. 0 

THE 

45. 0 

75. 0 

96. 0 

104. 0 

THE 

• • 

2 . 0 

64. 0 

83. 0 

97. 0 

103. 0 

I t 

i t 

IK 

16 

I t 

i t 

I t 

2( 

23 

i t 

11 

21 

21 

it 

I ) 

1) 

I ) 

nns* 

1) 

2) 

I ) 

3) 

AO.O 

Ri.O 

104. 0 

SVATUM* 

I t 

I t 

11 

; AT 

IMMEiTUMOP 

52. 0 

T2. 0 

101. 0 

riRSFRVATtflN! 

1) 

I ) 

I ) 

I ) 

I ) 

11 

2( 

I t 

. AT 

t TVMEtTUHOC 

9 . 0 

60. 0 

R7..1 

T3. 0 

104. 0 

l l 

"M 

l l 

l l 

l l 

I ) 

l l 

?5) 

LEVEL 

73. 0 

9 I. P 

104. 0 

21 

I t 

2( 

3 WITH A 

INDICATOR ( 

I ) 

I ) 

1) 

LFVEL 

69. 0 

8A.0 

102. 0 

I ) 

1) 

3) 

OCSF 

INUMRF.P)) 

11 

i t 

I t 

4 WITH A 

iNntCATriR 

11 

l l ' 

I ) 

? ) 

17) 

32. 0 

7«>.0 

13. 0 

100. 0 

I 14.0 

1) 

1) 

2) 

OOSE 

(NUMBER)) 

I t 

I t 

11 

I ( 

7.1 

I ) 

1) 

I ) 

1 ) 

R) 

«0 

97 

rip 

71 

* 9 

103 

OF 

57 

7? 

oc, 

10 I 

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•50 , 

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.0 

11 . 

11 

oooo 

2t 

I t 

it 

100.00 0 

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. 0 

• 0 

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11 

21 

11 

l l 

2) 

1) 

1) 

1) 

1) 

1) 

1) 

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8 1 . 

103. 

72 

9 6. 

104. 

62. 

83. 

97, 

102 

0 

0 

,0 

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.0 

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11 

It 

l l 

11 

It 

• -

2( 

11 

l l 

21 

1) 

1) 

I ) 

1) 

311 

— 

11 

i ; 

31 

i ; 

'•HE MAXIMUM LIKELIHOOD ESTIMATION OF OOSE COEFFICIENTS 

Ql 0)".0000000000000*00 

Ot l»«.2*R<>37l79396D-04 

.Ql 2)«.0000000000000*00 

Ql 3)».60029«942l060-09 

._.THE MAXIMUM LIKELIHOOD ESTIMATION OF TIME FUNCTION 

IT-.0000000000000*00)**1.00000000000 

A26 
P.74 

Oata from NTP (1983) 

Spedes and Sex: F344/N rats, females 

Endpoint: All squamous cell carcinomas 

Exposure Route: Gavage 

THE 5 OBSERVATIONS AT LEVEL I WITH A OC!E CF C.OCC0O0C»0O 

_ tTIMEiTUMOR CNCICATOR tNUM8.ER)l 

33.0 11 

._THE_.l2 

TeToHif"" 

88.0 I t 

1C3.0 21 

"THE 16 

.— 

45.0 I t 

72.0 i f 

96.0 21 

104.0 I f 

THE 21 

2.0 it 

64.0 I f 

93.0 If 

101.0 it 

IC4. 0 21 

I ) 93.0 If 11 <7.Q 11 11 

• • » 

CBSERVATICNS AT LEVEL 2 WITH A CCSE 

(TIME.TUMOR ISO IC A TOR (NLM8ER)) 

"ll 69.0 i f I ) 73.0 I I 1) 

1) 89.0 11 I ) 5!. 0 It 1) 

11 104.0 I f 38) 

CeSERV-MONS AT LEVEL 3 kl TH A OCSE 

tTIf»E,TUMCP INCICITCP IKUM8ERJ) 

I ) 52. 0 It 1) "CO If 11 

1) 75.0 I t 2) 82.0 I t 1) 

1) 101.0 21 I) IC2.0 I t I) 

34 1 

OBSERVATIONS AT LEVEL 4 WITH A CCSE 

ITI^EtTUPOR INCICATCR tNUMBER)) 

t l 9.0 It 1) 32.0 It I ) 

l l 69.0 l l l l 75.0 I t 2) 

