Detection
Limits
450a
01­
1
Introduction
Goal:
Examine
detection
limits,
their
purpose,
definition,
and
their
intended
use
There
are
many
potential
situations
in
which
data
censored
by
detection
limits
arise
One
place
censored
data
are
generated
is
through
the
analysis
of
survival
times
This
may
be
applicable
to
LD50
or
LC50
studies
that
are
performed
to
determine
the
toxicity
of
a
chemical
Our
focus
is
on
left
censoring
of
analytical
data
arising
from
the
use
of
detection
(
or
quantitation)
limits
450a
01­
2
Introduction
In
the
case
of
survival
times,
censoring
is
caused
by
not
being
able
to
observe
effect,

or
death,
after
some
point
in
time
In
the
case
of
"
detection
limits",
censoring
is
caused
by
not
reporting
data
below
some
threshold
concentration
Note
that
the
underlying
distributions
are
not
necessarily
truncated,
but
censoring
makes
it
difficult
to
estimate
parameters
450a
01­
3
Introduction
Let's
consider
the
following
right
and
left
censoring
of
a
joke
(
which
is
our
data
point):

Right
censoring:
A
statistician's
wife
had
twins.
He
was
delighted.
He
rang
the
minister
who
was
also
delighted.
"
Bring
them
to
church
on
Sunday
and
we'll
baptize
them,"

said
the
minister.
"
No,"
he
replied.
450a
01­
4
Introduction
Left
censoring:
He
rang
the
minister
who
was
also
delighted.
"
Bring
them
to
church
on
Sunday
and
we'll
baptize
them,"
said
the
minister.
"
No,"
he
replied.
"
Baptize
one.
We'll
keep
the
other
as
a
control."

Censoring
causes
some
loss
of
information.

The
consequences
are
lack
of
complete
understanding
450a
01­
5
Sensitivity
Indicator
Numerical
Definition
Definition
Common
Use
Instrument
Detection
Limit
(
IDL)
Usually
3
times
the
instrument
noise
level
Lowest
value
at
which
instrument
can
distinguish
from
zero
Provides
basis
for
determining
an
MDL
Method
Detection
Limit
(
MDL)
MDL
=
t
(
n­
1,
0.99)
x
s
s
=
standard
deviation
for
7
aliquots:

t
(
n­
1,
0.99)
=
3.14
Defined
40
CFR
Part
136
Appendix
B
Determines
the
theoretical
detection
limit
Practical
Quantitation
Limit
(
PQL)
PQL
=
5
x
MDL
or
PQL
=
10
x
MDL
(
more
precisely
defined
as
the
lowest
standard
on
the
instrument
calibration
curve)
"
the
lowest
concentration
of
an
analyte
that
can
be
reliably
measured
within
specified
limits
of
precision
and
accuracy
during
routine
laboratory
operating
conditions"
Provides
numerical
lower
limit
for
critical
data
Reporting
Limit
(
RL)
Laboratory
defined
(
often
the
RL
=
PQL)
Lowest
value
reported
by
laboratory
without
a
"
J"
flag
Laboratory
basis
for
data
reporting
Types
of
Detection
Limits
450a
01­
6
Detection
Limits
Two
types
of
detection
limits
are
of
particular
interest
and
will
be
presented
herein
1.
Method
Detection
Limit
(
MDL)

"
Imprecision
that
is
added
to
the
detection
capabilities
of
the
instrument
due
to
the
sample
processing
manipulations
and
the
sample
matrix"
­
US
EPA
NRMRL
450a
01­
7
Detection
Limits
2.
Practical
Quantitation
Limit
(
PQL)

"
Concentration
of
the
lowest
calibration
standard
(
by
default).
The
low
calibration
standard
is
usually
determined
by
accounting
for
the
sample
matrix,
dilutions
needed,
sample
volumes/
weight
used,
and
final
volumes
used.
It
is
usually
some
multiple
of
the
MDL"
­
EPA
QA/
G­
5i
450a
01­
8
Detection
Limits
Why
detection
limits?

Because
of
a
desire
to
avoid
erroneously
reporting
the
presence
of
an
analyte
(
i.
e.,
to
control
false
positives)

Because
of
measurement
variability
This
raises
the
question
of
when
does
a
positive
response
represent
a
detected
analyte?
450a
01­
9
Chemical
Measurement
In
general,
the
measurement
process
is
very
complex,
involves
many
details
(
e.
g.,
drift,

fluctuation,
baseline,
calibration),
and
varies
from
method
to
method
Calculation
of
detection
limits
have
largely
been
standardized,
perhaps
to
accommodate
the
many
intricacies
of
the
measurement
system
450a
01­
10
Method
Detection
Limit
The
MDL
has
a
regulatory
definition
in
40CFR136
Appendix
B:

"
The
minimum
concentration
of
a
substance
(
analyte)
that
can
be
measured
and
reported
with
99%
confidence
that
the
analyte
concentration
is
greater
than
zero,
and
is
determined
from
analysis
of
a
sample
in
a
given
matrix
type
containing
the
analyte."
450a
01­
11
Method
Detection
Limit
An
MDL
is
interpreted
in
terms
of
a
distribution
of
blanks
That
is,
we
determine
the
"
upper
99%

confidence
limit/
bound"
on
a
blank
distribution
We
use
the
MDL
as
the
threshold
concentration
that
determines
detect
status
for
future
individual
samples
450a
01­
12
Method
Detection
Limit
The
problems
­

The
MDL
is
not
usually
established
by
measuring
blanks,
but
by
measuring
standards
at
very
low
concentration,
and
then
extrapolating
through
assumption
to
the
blank
distribution
Lack
of
universal
understanding
of
"
confidence"
450a
01­
13
Method
Detection
Limit
Does
it
make
any
difference
that
we
use
low
concentration
standards
instead
of
blanks?

Perhaps
not
if
the
standard
deviation
is
the
same
in
both
cases
This
is
a
fundamental
assumption
of
this
approach
the
standard
deviation
is
the
same
within
a
range
of
low
concentrations
450a
01­
14
0.1
0.2
0.3
0.4
Distribution
of
the
blank
from
MDL
study
 
Assumption
of
Equivalent
Variances.

0
It
is
assumed
the
shape
is
the
same
despite
a
location
shift
450a
01­
15
Method
Detection
Limit
1.
A
known
standard
is
selected
at
a
concentration
that
is
expected
to
be
close
to
the
MDL
2.
Replicates
from
this
standard
are
analyzed
3.
A
(
preliminary)
MDL
is
determined
from
these
data
4.
If
the
preliminary
MDL
and
standard
are
"
close
enough",
then
use
the
preliminary
MDL,
otherwise
repeat
the
experiment
using
a
lower
standard
450a
01­
16
Method
Detection
Limit
The
MDL
defined
by
40CFR136
Appendix
B:

MDL
=
t(
n
­
1,
1
­
 
)
x
s
where,
s
=
the
estimated
standard
deviation
associated
with
the
sample
The
expression,
t(
n
­
1,
1
­
 ),
represents
a
specific
value
from
the
t­
distribution
associated
with
n
samples
(
or
n
­
1
degrees
of
freedom)
450a
01­
17
Method
Detection
Limit
 ,
the
false
positive
rate,
is
set
at
1%

(
corresponding
to
a
99%
value
from
the
t­
distribution)

Hence,
t(
n
­
1,
1
­
 ),
is
the
99th
percentile
of
the
standard
t­
distribution
with
n­
1
degrees
of
freedom
Hence,
the
MDL
(
t
x
s)
is
the
estimated
99
th
percentile
of
the
blank
distribution
450a
01­
18
MDL
Example
Suppose
an
MDL
study
was
performed
where
7
samples
were
used
to
establish
a
MDL
Suppose
the
standard
was
1
ppm,
and
we
are
given
the
following
data:

The
estimated
standard
deviation
is
s
=
0.264
0.7
0.8
0.9
1.0
1.1
1.2
1.4
450a
01­
19
­
4
­
2
0
2
4
0.1
0.2
0.3
0.4
3.14
0.99
0.01
t­
distribution
with
(
7­
1)=
6
Degrees
of
Freedom
450a
01­
20
MDL
Example
The
t­
statistic,
3.14
(
tabled
value
from
the
t­
distribution)
is
then
multiplied
by
the
sample
standard
deviation,
0.264,
to
obtain
the
MDL
MDL
=
t(
6,0.99)
x
s
=
3.14
x
0.264
=
0.83
In
this
example,
0.83
(
the
MDL)
is
probably
close
enough
to
1
ppm
(
the
standard),
that
further
iteration
is
not
required
450a
01­
21
MDL
Example
Interpretive
problem
­

There
is
no
statistical
concept
of
confidence
in
any
part
of
the
analysis
What
we
have
actually
estimated
is
a
percentile
of
a
distribution
There
isn't
anything
wrong
with
that,
but
it
has
nothing
to
do
with
statistical
confidence
intervals
450a
01­
22
MDL
Example
Suppose
we
get
a
reported
concentration
of
0.7
ppm
for
a
specific
analyte
Do
we
believe
that
the
analyte
is
present?

What
is
the
chance
that
the
analyte
is
present?

