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Appendix
A.
Benchmark
Dose
Modeling
Results
Introduction
Benchmark
dose
(
BMD)
modeling
was
performed
to
identify
potential
critical
effect
levels
as
alternatives
to
the
study
NOAEL/
LOAELs
for
derivation
of
the
HAs
for
DBAN,
DCAN,
and
TCAN.
No
adequate
studies
were
available
to
support
a
quantitative
dose­
response
assessment
for
BCAN.
Individual
modeling
output
for
each
endpoint
is
provided
in
Appendix
B.

Methods
Benchmark
Dose
The
haloacetonitrile
data
sets
considered
for
dose­
response
modeling
were
all
continuous
endpoints.
The
modeling
was
conducted
according
to
draft
EPA
guidelines
(
U.
S.
EPA,
2000c)

using
Benchmark
Dose
Software
(
BMDS
version
1.3.1),
available
from
the
U.
S.
EPA
(
U.
S.
EPA,

2001).
The
methods
and
models
applied
to
the
continuous
endpoints
are
presented
here.

The
continuous
endpoints
of
interest
with
respect
to
haloacetonitrile
toxicity
were
quantitatively
summarized
by
group
means
and
measures
of
variability
(
standard
errors
or
standard
deviations).
Since
all
of
the
endpoints
that
were
modeled
were
continuous
rather
than
quantal
(
e.
g.,
incidence
data)
in
nature,
the
Hill,
power,
and
polynomial
models
were
used
for
each
data
set.
Linear
fits
to
the
data
were
incorporated
into
the
analysis
by
allowing
the
power
and
polynomial
models
to
simplify
to
linear
equations
as
dictated
by
the
data
(
for
short­
term
studies).
The
linear
model
option
in
BMDS
was
also
run
separately
for
the
longer­
term
studies,
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since
this
provided
the
advantage
of
obtaining
goodness­
of­
fit
p­
values
(
since
the
number
of
parameters
is
smaller
for
the
linear
model)
for
the
longer­
term
data
sets
in
which
the
high
dose
was
removed;
insufficient
degrees
of
freedom
were
available
for
calculation
of
p­
values
for
the
power
or
polynomial
models
for
these
data
sets.
An
attempt
to
fit
the
data
using
a
hybrid
modeling
approach
for
the
longer­
term
studies
failed
to
compute
a
BMDL
estimate.
The
hybrid
approach
defines
the
benchmark
response
(
BMR)
directly
in
terms
of
risk,
as
opposed
to
the
standard
approach,
which
defines
the
BMR
in
terms
of
a
change
in
the
mean.
Furthermore,
the
hybrid
model
software
in
BMDS
is
still
undergoing
Beta­
testing,
and
was
not
considered
sufficiently
validated
to
have
used
a
BMDL
from
this
model
as
the
basis
for
the
quantitative
doseresponse
assessment.

These
mathematical
models
fit
to
the
data
are
defined
here.
In
all
cases,
µ
(
d)
indicates
the
mean
of
the
response
variable
following
exposure
to
dose
d.

The
polynomial
model
is
defined
as:

µ
(
d)
=
 
0
+
 
1
d
+
...
+
 
n
dn
where
the
degree
of
the
polynomial,
n,
was
set
less
than
or
equal
to
the
number
of
dose
groups
in
the
experiment
being
analyzed.
Note
that
U.
S.
EPA
(
2000c)
recommends
the
use
of
the
most
parsimonious
model
that
provides
an
adequate
fit
to
the
data.
It
may
appear
that
the
use
of
a
polynomial
model
with
degree
possibly
as
great
as
the
number
of
dose
groups
would
not
yield
the
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most
parsimonious
model.
However,
allowing
the
model
to
have
that
degree
is
not
the
same
as
forcing
the
model
to
have
that
degree;
in
the
model
fitting,
if
fewer
parameters
(
e.
g.,
a
lower
degree
polynomial)
is
adequate
and
consistent
with
the
data,
then
the
fitting
will
reflect
that
fact
and
a
more
parsimonious
model
will
be
the
result.
For
these
analyses,
the
values
of
the
 
parameters
allowed
to
be
estimated
were
constrained
to
be
either
all
nonnegative
or
all
nonpositive
(
as
dictated
by
the
data
set
being
modeled,
i.
e.,
nonnegative
if
the
mean
response
increased
with
increasing
dose
or
nonpositive
if
the
mean
response
decreased
with
increasing
dose).

The
power
model
is
represented
by
the
equation:

µ
(
d)
=
 
+
 d 
where
the
parameter
 
is
restricted
to
be
nonnegative.
[
The
linear
model
is
obtained
when
 
is
fixed
at
a
value
of
1.
The
linear
model
was
not
separately
fit
to
the
data;
if
the
result
of
fitting
the
power
model
does
not
result
in
the
linear
form,
 
=
1,
then
the
linear
model
does
not
fit
as
well
as
the
more
general
power
model,
by
definition.]

The
Hill
model
is
given
by
the
following
equation:

µ
(
d)
=
 
+
(
vdn)
/
(
dn
+
kn))

where
the
parameters
n
and
k
are
restricted
to
be
positive
(
in
fact,
n
>
1).
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In
the
case
of
continuous
endpoints,
one
must
assume
something
about
the
distribution
of
individual
observations
around
the
dose­
specific
mean
values
defined
by
the
above
models.
The
assumptions
imposed
by
BMDS
were
used
in
this
analysis:
individual
observations
were
assumed
to
vary
normally
around
the
means
with
variances
given
by
the
following
equation:

 
i
2
=
 2

[
µ
(
d
i)]
 
where
both
 2
and
 
were
parameters
estimated
by
the
model.

