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G. Appendix: TCE Cancer Dose-Response Analyses with Rodent Cancer Bioassay Data
G. Appendix: TCE Cancer Dose-Response Analyses with Rodent Cancer Bioassay Data G-l
G. 1. Data Sources G-2
G. 1.1. Numb ers at Ri sk G-2
G. 1.2. Cumulative Incidence G-2
G.2. Internal Dose Metrics and Dose Adjustments G-3
G.3. Dose Adjustments for Intermittent Exposure G-4
G.4. Rodent to Human Dose Extrapolation G-5
G.5. Combining data from related experiments in Maltoni et al. (1986) G-6
G.6. Dose-Response Modeling Results G-l2
G.7. Modeling to account for dose groups differing in survival times G-13
G.7.1. Time-to-tumor modeling G-13
G.7.2. Poly-3 calculation of adjusted number at risk G-14
G.8. Combined risk from multiple tumor sites G-15
G.S.I. Methods G-l 6
G.S.2. Results G-l 7
G.9. PBPK-model uncertainty analysis of unit risk estimates G-37
G.10. References G-39
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G.l. Data Sources
TCE cancer endpoints were identified in Maltoni et al. (1986), NCI (1976), NTP (1988,
1990), Fukuda et al. (1983) and Henschler et al. (1980). These data were reviewed and tabulated
in spreadsheets, and the numbers were verified. We tabulated all endpoint data identified by
authors as having a statistically significant response to dose, and we also reviewed data that had
marginally significant trends with dose. For all endpoints for which we present dose-response
model estimates, we verified trends using the Cochran-Armitage or the Poly-3 test.
G.l.l. Numbers at Risk
The numbers of animals at risk are not necessarily those used by the authors; instead, as
the number at risk, we used the number alive at 52 weeks (if the first cancer of the type of
interest was observed at later than 52 weeks) or the number alive at the week when the first
cancer of the type of interest was observed. In general, the data from Maltoni et al. (1986) were
presented in this way, in their tables titled "Incidence of the different types of tumors referred to
specific corrected numbers." In a few cases in Maltoni et al. (1986), the time of first occurrence
was later than 52 weeks, so we used an alternative number at risk from another column (for
another cancer) in the same table having a first occurrence close to 52 weeks. For NTP (1988,
1990) and for NCI (1976), the week of the first observation and the numbers alive at that week
were determined from the appendix tables. For Fukuda et al. (1983), we used the reported
"effective number of mice" in their Table 2, which is consistent with numbers alive at 40-42
weeks (when the first tumor, a thymic lymphoma, was observed) in their mortality curve. For
Henschler et al. (1980), we used the number of mice alive at week 36 (from their Figure 1),
which is when the first tumor was observed (according to their Figure 2).
G.1.2. Cumulative Incidence
Maltoni et al. (1986) conducted a lifetime study, in which rodents were exposed for 104
weeks (rats) or 78 weeks (mice), and allowed to live until they died 'naturally.' Maltoni et al.
(1986) reported cumulative incidence on this basis, and it was not possible for us to determine
incidence at any fixed time such as 104 weeks on study. For Henschler et al. (1980), we used the
number of mice with tumors observed by week 104 (their Figure 2). We used the cumulative
incidence reported by Fukuda et al. (1983) at 107 weeks (after 104 weeks of exposure). For the
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NCI (1976) and NTP (1988, 1990) studies, we used the reported cumulative incidence at 103 to
107 weeks (study time varied by study and species).
G.2. Internal Dose Metrics and Dose Adjustments
PBPK modeling was used to estimate levels of dose metrics corresponding to different
exposure scenarios in rodents and humans (Section 3.5). The selection of dose metrics for
specific organs and endpoints is discussed under Section 5.2. Internal dose metrics were selected
based on applicability to each major affected organ. The dose metrics used with our cancer
dose-response analyses are shown in the table below.
Table G.2.1 Internal dose metrics used in dose-response analyses, identified by "X".
The PBPK model requires the rodent body weight as an input. For most of the studies,
we used central estimates specific to each species, strain, and sex (and sub-study). These were
estimated by medians of body weights digitized from graphics in Maltoni et al. (1986), by
medians of weekly averages in NTP (1990, 1988), and by averages over the study duration of
weekly mean body weights tabulated in NCI (1976).
For the studies by Fukuda et al. (1983) and Henschler et al (1980), mouse body weights
were not available. After reviewing body weights reported for similar strains by two
laboratories1 and in the other studies reported for TCE, we concluded that a plausible range for
lifetime average body weight is 20 - 35 gm, with a median near 28 gm. For these two studies, we
computed internal dose metrics for these three average body weights (20, 28, and 35 gm). We
then evaluated the percentage differences between the internal dose metrics for the intermediate
body weight (BW) of 28 gm and the low and high average BW of 20 gm and 35 gm. Internal
1 http://phenome.iax.org/pub-
cgi/phenome/mpdcgi?rtn=meas%2Fdatalister&rea=Cbodv+weight&pan=2&noomit=&datamode=measavg.
http://www.hilltoplabs.com/public/growth.html.
dose.metric.units
ABioactDCVCBW34 (mg/wk-kgA3/4)
Liver Lung Kidney Other
0 0 X 0
0 0 X 0
X 0 0 0
OX 0 0
ox ox
0 0 XX
XX 0 0
AMetGSHBW34 (mg/wk-kgA3/4)
AMetLivl BW34 (mg/wk-kgA3/4)
AMetLngBW34 (mg/wk-kgA3/4)
AUCCBId (mg-hr/l-wk)
TotMetabBW34 (mg/wk-kgA3/4)
TotOxMetabBW34 (mg/wk-kgA3/4)
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dose metrics were little affected by choice of body weight. For all dose metrics, the differences
were less than ±13%.
The medians (from the MCMC posterior distribution) for each of the dose metrics for the
rodent were used in quantal dose-response analyses. The median is probably the most
appropriate posterior parameter to use as a dose metric, as it identifies a 'central' measure and it
is also a quantile, making it more useful in nonlinear modeling. The 'multistage' dose-response
functions are non-linear. We are interested in estimating the expected response. The expected
value of a nonlinear function of dose is under- or over-estimated when the mean (expected value)
of the dose is used, depending on whether the function is concave or convex. (This is Jensen's
Inequality: for a real convex function f(X), f[E(X)] <= E[f(X)]). For the dose-response function,
we are interested in E[f(X)], so using E(X) (estimated by the posterior mean) as the dose metric
will not necessarily predict the mean response. Using the posterior median rather than the mean
as the dose metric should lead to a response function that is closer to the median response.
However, if the estimated dose-response function is close to linear, this source of distortion may
be small and the mean response might be predicted reasonably well by using the posterior mean
as the dose metric. The mean and median are expected to be rather different because the
posterior distributions are skewed and approximately lognormal. Therefore, we compared
results based on the posterior median and the posterior mean dose metric before deciding to use
the median.
G.3. Dose Adjustments for Intermittent Exposure
The nominal applied dose was adjusted for exposure discontinuity (e.g., exposure for 5
days per week and 6 hours per day reduced the dose by the factor (5/7)*(6/24)), and for exposure
durations less than full study time (up to 2 years) (e.g., the dose might be reduced by a factor [78
wk / 104 wk]). The PBPK dose metrics took into account the daily and weekly discontinuity to
produce an equivalent dose for continuous exposure. The NCI (1976) gavage study applied one
dose for weeks 1-12 and another, slightly different dose for weeks 13-78; PBPK dose metrics
were produced for both dose regimes and then time-averaged (e.g., average dose = (12/78) x D1
+ (66/78) x D2). For Henschler et al. (1980), Maltoni et al. (1986), and NCI (1976), a further
adjustment of (exposure duration/study duration) was made to account for the fact that exposures
ended prior to terminal sacrifice, so that the dose metrics reflect average weekly values over the
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exposure period. Finally, for NCI (1976), the dose metrics were then adjusted for early sacrifice
(at 91 weeks rather than 104 weeks) by a factor of (91 wk /104 wk)3.2
G.4. Rodent to Human Dose Extrapolation
Adjustments for rodent-to-human extrapolation were applied to the final results - the
BMD, BMDL, and cancer slope factor (potency), which is calculated as BMR/BMDL, e.g.,
0.10/BMDLio.
