1. business and industrial
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CUN. CHEM.
22/2.
176-183
Sample
(1976)
Stability:
and Method
Ralph
We
E. Thiers,
propose
stituent
ly related
defining
stability
H. Reed,
of any
in terms
of the
chemical
measurement
when
the
average
change
suring
age.
over
the
concentration
experimental
stability.
and
range
statistical
The statistical
of
in question.
a graphical
for
the
for the proposal
the
is
presented.
quality
variation,
In clinical
control
#{149}
statistics
#{149}
stability
is a critical
consider-
the
approach
with
been
judgments
ulation
chemistry,
of
ing
stability
We
and
stability
that
a method
is
for test-
that
relatively
to
We,
by
application,
the
literature,
from
studies,
Proposed
definition
of sta-
and
derivation.
has
This
by
and
been
found
approach
comparison
with
by computer
sim-
reliable.
Definition
current
criteria
superficial,
of stability
and
that
are
fre-
conclusions
method.
Specifically,
one standard
is stable
under
demonstrate,
specified
with
conditions
prespecified
that
its mean
concentration
has changed
by less than
is a function
of the precision
in
an
of
the
as so defined.
believe
quently
of
chemistry
is related
measurement.
a simple
supporting
risks
of decision-error,
the
tested
specimens
amount,
5, where
for clinical
experimental
method
of testing
stability
that
and
objective.
It is presented
its
stability
We
suitable
of
tested
A constituent
when
measurements
to be lacking.
here
a definition
a given
differences
permits
ation,
but its assessment
seems
to have
been
neglected. We find
no literature
on an experimental
design
for doing
so. In fact,
even
an objective
definition
of
seems
propose
for
method
bility
and a standard
is statistically
simple
has
Keyphrases:
source
of
and
of detectable
seeks
differences
after
sample
stor-
therefore,
propose
to define
stability
in terms
of analytical
precision
after
Hagebush
(1 ) and to utilize
expenimental
designs
in which
one is used
to evaluate
the other.
here
Additional
terms,
size
precision
This
mea-
studies
one routinely
made
before
and
In practical
effort,
as the ap-
design
basis
its
in
number,
K,
by the measur-
K. Oliver
In stability
in measurements
by which
Based
on this definition
a technique
utilizing
truncated
normal
sequential
test is presented
propriate
con-
that are quantitative-
value
is less than a chosen
deviations
of the data obtained
ing method
and Lawrence
that a constituent
may be
for a stated
period and under exactly
conditions,
measured
standard
Allen
We suggest
stable,
defined
the
precision
it is determined.
considered
T. Wu,
samples
to the
Definition
of Determination
Gaw
of stored
A Suggested
we suggest
setting
deviation
(SD) of the
equal
analytical
t5
to
exactly
method
based
on them
depend
on subjective
judgment.
Measurement
errors
loom large
among
the practical
problems
involved
in measuring
any change
of concentration
attributable
to instability
on storage.
Among
used,
and we suggest
setting
deciding
that
a constituent
itive and 0.025 for negative
measurement
that
it is stable
when
it is in fact unstable.
Statisticians
call these
errors
of the first and second
kind,
respectively,
and symbolize
them
a and
fi.
Re-stated,
we are proposing
that
a constituent
be
errors
or inter-run
ed. These
we
have
biases
seem
are significant
disconcertingly
obvious,
ly serious
in measurements
trations
for
determination
but
where
and
which
precision
of hormones
knowledge
observed
to have
effects
that
been
that
they tend
of extremely
inter-day
underestimatare sometimes
to be especiallow concen-
is relatively
poor,
by radioimmunoassay-
of stability
stable,
is nonetheless
such
deemed
as
im-
portant.
setting
Laboratories,
Dept.
of Research,
7600 Tyrone
Calif.
91405;
and (A.H.R.)
Management
Science
Univ.
Northridge,
Northridge,
Calif.
91324.
Sept.
12, 1975; accepted
Nov. 10, 1975.
CLINICAL
CHEMISTRY,
Vol. 22, No. 2, 1976
Ave.,
Dept.,
at 0.05
stable
under
5% risk
of error
(if
This
the
may
for our
probability
of deciding
storage
is shown
to 1 SD and
conditions
to change
by
when
we allow
decision.