I) 94.0 It 1) 57.0 I f 4) 

t ) 101.0 2( 1) 102.0 ll 11 

I ) 

IC3.0 If 

CF 25.0000 

80.13 I f 

51.C 11 

CF 5C.CCCC 

65.Q 2( 

85.0 if 

102.0 2t 

CF 100.OCO 

57.0 I t 

83.0 It 

98.0 21 

IC3.C If 

l l 

21 

11 

11 

1) 

1) 

l l 

2) 

21 

1) 

104.0 

81.0 

1C3.0 

71.0 

96.0 

103.0 

62. 0 

87.0 

100.0 

104.0 

I t 

If 

i t 

I f 

it 

If 

if 

2( 

2( 

if 

..•61 

l i 

11 

11 

IJ 

11 

l i 

l i 

I 

24; 

THE MAXIfU* UKEI.IHCCC ESTIMfT'CN OF HOSE COEFFICIENTS 

Ct 0)«.0030000000000*00 

"Of Il«.l2l931«7f7"^880-C4 

Qt 2H.2931336872990-C7 

Qt 3)".CCCCCOCOOOOOO-OO 

THE MAXlinj" L1XEL1H0CC ESTIMITION OF TIME FUNCTION 

fT-2 .00000000006 T«fT.fl3fffiO"flfiCC0C~ 
Sata from NTP (1983) 

.Spedes and Sex: B6C3Fi mice, male 

Fnrfnolnt: Squamous cell carcinoma of the preputial gland 

i^Hu»ure Route: Gavage 

THE IB CBSEPVATICNS AT LEVEL 1 WITH A COSE OF C.CCCCCCD*0C 

I TIME,TUMOR INOICATCR tNLMEERI) 

3.9 U 

77.0 If 

8 J .0 1 t 

U2. 0 11 

"Trl'Fv" 

0.0 11 

44. 0 i t 

83.0 If 

94.0 i t 

102.0 If 

l l _ 36.0 I t 

M 81.0 It 

1) 92.0 It 

3) 103.0 I f 

C!SERV«TIONS AT 

tTIME.TUMCF 

1) 1.0 u 

1) 68. 0 I f 

l l E4.0 If 

I ) 96. 0 l l 

2) IC3.0 It 

1) 4 1.0 I t 2) 

I) 82.0 I f I ) 

I) 53.0 11 1) 

21 104.0 I f 281 

LEVEL 2 WITH A OOSE 

INOICATCR _tMJMeEP I I 

l l 26.0 If 11 

l l 74.0 I f I I 

t) U. O l l l l 

l l 9 7.0 I t l l 

2) 104.0 I f 20) 

43. 0 

85.0 

S7.C 

OF 25. 

3E.C 

79. 0 

86.0 

10C.0 

104.0 

It 

I f 

If 

CCCC 

If 

it 

i f 

11 

21 

1) 

l l 

11 

11 

1) 

2) 

1) 

3) 

55.0 

86.0 

99.0 

39.0 

8 1.0 

90.0 

ICl. C 

It 

if 

i t 

i f 

11 

i f 

it 

_ ll 

1 

21 

11 

li 

2 

21 

__THE 28 CeSERVATICNS AT LEVEL 3 «ITH A OOSE OF 5C.CCC0 

(TIME, TUMOR INOICATCR fNUMEERII 

"2976 it 

71.0 it 

85.0 i f 

93. 0 If 

99.0 If 

.1; "-'A..1 <.. 

THE 30 

3.0 I t 

76.0 21 

87.0 If 

93.0 2t 

47.0 2! 

101.0 21 

1) 

I) 

l l 

11 

11 

21 

43. 0 I t 

77.0 11 

87.0 It 

94.0 I t 

100.0 tt 

104.0 I t 

OBSERVATIONS AT 

ITIME,TUMOR 

1) 7.0 It 

1) 

I I 

2) 

4) 

1) 

78.0 I t 

ee.o 2t 

95.0 It 

98.0*21* 

102.0 a 

il 

I ) 

1) 

21 

2) 

41 

64.0 If 

78.0 I t 

ee.o K 

94.0 2f 

ICC.O 2( 

104.0 2( 

1) 

1) 

11 

I I 

l l 

14) 

LEVEL 4 WITH A OCSE 

INCICATCR fNUMBER)) 

I) 2<.0 It 1) 

I ) 

2) 

3) 

I) 

1) 