For the PBPK dose metrics, a ratio between human and laboratory animal internal dose
was determined by methods described in Section 3.5. The cancer slope factor is relevant only for
very low extra risk (typically on the order of 10"4 to 10"6), thus very low dose, and it was
determined that the relation between human and animal internal dose was linear in the low-dose
range for each of the dose metrics used, hence this ratio was multiplied by the animal dose (or
divided into the cancer slope factor) to extrapolate animal to human dose or concentration.
For the experimentally applied dose, default interspecies extrapolation approaches were
used. These are provided for comparison to results based on PBPK metrics. To extrapolate
animal inhalation exposure to human inhalation exposure, the "equivalent" human exposure
concentration (i.e., the exposure concentration in humans that is expected to give the same level
of response that was observed in the test species) was assumed to be identical to the animal
inhalation exposure concentration, i.e., "ppm equivalence." This assumption is consistent with
EPA recommendations (U.S. EPA, 1994) for deriving a human equivalent concentration for a
Category 3 gas for which the blood:air partition coefficient in laboratory animals is greater than
that in humans (see Section 3.1 for discussion of the TCE blood:air partition coefficient). To
extrapolate animal oral exposure to equivalent human oral exposure, animal dose was scaled up
by body weight to the 3/4-power using the factor (BWHuman / BWAnimai)A0.75. To extrapolate
animal inhalation exposure to human oral exposure, we used the following equation3:
Animal, equivalent oral intake, mg/kg/day =
ppm * [MWtce / 24.45 4] * MV * (60 min/hr) * (103 mg/g) * [24hr / BWkg ]
with units: ppm * [g/mol ^ L/mol ] * L/min * (min/hr) * (mg/g ) * [ hr/day ^ kg ]
2 For studies of less than 2 years (i.e., with terminal kills before 2 years), the doses are generally adjusted by the
study length ratio to a power of 3 (i.e., a factor [length of study in wks/104 wks]3) to reflect the fact that the animals
were not observed for the full standard lifetime (U.S. EPA, 1980).
3 ToxRisk version 5.3, © 2000-2001 by the KS Crump Group, Inc.
4
Molecular weight of TCE is 131.39; there are 24.45 liters of perfect gas per g-mol at standard temperature &
pressure, USEPA (1994).
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which reduces to ppm * [ 7.738307 * MV / BW.kg ]
where
ppm = Animal inhalation concentration, 1/106 , unitless
MV = minute volume (breathing rate) at rest, liters / minute.
Minute volume (MV) was estimated using equations from U.S. EPA (1994, p.4-27),
Mouse: ln(MV) = 0.326 + 1.05 * ln(BWkg)
Rat: ln(MV) = -0.578 + 0.821 * ln(BWkg) .
Animal equivalent oral intake was converted to human equivalent oral intake by
multiplying by the rodent to human ratio of body weights to the power +0.255.
To extrapolate animal oral exposure to equivalent human inhalation exposure, we
reversed the calculation above to extrapolate the animal inhalation exposure.
G.5. Combining data from related experiments in Maltoni et al. (1986)
Data from Maltoni et. al. (1986) required decisions by us regarding whether to combine
related experiments for certain species and cancers.
In experiment BT306, which used B6C3F1 mice, males experienced unusually low
survival, reportedly because of the age of the mice at the outset and resulting aggression. The
protocol was repeated (for males only), with an earlier starting age, as experiment BT306bis, and
male survival was higher (and typical for such studies). The rapid male mortality in experiment
BT306 apparently censored later-developing cancers, as suggested by the low frequency of liver
cancers for males in BT306 as compared to BT306bis. Data for the two experiments clearly
cannot legitimately be combined. We therefore used only experiment BT306bis males in our
analyses.
Experiments BT304 and BT304bis, on rats, provide evidence in male rats of leukemia,
carcinomas of the kidney, and testicular (Leydig cell) tumors, and provide evidence in female
rats for leukemia. Maltoni et al. (1986, p.46) stated "Since experiments BT304 andBT 304bis
on Sprague-Dawley rats were performed at the same time, exactly in the same way, on animals
5 Find whole animal intake from mg/kg-day * BWAmmai • Scale this allometrically by (BWHuman / BW,\mi„;,i)A0.75 to
extrapolate whole human intake. Divide by human body weight to find mg/kg-day for the human. The net effect is
Animal mg/kg-day * (BWAnllIllli / BW, )A0.25 = Human mg/kg-day.
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1 of the same breed, divided by litter distribution within the two experiments, they have been
2 evaluated separately and comprehensivelyWe also analyzed the data separately and in
3 combination.
4 The data and modeling results for these tumors in the BT304 and BT304bis experiments
5 is tabulated below. We decided that it was best to combine the data for the two experiments.
6 There were no consistent differences between experiments, and no firm basis for selecting one of
7 them. Our final analyses are therefore based on the combined numbers and tumor responses for
8 these two experiments.
9
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Table G.5.1. Experiments BT304 and BT304bis, female Sprague-Dawley rats, Maltoni et
al. (1986)
Number alive is reported for week of first tumor observation in either males or females 1
These data were not used for dose-resoonse modeling because there is no consistent trend
(for the combined data, there
is no significant trend by the Cochran-Armitage test, and no
significant differences between control and dose groups by Fisher's exact test).
Exposure
Concen.
(ppm)
No.
No. rats
Proportion
Multistage model fit statistics 2
alive
with
this
cancer
with
cancer
Model
order
P
value
AIC
BMDio
BMDL io
Experiment BT304, female rats, leukemias, N alive at 7 weeks
0
105
7
0.067
No adequately fitting model
100
90
6
0.067
300
90
0
0.000
600
90
7
0.078
Experiment BT304bis, female rats, leukemias, N a
ive at 7 weeks
0
40
0
0.000
1
0.202
70.4
127
58.7
100
40
3
0.075
300
40
2
0.050
600
40
4
0.100
Experiments BT304 & BT304bis, female rats, leukemias, combined data
0
145
7
0.048
3
0.081
227
180
134
100
130
9
0.069
300
130
2
0.015
600
130
11
0.085
1 First tumor occurrences were not reported separately by sex
2 Models of orders 3 were fitted; the highest-order non-zero coefficient is reported in
column "Model order". BMDL was estimated for extra risk of 0.10 and confidence level
0.95. Exposure concentrations were multiplied by (7/24)*(5/7) = 0.20833 before fitting
the models, to adjust for exposure periodicity (i.e., the time-averaged concentrations were
about 20% of the nominal concentrations).
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1
Table G.5.2. Experiments BT304 and BT304bis, male Sprague-Dawley rats, Maltoni et al.
(1986): leukemias.
Number alive is reported for week of first tumor observation in either
males or females 1
Exposure
Concen.
(ppm)
No.
No. rats
Proportion
Multistage model fit statistics 2
alive
with
this
with
cancer
Model
order
P
value
AIC
BMD io
BMDL io
cancer
Experiment BT304, male rats, leukemias, N alive at 7 wee
cs
0
95
6
0.063
1
0.429
238
NA
NA
100
90
10
0.111
300
90
11
0.122
600
89
9
0.101
Experiment BT304bis, male rats, leukemias, N alive at 7 weeks
0
39
3
0.077
3
0.979
102
143
71.9
100
40
3
0.075
300
40
3
0.075
600
40
6
0.150
Combined data for BT304 & BT304bis, male rati, leukemias
0
134
9
0.067
1
0.715
337
269
111
100
130
13
0.100
300
130
14
0.108
600
129
15
0.116
1 First tumor occurrences were not reported separately by sex
2 Models of orders 3 were fitted; the highest-order non-zero coefficient is reported in
column "Model order". BMDL was estimated for extra risk of 0.10 and confidence level
0.95. Exposure concentrations were multiplied by (7/24)*(5/7) = 0.20833 before fitting
the models, to adjust for exposure periodicity (i.e., the time-averaged concentrations were
about 20% of the nominal concentrations). "NA" indicates the BMD or BMDL could not
be solved because it exceeded the highest dose.