Given
those
assumptions
about
variation
around
the
means,
maximum
likelihood
methods
were
applied
to
estimate
all
of
the
parameters,
where
the
log­
likelihood
to
be
maximized
is
(
except
for
an
additive
constant)
given
by
L
=
 
[(
N
i/
2)

ln(
 
i
2)
+
(
N
i
­
1)
s
i
2/
2 
i
2
+
N
i{
m
i
­
µ
(
d
i)}
2/
2 
i
2]

where
N
i
is
the
number
of
individuals
in
group
i
exposed
to
dose
d
i,
and
m
i
and
s
i
are
the
observed
mean
and
standard
deviation
for
that
group.
The
summation
runs
over
i
from
1
to
k
(
the
number
of
dose
groups).

Goodness
of
Fit
Analyses
For
these
continuous
models,
goodness
of
fit
was
determined
based
on
a
likelihood
ratio
statistic.
In
particular,
the
maximized
log­
likelihood
associated
with
the
fitted
model
was
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If
and
when
BMDS
suggested
that
a
homogeneous­
variance
model
was
appropriate,
the
log­
likelihood
of
the
fitted
model
was
compared
to
the
likelihood
maximized
assuming
independent
means
but
a
single,
constant
variance
for
all
dose
groups
(
the
fitted
model
also
assumed
that
to
be
the
case
in
such
cases).

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compared
to
the
log­
likelihood
maximized
with
each
dose
group
considered
to
have
a
mean
and
variance
completely
independent
of
the
means
and
variances
of
the
other
dose
groups.
1
It
is
always
the
case
that
the
latter
log­
likelihood
will
be
at
least
as
great
as
the
model­
associated
loglikelihood
but
if
the
model
does
a
reasonable
job
of
fitting
the
data,
the
difference
between
the
two
log­
likelihoods
will
not
be
too
great.
A
formal
statistical
test
reflecting
this
idea
uses
the
fact
that
twice
the
difference
in
the
log­
likelihoods
is
distributed
as
a
chi­
square
random
variable.
The
degrees
of
freedom
associated
with
that
chi­
squared
test
statistic
are
equal
to
the
difference
between
the
number
of
parameters
fit
by
the
model
(
including
the
parameters
 2
and
 
defining
how
variances
change
as
a
function
of
mean
response
level)
and
twice
the
number
of
dose
groups
(
which
is
equal
to
the
number
of
parameters
estimated
by
the
model
assuming
independence
of
dose
group
means
and
variances).
Parameters
hitting
boundary
values
were
not
included
for
determining
degrees
of
freedom.

Acceptable
fit
was
defined
as
a
goodness­
of­
fit
p­
value
greater
than
or
equal
to
0.1,
or
a
perfect
fit
when
there
were
no
degrees
of
freedom
for
a
statistical
test
of
fit.
Choice
of
0.1
is
consistent
with
current
U.
S.
EPA
guidance
for
BMD
modeling
(
U.
S.
EPA,
2000c).
If
a
model
was
judged
to
provide
a
reasonable
BMDL
estimate,
but
the
p­
value
criterion
of
0.1
was
not
met,

the
rationale
for
waiving
the
p­
value
criterion
is
provided
in
the
discussion
of
the
results.
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Goodness­
of­
fit
statistics
are
not
designed
to
compare
different
models,
particularly
if
the
different
models
have
different
numbers
of
parameters.
Within
a
family
of
models,
adding
parameters
generally
improves
the
fit.
BMDS
reports
the
Akaike
Information
Criterion
(
AIC)
to
aid
in
comparing
the
fit
of
different
models.
The
AIC
is
defined
as

2L+
2p,
where
L
is
the
loglikelihood
at
the
maximum
likelihood
estimates
for
the
parameters,
and
p
is
the
number
of
model
parameters
estimated
(
ignoring
parameters
assuming
values
at
the
boundaries
of
their
allowable
ranges).
When
comparing
the
fit
of
two
or
more
models
to
a
single
data
set,
the
model
with
the
lesser
AIC
was
considered
to
provide
a
superior
fit.

Definition
of
the
BMR
and
Corresponding
BMD
and
BMDL
For
the
continuous
models,
BMDs
were
implicitly
defined
as
follows:

 
µ
(
BMD)
­
µ
(
0)
 
=
  
1
where
 
1
is
the
model­
estimated
standard
deviation
in
the
control
group.
In
other
words,
the
BMR
was
defined
as
a
change
in
mean
corresponding
to
some
multiplicative
factor
of
the
control
group
standard
deviation.

The
value
of
 
used
in
this
analysis
was
1.0.
This
value
was
chosen
based
on
EPA
draft
guidelines
for
BMD
analyses
(
U.
S.
EPA,
2000c),
in
the
absence
of
a
clear
biological
rationale
for
selecting
an
alternative
response
level.
It
is
roughly
consistent
with
(
though
slightly
more
conservative
than)
a
choice
of
1.1,
which
according
to
Crump
(
1995)
corresponds
to
an
additional
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risk
of
10%
when
the
background
response
rate
was
assumed
to
be
1%,
with
normal
variation
around
the
mean
(
and
constant
standard
deviation).