8 1.0 I I 

89.0 I t 

9'. 0 21 

99.0 ,2 1 

1C2. 0 2( 

2) 

l l 

2) 

2 ) 

4) 

6C.0 If 

83.0 I f 

85.0 If 

95. 0 It 

101.0 21 

CF IOC.COO 

54.C If 

81.0 21 

9C.0 I t 

Sc.C It 

100.0 2( 

104.0 I f 

1) 

1) 

11 

tl 

1) 

1) 

1) 

1) 

11 

2) 

3) 

65.0 

84.0 

91.0 

97. 0 

102.0 

74.0 

82.0 

90. 0 

96.0 

" T/OI.O 

104.0 

if 

It 

I t 

It 

I f 

I f 

11 

21 

21 

It " 

2( 

1. 

1 

21 

21 

2 

2 

i; 

l 

n 

t.i 

4 

THE MAXIMUM LIKELIHOOO ESTIMATICK OF COSE COEFFICIENTS 

Of 0)«.CCCCCC0000C0O»CC 

Qt if".3460089365780-20 

Qt 2I« . 1286267493160-20 

~QI 3}-".~OCCC000COOC0O+00 

Tr"E MAXIMUM LIKELIHOOO ESTIMTICN HF 1IPE FUSTIC* 

IT-.CC:CCeCCCCCCO*OCI«*e.3330C36 8244 
P.76 

Data from NTP (1983) 

Spedes and Sex: B6C3F]. mice, male 

Endpoint: All squamous cell carcinomas 

Exposure Route: Gavage.. 

THE 18 OBSERVATIONS AT LEVEL f'"U*£TH A DolE*" dF O.OOOOOOD+OO 

(TIME.TUMOR INDICATOR (NUMBER)) 

?• rt 1 f 

77-.crrr 

87. 0 K 

02. 0 1( 

THE 24 

0 . 0 1( 

44. 0 IC 

63. 0 K 

94. 0 2( 

02. 0 1( 

THE 30 

29. 0 1( 

7J..0. l.(._ 

85. 0 1( 

91. 0 2( 

97. 0 1( 

02. 0 1( 

THE 27 

3 . 0 1( 

76. 0 2( 

87. 0 2< 

95. 0 1( 

98 ."6 2< 

C2. 0 2( 

THE MAX 

1) 36. 0 1( 1) 41. 0 "if 2) 43. 0 1< 

1) 81. 0 1< 1) 82. 0 1( 1> 85."0~1( 

1) 92. 0 1< 1) 93. 0 1< 1) 97. 0 1( 

3 ) 103. 0 1( 2 ) 104. 0 i< 28 ) ~ 

OBSERVATIONS AT LEVEL 2 "WT'TH A T>C*sr*3*F 55.000 0 

(TIME.TUMOR INDICATOR (NUMBER)) 

1) 1.0 t( 1) 28. 0 1( 1) 38. 0 1( 

1) 68. 0 1( 1) 74. 0 1( 1) 79. 0 1( 

1) 84. 0 1( 1) 85. 0 1( .1 ) 86. 0 1( 

1) 96. 0 1( 1) 97, 0 1( 1) 100. 0 1( 

. 2 ) 103. 0 1( 2 ) 104. 0 1( £0> 104, 0 2( 

OBSERVATIONS AT LEVEL 3 WITH A DOSE OF 50.000 0 

(TTMEfTUMOR INDICATOR (NUMBER)) 

1) 43. 0 1( 1) 647b" If 1)~ 66. 0 l"( 

1) 77. 0 1( 1) . 78...0_1C L> 83.0_1(_ . 

1) 87. 0 1( 1) 88. 0 1( 1) 89. 0 1( 

1) 93. 0 1( 1) 94. 0 1( 2) 94. 0 2( 

2) 99. 0 1( 1) 100. 0 1( 2 ) ' 100. 0 2( 

2) 103. 0 1( 1) 103. 0 2( 1) 104. 0 1( 

OBSERVATIONS AT LF'.TL 4 WITH A DOSE OF 100.00 0 

(TIMF » TUMOR INlUCnrOR tNUMBER>> 

1) 7. 0 1( 1) 24. 0 l< 1) 54. 0 1( 

1) 78. 0 2( 1) 81. 0 1( 2).... 81. 0 2( _ 

1) 88. 0 2< 2 ) 89. 0 1( 1) 90. 0 2( 

1) 95. 0 2( 4) 96. 0 1( 1) 96. 0 2( 

1) 99. 0 2( 2 ) iOO.O 2< ?.) 101. 0 It 

. 5 ) 104. 0 2( 7) _ 

IMUM LIKELIHOOD ESTIMATION~~d"F TJOSE ToTFFfCIENTS~" 

1) -

1) 

1) 

1) 

1> 

2) 

1) 

.3).... 