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Table G.5.3. Experiments BT304 and BT304bis, male Sprague-Dawley rats, Maltoni et al.
(1986): kidney adenomas + carcinomas. Number alive is reported for week of first tumor
observation in either males or females 1
Exposure
Concen.
(ppm)
No.
No. rats
Proportion
Multistage model fit statistics 2
alive
with
this
cancer
with
cancer
Model
order
P
value
AIC
BMD io
BMDL io
Experiment BT304 male rats, kidney adenomas + carcinomas, N alive at 47
weeks
0
87
0
0.000
3
0.318
50.1
173
134
100
86
1
0.012
300
80
0
0.000
600
85
4
0.047
Experiment BT304bis, male rats, kidney adenomas + carcinomas, N
alive at
53 weeks
0
34
0
0.000
3
0.988
13.0
266
173
100
32
0
0.000
300
36
0
0.000
600
38
1
0.027
Combined data for BT304 & BT304bis, male rats, kidney adenomas
+
carcinomas
0
121
0
0.000
3
0.292
60.5
181
144
100
118
1
0.008
300
116
0
0.000
600
123
5
0.041
1 First tumor occurrences were not reported separately by sex
2 Models of orders 3 were fitted; the highest-order non-zero coefficient is reported in
column "Model order". BMDL was estimated for extra risk of 0.10 and confidence level
0.95. Exposure concentrations were multiplied by (7/24)*(5/7) = 0.20833 before fitting
the models, to adjust for exposure periodicity (i.e., the time-averaged concentrations were
about 20% of the nominal concentrations). "NA" indicates the BMD or BMDL could not
be solved because it exceeded the highest dose.
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Table G.5.4. Experiments BT304 and BT304bis, male Sprague-Dawley rats, Maltoni et al.
(1986): testis, Leydig cell tumors. Number alive is reported for week of first tumor
observation1.
Exposure
Concen.
(ppm)
No.
No. rats
Proportion
Multistage model fit statistics 2
alive
with
this
with
cancer
Model
order
P
value
AIC
BMD io
BMDL io
cancer
Experiment BT304, male rats, Leydig cell tumors, N alive at 47 weeks
0
87
5
0.057
1
0.0494
309
41.5
29.2
100
86
11
0.128
300
80
24
0.300
600
85
22
0.259
Experiment BT304bis, male rats, Leydig cell tumors , N alive at 53 weeks
0
34
1
0.029
1
0.369
117
54.5
30.9
100
32
5
0.156
300
36
6
0.167
600
38
9
0.237
Combined data for BT304 & BT304bis, male rati, Leydig cell tumors
0
121
6
0.050
1
0.0566
421
44.7
32.7
100
116
16
0.138
300
116
30
0.259
600
122
31
0.254
1 Numbers alive reported for weeks as close as possible to week 52 (first tumors observed
at weeks 81, 62, respectively, for the two experiments).
2 Models of orders 3 were fitted; the highest-order non-zero coefficient is reported in
column "Model order". BMDL was estimated for extra risk of 0.10 and confidence level
0.95. Exposure concentrations were multiplied by (7/24)*(5/7) = 0.20833 before fitting
the models, to adjust for exposure periodicity (i.e., the time-averaged concentrations were
about 20% of the nominal concentrations). "NA" indicates the BMD or BMDL could not
be solved because it exceeded the highest dose.
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G.6. Dose-Response Modeling Results
Using BMDS software, we fitted the multistage quantal model using the applicable dose
metrics for each combination of study, species, strain, sex, organ, and BMR (extra risk) value
under consideration. A multistage model of order one less than the number of dose groups (g)
was fitted. This means that in some cases the fitted model could be strictly nonlinear at low dose
(estimated coefficient "bl" was zero), and in other cases, higher-order coefficients might be
estimated as zero so the resulting model would not necessarily have order (#groups-l). Because
more parsimonious, lst-order models often fit such data well, based on our extensive experience
and that of others (Nitcheva et al., 2007), if the resulting model was not a lst-order multistage, we
then also fitted lower-order models, down to a lst-order multistage model. This permitted us to
screen results efficiently.
The document Appendix.linked.files\AppG.Cancer.Rodents.Plots.TCE.DRAFT.pdf
shows the fitted model curves. The graphics include observations (as proportions, i.e.,
cumulative incidence divided by number at risk), the estimated multistage curve (solid red line)
and estimated BMD, with a BMDL. Vertical bars show 95% confidence intervals for the
observed proportions. Printed above each plot are some key statistics (necessarily rounded) for
model goodness of fit and estimated parameters. Printed in the plots at upper left are the BMD
and BMDL for the rodent data, in the same units as the rodent dose. Within the plot at lower
right are human exposure values (BMDL and cancer slope factor for continuous inhalation and
oral exposures) corresponding to the rodent BMDL. For applied doses, the human equivalent
values were calculated by "default" methods6, as discussed above, and then only for the same
route of exposure as the rodent, and they are in units of rodent dose. For internal dose metrics,
the human values are based upon the PBPK rodent-to-human extrapolation, as discussed in
Section 5.2.1.2.
The document Appendix.linked.files\AppG.Cancer.Rodents.Results.TCE.DRAFT.pdf
presents the data and model summary statistics, including goodness-of-fit measures (Chi-square
goodness-of-fit P-value, AIC), parameter estimates, BMD, BMDL, and "cancer slope factor"
("CSF"), which is the extra risk divided by the BMDL. Much more descriptive information
appears also, including the adjustment terms for intermittent exposure, and the doses before
applying those adjustments. The group numbers "GRP" are arbitrary, and are the same as GRP
6 For oral intake, dose (BMDL) is multiplied by the ratio of animal to human body weight (60 kg female, 70 kg
male) taken to the 'A power. For inhalation exposures, ppm equivalence is assumed.
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1 numbers in the plots. There is one line in this table for each dose-response graph in the
2 preceding document. Input data for the analyses are in the file
3 Appendix.linked.files\AppG.Cancer.Rodents.Input.Data.TCE.DRAFT.pdf. Finally, the values
4 and model selections for the results used in Section 5.2 are summarized in the file
5 Appendix.linked.files\AppG.Cancer.Rodents.model.selections.TCE.DRAFT.pdf (primary dose
6 metrics in bold).
7 G.7. Modeling to account for dose groups differing in survival times
8 Differential mortality among dose groups can potentially interfere with (i.e., censor) the
9 occurrence of late-appearing cancers. Usually the situation is one of greater mortality rates at
10 higher doses, caused by toxic effects, or sometimes by cancers other than the cancer of interest.
11 Statistical methods of estimation (for the cancer of interest) in the presence of competing risks
12 assume uninformative censoring.
13 For bioassays with differential early mortality occurring primarily before the time of the
14 1st tumor or 52 weeks (whichever came first), the effects of early mortality were largely
15 accounted for by adjusting the tumor incidence for animals at risk, as described above, and the
16 dose-response data were modeled using the multistage model.
17 If, however, there was substantial overlap between the appearances of cancers and
18 progressively differential mortality among dose groups, it was necessary to apply methods that
19 take into account individual animal survival times. Two such methods were used here: time-to-
20 tumor modeling and the poly-3 method of adjusting numbers at risk. We identified three such
21 studies, all with male rats (see Table 5.2.3). Using both survival-adjustment approaches, BMDs
22 and BMDLs were obtained and unit risks derived. A comparison of the results for the three
23 datasets and for various dose metrics is presented in Section 5.2.1.3.