Choice
of
BMDL
The
following
guidance
was
followed
with
regard
to
the
choice
of
the
BMDL
to
use
as
a
point
of
departure
for
calculation
of
a
health
advisory.
This
guidance
is
consistent
with
recommendations
in
U.
S.
EPA
(
2000c).
For
each
endpoint,
the
following
procedure
is
recommended:

1.
Models
with
an
unacceptable
fit
are
excluded.

2.
If
the
BMDL
values
for
the
remaining
models
for
a
given
endpoint
are
within
a
factor
of
3,

no
model
dependence
is
assumed,
and
the
models
are
considered
indistinguishable
in
the
context
of
the
precision
of
the
methods.
The
models
are
then
ranked
according
to
the
AIC,
and
the
model
with
the
lowest
AIC
is
chosen
as
the
basis
for
the
BMDL.

3.
If
the
BMDL
values
are
not
within
a
factor
of
3,
some
model
dependence
is
assumed,
and
the
lowest
BMDL
is
selected
as
a
reasonable
conservative
estimate,
unless
it
is
an
outlier
compared
to
the
results
from
all
of
the
other
models.
Note
that
when
outliers
are
removed,
the
remaining
BMDLs
may
then
be
within
a
factor
of
3,
and
so
the
criteria
given
in
item
2.
would
be
applied.

4.
The
BMDL
values
from
all
modeled
endpoints
are
compared,
along
with
any
NOAELs
or
LOAELs
from
data
sets
that
were
not
amenable
to
modeling,
and
the
lowest
NOAEL
or
BMDL
is
chosen.
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Modeling
Results
for
Short­
term
Studies
This
modeling
was
done
to
support
the
derivation
of
the
Ten­
Day
HAs.
BMD
modeling
was
conducted
only
for
toxicologically­
relevant
endpoints
that
could
be
used
to
derive
the
HAs.

Adequate
short­
term
studies
for
modeling
were
available
only
for
DBAN,
DCAN,
and
TCAN.

No
suitable
studies
were
available
for
derivation
of
the
Ten­
day
HA
for
BCAN.
As
a
result,

BMD
modeling
was
not
performed
for
BCAN.
The
BMD
modeling
results
for
the
short­
term
studies
are
presented
in
Table
A­
1
and
described
below.

DBAN
The
endpoints
modeled
for
DBAN
in
the
Hayes
et
al.
(
1986)
14­
day
study
were
body
weight
in
males
and
relative
liver
weight
in
females.
Modeling
was
done
for
relative
liver
weight
for
completeness,
although
as
discussed
in
Chapter
V,
the
relative
liver
weight
changes
for
DBAN
were
not
considered
to
be
sufficiently
adverse
to
serve
as
the
basis
for
the
HA.

The
body
weight
response
to
DBAN
in
males
did
not
appear
to
have
constant
variance;

the
variability
in
the
highest
dose
group
was
much
greater
than
that
observed
in
the
other
groups.

Even
when
a
dose­
dependent
variance
was
included,
however,
the
polynomial
model
did
not
predict
standard
deviations
that
matched
well
with
the
observed
values,
contributing
to
the
significant
lack
of
fit
of
that
model
(
p
=
0.004).
The
power
model
did
a
much
better
job
of
fitting
the
observed
standard
deviations,
as
well
as
the
observed
means,
yielding
a
p­
value
for
goodnessof
fit
of
0.07.
The
Hill
model
did
not
provide
an
adequate
fit.
The
BMD
and
BMDL
(
26
and
16
mg/
kg/
day,
respectively)
from
the
power
model
are
preferred
for
this
data
set.
The
goodness­
of­
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fit
statistic
for
the
power
model
was
below
the
current
p­
value
criterion
of
0.1
recommended
in
current
EPA
guidance
(
U.
S.
EPA,
2000c).
However,
the
results
of
the
power
model
were
considered
adequate
for
use
in
the
quantitative
dose­
response
assessment.
This
consideration
was
based
on
the
observation
that
the
visual
fit
to
the
data
was
reasonably
good,
and
that
the
modelpredicted
means
and
standard
deviations
were
similar
to
the
observed
values
(
i.
e.
as
indicated
by
low
values
for
the
chi­
square
residuals).

For
the
relative
liver
weight
in
female
rats,
all
the
models
fit
the
data
extremely
well
(

pvalues
all
greater
than
0.45).
Because
of
the
extra
parameters
in
the
Hill
model
(
which
visually
looked
essentially
the
same
as
the
polynomial
or
power
models),
the
AIC
for
the
Hill
model
was
substantially
higher
than
the
AICs
for
the
polynomial
or
power
models.
In
addition,
the
BMDL
calculation
failed
for
the
Hill
model.
The
polynomial
mode
gave
a
slightly
better
fit
than
the
power
model,
and
consequently
the
BMD
and
BMDL
from
the
polynomial
model
(
31
and
17
mg/
kg/
day,
respectively)
are
the
estimates
of
choice
for
this
data
set.

In
summary,
for
the
DBAN
Ten­
day
HA,
only
the
modeling
results
for
decreased
body
weight
reported
in
Hayes
et
al.
(
1986)
were
considered
for
use
in
the
quantitative
dose­
response
assessment.
The
estimate
of
choice
for
this
data
set
was
the
BMD
of
26
mg/
kg/
day
with
the
corresponding
BMDL
of
16
mg/
kg/
day
obtained
from
the
power
model.
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
OW/
OST/
HECD
Final
Draft
A­
10
DCAN
The
endpoints
modeled
for
DCAN
in
the
Hayes
et
al.
(
1986)
14­
day
study
were
body
weight
in
males
and
relative
liver
weight
in
males
and
females.
Modeling
was
done
for
each
of
these
effects
since
they
were
considered
to
be
toxicologically
relevant.