Design
definition
constituent
presume
the
specified
when
its mean
concentration
less than
an amount
equal
Experimental
Bio-Science
Van
Nuys,
‘Calif.
State
Received
176
and
at 0.05 the probability
of
is unstable
(0.025
for poschanges)
when
it is in fact
implies
a single
is unchanged
that
it has
been
stable
duration
at that
until
of storage
time,
one
that
time).
Also,
carefully
and
stated
storage
conditions
must
definition.
be
Finally,
state
of the
test
ben
stability,
as
of determinations
of inter-nun
art
minimize
definition
permits.
defined,
bias,
in the
makes
and
implies
should
required,
can use the known
simply
divides
each
Day
to
the
the
numeffect
period
in the
being
same
aliquot-pairs
quots
can
of each
bias
and
tested
analytical
be
the
are
measured
S,
S3
5
F6
S4
stathat
6
7
.
because
one
comparison.
two aliquots
One
im-
8
8
not suffer
of conditions
constituent
is stable
from
oven
inter-run
bias cannot
final
determinations
runs.
creased
design.
is divided
analyzed
some
in
time
etc.
two
and
All
analyzed
according
in Table
to
is a design
constituent
at the
under
in the
the
“stoned”
of the
measured
under
ith
like
that
the
test
exempli-
determining
sta-
concentration
whether
after
it has
F
Let
conditions
of the
analyzed
been
represent
aliquot.
of the
stored
the
Simiith ali-
be S.
in the runs
in each run.
determination
is compensated
by having
two aliThe effect
for one aliquot
is on the
(F) and for the other
aliquot
on
the final
determination
is to substantially
cancel
sumption
in Table
(5). Therefore,
the net effect
the bias in that
nun. The as-
1 is that
merely
one
run
on fresh
sample
on stored
5,,
number
sample
of other
have
1.
number
is made
every
than
1.
this
two
F and
the
number
desired.
an analysis
be
without
regard
of days
days,
an
initial
nun
the
sample
corresponding
experimental
design
is decreased
of another,
given
statistical
mend
is
the
in which
it is used
When
the
that
the
pending
below).
The
on
test
statistic
should
which
statistic
We
propose
be the
for ei-
design
de-
F1 and
data
plotted
marked
a boundary
is stable
of
that
same
of analytical
boundary
recomtest
experimental
crosses
cancellawe
is calculated
and
preset
boundaries
constituent
error
sequential
(2).
one
inter-run
process
Armitage
same
is only
as by some
normal
statistic,
T.S.,
(Figure
1) with
is in the
there
as well
decision-making
Si, a test
cide
sample
case
ther
of the
two
types
of
scribed
above,
as follows:
For each
successive
pain
graph
that
of the effect
of
weekends
inso that
either
In this
truncated
and
form
by
to the
demands
or else
run.
by averaging
tion.
The
the
on one
final
in any
schedoffset
run every
day,
or at regular
intervals,
to weekends
or holidays.
An effective
determination
with
the
S columns
but slightly
less complete
cancellation
inter-run
bias
can be achieved,
where
tenvene,
by spacing
the determinations
jt.i
1, aliquot
F1 is assayed
1, and so on. On day 2,
3, F3, and
the
final
assay
on specimen
1, S1, are run concurrently.
On all
subsequent
days
two assays
are run, one on a stored
and one on a control
aliquot.
Therefore,
in all runs
except
the first
two and the last two,
bias that
may
exist
quots
initial
a period
Schneiderman
such
control
concentration
In the case shown
in Table
on day 0, aliquot
F2 on day
the
initial
assay
on specimen
aliquots
for different
collected
and
aliquot,
time
of collection
or
conditions
of stability.
concentration
lanly,
let
quot
control
is
times
are
for
bility
over a two-day
period.
Let F represent
the measured
for
other
of the
a schedule
1, which
is stored
the
treatment
storage
time
and starting
must
be identical.