. ___ . 

.U- . 

1) 

1) 

1) 

3) 

1)" " 

1) _ 

2) 

1) 

1 > 

59. 0 1( 

86. 0 1< 

99. 0 1^ _ 

. 39.0.1 ( 

81.01~ f 

.90. 0 IC . 

101. 0 1( 

. .... . — 

69. 0 1( 

84^o_ic; 

91. 0 1( 

95. 0 1( 

101. 0 2( 

104. 0 2_(._ 

74. 0 1( 

...82j0..1t . 

93. 0 2( 

97. 0 2( 

iOi. O 2< 

1) 

1) 

_2) 

_ 1 ) 

~f) 

. 2 ) . . 

2) 

- — 

1) 

1> 

1) 

1) 

1) 

.15.) 

2) 

2 ) 

4> O • 

1) V 

Q( O)-.0O0OOOOOOOO0D+OO 

0("l)=.0000000000000+00 

Q( 2)-.387387062466D-22 

0("3)=.426343280969D-24 

_JHE_MAXIMUM LIKELIHOOD ESTIMATION J3F_TIME_FUNCTipN_ 

<f-.00b000600000D+00>**9.30674412063 

A29 
Oata from NTP (1983) . 

Species and Sex: B6C3FX mice, male , 

Endpoint: Alveolar/Bronchiolar carcinoma 

•%-"-!«yre acute: Gavage 

THE 20 CBSERVATICNS AT LEVEL I WITH A CCSE CF O.OOOOOOCOO 

fTIMEtTUHOR INDICATOR tNUMBERII 

3,0 1( 

77. 0 I t 

•T. n 1t 

99. 0 2( 

"THE 24 

0 . 0 l l 

44. 0 If 

83.0 21 

94. 0 I f 

JliUj&JUL-

—THE.- 29 

"T97b"if" 

71.0 I f 

85.0 i t 

—?3f.0_.lt . 

97.0 2 f 

.U3JJL11 _ 

THE 34 

3.0 I t 

74.0 2t 

8 2.0 I f 

90.0 21 

96.0 21 

99.0 21 

102.0 i t 

THE MAX 

17 

l l 

» » 

I) 

.36.0 .I t . 

81.0 I t 

92.0 t t 

IC2.0 It 

CeSERVATICNS AT 

l l 

t ) 

l l 

l l 

_ 2 I 

fTIMEiTUMOR 

, i 

I .0 t I 

68.0 I t 

84.0 2( 

96. 0 I f 

103.0 If 

QBSERVATICNS AT 

11 

1) 

11 

t l 

l l 

_u. 

tTIME,TUMOR 

43.9 I f 

77.0 21 

87.0 I t 

54.0 If 

99.0 It 

10 3.0 21 

CBS ERV AT I CNS AT 

t 1I>EtTUM0S 

l l 7.0 l l 

1) 

" I ) 

l l 

11 

I ) 

IMLM 

76.0 11 

87.0 If 

93.0 I t 

57.0 It 

100.0 I t 

L02.0 2( 

LIKELIHCCO ( 

11 41.0 l l 21 

1) 82.0 I t I ) 

11 93.0 2\ l l 

31 IC3.0 i f 21 

LEVEL 2 WITH A OCSE 

INOICATCR fNUMBERII 

l l

 V2B.O I t l l 

l l I'.O I t I) 

I ) t«. 0 I f l l 

t ) 57.0 I f H 

2) IC4.0 It 18) 

y 

LEVEL 3 WITh A CCSE 

INDICATOR tKUMBERM 

l l 64.0 2 t l l 

l l 76.0 I t t) 

l l 8 8.0 I t l l 

21 94.0 21 1) 

l l ICC.O I f 3) 

1) 1C4.0 I t 14) 

LEVEL 4 WITH A OOSE 

INC1CATCR INUMeEP)) 

I) 24.0 I t I ) 

1) 73.0 I t I ) 

l l 6 E.O 11 2) 

2) 95.0 I t 2) 

3) 5 7.0 21 1) 