24 G.7.1. Time-to-tumor modeling
25 The first approach we used to take into account individual survival times was application
26 of the multistage Weibull (MSW) time-to-tumor model. This model has the general form
27
P(d,t) = 1 - exp[-(q0 + qid + q2d2 + ... + qkdk) * (t - t0)z],
28
29 where P(d,t) represents the probability of a tumor by age t for dose d, and parameters z >1, to > 0,
30 and q; > 0 for i = 0,1,...,k, where k = the number of dose groups; the parameter to represents the
31 time between when a potentially fatal tumor becomes observable and when it causes death. The
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MSW model likelihood accounts for the left-censoring inherent in "Incidental" observations of
non-fatal tumors discovered upon necropsy and the right-censoring inherent in deaths not caused
by fatal tumors. All of our analyses used the model for incidental tumors, which has no t0 term,
and which assumes that the tumors are nonfatal (or effectively so, to a reasonable
approximation). This seems reasonable because the tumors of concern appeared relatively late in
life and there were multiple competing probable causes of death (esp., toxic effects) operating in
these studies (also note that cause of death was not reported by the studies we used). It is
difficult to formally evaluate model fit with this model because there is no applicable goodness-
of-fit statistic with a well-defined asymptotic distribution. However, plots of fitted vs. observed
responses were examined.
A computer program ("MSW") to implement the multistage Weibull time-to-tumor
model was designed, developed and tested for EPA by Battelle Columbus (Ohio). The MSW
program obtains maximum likelihood estimates for model parameters and solves for the BMDL
(lower confidence limit for BMD) using the profile-likelihood method. The model, with
documentation for methodology (statistical theory and estimation, and numerical algorithms) and
testing, was externally reviewed by experts in June, 2007. Reviews were generally positive and
confirmed that the functioning of the computer code has been rigorously tested. (EPA and
Battelle confirmed that MSW gave results essentially identical to those of "ToxRisk", a program
no longer commercially issued or supported). EPA's BMDS web site provided reviewers'
comments and EPA's responses.7 The MSW program and reports on statistical & computational
methodology and model testing will be made available in mid 2009 (after implementing some
changes to reporting features and error-handling).
Results of this modeling are shown in the file
Appendix.linked.files\AppG.Cancer.Rodents.TimetoTumor.Results.TCE.DRAFT.pdf.
G.7.2. Poly-3 calculation of adjusted number at risk
To obtain an independent estimate of a POD using different assumptions, it was thought
desirable to compare time-to-tumor modeling to an alternative survival-adjustment technique,
"poly-3 adjustment" (Portier and Bailer, 1989), applied to the same data. This technique was
used to adjust the tumor incidence denominators based on the individual animal survival times.
The adjusted incidence data then served as inputs for EPA's BMDS multistage model, and
multistage model selection was conducted as described in Section 5.2.
7
At http://www.epa.gov/ncea/bmds/response.html under title "2007 External Review of New Quantal Models"; use
links to comments and responses.
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A detailed exposition is given by Piegorsch and Bailer (1997), Chapter 6.3.2. Each
tumor-less animal is weighted by its fractional survival time (survival time divided by the
duration of the bioassay) raised to the power of 3 to reflect the fact that animals are at greater
risk of cancer at older ages. Animals with tumors are given a weight of 1. The sum of the
weights of all the animals in an exposure group yields the effective survival-adjusted
denominator. We assumed the 'default' power of 3 (thus, "poly-3"), which was found to be
representative for a large number of cancer types (Portier et al., 1986). Algebraically,
Nadj - L w; where w, = 1 if tumor is present and
w; = (t; /T)3 if tumor is absent at time of death (t,),
and T = duration of study. N was rounded to the nearest integer.8
Calculations are reproduced in the spreadsheets above.
G.8. Combined risk from multiple tumor sites
For bioassay s that exhibited more than one type of tumor response in the same sex and
species (these studies have a row for "combined risk" in the "Endpoint" column of Table 5.2.3,
Section 5.2), the cancer potency for the different tumor types combined was estimated. The
combined tumor risk estimate describes the risk of developing tumors for any (not all together)
of the tumor types that exhibited a TCE-associated tumor response; this estimate then represents
the total excess cancer risk. The model for the combined tumor risk is also multistage, with the
sum of the stage-specific multistage coefficients from the individual tumor models serving as the
stage-specific coefficients for the combined risk model (i.e., for each q., q. ,. , = q. + q. + ...
° r v ' V ni [combined] nil ni2
+ q.k, where the q.s are the coefficients for the powers of dose and k is the number of tumor types
being combined) (Bogen, 1990; NRC, 1994). This model assumes that the occurrences of two or
more tumor types are independent. The resulting model equation can be readily solved for a
given BMR to obtain an MLE (BMD) for the combined risk. However, the confidence bounds
for the combined risk estimate are not calculated by available modeling software. Therefore, we
used a Bayesian approach to estimate confidence bounds on the combined BMD. This approach
was implemented using the freely available WinBugs software (Spiegelhalter et al., 2003), which
g
Notice that the assumptions required for significance testing and estimating variances of parameters are changed
by this procedure. The Williams-Bieler variance estimator is described by Piegorsch and Bailer, 1997. Our
multistage modeling did not take this into account, so the resulting BMDL (lower confidence limit of BMD) may be
somewhat lower than could be obtained by more laborious calculations.
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applies Markov chain Monte Carlo computations. Use of WinBugs has been demonstrated for
derivation of a distribution of BMDs for a single multistage model (Kopylev et al., 2007) and can
be straightforwardly generalized to derive the distribution of BMDs for the combined tumor
load.
G.8.1. Methods
G.8.1.1. Single tumor sites
Cancer dose-response models were fitted to data using BMDS software. These were
multistage models with coefficients constrained to be non-negative. The order of model fitted
was g-1, where g is the number of dose groups. For internal dose metrics, we used the values
shown in tables above.
The multistage model was modified for EPA.NCEA by Battelle (under contract
EPC04027) to provide model-based estimates of extra risk at a user-specified dose and profile-
likelihood confidence intervals for that risk. Thus, we were able to report confidence intervals for
extra risk in addition to BMDs.
G.8.1.2. Combined risk from multiple tumor sites
The multistage model identified by BMDS (example: gamma = 0, beta.l > 0, beta.2 = 0,
beta.3 >0) was used in a WinBUGs script to generate posterior distributions for model
parameters, the benchmark dose (BMD) and extra risk at the same dose specified for the BMDS
estimates. We used a burn-in of length 10,000, then 100,000 updates, and thinned the latter to
every 10th update for sample monitoring. From a WinBUGs run, we archived the sample
histories, posterior distribution plots, summary statistics, and codas.
Codas were then imported to R and processed using R programs to compute BMD, and
the extra risk at a specific dose, for each tumor type. We also computed BMD and extra risk for
the combined risk function (assuming independence) following Bogen.9 Results were
summarized as percentiles, means and modes (of the smoothed posterior distributions). We also
summed the extra risks across tumor types at a specific dose (we used 10 or 100).
BMDLs for rodent internal doses, reported below, were converted to human external
doses using the conversion factors in the following Tables (based on PBPK model described in
Section 3.5).
Table G.8.1
Rodent to human conversions for internal dose metric TotOxMetabBW34
9 Bogen, K.T. 1990. Uncertainty in Environmental Health Risk Assessment. London: Taylor & Francis [Chapter
IV]. NRC (National Research Council). 1994. Science and Judgement in Risk Assessment. Washington, DC:
National Academy Press [Chapter 11, Appendix 1-1, Appendix 1-2]
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Route
Inhal, ppm
Oral, mg/kg-day
sex
F
M
F
M
human (mean)
9.843477
9.702822
15.72291
16.4192
Table G.8.2
Rodent to human conversions for internal dose metric TotMetabBW34
route
Inhal, ppm
F
sex
human (mean)
11.84204
M
Oral, mg/kg-day F
M
11.69996
18.76327
19.6
Application of rodent to human conversion factors:
Given rodent internal dose D in some units of TotOxMetabBW34, divide by tabled value Y
above to find human exposure in ppm or mg/kg-d.
