"
Smith,
Anne"
<
ASmith@
crai.
com>

07/
08/
2006
07:
20
AM
T
o
Johnd
Bachmann/
RTP/
USEPA/
US@
EPA
c
c
clangworthy@
hunton.
com
S
u
b
j
e
c
t
Follow
up
on
your
question
about
rollbacks
Dear
John,

On
June
19,
you
asked
for
information
on
how
we
had
performed
the
annual
standard
rollbacks
in
a
sensitivity
analysis
on
Figure
5­
1
of
the
Staff
Paper.
Due
to
an
oversight,
the
information
did
not
get
sent
to
you
promptly.
I
apologize
for
that,
and
am
sending
you
some
more
detailed
information
on
that
sensitivity
analysis
now.

The
attached
file
shows
a
breakdown
of
the
three
elements
of
the
sensitivity
analysis.
The
upper
left
of
the
attached
slide
shows
the
figure
as
it
is
in
the
Staff
Paper.
The
upper
right
shows
the
effect
of
JUST
revising
the
method
of
rollback
to
exactly
attain
the
annual
average.
It
is
that
single
step
that
you
asked
about,
and
which
I
will
describe
below.
However,
the
two
figures
on
the
lower
part
of
the
graph
show
the
effect
of
then
also
calculating
mortality
to
background
rather
than
to
LML
(
lower
left)
or
then
also
performing
the
alternative
peak
rollback
for
attaining
the
daily
standard
(
lower
right).
(
The
bottom
two
figures
are
thus
two­
way
sensitivities
on
Figure
5­
1,
or
one­
way
sensitivities
on
the
figure
in
the
upper
right,
as
the
arrows
on
the
figure
indicate).
The
combined
effect
of
all
three
elements
was
the
figure
in
the
June
19
presentation
(
on
slide
8).

I
will
now
summarize
how
these
sensitivity
cases
were
developed.

We
did
not
use
daily
data
for
each
monitor
in
the
city,
as
EPA
has
done.
Instead,
we
found
that
a
lognormal
distribution
could
be
fitted
to
the
distributional
summary
statistics
reported
in
EPA's
Risk
Assessment
for
"
just
attaining"
the
current
standard,
and
that
proportional
rollbacks
of
this
fitted
distribution
using
the
rollback
factors
that
EPA
reported
would
very
closely
reproduce
the
entire
set
of
percent
mortality
changes
in
Figure
5­
1
for
each
city.
This
method
was
reasonable
as
a
sensitivity
analysis
to
understand
the
determinants
and
responsiveness
of
the
information
in
Figures
5­
1
and
5­
2.
For
this
purpose,
it
did
not
need
to
provide
a
precise
reproduction
of
the
calculations
that
EPA
would
perform
using
exact
daily
data
from
each
individual
monitor
in
the
city.
(
However,
I
do
not
believe
such
precision
is
meaningful
even
for
EPA's
final
risk
assessment.)
Sensitivity
to
Annual
Standard
Rollback
("
Exact
Attainment").
By
applying
the
EPA
rollback
factors
for
each
alternative
annual
standard
where
the
daily
standard
was
not
controlling,
we
were
able
to
confirm
that
EPA's
simulation
of
"
just
attaining"
the
annual
standards
produced
annual
average
values
that
were
substantially
lower
than
the
annual
standard.
In
our
sensitivity
case,
we
then
used
an
alternative
rollback
factor
that
would
cause
the
annual
average
of
the
fitted
lognormal
distribution
to
be
exactly
equal
to
the
annual
standard
itself.
This
new
distribution
would
then
be
rolled
back
again
to
meet
each
of
the
daily
standards,
if
they
were
not
also
met
as
a
result
of
the
annual
standard
rollback.
For
graphs
that
show
the
effect
of
only
the
change
in
the
annual
standard
rollback,
(
e.
g.,
the
upper
right
of
the
attached
file)
the
daily
rollbacks
were
still
performed
using
EPA's
method
of
proportional
rollback
of
the
full
distribution
The
rollback
factor
for
the
latter
was
determined
by
the
value
of
the
98th
percentile
on
the
revised
lognormal
distribution.
As
the
figures
we
have
supplied
reveal,
the
alternative
annual
standard
rollback
has
the
least
impact
of
the
three
on
the
percent
risk
changes.
Sensitivity
to
Daily
Standard
Rollback
("
Minimum
Rollback
of
Peak
Days
to
Just
Attain
Daily
Standard").
After
performing
the
rollbacks
necessary
for
exactly
attaining
the
annual
standard,
it
can
be
determined
if
additional
rollback
is
necessary
to
attain
the
daily
standard.
This
was
done
by
looking
at
the
value
at
the
98th
percentile
of
the
new
distribution.
Under
our
sensitivity
case,
we
reduced
all
daily
values
above
the
24­
hour
standard
down
to
just
below
the
level
of
that
standard
(
in
our
discretized
analysis,
those
days
were
assigned
an
average
PM2.5
value
of
0.5
µ
g/
m3
below
the
level
of
the
standard.)
The
figures
provided
show
this
sensitivity
only
in
combination
with
"
Exact
Attainment"
of
the
annual
standard,
and
should
therefore
be
compared
to
the
"
Exact
Attainment"
figure
to
observe
its
individual
sensitivity.
As
can
be
seen,
this
has
a
substantial
effect,
particularly
by
"
flattening"
the
apparent
"
knee
in
the
curve"
of
Figure
5­
1.
Sensitivity
to
Use
of
LML
in
place
of
Background
("
Calculation
Mortality
to
Background").
The
calculation
of
risks
(
and
percent
reduction
in
risks)
was
done
by
EPA
only
down
to
the
LML
of
7.5
µ
g/
m3.
When
reproducing
EPA's
figures,
we
also
used
that
LML
unless
otherwise
noted.
In
our
sensitivity
case
for
the
LML,
we
replaced
the
LML
value
in
the
calculation
with
the
city's
assumed
background
level
(
2.5
µ
g/
m3
for
Los
Angeles
and
3.5
µ
g/
m3
for
Philadelphia).
This
change
also
has
a
significant
effect,
particularly
by
"
lowering"
the
percentage
reduction
achieved
across
the
entire
figure.
It
raises
the
absolute
number
of
deaths
estimated
at
the
current
standard
(
simply
because
it
counts
all
that
are
supposedly
due
to
anthropogenic
PM2.5)
but
doing
so
also
dramatically
alters
the
suggestion
of
Figure
5­
1
that
very
much
of
that
risk
can
be
eliminated
by
changing
the
standard
within
the
ranges
being
considered.
As
CASAC
was
striving
for
a
standard
that
would
achieve
a
risk
reduction
in
the
range
of
40
to
70
percent
in
each
of
the
cities,
the
fact
that
this
could
only
be
done
by
not
counting
risks
below
the
LML
is
a
highly
relevant
piece
of
information.

I
hope
this
helps,
and
I
am
sorry
again
for
the
delay
in
my
response.
Let
me
know
if
you
have
any
questions.
Anne
Smith
CRA
International
(
202)
662­
3872