I ) 10C.0 7( 11 

43. 0 I t 

85.0 I t 

97. 0 It 

104.0 I f ; 

OF 25.CCCC 

38. 0 I t 

75.0 I t 

B«.0 If 

109.0 I f 

104. C 2 ( 

OF 50.0000 

66.0 I t 

83.0 I t 

89.0 I f 

95.0 I f 

IC1.C If 

104.0 21 

OF ICC.CCO 

54.C It 

8 1.0 I t 

85.C I t 

. 95.0 2t 

98.0 l l " 

10UC ! ' 

' l l ' 1C4.0 \ t 5 1 104T.0 :-

•STIMIT1CN OF COS E _ CO € F FIC I EN T S 

11 

I) 

I) 

IS) 

11 

2) 

I) 

3) 

I ) 

») 

2) 

.59.0 

86.0 

55.0 

104,0 

35.0 

81.0 

9C.0 

101.0 

. . 

69.0 

84.0 

91.0 

97 X 

1C2.0 

74.0 

81.0 

9C.0 

56.0 

'" "99.0 

K UO 

- — 

If 

I t 

If 

21 

i f 

2( 

2( 

2t 

If 

2 t 

21 " 

l i 

i f 

i f 

2( 

I t 

11 

"it Z3 

1) 

11 

1) 

31 

. . .. 

1) 

" l l 

1) 

2) 

—— 

1) 

1) 

2) 

11 

2) 

. .. 

1) 

1! 

r

 1 i 

i l 

1 

1 ! 

Qt 0l«.346C443927500-03 

Qt U«.6441939503e20-C3 

Qt 2 I-.0000000000000*00 

_QL3i«.CCCCC000GOOOO»0O_ 

THE BATTPUP- ifKELfHCOO EST IMIT ICK OF TIFF. FUNCTION 

IT-.flQOOOaoOQ0OQP*O0 !*>•! .31898771565 

A30 
P.78 

Oata from NTP (1983) 

•>n«»des and Sex: B6C3FV mice, male 

tndpolnt: Lymphoma, NOS 

* Exposure Route: Gavage -

THC 20 CB5F.RVATICNS AT LEVEL I WITH A CCSE CF O.O00000C*OO 

f TIME, TUMOR INDICATOR t NUMBER ) I 

_3_J3_1L _ 

•» •» A • # 

• . +* 4 6 

.87.0.I f 

102.0 If 

ifHE 2~4 

0, 0 .if.. 

44.0 It 

.83. 0 I f 

94.0 If 

AOj___,l_t_ 

THE.. .2 6 

• 

29.0 tt 

71.0 I f 

85.0 If 

_93. 0 l l 

100.0 I t 

X 04».0_2t . 

THE 28 

~ 37611 

76.0 If 

88.0 I t 

95.0 If 

98.0 It 

102.0 2( 

__n_ 

4 ' 

t l 

31 

_ . 36.0.1 1 

81.0 It 

92.0 I f 

103.0 If 

OBSERVATIONS AT 

t l 

l l 

l l 

1) 

—21 

..f TIME, TUMOR 

1.0 i t 

68.0 If 

S4.0 tt 

96.0 It 

103.0 It 

OBSERVATIONS AT 

I) 

I ) 

1) 

l l 

3) 

. 5 1 

CBSE 

l l 

tl 

21 

41 

I ) 

21 

f TIME, TUMOR 

43.0 It 

77.0 If 

87.0 I t 

94.0 tf 

toi. o I t 

RV ATI CNS AT 

"tfi>E , TUMOR 

7.0 i t 

78. C ll 

89.0 l l 

95.0 2t 

99.0 ll 

104.0 11 

_l>_ . 41.0 t t 

l ) 82.0 2( 

1) 9 3.0 I t 

I) 103.0 21 

LEVEL 2 WITH A 

2) 

U 

I ) 

11 

OCSE 

INOICATCR tNUMBERII 

l l 28.0 I f t l 

I) 74.0 It 

L) 85.0 I t 

l l 57.0 2t 

2) IC4.0 It 

LEVEL 3 WITH A 

l l 

I ) 

l l 

19) 

OCSE 

INOICATOR tNUMBERII 

1) 64.0 I t t ) 

l l 78.0 I t 

I) 88.0 I t 

1) 5 5.0 21 

l l 102.0 It 

l l 

11 

11 

21 

LEVEL 4 WITH A OOSE 

INOICA'TCR tNUMBERII 

l l 24.0 If 

I) 81.0 I I 

I ) 9C.0 ll 

I ) 96.0 2 ( 

2) ICC. 0 If 

:•» io<?cO 2t 

l l 

3) 

l l 

I I 

2) 

21 

43.0 If 

85.0 If 

97.0 If 

11 

1) 

11 

104.0 I t 27} 

OF 25.COCO 

38.0 I t 

79.0 I t 

86.0 If 

100.0 If 

104.0 21 

CF 50.0000 

66. 0 I t 

83.0 tt 

89.0 It 

97.0 I t 

103.0 If 

OF 100.000 

54.0 2t 

8 2.0 I t 

9C.0 2( 

97. 0 It 

101.0 11 

• 

1) 

11 

21 

11 

41 

... . 