Example: ppm (human) = D(rodent) / Y
ppm (human female mean) = 500 (internal units) / 9.843477
= 50.80 ppm
G.8.2. Results
Results follow in this order:
Applied doses
NCI, 1976, Female B6C3F1 mice, oral gavage, Liver & Lung tumors and Lymphomas
Maltoni 1986 Female B6C3F1 mice, inhalation (expt. BT306), Liver & Lung tumors
Maltoni 1986 Male Sprague-Dawley rats, inhalation (expt. BT304), Kidney tumors, Testis
Leydig Cell tumors, and Lymphomas
Internal Doses
NCI, 1976, Female B6C3F1 mice, oral gavage, Liver & Lung tumors and Lymphomas
Maltoni 1986 Female B6C3F1 mice, inhalation (expt. BT306), Liver & Lung tumors
Maltoni 1986 Male Sprague-Dawley rats, inhalation (expt. BT304), Kidney tumors, Testis
Leydig Cell tumors, and Lymphomas
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NCI, 1976: Female B6C3F1 mice
- applied doses : DATA
Dose*
N **
Liver
hepatocellular
carcinomas
Lung adenomas +
carcinomas
Hematopoietic
Lymphomas +
Sarcomas
0
18
0
1
1
356.4
45
4
4
5
713.3
41
11
7
6
* Doses adjusted by a factor 0.41015625, accounting for exposure 5/7 days/week, exposure
duration 78/91 weeks, and duration of study (91/104)A3. Averaged applied gavage exposures were:
low-dose 869 mg/kg-day, high-dose 1739 mg/kg-day. ** Numbers at risk are the smaller of (a) time
of first tumor observation or (b) 52 weeks on study
2
NCI, 1976: Female B6C3F1 mice - applied doses : MODEL SELECTION
comparison of model fit statistics for multistage models of increasing order
Tumor Site
Model
Order,
* selected
Coeff.
estimates
equal
zero
AIC
Largest*
Scaled
Residual
Goodness
of Fit P-
value
Liver
2
Y
78.68
0
1
1*
Y
77.52
-0.711
0.6698
Lung
2
NA
78.20
0
1
1*
NA
76.74
-0.551
0.4649
Lymphomas + sarcomas
2
(32
77.28
0.113
0.8812
1*
NA
77.28
0.113
0.8812
* largest in absolute value
3
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NCI, 1976: Female B6C3F1 mice - applied doses : BMD AND RISK ESTIMATES (inferences for
BMR of 0.05 extra risk at 95% confidence level)
Liver
hepatocellular
carcinomas
Lung adenomas +
carcinomas
Hematopoietic
Lymphomas +
Sarcomas
Parameters used in model
qO, ql
qO, ql
qO, ql
P-value for BMDS model
0.6698
0.6611
0.8812
BMD05 (from BMDS)
138.4
295.2
358.8
BMD05 (median, mode - WinBugs)
155.5, 135.4
314.5,212.7
352.3,231.7
BMDL (BMDS)*
92.95
144.3
151.4
BMDL (5th%-ile, WinBugs)
97.48
150.7
157.7
BMD05 for Combined Risk (median,
mode, from WinBugs)
84.99, 78.95
BMDL for Combined Risk (5th%-ile,
WinBugs)
53.61
BMDS maximum likelihood risk estimates
Risk at dose 100
0.03640
0.01722
0.01419
Upper 95% C.L.
0.05749
0.03849
0.03699
Sum of risks at dose 100
0.06781
WinBUGs Bayes risk estimates
Risk at dose 100: mean, median
0.0327, 0.0324
0.0168,0.0161
0.0152, 0.0143
Upper 95% C.L.
0.0513
0.0334
0.0319
Comb, risk at dose 100 mean, median
0.06337, 0.0629
Comb, risk at dose 100, upper 95% CL
0.09124
* all confidence intervals are at 5% (lower) or 95% (upper) level, one-sided
2
3
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Figure G.8.1. Combined and Individual Tumor Extra Risk Functions
4
5
6
7
Extra Risk
CM
O
oo
o
o
o
o
o
o
o
vertical solid, BMDc
vertical dash, BMCLc
0
50
100
150
200
Dose
Figure G.8.2. Distribution of BMDc for combined risk
Density
0 200 400 600 800 1000
N = 300000 Bandwidth = 1.602
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Maltoni 1986 B6C3F1 female mice inhalation expos - applied doses
Dose*
Liver hepatomas
/N**
Lung adenomas +
carcinomas /N**
0
3/88
2/90
15.6
4/89
6/90
46.9
4/88
7/89
93.8
9/85
14/87
* Doses adjusted by a factor 0.133928571, accounting for exposure 7/24 hours/day x 5/7
days/week, and exposure duration 78/104 weeks. Applied doses were 100, 300, and 600 ppm. **
Numbers at risk are the smaller of (a) time of first tumor observation or (b) 52 weeks on study
2
Maltoni 1986 B6C3F1 female mice - applied doses : MODEL
SELECTION comparison of model fit statistics for multistage models of
increasing order
Tumor Site
Model
Order,
* selected
Coeff.
estimates
equal
zero
AIC
Largest*
Scaled
Residual
Goodness
of Fit P-
value
Liver
3
(32
154.91
0.289
0.7129
2
PI
153.02
0.330
0.8868
1*
NA
153.47
-0.678
0.7223
Lung
3
(32
195.91
0.741
0.3509
2
(32
193.91
0.714
0.6471
1*
NA
193.91
0.714
0.6471
* largest in absolute value
3
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Maltoni 1986 B6C3F1 female mice inhalation exposure - applied doses (inferences for 0.05 extra
risk at 95% level)
Liver hepatomas
Lung adenomas +
carcinomas
Parameters used in model
qO, ql
qO, ql
P-value for BMDS model
0.7223
.06471
BMD05 (from BMDS)
72.73
33.81
BMD05 (median, mode - WinBugs)
71.55,56.79
34.49,31.65
BMDL (BMDS)*
37.13
21.73
ms_combo.exe BMD05c, BMDLc
32.12, 16.22
BMD05 (5th %-ile, WinBugs)
37.03
22.07
BMD05 for Combined Risk (median,
mode, from WinBugs)
23.07, 20.39
BMDL for Combined Risk (5th %-ile,
WinBugs)
15.67
BMDS maximum likelihood risk estimates
Risk at dose 10
0.0070281
0.0150572
Upper 95% C.L.
0.0151186
0.0250168
Sum of risks at dose 10
0.0220853
WinBUGs Bayes risk estimates: means (medians)
Risk at dose 10: mean, median
0.007377,0.007138
0.01489, 0.01476
Upper 95% C.L.
0.01374
0.02
Comb, risk at dose 10 : mean, median
0.02216, 0.02198
Comb, risk at dose 10: upper 95% CL
0.03220
* all confidence intervals are at 5% (lower) or 95% (upper) level, one-sided
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Figure G.8.3. Combined and Individual Tumor Extra Risk Functions
Extra Risk
vertical solid, BMDc
vertical dash, BMDLc
o
CO
o
o
CM
o
o
o
o
o
o
0
50
100
150
200
Dose
Figure G.8.4. Distribution of BMDc for combined risk
Density
0 100 200 300
N = 300000 Bandwidth = 0.4731
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Maltoni Sprague-Dawley Male Rats - applied doses
Dose*
Kidney
adenenomas +
carcinomas /N**
Leukemias /
N**
Testis, Leydig
Cell Tumors /
N**
0
0/121
9/134
6/121
20.8
1/118
13/130
16/116
62.5
0/116
14/130
30/116
125
5/123
15/129
31/122
* Doses adjusted by a factor 0.208333333, accounting for for exposure 7 hours/day x 5/7
days/week. Applied doses were 100, 300, and 600 ppm. ** Numbers at risk are the smaller of (a)
time of first tumor observation or (b) 52 weeks on study
2
Maltoni Sprague-Dawley Male Rats - applied doses : MODEL
SELECTION comparison of model fit statistics for multistage models of
increasing order
Tumor Site
Model
Order*
Coeff.