Specimens
de-
experimental
after
it is colone
For
would
Obviously
and
be in
drastically
analyzed,
result
the appropriate
length
of time
the
initial
must
aliquots;
then
F#{247}2
result
analytical
ule
which
because
sample
be
S,:
day.
concentra-
in question,
however,
analytical
F,:
S.
ali-
period
by the following
immediately
into
time
both
inter-run
in their
55
are anaof such
this error.
is known
under
the
can,
immediately.
except
pairs
fled
Bias
designated
Thus
same
be avoided,
on any one
and minimized
Each
specimen,
lected,
the
run.
to the
difference
tions
should
If no set
different
given
subject
F,
F,
the two aliquots
run. Any number
in any
pair
Stored
4
to know
constituent
for
into
F,
S,
bias
conditions
specimen
Fresh
0
1
2
3
F4
is definitely
experiments
inter-run
no.
assayed
F3
to execute.
matrix
design
Design-
.
Aliquots
mediately
after
it is collected
and stores
one under
the conditions
of known
stability
while
the other
is
stored
under
the test
conditions.
At the end of the
time
lyzed
1 Example of Experimental
Testing 2-Day Stability
the analytas small
as
designed
is fortunate
enough
under
which
the
of
Table
of this
a known,
for
be
minimize
minimize
be simple
effects
handling
of use
Experiments
given
sample
it easy
to
the
sample
part
standard
deviation
used,
which
should
Sometimes
one
set
of conditions
question
ble. This
for
integral
the
stated,
unchanging
ical method
being
the
an
one
or
on a
on
can
unstable,
is crossed
(as
dede-
explained
is:
:
Nd
T.S.
=
(S,
-
F1)/SD
i=1
where
Si
after
=
the
measured
concentration
of the
ith
sample
storage,
1 The
statistical
derivation
of this approach
boundaries
in the
various
graphs
is available
reader
from
the authors
or the Executive
Editor
CLINICAL
CHEMISTRY,
Vol.
and
of the decisionto the
interested
of this journal.
22,
No.
2, 1976
177
0.5
/
/
I
I
0.4
I
/
Proportional
0.3
Error
I
-
a)
p..
z
0
a)
SAMPLE
NUMBER.
i
Fig. 1 Graphical presentation
of truncated
test-stability
of creatine kinase for 4 days
normal sequential
.
Line A, 30 #{176}C,
line B, 4 #{176}C,
line C, -20
0.2
#{176}C.
Samples
were
0.1
quick-frozen
I
I
00
,
I__
I
2
CREATINE
F1
the
fresh,
=
when
bility
SD
measured
on stoned
(the
“control”
overall
the
=
concentration
of the ith sample
under
conditions
of known
sta-
cal method,
aliquot).
standard
sion is made.
As each pair
calculated
This
new
ure
1.
of sample
of analyses
and
sum
As
long
as
experiment
in either
for
the
sum
be
1, Line
2 and
ended
0.05.
that
by
not
an
a test
a single
of concentrations
centration.
exist.
error
assumed
178
the actual
n
20
coefficient
portional
and errors
(3).
These
error
to concentration
curve
show the confidence
limits
for
of variation
(CV)
is constant,
error
is proto concentration
(the
proportion
model),
are assumed
to be distributed
lognonmally
are
characterized
by the
relationships
shown
in Figure
2.
In the proportional
gous to that
presented
model
above
:
instability
has
our
an
definition
of Table
of aliquots
creatine
=
#{244}
is defined
as 1.0 CV rather
than
1.0 SD.
two models
were used in the computer
simulation
studies
described
below
and it was found
that
the additive
model
was quite
effective
for all practi-
These
cal
uses.
Experiments,
that
The
penimentally
(EC
lytical
Line
B
22 ali-
stability
is not stable
at 4
24 aliquot-pairs,
at -20
#{176}C
it is
formed
presented
for
that
may
be inappropriate
is chosen
for
extremes,
and
SD
two
is constant
additive
SD
may
while
vary
conditions
with
model),
normally.
universal
with
Vol. 22, No. 2, 1976
of
with
and
proposed
vac Spectra
were chosen
Simulation
70 computer.
to represent
and
of stability
and
or in-
distributions
studies
IV computer
(control
and
language
were
with
Values
error-free
designated
concentrations
stored,
respectively)
of different
pera Uni-
f
and
s
of
under
degrees
A gaussian
random-number-generating
was used to provide
numbers
which
were
combined
with
ex-
of ana-
of stability
amounts
error.