11 

11 

11 

21 

21 

59.0 

86.0 

95.0 

104.0 

39.0 

81.0 

9C.0 

101.0 

-

69.0 

84.0 

91.0 

99.0 

104.0 

74.0 

87.0 

93.0 

97.0 

'102.0 

It 

I t 

it 

2t 

it 

I t 

if 

11 

i t 

1< 

It 

I f 

It 

11 

if 

i t 

2( 

1< 

1 

1 . 

21 

1 

ll 

1. 

2) 

2 

—... 

• 

1 

11 

21 

1. 

13) 

21 

1 

2) 

2; 

3 

THE MAXIMUM IIKELIHOQO ESTIMATION OF COSE COEFFICIENTS 

CJLft!*L»429

 T ' 64>56659 0-0 7 

Qt U- . 1010121803870-08 

gt_2 l-jJOOOOOQOOOOOOD •00 

Qt 3I«.3163454944710-13 

THE MAXIMUM LIKELIHOOO EST IMAT ION OF Tt ME FUNCTION 

(T-.OOOOOOCO0O00C*OOM*3.UO345 3C8 3 7 

A31 
P.79 

Data from NTP (1983) 

Spedes and Sex: B6C3F! mice, female 

Endpoint: All squamous cell carcinomas 

Exposure Route: Gavage 

THE 16 OBSERVATIONS AT LEVEL 1 WITH A DOSE OF O.OOOOOOD+OO 

(TIME,TUMOR INDICATOR (NUMBER)) 

3.0 1( 

ft. r» 1 t 

93.0 1( 

104.0 1( 

THE 17 

.. 

1.0 1( 

81.0 1( 

93.0 1( 

103.0 1( 

THE 22 

67.0 1( 

85.0 1( 

93.0 1( 

99.0 1( 

104.0 1( 

THE 26 

3.0 1( 

72.0 1( 

84.0 1( 

93.0 1( 

97.0 2( 

104.0 2( 

1) 

!) 

1) 

30) 

29.0 1( 

74.0 1( 

95.0 1( 

OBSERVATIONS AT 

5) 

2) 

1) 

1) 

<TIME*TUMOF 

32.0 1( 

83.0 1( 

94.0 1( 

104.0 1( 

OBSERVATIONS *T 

1) 

2) 

1) 

1) 

1) 

1) 

1) 

LEVEL 

30.0 1( 1) 

80.0 1( 1) 

.99.0 i(. _2) _ 

2 WITH A DOSE 

* INDICATOR (NUMBER)). 

1) 

1) 

2) 

24) 

LEVEL 

70.0 1( . 1) 

87.0 1( 1) 

97.0 1( 1) %m 

3 WITH A DOSE 

(TIME»TUMOR INDICATOR (NUMBER)) 

68.0 1( 

87.0 1( 

94.0 1( 

100.0 1( 

1) 

1) 

1) 

1) 

70.0 K 1) 

90.0 1 (" 1 )* 

95.0 1( 2) 

101.0 1( 1) 

23) 104.0 2( 1) 

.OBSERVATIONS AT LEVEL _4_UITH_A DOSE 

(TIME.TUMOR INDICATOR (NUMBE*R)) 

1) 

1) 

2) 

2) 

1) 

4) 

"THE MAXIMUM 

48.0 i< 

76.0 1( 

87.0 1( 

94.0 1( 

99.0 1( 

LIKELIHOOD 

1) 

1 » 

3) 

1) 

1) 

64.n 2( t ) 

77. 0 J* < 1 • 

8fl . 0 1 ( 1 ) 

94,0 2( 1) 

100.0 t( 1) 

... . 

38.0 K 

87.0 1( 

.100.0.K ... 

OF 25.0000 

78.0 1( 

88*0 1( 

101.0 l/_. 