A
constant
variance
model
was
used
for
the
analysis
of
the
DCAN
body
weight
endpoint
in
male
rats
(
Hayes
et
al.,
1986).
The
mean
weights
showed
a
non­
monotonic
dose
response,

with
the
lowest
positive
dose
group
having
a
mean
weight
greater
than
that
in
controls.
This
caused
some
difficulty
in
fitting
the
models
(
p­
values
all
less
than
or
equal
to
0.02).
However,
in
this
case,
the
fits
might
be
judged
to
be
adequate
for
BMD
estimation
for
several
reasons.
First,

the
poor
statistical
fit
was
driven
largely
by
one
point,
while
the
visual
fits
were
reasonable.

Second,
the
BMD
estimates
(
ranging
from
32­
36
mg/
kg/
day)
were
very
consistent
among
the
models,
suggesting
that
the
fits
were
not
model­
dependent.
Third,
the
BMDL
estimates
were
associated
with
a
response
that
corresponded
almost
exactly
to
one
standard
deviation
below
the
control
group
mean,
using
the
observed
values
of
the
control
group
mean
and
standard
deviation.

The
AIC
for
the
power
model
was
slightly
better
than
those
for
the
other
models,
and
the
BMD
of
36
mg/
kg/
day
and
BMDL
of
25
mg/
kg/
day
from
the
power
model
are
recommended
as
the
best
estimates
for
this
data
set.

For
the
female
rats
exposed
to
DCAN,
a
non­
monotonic
dose­
response
was
observed
for
increased
relative
liver
weight
(
with,
essentially,
a
plateau
of
effect
for
the
highest
three
dose
groups
after
little
change
in
the
low­
dose
group
compared
to
controls).
Moreover,
the
observed
Drinking
Water
Criteria
Document
for
Haloacetonitriles
2
A
bug
in
BMDS
resulted
in
three
different
values
for
the
log­
likelihood
of
model
A3
(
independent
means
but
modeled
variances)
across
the
three
model
runs.
The
fit
of
model
A3
should
be
the
same
regardless
of
the
model
being
fit,
so
it
is
not
possible
to
know
with
certainty
what
the
correct
likelihood
for
A3
is.
In
all
cases,
however,
it
was
significantly
worse
than
that
for
model
A2
(
independent
means
and
independent
variances).

EPA/
OW/
OST/
HECD
Final
Draft
A­
11
standard
deviation
in
the
high­
dose
group
was
three
to
four
times
greater
than
the
standard
deviation
in
the
other
groups.
As
a
result,
the
variance
modeling
approaches
available
in
BMDS
were
not
capable
of
fitting
the
observed
dose­
variance
pattern.
2
The
linear
models
to
which
the
polynomial
and
power
models
defaulted
could
not
fit
the
dose­
response
pattern.
However,
the
Hill
model
did
reflect
the
dose­
response
pattern
well
enough
and
the
predicted
standard
deviation
was
reasonably
close
to
the
observed
standard
deviation
for
the
control
group,
which
would
make
that
model
acceptable
for
BMD
estimation.
The
BMD
estimate
was
14
mg/
kg/
day,
but
the
Hill
model
failed
to
derive
a
BMDL
estimate.
As
an
alternative,
the
high
dose
group
was
removed
and
the
dose­
response
models
were
refit
to
the
reduced
data
set.
Without
the
highest
group,

BMDS
suggests
that
a
constant
variance
model
is
appropriate.
The
polynomial
and
power
models
still
defaulted
to
linearity,
and
still
did
not
fit
the
data
(
p
=
0.002).
However,
the
Hill
model
passes
exactly
through
all
of
the
observed
means
and
yields
a
BMD
and
BMDL
of
13
and
11
mg/
kg/
day,
respectively.
These
estimates
are
reasonable
values
to
use
for
this
data
set,
given
the
similarity
of
the
BMD
estimate
for
the
truncated
data
set
as
compared
to
that
of
the
Hill
model
fit
to
all
the
doses.

For
the
male
rats
exposed
to
DCAN,
a
monotonic
dose­
response
pattern
was
observed
for
the
relative
liver
weight,
but
again
the
responses
tended
to
plateau
at
the
top
two
dose
levels.
The
best
estimates
that
the
polynomial
or
power
models
can
produce
in
such
cases
are
based
on
a
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
OW/
OST/
HECD
Final
Draft
A­
12
linear
fit
which,
in
this
case,
severely
over­
estimated
the
response
observed
at
the
high
dose
and
underestimated
the
response
at
the
penultimate
dose.
The
Hill
model
provides
an
excellent
fit
to
the
data,
but
failed
to
estimate
a
BMDL
estimate
to
go
with
the
BMD
estimate
of
8.4
mg/
kg/
day.

For
consistency,
the
male
data
were
also
considered
with
the
high
dose
group
ignored
(
as
was
done
for
the
females
exposed
to
DCAN).
The
results
of
analyzing
the
reduced
male
data
set
were
as
follows.
The
linear
model
to
which
the
polynomial
and
power
models
defaulted
provided
an
adequate
fit
to
the
data
(
p
=
0.14).
The
Hill
model
also
fit
the
data
pretty
well
(
p
=
0.06),
but
because
it
required
additional
parameters,
its
AIC
value
was
slightly
greater
than
that
for
the
linear
model.
The
elimination
of
the
highest
dose
resulted
in
an
acceptable
linear
model
fit
but
reduced
the
BMD
to
7.8
mg/
kg/
day,
which
was
similar
to
the
BMD
from
the
Hill
model
that
fit
the
complete
data
set
very
well.
Given
that
similarity,
that
BMD
and
the
associated
BMDL
of
5.0
mg/
kg/
day
from
the
linear
model
fit
to
the
reduced
data
set
are
considered
to
be
adequate
values
to
characterize
this
data
set.