was
simulation
conditions
known
in Fortran
approaches
by computer
known
with
of experimental
stability.
routine2
tal error,
the
verified
runs
analyte
and Discussion
of in-
subfor expenimenthe error-free
actually
concentration,
and errors
In the
con-
Results,
validity
conditions
a range
ln (S/F1)/CV
and
were
kinase
days.
after
(analocase)
is:
i=i
an
we have
value
CHEMISTRY,
data
at 30 #{176}C
for four
that
showed,
statistic
to be distributed
proved
definition,
experiment
pairs
assayed,
that
it also
Line C shows,
after
freezing
and storage
In one the SD
is additive
(the
been
by the
three
statistic
experiment
of our
the test statistic
for the additive
Nd
T.S.
increase
test
the
terms
A shows
is used,
As
CLINICAL
plotted
an
if the
stability
only
by our definition.
can argue
that
because
is
data.
in Fig-
the
(i.e.,
line
is illustrated
stable
experiment
quot-pairs
were
#{176}C
for four days.
that
with
quick
application
F1)/SD
-
because
hand,
the
1. Line
was
stable
One
UNITS
ACTIVITY,
a deci-
previous
shown
within
direction
other
because
after
illustrates
is
boundary
This
Figure
2.7.3.2)
the
C), within
demonstrated,
assayed,
(5,
of the
graph
be ended,
curved
(Figure
=
until
can be made
regarding
stabilshould
be continued.
If and
either
straight-line
boundary,
or falling
On
the
f3
The vertical
ranges around
the line at 95% confidence,
analyti-
the
constituent)
has
been
demona
0.025
(each
way) (Figure
1, Line
A).
lines thus represent
indices
for decisions
should
with
I
5
(U/liter)
in
instability.
crosses
run
is completed,
should
a rising
or decrease
strated
with
The straight
pairs
added
to the sum
is plotted
on the
boundaries,
no decision
ity, and the experiment
when
the line crosses
the
of the
KINASE
of measurement
I
4
and
the number
Nd
deviation
Fig. 2. Relationships
3
other
2
are
the
Random
variable
generators
used
were:
Package,
Health
Science
Computing
Facility
tem/360
Scientific
Subroutine
Package.
(3)
tion from
R. B. Koger.
(1)
Random
UCLA.
Personal
Number
(2) IBM
Syscommunica-
Table
2. Three
Examples
of Tests of Stability:
Creatine
Kinase
-20#{176}C
Sample
no.
Stored
concn.
S
Fresh
concn.
F,
i
at -20,
Test
statistic
Test
S
statistic
30
Stored
concn.
3.3
3
2.1
1
1.1
1.0
2
4.0
4.1
3
8.7
8.4
-1.5
8.8
1.5
4
1.1
1.1
-1.5
1.3
2.5
cCand4
-0.5
0.0
-0.5
4.3
1.0
5
2.2
2.4
0
2.4
3.4
5.6
3.4
2.0
2.8
5.1
3.7
1.8
-3.0
-5.5
-4.0
-5.0
2.5
5.1
3.7
1.4
-1.0
-3.5
-2.0
-5.0
10
2.1
2.0
-5.5
2.0
-5.5
11
12
13
14
15
2.8
2.3
1.6
2.3
2.3
2.7
2.3
1.7
2.4
2.3
-6.0
-6.0
-5.5
-5.0
-5.0
2.6
2.4
1.6
2.3
2.4
-6.5
-6.0
-6.0
-6.0
-5.5
16
17
18
19
5.5
3.7
1.1
3.0
4.5
3.9
1.2
3.5
-10.0
-9.0
-8.5
-6.5
4.5
3.1
1.1
3.2
-10.5
-13.5
-13.5
-12.5
20
21
22
23
1.5
2.6
0.9
0.9
1.3
2.4
0.7
0.9
-7.5
-8.5
-9.5
-9.5
1.1
2.1
0.6
-14.5
-17.0
-18.5
Unstable,
decision
after 22 samples
24
1.8
2.3
-5.0
concentration
values
situations
Units.
SD
=
to produce
0.2
described
above
and
decision
after
24 samples
Units.
simulated
S. The
experiments
of the
additive
and
3.5
-
Stable,
in BSL
analytical
were
divided
proportional
in each
was
into
error
of these
two
taken
successive
in this
case
compared
inner
and
sion
in
sen
and
the
of SD.