estimates
equal
zero
AIC
Largest+
Scaled
Residual
Goodness
of Fit P-
value
Kidney
3
(31,(32
60.55
1.115
0.292
2
Y
61.16
-1.207
0.253
1*
Y
59.55
-1.331
0.4669
Leukemia
3
(32, (33
336.8
0.537
0.715
2
(32
336.8
0.537
0.715
1
NA
336.8
0.537
0.715
dropping high dose
2
(32
243.7
0.512
0.529
1*
NA
243.7
0.512
0.529
Testis
3
(32, (33
421.4
-1.293
0.057
2
(32
421.4
-1.293
0.057
1
NA
421.4
-1.293
0.057
dropping high dose
2
(32
277.6
0.291
0.728
1*
NA
277.6
0.291
0.728
* model order selected + largest in absolute value
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Maltoni Sprague-Dawley Male Rats - applied doses
Kidney
adenenomas +
carcinomas
Leukemia (high
dose dropped)
Testis, Leydig
Cell Tumors
(high dose
dropped)
Parameters used in models
qO, ql
qO, ql
qO, ql
P-value for BMDS model
0.4669
0.5290
0.7277
BMD01 (from BMDS)
41.47
14.5854
2.46989
BMD01 (median, mode - WinBugs)
46.00,35.71
12.32, 8.021
2.497, 2.309
BMDL (BMDS)*
22.66
5.52597
1.77697
BMDL (5th%-ile, WinBugs)
23.23
5.362
1.789
BMD01 for Combined Risk
(median, mode, from WinBugs)
1.960, 1.826
BMDL for Combined Risk (5th Vo-
ile, WinBugs)
1.437
BMDS maximum likelihood risk estimates
Risk at dose 10
0.0024208
0.0068670
0.0398747
Upper 95% C.L.
0.0048995
0.0202747
0.0641010
Sum of risks at dose 10
Risk at dose 1
0.0002423
0.0006888
0.0040609
Upper 95% C.L.
0.0004911
0.0020462
0.0066029
Sum of risks at dose 1
WinBUGs Bayes risk estimates: means (medians)
Risk at dose 10: mean, median
0.002302, 0.002182
0.008752,
0.008120
0.03961, 0.03945
Upper 95% C.L.
0.004316
0.01860
0.05462
Comb, risk at dose 10, mean,
median
0.05020, 0.04998
Comb, risk at dose 10, upper 95%
CL
0.06757
Risk at dose 1: mean median
2.305e-04, 2.184e-
04
8.800e-04,
8.150e04
0.004037,
0.004017
Upper 95% C.L.
4.325e-04
1.876e-03
0.005601
Comb, risk at dose 1, mean, median
0.005143,0.005114
Comb, risk at dose 1, upper 95% CL
0.006971
* all confidence intervals are at 5% (lower) or 95% (upper) level, one-sided
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Figure G.8.5. Combined and Individual Tumor Extra Risk Functions
Extra Risk
"vT
O - —
vertical solid, BMDc
vertical dash, BMDLc
CO
o
(N
6
o
o
o
0
20
40
60
80
100
Dose
Figure G.8.6. Distribution of BMDc for combined risk
Density
2
4
6
8
10
12
14
N = 300000 Bandwidth = 0.03059
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NCI, 1976: Female B6C3F1 mice - Internal Dose Metric (Total Oxidative Metabolism) : DATA
Internal Dose*
N **
Liver
hepatocellular
carcinomas
Lung adenomas +
carcinomas
Hematopoietic
Lymphomas +
Sarcomas
0
18
0
1
1
549.8
45
4
4
5
813.4
41
11
7
6
* Internal dose, Total Oxidative Metabolism, adjusted for body weight, units (mg/(wk-kgA3/4)).
Internal doses were adjusted by a factor 0.574219, accounting for exposure duration 78/91 weeks,
and duration of study (91/104)A3. Before adjustment, the median internal doses were: 957.48 and
1416.55 (mg/wk-kgA3/4). ** Numbers at risk are the smaller of (a) time of first tumor
observation or (b) 52 weeks on study
2
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comparison of model fit statistics for multistage models of increasing order
Tumor Site
BMD,
BMDL
Model
Order *
Coeff.
estimates
equal
zero
AIC
Largest+
Scaled
Residual
Goodness
of Fit P-
value
Liver
505,284
2*
y, P1
77.25
-0.594
0.7618
367, 245
1
Y
78.86
-1.083
0.3542
Lung
742, 396
2*
PI
76.33
-0.274
0.7197
780,380
1
NA
76.74
-0.551
0.4649
Lymphomas + sarcomas
870,389
2
NA
79.26
0
1
839,390
1*
NA
77.27
-0.081
0.9140
* model order selected + largest in absolute value
3
4
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NCI, 1976: Female B6C3F1 mice - Internal Dose Metric (Total Oxidative Metabolism) : BMD
AND RISK ESTIMATES (values rounded to 4 significant figures) (inferences for BMR of 0.05
extra risk at 95% confidence level)
Liver
hepatocellular
carcinomas
Lung adenomas +
carcinomas
Hematopoietic
Lymphomas +
Sarcomas
Parameters used in models
qO, ql, q2
qO, ql, q2
qO.ql
P-value for BMDS model
0.7618
0.7197
0.9140
BMD05 (from BMDS)
352.4
517.8
423.8
BMD05 (median, mode from WinBugs)
284.8, 292.5
414.3,299.9
409.8, 382.6
BMDL (BMDS)*
138.1
193.0
189.5
BMDL (5.h %-ile, WinBugs)
162.6
195.4
226.2
BMD05 for Combined Risk (median,
mode, from WinBugs)
136.1, 121.1
BMDL for Combined Risk (5th %-ile,
WinBugs)
85.65
BMDS maximum likelihood risk estimates
Risk at dose 100
0.004123
0.001912
0.0120315
Upper 95% C.L.
0.04039
0.02919
0.0295375
Sum of risks at dose 100
WinBUGs Bayes risk estimates
Risk at dose 100: mean, median
0.01468, 0.01311
0.01284, 0.01226
0.009552,
0.008286
Upper 95% C.L.
0.03032
0.02590
0.021410
Comb, risk at dose 100 mean, median
0.03663, 0.03572
Comb, risk at dose 100, upper 95%
CL
0.05847
* all confidence intervals are at 5% (lower) or 95% (upper) level, one-sided
1
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Figure G.8.7. Combined and Individual Tumor Extra Risk Functions
Extra Risk
ZllflElLagl.lEl,
CO
O
O
O
O
0
200
400
600
800
Dose
Figure G.8.8. Distribution of BMDc for combined risk
Density
CO
o
o -
b
*3"
o
o
b
o
o
o
b
100
200
300
400
500
600
N = 300000 Bandwidth = 3.023
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Maltoni 1986 B6C3F1 female mice inhalation expos - Internal Dose Metric (Total Oxidative
Metabolism)
Intern al Dose*
Liver hepatomas
/N**
Lung adenomas +
carcinomas /N**
0
3/88
2/90
280.946
4/89
6/90
622.530
4/88
7/89
939.105
9/85
14/87
* Internal dose, Total Oxidative Metabolism, adjusted for body weight, units (mg/(wk-kgA3/4)).
Internal doses were adjusted by a factor 0.75, accounting for exposure duration 78/104 weeks.
Before adjustment, median internal doses were 374.5945, 830.0405, 1252.14 (mg/(wk-kgA3/4)). **
Numbers at risk are the smaller of (a) time of first tumor observation or (b) 52 weeks on study
2
Maltoni 1986 B6C3F1 female mice - Internal Dose: MODEL SELECTION
comparison of model fit statistics for multistage models of increasing order
Tumor Site
Model
Order,
* selected
Coeff.
estimates
equal
zero
AIC
Largest+
Scaled
Residual
Goodness
of Fit P-
value
Liver
3*
(31,(32
153.1
-0.410
0.8511
2
PI
153.4
-0.625
0.7541
1
NA
154
-0.816
0.5571
Lung
3
(32
195.8
-0.571
0.3995
2
NA
195.9
-0.671
0.3666
1*
NA
194
-0.776
0.6325
* model order selected + largest in absolute value
3
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Maltoni 1986 B6C3F1 female mice inhalation expos - Internal Dose Metric (Total Oxidative
Metabolism) (inferences for 0.05 extra risk at 95% level)
Liver hepatomas
Lung adenomas +
carcinomas
Parameters used in models
qO, ql, q2, q3
qO, ql
P-value for BMDS model
0.5571
0.6325
BMD05 (from BMDS)
813.7
366.7
BMD05 (median, mode - WinBugs)
672.9, 648.0
382.8,372.1
BMDL (BMDS)*
419.7
244.6
ms combo BMD05c, BMDLc
412.76, 189.23
BMDL (5th%-ile, WinBugs)
482.7
251.1
BMD05 for Combined Risk (median,
mode, from WinBugs)
286.7, 263.1
BMDL for Combined Risk (5th%-ile,
WinBugs)
199.5
BMDS maximum likelihood risk estimates
Risk at dose 100
0.006284
0.01389
Upper 95% C.L.