In
summary,
for
the
Ten­
day
HA
for
DCAN,
the
modeling
results
for
the
endpoints
of
decreased
body
weight
and
increased
relative
liver
weight
(
Hayes
et
al.,
1986)
were
considered
for
use
in
the
quantitative
dose­
response
assessment.
Changes
in
relative
liver
weight
in
males
was
the
most
sensitive
endpoint.
The
estimate
of
choice
for
the
short­
term
data
sets
for
DCAN
was
the
BMD
of
7.8
mg/
kg/
day
with
the
corresponding
BMDL
of
5.0
mg/
kg/
day
obtained
from
the
power
and
polynomial
models
for
increased
relative
liver
weight
in
males.
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
OW/
OST/
HECD
Final
Draft
A­
13
TCAN
For
TCAN,
the
developmental
study
by
Christ
et
al.
(
1996)
was
selected
as
the
most
appropriate
basis
for
deriving
the
Ten­
day
HA.
A
number
of
maternal
and
developmental
parameters
were
affected
by
TCAN.
Comparison
of
NOAELs
across
these
endpoints
suggested
that
adjusted
maternal
body
weight
gain
was
the
most
sensitive
effect.
Therefore,
BMD
modeling
results
are
described
in
detail
for
this
endpoint.
Results
of
modeling
with
BMDS
suggested
a
constant­
variance
approach.
The
polynomial
model
defaulted
to
a
linear
fit,
which
was
very
good
(
p
=
0.70).
The
power
model
estimated
a
power
just
greater
than
1
(
1.04),
and
so
was
not
exactly
linear.
The
power
model
fit
was
not
substantially
better
than
the
polynomial
model,
so
the
AIC
for
the
power
model
was
greater
than
that
for
the
linear
model
(
because
of
the
extra
parameter).
Similarly,
the
Hill
model
used
extra
parameters
to
achieve
a
marginally
better
fit
to
the
data;
it
too
yielded
an
AIC
greater
than
that
for
the
linear
(
polynomial)
model.
Since
the
extra
parameters
resulted
in
only
marginal
improvements
in
fit,
the
linear
model
estimates
derived
from
the
polynomial
model
run
are
the
preferred
ones,
with
a
BMD
of
21
mg/
kg/
day
and
a
BMDL
of
17
mg/
kg/
day.

Visual
inspection
of
the
data
for
other
maternal
or
developmental
endpoints
affected
by
TCAN
in
this
study
suggested
that
the
critical
effect
levels
for
these
additional
endpoints
would
likely
be
greater
than
for
adjusted
maternal
body
weight
gain.
To
verify
this,
BMD
modeling
was
performed
for
the
following
endpoints:
maternal
relative
liver
weight,
post­
implantation
loss,
live
fetuses/
litter,
male
and
female
fetal
body
weight,
male
and
female
crown­
rump
length,
and
incidence
of
external
malformations.
Best­
fit
BMDL
estimates
for
all
of
these
endpoints
were
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
OW/
OST/
HECD
Final
Draft
A­
14
greater
than
the
BMDL
of
17
mg/
kg/
day
for
maternal
adjusted
weight
gain,
and
thus
these
other
endpoints
would
not
be
appropriate
as
the
basis
for
deriving
the
Ten­
day
HA.
For
this
reason,
we
do
not
describe
these
additional
modeling
results
in
detail
here,
but
the
output
from
BMDS
for
these
endpoints
are
presented
in
Appendix
B.

In
summary,
for
the
TCAN
Ten­
day
HA
modeling
results
for
numerous
maternal
and
developmental
endpoints
reported
in
Christ
et
al.
(
1996)
were
considered
for
use
in
the
quantitative
dose­
response
assessment.
The
most
appropriate
endpoint
to
serve
as
the
basis
for
the
Ten­
day
HA
was
adjusted
maternal
body
weight
gain.
The
BMD
was
21
mg/
kg/
day
with
a
corresponding
BMDL
of
17
mg/
kg/
day,
derived
using
the
linear
model
estimates
from
the
polynomial
model.
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
OW/
OST/
HECD
Final
Draft
A­
15
Table
A­
1
Benchmark
Dose
Modeling
Results
for
DBAN,
DCANa,
and
TCANb
Endpoint
and
Model
AIC
P­
value
BMDc
BMDL
DBAN
­
Body
Weight
Males
Hill
323.095
<
0.001d
Failede
Failede
Power
279.347
0.07
26
16
Polynomial
284.303
0.004
30
15
DBAN
­
Relative
Liver
Weight
Females
Hill
­
11.853
0.52d
32
Failed
Power
­
13.885
0.45
31
17
Polynomial
­
14.037
0.53
31
17
DCAN
­
Body
Weight
Males
Hill
343.446
0.01
32
22
Power
343.290
0.02
36
25
Polynomial
343.538e
0.02
33
25
DCAN
­
Relative
Liver
Weight
Females
Hill
61.811
0.06
14
Failed
Power
65.850
0.04e
13
8.4
Polynomial
65.582
0.01e
13
8.4
DCAN
­
Relative
Liver
Weight
Females
(
without
highest
dose)