How
does
the
relationship
between
the
reported
concentration
and
the
MDL
affect
the
chance
the
analyte
is
present?
450a
01­
23
MDL
Example
This
can
be
interpreted
as
a
98%
probability
that
the
analyte
reported
at
0.7
is
actually
present
Even
a
reported
value
of
0.2
has
a
probability
that
the
analyte
is
present
of
about
0.75
However,
one
should
realize
that
a
reported
value
of
0,
using
this
model,
has
a
probability
that
the
analyte
is
present
of
0.5
450a
01­
24
­
1.0
­
0.5
0.0
0.5
1.0
0.0
0.5
1.0
1.5
0.7
Probability
of
Observing
0.7
ppm
(
or
Greater)

0.02
0.02
450a
01­
25
­
1.0
­
0.5
0.0
0.5
1.0
0.0
0.5
1.0
1.5
0.7
Probability
of
Observing
Small
Concentrations
0.02
0.2
0.50
0.25
450a
01­
26
Practical
Quantitation
Limit
There
are
many
types
of
quantitation
limits,

the
intention
of
all
of
them
is
to
provide
some
more
"
confidence"
in
reported
concentrations
Practical
quantitation
limits
are
defined
as
"
the
lowest
concentration
of
an
analyte
that
can
be
reliably
measured
within
specified
limits
of
precision
and
accuracy
during
routine
laboratory
operating
conditions"

­
US
EPA
QA/
G­
5i
450a
01­
27
Practical
Quantitation
Limit
Some
are
defined
as
a
multiple
of
the
MDL
between
2
and
5
are
common
Some
are
defined
as
a
number
of
standard
deviations
from
zero
around
10
standard
deviations
is
common
450a
01­
28
Relationship
of
Detection
Limits
3 
10
 
Zero
Analyte
Concentration
Region
of
high
uncertainty
Region
of
more
certain
detection
Region
of
less
certain
quantification
Approximate
MDL
Level
Region
of
more
certain
quantification
Instrument
signal,
standard
deviation
units
Matrix/
method
blank
Approximate
PQL
Level
 
=
population
standard
deviation
0
450a
01­
29
Practical
Quantitation
Limit
Given
the
MDL
discussion,
it
would
appear
that
PQLs
are
a
very
conservative
censoring
mechanism.
Why
are
they
used?

The
purpose
relates
to
the
desire
to
define
a
linear
range
(
a
calibration
range)
that
is
sufficiently
far
from
noise
levels,
but
still
likely
to
serve
the
purposes
of
the
study,
and
to
which
all
analyses
are
targeted
That
is,
the
PQL
defines
the
lower
end
of
the
concentration
range
for
which
reported
concentrations
are
not
flagged
450a
01­
30
MDL/
PQL
Example
Let's
revisit
the
study
where
7
samples
were
used
to
establish
a
MDL
The
estimated
standard
deviation
was
s
=
0.264
Recall
that
the
MDL
was
calculated
to
be
0.83
ppm
The
PQL
was
set
at
10 
=
2.64
ppm
0.7
0.8
0.9
1.0
1.1
1.2
1.4
450a
01­
31
Data
Reporting
Data
within
the
calibration
range
are
reported
without
flags
If
high
concentration
samples
are
not
diluted
and
re­
analyzed,
then
they
are
flagged
as
estimated
(
J)

Values
below
the
PQL
are
flagged
as
estimated
(
J)

Values
less
than
the
MDL
are
flagged
as
not
detected
(
U)
450a
01­
32
MDL/
PQL
Example
In
our
example
­

Data
reported
below
0.83
ppm
is
flagged
with
a
"
U"
to
indicate
that
the
analyte
was
not
detected
Data
reported
above
0.83
ppm,
but
below
2.64
ppm,
is
flagged
with
a
"
J"
to
indicate
that
the
value
is
estimated
Data
reported
above
2.64
ppm
is
not
flagged
450a
01­
33
Conclusions
From
a
statistician's
perspective,
censoring
both
results
in
a
loss
of
information
and
causes
difficulties
in
statistical
analysis
The
decision
focus
is
on
data
From
a
chemist's
perspective,
censoring
more
realistically
reflects
their
knowledge
about
the
analytical
process
Their
focus
is
on
each
datum
If
all
the
information
is
provided
and
couched
appropriately,
then
it
is
possible
to
accommodate
both
concerns
450a
01­
34
Conclusions
How
detection
limits
are
used
and
their
impact
on
analysis
depends
not
only
on
the
objectives
of
the
study,
but
also
on
the
magnitude
of
the
concentrations
of
interest
For
many
analytes
detection
limits
are
not
of
concern
because
the
reporting
values
are
well
above
this
limit
Detection
limits
are
also
not
a
concern
when
the
threshold
concentrations
of
interest
are
much
greater
than
this
limit
450a
01­
35
For
other
analytes,
the
detection
limits
are
similar
to
reporting
values,
so
they
are
a
concern
Detection
limits
are
a
concern
when
they
are
close
to
the
threshold
concentrations
of
interest
Many
methods
are
available
for
handling
detection
limits
in
data
analyses
Conclusions
450a
01­
36