OF 50.0000 

71.0 1( 

"91.0"l(" "* 

96.0 1( 

102.0 1( 

0F__ 100 ..000 

*A.O 1( 

fl.7.0 1( 

90.0 1( 

95.0 1( 

103.0 1( 

— - -

ESTIMATION OF "til*E~CUE r F1CIE NT S ' 

1) 

2) 

1) 

1) 

1) 

1) 

1) 

"2") 

2) 

3) 

-r • • 

1 ) ' 

1) 

1) 

3) 

1) 

_ 

58.0 1( 

90.0 1( 

.103.0 1( 

80,0 1( 

89.0 1( 

_102_L0__1_(_ 

• • . ~ 

. .__ ..... 

8.0.0 1( 

92"."0 1( " 

97,0 1( 

103.0 1( 

71.0 1( 

83.0 1( 

91.0 1( 

97.0 K 

104.0 1( 

• 

1) 

1) 

4) 

_ 

X) . 

1) 

J2>._; 

-

____ 

1) 

i) 

l) 

l) 

~~2)~ 

2) 

1) 

1) 

14) 

- -

0( 0)-.000000000000D+00 

0(" 1)«.OOO0OO000O00D+00 

Q( 2)«.O0O0O0OO000OD+OO 

Q( 3>-.18A337667410D-ll 

THE MAXIMUM LIKELIHOOD ESTIMATION OF TIME FUNCTION 

(t'-.000000000000n+00)**2,49169151405 

A32 
Oata from NTP (1982) 

Spedes and Sex: B6C3Fi mice, female 

Endpoint: Mammary aland carcinoma, NOS 

exposure Route: Gavage 

Tl-E 10 QUSERVAT10NS AT LEVEL 1 WI TH A OCSE CF C.CC0000C*O0 

fTt»E,TUNCR INDICATOR tNUMBERII 

_ 3,0 If 71 25.0 I I l l . 3C.0 I f I I 3e.O I f 11 87.0 It 2 

95.0 I t l l 99. 0 If 2) ICC.O It 11 103.C It 41 1C4.0 It 281 

TME 12 OBSERVATIONS AT LEVEL 2 Wt TH A CCSE CF 25.COCO 

tTIWE.TUMCR INCICITCR tNUMBERII 

1.0 If 21 

94. 0 I t 21 

.103. 0 2i II 

70.0 tf 

97.0 I t 

IC4.0 It 

1) 

1) 

171 

7!. 0 If 

99.0 I f 

11 

11 

81.0 I t 

101.0 2( 

11 

1) 

87.0 I t 

102.0 It 

1. 

21 

. THE 17 CESERVATICNS AT LEVEL 3 WITH A COSE OF 5C.0CC0 

(TIME,TUMOR INOICATCR fMMBEPII 

68.0 

90.0 

96. 0 

IC4. 0 

i f 

if 

i t 

if 

n i i 

n i e i 

70.0 

91. 0 

100.0 

104.0 

21 

It 

It 

2( 

1) 

21 

l l 

2) 

71.0 

54.0 

101.0 

I t 

I t 

It 

11 

11 

I) 

8C.0 

95.0 

IC2.0 

If 

I f 

tt 

1) 

1) 

21 

£1.0 

95.0 

1C2.0 

ll 

Zi 

2f 

21 

I 

l i 

THE 16 OBSERVATIONS AT LEVEL 4 WITH A COSE OF ICC.CCO 

fTIME,TUfCR INCICATCP tNUMBEPIl 

64. 0 i t 11 

_87. 0 It 2) 

95.0 21 11 

104.0 2( 3) 

71.0 It 

88.0 21 

57. 0 11 

2) 

I) 

I) 

• 7«.0 

90.0 

55.0 

21 

1 t 

ll 

1) 

11 

1) 

83.0 

9 3.0 

10C.0 

21 

It 

It 

1) 

11 

1) 

84.0 

94. 0 

104.0 

It 

2( 

it 

11 

li 

15 

THE M4XIPUP LIKELIHCCC ESTIMATION OF COSE COEFFICIENTS 

Cf 0I«.0000000000000*00 

Qt ll«.2S4C058399340-04 

Qf_2l-.0CCC000C0OCOOtQ0 

Ql 3l«.OCQ0O0OOOOOO0«OO 

THE MAXIMUM LIKELIICOC ESTIMATION OF TIME FUNCTION 

tT-.OOOOC0C00CCaC+0OI»*l.0OC0OO0000Q 

A33 
P.81 

I I 

Cata from NTP (1983) 