Hill
15.440
1.0f
13
11
Power
24.058e
0.002e
15
11
Polynomial
24.058e
0.002e
15
11
DCAN
­
Relative
Liver
Weights
Males
Hill
10.291
0.93
8.4
Failed
Power
26.962
0.0001
16
8.4
Polynomial
26.962
0.0001
16
8.4
DCAN
­
Relative
Liver
Weight
Males
(
without
highest
dose)

Hill
4.948
0.06d
8.4
Failed
Drinking
Water
Criteria
Document
for
Haloacetonitriles
Endpoint
and
Model
AIC
P­
value
BMDc
BMDL
EPA/
OW/
OST/
HECD
Final
Draft
A­
16
Power
4.859e
0.14e
7.8
5.0
Polynomial
4.859
0.14e
7.8
5.0
TCAN
­
Adjusted
%
Maternal
Weight
Gain
Hill
320.867
0.89d
22
14
Power
319.562e
0.40
21
17
Polynomial
317.582e
0.70e
21
17
a
Modeling
for
BCAN
and
DCAN
based
on
data
from
Hayes
et
al.
(
1986).

b
Adjusted
%
Weight
Gain
for
TCAN
based
on
data
from
Christ
et
al.
(
1996).

c
BMD
and
BMDL
are
based
on
benchmark
response
of
1SD.
Results
are
presented
in
units
of
mg/
kg/
day.
BMD
and
BMDL
estimates
in
bold
type
are
the
estimates
judged
to
be
the
best
estimates
to
use
for
the
quantitative
dose­
response
assessment
for
each
chemical.
Failed
indicates
that
BMDS
was
unable
to
produce
the
estimate
or
the
information
required
to
be
able
to
present
a
value.

d
Based
on
a
comparison
of
the
fitted
model
to
the
model
maximizing
the
likelihood
(
i.
e.
model
with
independent
means
and
variances
for
each
dose
group,
model
A2
from
BMDS).

e
Corrected
from
erroneous
BMDS
output.
Errors
were
identified
in
the
degrees
of
freedom
(
DF)
provided
in
the
output
for
the
fitted
model
in
several
cases.
For
these
cases,
the
AIC
was
calculated
independently
using
the
log
likelihoods
provided
in
the
output
and
the
correct
number
of
DF.
Similarly,
the
goodness­
of­
fit
p­
values
were
corrected
by
calculating
manually
the
chi
square
p­
value
using
the
appropriate
number
of
DF.

f
A
fit
that
maximizes
the
likelihood
is
assigned
a
p­
value
of
1.0,
even
if
there
were
no
degrees
of
freedom
for
a
formal
statistical
test.
The
maximized
likelihood
is
given
by
model
A1
for
constant
variance
models
and
model
A2
for
non­
constant
variance
models.
Models
A1
and
A2
are
independent
of
the
model
chosen
to
fit
the
data
(
e.
g.,
power,
polynomial,
Hill
model)
and
provide
the
best
match
possible
to
the
mean
and
standard
deviation
for
each
dose
level.

Modeling
Results
for
Longer­
term
Studies
BMD
modeling
was
done
to
support
the
derivation
of
the
Longer­
term
and
Lifetime
HAs.

Adequate
longer­
term
studies
that
would
support
BMD
modeling
were
available
only
for
DBAN
and
DCAN.
No
studies
of
suitable
duration
were
available
for
derivation
of
Longer­
term
or
Lifetime
HAs
for
BCAN
or
TCAN.
As
a
result,
BMD
modeling
was
not
performed
for
these
two
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
OW/
OST/
HECD
Final
Draft
A­
17
HANs.
The
BMD
modeling
results
for
the
longer­
term
studies
are
presented
in
Table
A­
2
and
described
below.

DBAN
As
noted
in
Chapter
V,
the
only
endpoint
that
was
considered
to
be
toxicologically
relevant
for
DBAN
in
the
single
available
subchronic
study
(
Hayes
et
al.,
1986)
was
the
observed
decrease
in
body
weight
in
male
rats.
A
constant
variance
model
was
appropriate
for
modeling
the
data
set.
The
Hill,
polynomial,
and
power
models
all
gave
similar
BMD
and
BMDL
estimates.

Visual
inspection
in
the
region
of
the
BMDL
indicated
that
the
fit
was
adequate
for
all
three
of
these
models,
and
was
better
for
these
models
than
for
the
linear
model.
The
goodness­
of­
fit
pvalues
for
the
polynomial
and
power
models
were
very
good,
and
model
fit
for
the
Hill
model
was
not
very
good.
The
polynomial
model
provided
a
slightly
better
fit
than
the
polynomial
model,

with
fewer
parameters
as
indicated
by
the
lower
AIC
and
higher
p­
value,
and
the
BMD
of
29
mg/
kg/
day
and
the
BMDL
of
20
mg/
kg/
day
for
the
polynomial
model
was
selected
as
the
best
estimate
for
this
data
set.