0.01335
0.02215
Sum of risks at dose 100
0.02017
WinBUGs Bayes risk estimates: means (medians)
Risk at dose 100: mean, median
0.003482, 0.00 2906
0.01337,0.01331
Upper 95% C.L.,
0.008279
0.02022
Comb, risk at dose 100 mean, median
0.01637,0.01621
Comb, risk at dose 100, upper 95% CL
0.02455
* all confidence intervals are at 5% (lower) or 95% (upper) level, one-sided
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Figure G.8.9. Combined and Individual Tumor Extra Risk Functions
Extra Risk
— vertica
~ vertica
solid, BM )e
dash, BMJLc
ID
O
o
o
o
o
ci
0
200
400
600
800
Dose
Figure G.8.10. Distribution of BMDc for combined risk
Density
o
o -
ci
o
o -
O
O
O
O
O
O
O
ci
200 400 600 800 1000 1200
N = 300000 Bandwidth = 5.053
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Maltoni Sprague-Dawley Male Rats - Internal Dose Metric (Total Metabolism)
Internal Dose*
Kidney
adenenomas +
carcinomas /N**
Leukemias /
N**
Testis, Leydig
Cell Tumors /
N**
0
0/121
9/134
6/121
214.6540
1/118
13/130
16/116
507.0845
0/116
14/130
30/116
764.4790
5/123
15/129
31/122
* Internal dose, Total Oxidative Metabolism, adjusted for body weight, units (mg/(wk-kgA3/4)). **
Numbers at risk are the smaller of (a) time of first tumor observation or (b) 52 weeks on study
2
Maltoni Sprague-Dawley Male Rats - Internal Dose : MODEL
SELECTION comparison of model fit statistics for multistage models of
increasing order
Tumor Site
Model
Order,
*selected
Coeff.
estimates
equal
zero
AIC
Largest*
Scaled
Residual
Goodness
of Fit P-
value
Kidney
3
Y,P2
61.35
-1.264
0.262
2
Y
61.75
-1.343
0.246
1*
Y
60.32
-1.422
0.370
Leukemias
3
(32, (33
336.5
0.479
0.828
2
(32
336.5
0.479
0.828
1*
NA
336.5
0.479
0.828
Testis, Leydig Cell Tumors
3
(32, (33
417.7
1.008
0.363
2
(32
417.7
1.008
0.363
1*
NA
417.7
1.008
0.363
* largest in absolute value
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Maltoni Sprague-Dawley Male Rats - Internal Dose Metric (Total Metabolism) (inferences for 0.01
extra risk at 95% level)
Kidney adenomas
+ carcinomas
Leukemias
Testis, Leydig Cell
Tumors
Parameters used in models
qO.ql
qO.ql
qO.ql
P-value for BMDS model
0.3703
0.8285
0.3626
BMD01 (from BMDS)
295.1
145.8
26.65
BMD01 (median, mode - WinBugs)
BMDL (BMDS)*
161.3
65.29
20.32
BMDL (5th%-ile, WinBugs)
BMD01 for Combined Risk (median,
mode, from WinBugs)
20.97, 19.73
BMDL for Combined Risk (5th%-ile,
WinBugs)
16.14
BMDS maximum likelihood risk estimates
Risk at dose 100
0.003400
0.0068694
0.0370162
Upper 95% C.L.
0.0068784
0.0169134
0.0504547
Sum of risks at dose 100
0.04729
Risk at dose 10
0.0003406
0.0006891
0.0037648
Upper 95% C.L.
0.0006900
0.0017044
0.0051638
Sum of risks at dose 10
0.004795
WinBUGs Bayes risk estimates: means (medians)
Risk at dose 100: mean, median
0.003191,
0.003028
7.691e-03,
7.351e-03
0.03641, 0.03641
Upper 95% C.L.
0.006044
1.539e-02
0.04769
Comb, risk at dose 100 - mean, median
0.04688, 0.04680
Comb, risk at dose 100, upper 95% CL
0.060380
Risk at dose 100 - mean, median
3.196e-04,
3.032e04
7.726e-04,
7.376e04
0.003705,
0.003703
Upper 95% C.L.
6.060000e-04
1.550000e-03
0.004874000
Comb, risk at dose 10 - mean, median
0.004793, 0.0047820
Comb, risk at dose 10, upper 95% CL
0.006208
* all confidence intervals are at 5% (lower) or 95% (upper) level, one-sided
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Figure G.8.11. Combined and Individual Tumor Extra Risk Functions
Extra Risk
o
CM
O
ID
O
O
ID
O
o
o
o
o
vertical solid, BMDc
vertical dash, BMDLc
0
100
200
300
400
500
Dose
Figure G.8.12. Distribution of BMDc for combined risk
Density
00
o
o
o
o
o
o _
20 40
N = 300000 Bandwidth = 0.2732
60
80
100
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G.9. PBPK-model uncertainty analysis of unit risk estimates
As discussed in Chapter 5.2, an uncertainty analysis was performed on the unit risk
estimates derived from rodent bioassays to characterize the impact of pharmacokinetic
uncertainty. In particular, two sources of uncertainty are incorporated: (i) uncertainty in the
rodent internal doses for each dose group in each chronic bioassay and (ii) uncertainty in the
relationship between exposure and the human population mean internal dose at low exposure
levels.
A Bayesian approach provided the statistical framework for this uncertainty analysis.
Rodent bioassay internal dose-response relationships were modeled with the multistage model,
with general form
P(id) = 1 - exp[-(q0 + qiid + q2id2 + ... + qkidk)],
where P(id) represents the lifetime risk (probability) of cancer at internal dose id, and multistage
parameters q; > 0, for i = 0, 1, ..., k. Since the BMD (in internal dose units) for a given BMR can
be derived from the multistage model parameters qH it is sufficient to estimate the posterior
distribution of q, given the combined bioassay data (for each dose group j, the number
responding yj, the number at risk nj, and the administered dose dj) and the rodent
pharmacokinetic data, for which the posterior distribution can be derived using the Bayesian
analysis of the PBPK model described in Section 3.5. In particular, the posterior distribution of
q; can be expressed as:
P(q[i]|Dbioassay Dpk) oc P(qti]) P(y[j]| qti] n^) P(id[j]|d[j], Dpk)
Here, the first term after the proportionality P(qp]) is the prior distribution of the multistage
model parameters (assumed to be non-informative), the second term P(y^]| q[i] n^) is the
likelihood of observing the bioassay response given a particular set of multistage parameters and
the number at risk (the product of binomial distributions for each dose group), and P(id[j]|d[j],
Dpk) is the posterior distribution of the rodent internal doses id[j], given the bioassay doses and
the pharmacokinetic data used to estimate the PBPK model parameters.
The distribution of unit risk (URid = BMR/BMD) estimates in units of "per internal dose"
is then derived deterministically from the distribution of multistage model parameters:
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P(URid|Dbioassay Dpk-rodent) JP(C[[i]|Dbioassay Dpk-rodent) S(UR BMR/BMD(C]|j|)) t/c]|j |
Here 8 is the Dirac delta-function. Then, the distribution of unit risk estimates in units of "per
human exposure" (per mg/kg/d ingested or per continuous ppm exposure) is derived by
converting the unit risk estimate in internal dose units:
P(URj1uman|Dbioassay Dpk-rodent) 1 P(UR.jclDbioassay Dpk-rodent) P(idconversion|Dpk-human)
S(URhuman URid x id conversion
)cM
conversion
Here, idconversion is the population mean of the ratio between internal dose and administered
exposure at low dose (0.001 ppm or 0.001 mg/kg/d), and P(idconversion|Dpk-human) is its posterior
distribution from the Bayesian analysis of the human PBPK model.