Spedes and Sex: B6C3Fi mice, female 

Endpoint: Alveolar/Bronchiolar carcinoma 

"Exposure Route: Gavage 

THE 16 CASER'ATIONS AT LEVEL 1 M TH A CCSE CF 0.O00O00CM30 

»T1ME, TUMOR INDICATOR tNUMBERII 

J^Q-LL -

T3,0 I f 

53.0 I t 

104. 0 It 

THE 18 

1.0 It 

81.0 If 

. 93. 0 I f 

103.0 It 

. THE 23 

..... . -

67.0 I t 

85.0 It 

92. 0 I t 

97.0 I t 

JLP.3_.C_lt_ 

THE 25 

3 . 0 It 

72. 0 I t 

£4.0 i t 

93.0 If 

99 .0 i t 

__11 29. 0 i t 

11 74. 0 If 

11 95. 0 I t 

301 

CBSERVATICNS AT 

t TIME, TUMOR, 

5) 32. 0 I f 

21 83. 0 If 

11 94.0 1t 

11 1C4.0 If 

CeSERVATICNS AT 

t TIME,TUMOR 

1) 68. 0 I 1 

21 67. 0 If 

I ) 93. 0 I t 

1) 99. 0 I t 

„ t l 104.0 11 

CBSERVATICNS AT 

tTIME,TUMOR 

I) 48.0 I t 

11 76. 0 It 

21 87. 0 l l 

2) 54. 0 IC 

I ) • 100,0 c 

11 

1) 

11 

LEVEL 

3C. 0 I t 

S C O 11 

99. 0 I t 

2 WITH A 

It 

1) 

2) 

CCSE 

INOICATCR fNLMBERI) 

I ) 7C.0 I t I ) 

11 

21 

21) 

LEVEL 

(7. 0 l l 

9 7c 0 I t 

104.0 21 

3 WITK A 

I ) 

I ) 

31 

CCSE 

INOICATCR tKLMBERII 

1) 

I) 

l l 

11 

19) 

LEVEL 

70. 0 11 

90. 0 I t 

54. 0 I t 

I OCO I t 

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17.0 If 

100.0 i t 

OF 25.0000 

78.0 if 

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THE MAXIMUM LIKELIHOOD ESTIMATION OF OOSE COEFFICIENTS 

Qt OI«.OC0C0C0C0OQO0*O0 

Qt l)«.56C2 6 84 9 72 88 0^17 

Qt 2)-.CCCCCCCCC0C0O*C0 

C t_3 )•.000000000000 C «00 

THE MAXIMUM LIKELIHOOD ESTIMATION OF TIPE FUNCTICN 

J_T-,00O0CC00000CO»O0|4«7.295483€2e9C 

A34 
THE 

Data from NTP (1983) 

So-des and Sex: B6C3FJ mice, female 

Endpoint: Malignant lymphoma 

Exposure Route: Gavage 

IB 0*Sf-RVATI C>VS AT LFVEL I WITH A QOSr 

|T1MF,TIJMO«» INDICATOR INIJMBER)) 

rr o.ooooooc*oo 

3.0 11 

73,0 !» 

93.0 i t 

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100.0 

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THE 19 flSSFRVATIONS AT LEVEL 2 WITH A OOSF OF 

ITIMF,TUMOR INOICATOR tNUMBFR)) 

1.0 

41.0 

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25.0000 

78.0 I t 

88.0 I t 

101.0 I t 

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THE 25 OPNrRVATIONS AT LEVEL 3 WITH A OOSF OF 50.0000 

tTIMF.TUMOP INOICATCR fNUMREF.II 

80. 0 It 

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THE 27 CBSERVATTONS AT LEVEL 4 WITH A OOSE OF 

fTIMF,TUMOR INOICATOR {NUMBER)) 

100.00 0 

3 . 0 

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THE .MAXIMUM LIKELlHfiOD ESTIMATION QF COSE CO Ei-

 : I C 16NTS 

Qt 0I«.2472739286150-03 

Qt D-.OOOOOOOOOOOOO+O O 

Qt 2 )«.0000000000000*00 

Qt 3)«.0000000000000*00 

THE .MAXIMUM L IK EL tHOOO. ESTIMATION OF TIME.. FUNCT ION.. __ 

tT-i.OOOOUOOOOOO I•*!.59972385*66 

A35