In
summary,
decreased
body
weight
in
males
was
the
only
endpoint
judged
to
be
of
sufficient
toxicological
significance
to
be
modeled
for
DBAN.
Therefore,
the
BMDL
of
20
mg/
kg/
day
for
this
endpoint
is
the
most
appropriate
basis
for
the
Longer­
term
and
Lifetime
HAs.
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
OW/
OST/
HECD
Final
Draft
A­
18
DCAN
Decreased
body
weight
reported
in
Hayes
et
al.
(
1986)
was
considered
to
be
a
toxicologically­
relevant
response
to
DCAN.
A
constant­
variance
model
was
appropriate
for
modeling
the
data
set
for
body
weight
in
males.
However,
none
of
the
continuous
models
provided
an
adequate
visual
fit
in
the
dose
range
of
interest.
Only
the
Hill
models
had
an
adequate
goodness­
of­
fit
statistic,
but
this
model
was
not
selected
due
to
the
model
dependence
of
the
BMDL
estimate,
which
relied
on
a
sigmoid
curve
that
could
not
be
supported
based
on
the
underlying
biology.
The
poor
fits
were
due
to
the
non­
monotonic
nature
of
the
data;
the
mean
body
weight
was
higher
in
the
low
dose
group
than
in
the
controls.
Therefore,
no
adequate
BMDL
estimate
for
decreased
body
weight
in
males
was
obtained.
Further
optimization
of
the
models
for
decreased
body
weight
that
provided
poor
fits
was
not
done
since
it
became
apparent
in
the
course
of
the
preliminary
modeling
that
increased
relative
liver
weight
would
yield
significantly
lower
BMDLs
than
decreased
body
weight,
and
thus
the
modeling
for
body
weight
would
not
drive
the
assessment.

Initial
modeling
for
body
weight
in
females
was
conducted
separately
assuming
either
constant
or
non­
constant
variance.
For
all
four
mathematical
models
fit
to
the
data,
modeling
results
using
the
constant
variance
model
suggested
that
a
non­
homogenous
variance
model
should
be
used.
However,
when
this
was
done,
the
test
statistic
for
the
variance
model
(
test
3)

was
inadequate.
This
result
is
consistent
with
the
absence
of
a
clear
dose­
dependent
(
i.
e.

meandependent
trend
in
the
group
standard
deviations.
The
outcome
of
these
modeling
efforts
indicates
that
neither
the
constant
variance
nor
modeled
variance
options
in
BMDS
provided
an
Drinking
Water
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OST/
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A­
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adequate
estimate
of
the
variance
around
the
best
fit
curve.
An
adequate
estimate
of
the
variances
is
critical
for
relying
on
the
BMDL,
since
the
computation
of
the
BMDL
is
dependent
on
the
estimated
variance
for
the
fitted
model.
(
As
noted
above,
the
BMR
was
defined
as
a
change
in
the
mean
of
one
standard
deviation,
a
measure
related
to
the
variance.)
As
a
result,
even
though
the
linear,
power,
and
polynomial
models
yielded
adequate
goodness­
of­
fit
p­
values
ranging
from
0.11
to
0.22,
none
of
these
models
was
viewed
as
providing
a
reliable
estimate
of
the
BMDL.

The
NOAEL/
LOAEL
analysis
indicated
that
increased
relative
liver
weight
was
the
most
sensitive
indicator
of
toxicity
for
DCAN
(
see
discussion
in
Chapter
V).
Since
increases
in
liver
weight
were
observed
in
both
males
and
females
and
this
effect
was
judged
to
be
toxicologically
relevant,
modeling
was
performed
for
the
relative
liver
weight
data
for
both
sexes.

The
relative
liver
weight
data
for
males
was
modeled
using
a
non­
constant
variance
model,

based
on
visual
inspection
of
the
group
standard
deviations
and
BMD
modeling
results
in
initial
runs.
The
overall
fit
to
the
data
achieved
using
the
full
data
set
was
inadequate
for
all
of
the
continuous
models
that
were
run,
except
the
Hill
model,
which
did
not
calculate
a
BMDL
estimate.
The
poor
model
fits
appeared
to
arise
from
the
inability
of
these
models
to
accommodate
the
plateau
in
the
dose­
response
curve
at
high
doses.
Therefore,
consistent
with
the
approach
used
for
the
short­
term
studies,
modeling
was
done
using
a
truncated
data
set
(
i.
e.

without
the
high
dose).
The
Hill
model
was
not
run
using
the
truncated
data
set,
since
this
model
requires
at
least
four
data
points
to
calculate
a
BMDL
estimate
and
the
truncated
data
set
contained
only
three
doses.
The
linear,
power,
and
polynomial
models
performed
very
well
when
Drinking
Water
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Document
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the
high
dose
data
were
removed,
based
on
visual
inspection
and
review
of
the
chi­
square
values
for
residuals
at
the
individual
data
points.
Although
goodness­
of­
fit
statistics
were
not
calculated
by
BMDS
for
the
polynomial
and
power
models,
independent
calculation
of
the
p­
values
(
as
presented
in
Table
A­
2)
confirms
the
good
statistical
fit.
Since
the
BMDL
estimates
were
the
same
for
all
three
models,
the
model
with
the
lower
AIC
was
selected
as
providing
the
best
estimate.
Therefore,
the
BMD
of
6
mg/
kg/
day
and
the
BMDL
of
4
mg/
kg/
day
for
the
linear
model
were
selected
as
the
best
estimates
for
the
dose­
response
assessment.

For
modeling
of
relative
liver
weight
in
females,
the
initial
BMDS
results
indicated
that
a
non­
constant
variance
model
would
be
most
appropriate.
However,
for
all
four
of
the
mathematical
models
fit
to
the
data,
the
test
statistic
for
the
variance
model
was
inadequate
with
this
option
selected,
reflecting
the
absence
of
a
clear
dose­
dependent
(
i.
e.
mean­
dependent)
trend.

As
described
above
for
modeling
of
female
body
weight
for
DCAN,
the
inability
to
get
an
appropriate
model
of
the
variance
precludes
identifying
the
BMDL
estimate
with
confidence.