The
fractions
chosen
were
0, 0.2,
0.4, 0.6, 0.8, 1.0, 1.2, 1.5, and 2.0. The first of these,
course,
represents
absolute
stability,
and the sixth
seq. represent
instability
according
to our suggested
definition.
In the
additive
model
grammed
to select
from
a normally
values
distributed
equal
to zero
the first
case,
standard
difference
and
the
the
computer
was
of
et
pro-
of error
of F and error
of S
population
with
mean
deviation
between
equal
E(F)
to 1. In
and E(S)
passed
printed
97%
that
boundary
test
of only
the
the
of aliquot-pairs
particular
the
of the
value
obtained
boundaries.
decision
out
experiment.
that
the
0.4, etc.,
print-out.
The
is a reflection
Nd,
0) and
=
values
the
outer
any
number,
shown
existed,
(E(Z)
as zero
culated
cases
various
degrees
of actual
instability
were simulated.
This
was done
by assuming
that
the average
difference
E(Z)
between
the expected
values
of F,
designated
E(F),
and S, designated
E(S),
was a chofraction
-1.5
-2.5
-10.5
Unstable,
decision after
3 samples
CC experiment
1.0
6
7
8
9
data,
F1 and
simulations
Test
statistic
1.2
3.1
0.5
2
-20
Daysa
#{176}C
experiment
1.5
Activity
for Four
oC
30 #{176}C
Stored
concn.
1
aMeasured
4, and 30
4 #{176}C
terms,
computer
recorded
to reach
This
against
Nd,
number,
stability
then
of the
than
as Figure
3, Line
A.
the proposed
method
of the
time.
When
CLINICAL
serial
were
except
as 0.2,
of one
run.
more
the
the
a deci-
number
of
opposite
and
for the
statistic
Subsequent
cases
were
identical,
average
differences,
E(Z),
were taken
times
SD. Table
3 shows
an example
In each case 1000 experiments
were
results
in a list
error
required
or
calwhich
with
values
When
the test
experiment.
for
computer
statistic,
10 000
simulations
are
When
absolute
stability
identified
it as stability
instability
CHEMISTRY,
to the
Vol.
22,
No.
extent
2, 1976
of
179
Figure
Table
3. Computer
Simulation,
Example
Printout
of Results
Experiments
Exp
with
E(Z)
because
meaning
Instability
1
11
20
x
3
15
x
4
37
5
34
essence
of our
necom-
in quantitative
terms
combination
of the sug-
the
that
proposed
a constituent
method.
The
is stable
is
expressed
by the percentage
of the simulation
ments
that
give a decision
for stability.
This
bility
is shown
in Line A as a function
of actual
Nd
2
the
it expresses
of the
gested
definition
and
probability
of deciding
type
Stability
A presents
3, Line
mendation
the effective
X SD
Decision
No. samples
run
until decision
no.
0.6
of
X
bility.
For
conditions
x
for
X
example,
exceeds
stability
if the instability
1.3 SD the probability
is essentially
the
probability
65%. Thus the
zero.
and
are
the test
of deciding
If instability
of a decision
definition
and
quantitative
under
is 0.5
for stability
treatment
more
expeniprobainsta-
SD
is 0.65,
or
together
are
conservative
than
one
might
infer
from
the definition
alone-which
sounds
qualitative-because
the definition
can be taken
to
imply
that
any instability
of less than
1.0 SD will be
998
21
999
27
1000
16
No. of runs
x
called
X
x
504
1000
stability,
Figure
One
496
can
estimates
the
chances
na less
of deciding
stringent.
SD
the
probabilities
method
one
(this
the
greatly
of
seems
of in-
If one
over-
improves
to be the
it actually
that
is not
is absolutely
of SD
his
more
of deciding
constituent
in estimation
effect
by making
the cniteif one underestimates
chances
when
3 the
of a method.
for stability,
Conversely,
then
If the
Figure
SD
then
is stable
errors
15 and 38
from
the
SD
of the
error)
markedly.