This statistical model was implemented via Monte Carlo as follows. For each bioassay,
for a particular iteration r (r= 1... //,),
(1) A sample of rodent PBPK model population parameters (|i,X)rodenLr was drawn from the
posterior distribution. Using these population parameters, a single set of group rodent
PBPK model parameters 0rodent,r was drawn from the population distribution. As
discussed in Section 3.5, for rodents, the population model describes the variability
among groups of rodents, and the group-level parameters represent the "average"
toxicokinetics for that group.
(2) Using 9rodent,r, the rodent PBPK model was run to generate a set of internal doses idy^ for
the bioassay.
(3) Using this set of internal doses idy^r, a sample q|,|.r was selected from the distribution
(conditional on id[j],r) of multistage model parameters, generated using the WinBUGS,
following the methodology of Kopylev et al. (2009).
(4) The unit risk in internal dose units URid,r = BMR/BMD(q[i]r) was calculated based on the
multistage model parameters.
(5) A sample of human PBPK model population parameters (|i,S)iUmian.r was drawn from the
posterior distribution. Using these population parameters, multiple sets of individual
human PBPK model parameters 9human,r,[s] (s=l.. .ns) were generated. A continuous
exposure scenario at low exposure was run for each individual, and the population mean
internal dose conversion was derived by taking the arithmetic mean of the internal dose
conversion for each individual: idiversion,r = Sum( idConversion,r,s )/ns.
(6) The sample for the unit risk in units per human exposure was calculated by multiplying
the sample for the unit risk in internal dose units by the sample for the population internal
dose conversion: URhumanr URidr x idc
-^conversions-
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In practice, samples for each of the above distributions was "pre-calculated," and
inferences were performed by re-sampling (with replacement) according to the scheme above.
For the results described in Chapter 5.2, a total of nr = 15,000 samples was used for deriving
summary statistics. For calculating the unit risks in units of internal dose, the BMDs derived by
re-sampling from a total of 4.5xlO6 multistage model parameter values (1500 rodent PBPK
model parameters from the Bayesian analysis described in Chapter 3.5, for each of which there
were conditional distributions of multistage model parameters of length 3000 derived using
WinBUGS). The conversion to unit risks in units of human exposure was re-sampled from 500
population mean values, each of which was estimated from 500 sampled individuals.
The file
Appendix.linked.files\AppG.Cancer.Rodents.Uncertaintv.Analvsis.TCE.DRAFT.pdf contains
summary statistics (mean, and selected quantiles from 0.01 to 0.99) from these analyses, and is
the source for the results presented in Chapter 5 (Tables 5.2.10 and 5.2.11). Histograms of the
distribution of unit risks in per unit human exposure are in the file
Appendix.linked.files\AppG.Cancer.Rodents.uncertaintv.CSF-
inhal.histograms.inhalation.bioassavs.TCE.DRAFT.pdf for the rodent inhalation bioassays and
Appendix.linked.files\AppG.Cancer.Rodents.uncertaintv.CSF-
oral.histograms.oral.bioassavs.TCE.DRAFT.pdf for the rodent oral bioassays. Route-to-route
extrapolated unit risks are in the files
Appendix.linked.files\AppG.Cancer.Rodents.uncertaintv.CSF-
inhal.histograms.oral.bioassavs.TCE.DRAFT.pdf (inhalation unit risks extrapolated from oral
bioassays) and Appendix.linked.files\AppG.Cancer.Rodents.uncertainty.CSF-
oral.histograms.inhalation.bioassavs.TCE.DRAFT.pdf (oral unit risks extrapolated from
inhalation bioassays). Each figure shows the uncertainty distribution for the male and female
combined population risk per unit exposure (transformed to base-10 logarithm), with the
exception of testicular tumors, for which only the population risk per unit exposure for males is
shown.
G.10. References
Bogen, K.T. 1990. Uncertainty in Environmental Health Risk Assessment. London: Taylor &
Francis.
Fukuda, K; Takemoto, K; Tsuruta, H. (1983) Inhalation carcinogenicity of trichloroethylene in
mice and rats. Ind Health 21:243-254.
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Henschler D, Romen W, Elsasser HM, Reichaert D, Eder E, Radwan Z. 1980. Carcinogenicity
study of trichloroethyleneby longterm inhalation in three animal species. Arch Toxicol
43: 237-248 (1980).
Kopylev, L; Chen, C; White, P. (2007) Towards quantitative uncertainty assessment for cancer
risks: central estimates and probability distributions of risk in dose-response modeling.
Regul Toxicol Pharmacol 49(3):203-207.
Maltoni, C; Lefemine, G; Cotti, G. (1986) Experimental research on trichloroethylene
carcinogenesis. In: Maltoni, C; Mehlman MA., eds. Vol. 5. Archives of research on
industrial carcinogenesis. Princeton, NJ: Princeton Scientific Publishing;
NCI (National Cancer Institute). (1976) Carcinogenesis bioassay of trichloroethylene. Division
of Cancer Cause and Prevention, National Cancer Institute, U.S. Department of Health,
Education, and Welfare, DHEW Publication No. (NIH) 76-802, Technical Report Series
No. 2, 218 pages; NCI-CG-TR-2; NTIS PB254122.
http://ntp.niehs.nih.gov/ntp/htdocs/LT_rpts/tr002.pdf.
Nitcheva DK, Piegorsch WW, West RW. (2007). On use of the multistage dose-response model
for assessing laboratory animal carcinogenicity, Regulatory Toxicology and
Pharmacology 48:135-147.
NRC (National Research Council). 1994. Science and Judgment in Risk Assessment.
Washington, DC: National Academy Press
NTP (National Toxicology Program). (1988) Toxicology and carcinogenesis studies of
trichloroethylene (CAS no. 79-01-6) in four strains of rats (ACI, August, Marshall,
Osborne-Mendel) (gavage studies). Public Health Service, U.S. Department of Health
and Human Services; NTP TR-273; NIH Publication No. 88-2529. Available from the
National Institute of Environmental Health Sciences, Research Triangle Park, NC, and
the National Technical Information Service, Springfield, VA; PB88-218896.
http://ntp.niehs.nih.gov/ntp/htdocs/LT_rpts/tr273.pdf.
NTP (National Toxicology Program). (1990) Carcinogenesis Studies of Trichloroethylene
(Without Epichlorhydrin) (CAS No. 79-01-6) in F344/N Rats and B6C3F1 Mice (Gavage
Study). NTP TR 243. Research Triangle Park, NC: U.S Department of Health and
Human Services.
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Piegorsch WW, Bailer AJ, 1997, Statistics for Environmental Biology and Toxicology
(Chapman & Hall, London). See Ch. 6.3.2
Portier CJ, Bailer AJ. 1989. Testing for increased carcinogenicity using a survival-adjusted
quantal response test. Fund Appl Toxicol 12:731-737. Bailer, AJ, and CJ Portier. 1988.
Effects of treatment-induced mortality and tumor-induced mortality on tests for
carcinogenicity in small samples. Biometrics 44:417-431.
Portier CJ, Hedges JC, Hoel DG. 1986. Age-specific models of mortality and tumor, onset for
historical control animals in the National Toxicology Program's carcinogenicity
experiments. Cancer Research 46:4372-4378.
Spiegelhalter, D; Thomas, A; Best, N; et al. (2003) WinBUGS user manual. Version 1.4.
Available online atwww.mrc-bsu.cam.ac.uk/bugs/winbugs/manuall4.pdf.
U.S. EPA. 1980. Water Quality Criteria Documents; Availability. Fed Reg 45(231), page 79352.
U.S. EPA (Environmental Protection Agency). (1994) Methods for derivation of inhalation
reference concentrations and application of inhalation dosimetry. Environmental Criteria
and Assessment Office, Office of Health and Environmental Assessment, Washington,
Washington, DC; EPA/600/8-90/066F. Available from: National Technical Information
Service, Springfield, VA; PB2000-500023.
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