Regardless
of
this
consideration,
none
of
the
modeling
results
using
the
full
data
set
provided
an
adequate
fit
to
the
data.
Although
the
Hill
model
yielded
a
curve
that
went
through
the
points,

the
curve
had
a
sigmoid
shape
that
was
highly
dependent
on
the
model
and
that
could
not
be
supported
based
on
the
underlying
biology.
Since
there
was
an
apparent
plateau
in
the
doseresponse
data,
a
truncated
data
set
was
modeled
with
the
high
dose
group
removed.
This
approach
provided
an
adequate
visual
fit.
However,
similar
to
the
modeling
with
the
full
data
set,

the
variance
model
could
not
adequately
describe
the
data.
Therefore,
none
of
these
models
was
viewed
as
providing
a
reliable
estimate
of
the
BMDL.
Drinking
Water
Criteria
Document
for
Haloacetonitriles
EPA/
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A­
21
In
summary,
based
on
the
evaluation
of
these
BMD
modeling
results
for
DCAN,
increased
relative
liver
weight
in
males
is
the
most
sensitive
endpoint.
The
BMD
of
6
mg/
kg/
day
and
the
corresponding
BMDL
of
4
mg/
kg/
day
for
the
linear
model
was
selected
as
the
most
appropriate
basis
for
the
Longer­
term
and
Life­
time
HAs.
Drinking
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Table
A­
2
Benchmark
Dose
Modeling
Results
for
DBAN
and
DCANa
Endpoint
and
Model
AIC
P­
value
BMDb
BMDL
DBAN
­
Body
Weight
in
Males
Linear
716.297e
0.15
20
16
Hill
716.713
0.06c
30
21
Power
714.705
0.61
30
20
Polynomial
714.681e
0.63
29
20
DCAN
­
Body
Weight
in
Males
Linear
777.801e
0.022
17
15
Hill
775.374
0.12c
32
21
Power
776.405
0.028
25
18
Polynomial
777.462e
0.015
24
16
DCAN
­
Body
Weight
in
Femalesd
Linear
717.621e
0.22
46
34
Hill
721.120
<
0.001c
55
31
Power
719.090
0.11
55
35
Polynomial
718.907e
0.13
52
33
DCAN
­
Liver
Weight
in
Males
Linear
117.429
<
0.0001
7
5
Hill
118.869
0.59c
8
Failed
Power
117.429e
0.02e
7
5
Polynomial
117.974
<
0.0001
6
4
DCAN
­
Liver
Weight
in
Males
(
without
highest
dose)

Linear
37.993
0.44
6
4
Power
39.388
1.0f
7
4
Polynomial
39.388
1.0f
7
4
DCAN
­
Liver
Weight
in
Femalesd
Linear
86.720e
0.00039
32
25
Drinking
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Endpoint
and
Model
AIC
P­
value
BMDb
BMDL
EPA/
OW/
OST/
HECD
Final
Draft
A­
23
Hill
75.031
1.0f
8
6
Power
86.720e
0.0004e
32
25
Polynomial
86.720e
0.0004e
32
25
DCAN
­
Liver
Weight
in
Females
(
without
highest
dose)
d
Linear
64.218e
0.50
16
12
Power
64.218e
0.50
16
12
Polynomial
65.757e
1.0f
12
6
a
Modeling
was
performed
based
on
body
and
organ
weight
at
terminal
sacrifice
in
the
subchronic
study
by
Hayes
et
al.
(
1986).

b
BMD
and
BMDL
are
based
on
benchmark
response
of
1SD.
Results
are
presented
in
units
of
mg/
kg/
day.
BMD
and
BMDL
estimates
in
bold
type
are
the
estimates
judged
to
be
the
best
estimates
to
use
for
the
quantitative
dose­
response
assessment
for
each
chemical.
Failed
indicates
that
BMDS
was
unable
to
produce
the
estimate
or
the
information
required
to
be
able
to
present
a
value.

c
Based
on
a
comparison
of
the
fitted
model
to
the
model
maximizing
the
likelihood
(
i.
e.
model
with
independent
means
and
variances
for
each
dose
group,
model
A2
from
BMDS).

d
The
modeling
results
for
DCAN
shown
here
are
for
the
constant
variance
model.
Neither
the
constant
nor
non­
constant
variance
models
yielded
a
reliable
BMDL
estimate.

e
Corrected
from
erroneous
BMDS
output.
Errors
were
identified
in
the
degrees
of
freedom
(
DF)
provided
in
the
output
for
the
fitted
model
in
several
cases.
For
these
cases,
the
AIC
was
calculated
independently
using
the
log
likelihoods
provided
in
the
output
and
the
correct
number
of
DF.
Similarly,
the
goodness­
of­
fit
p­
values
were
corrected
by
calculating
manually
the
chi
square
p­
value
using
the
appropriate
number
of
DF.

f
A
fit
that
maximizes
the
likelihood
is
assigned
a
p­
value
of
1.0,
even
if
there
were
no
degrees
of
freedom
for
a
formal
statistical
test.
The
maximized
likelihood
is
given
by
model
A1
for
constant
variance
models
and
model
A2
for
non­
constant
variance
models.
Models
A1
and
A2
are
independent
of
the
model
chosen
to
fit
the
data
(
e.
g.,
power,
polynomial,
Hill
model)
and
provide
the
best
match
possible
to
the
mean
and
standard
deviation
for
each
dose
level.