>-
actually
deduce
estimating
quent
stituent
0.
also
correctly
the
.0
whereas
3 apply.
should
frea con-
decrease
stable
have
then
little
effect,
=1(1)
on the average,
because
the expected
value
merator
of the test statistic
is zero.
Obviously
a statement
of the analytical
U)
0.
of the
method
stability
must
by this
any
stability
It is useful
as observed
this enables
any
E(Z)
Fig. 3. Fraction
bility
Instability
is expressed
of analytical
E(Z)
the
of decisions
as actual
in concentration,
E(Z),
of instaas a fraction
1 SD existed
proposed
method
of
The
cance.
However,
experiments
in
random
numbers
algorithms,
and
fered
slightly
slight
discrepancy
by Schneiderman
CLINICAL
criterion
identified
course,
zero abscissa
1.0 at 5% (3
observed.
(by the
Line
it as
A
at 95% (2a
0.05), instead
=
difference
is
of #{244}
=
1.0 SD)
of
of
instability
Figure
0.05)
=
of the
likely
to come
ly number
no
practical
signifi-
we repeated
thousands
of simulation
each
of these
two cases,
with
use
generated
by three
quite
different
we
continued
from
the
was
and
CHEMISTRY,
to get
theoretical
also
observed,
Armitage
Vol.
results
22,
(2).
No.
that
prediction.
2, 1976
and
of
dif-
This
explained,
quickly,
of runs
unstable
with
exists,
eight
required.
the
with
16 being
of
if insta-
decision
the
most
constituent
will
most
to
likely
is
like-
is even
come
is absolutely
still
likely
the
4A,
the
being
If the
decision
quickly,
even
more
(E(Z)
stable
come
rather
number
(Fig-
4B).
Figure
4 illustrates
(4, 5).
the
sequential
t-test
For
value
of 0.05
26 aliquot-pairs.
greater
late.
37
experimental
statistical
or to U, the
example,
where
with
5
With
approach
standardized
the
1 SD one
this number,
shown
in line B of Figure
3 would
Incidentally,
it is noteworthy
incorrect
decisions
for instability
=
about
requirement
in Figure
1 SD
If the constituent
the
decision
is
test
6%
exactly
quickly.
=
zero)
ure
precision
statements
an implied
As shown
to
omy of the
to Student’s
should
97% and
experiment.
equal
94%
3 should
and
definition,
any
nu
statement.
to note the frequency
distribution
of Nd
in the
simulations
(Figure
4), because
one to predict
the probable
duration
of
bility
more
of the time.
In theory,
180
change
as a function
SD
=
cross
cross
for stability
one
accompany
of the
latter,
would
the
to obtain
a /3
need
to run
relationship
hold
(5).
in Figure
4 that
the
are likely
to come
It is also noteworthy
that
decisions
or 38 tend
to be much
more
prone
the average
decision.
This
can
4, where
13 of the 21 decisions
econcompared
normal
made
to error
be observed
made
at Nd
at Nd
than
in Figure
38 are
A
Known
5F
Unstable
E(Z).
Cases
Proportional
errors
each
concentrations,
of these
C,)
tnibuted
0
0.05. Then
z
population
:::
Correct
-
Incorrect
decisions
The
LI-
0
chosen
0
results
choosing
especially
F-
z
LU
0
randomly
for
in
95%
mean
a log-normally
equal
to 1 and
are
shown
in Table
dis-
CV
4. It
the wrong test statistic
is not
when the additive
statistic
values
LU
0.
from
equal
to
additive
test
statistic
was applied
to
F and S values,
with
SD
60 mg/liter.
of SD is, of course,
correct
only
at the
the resultant
This
value
mean
value.
decisons
.1
0
I.-
also
the
U)
0
LU
0
were
0 SD
Table
4 do
the
concentration
until
not
depart
is clear
that
a serious
is chosen.
error,
The
significantly
range
gets
from
quite
broad
indeed.
The
Fig. 4. Frequency
distribution
effect
truncated
(2). In
of Nd
sary
to
these
incorrect,
and
seven
periments
should
Simulation
run
with
CV
distribution
of
for
used
in
the
and
fact
vice
of 38
place
random
versa,
randomly.
means
All
population
tively.
Thus
more
than
with
should
course,
this
be
the
case
additive
model
by
were
model
fits
the
simulation.
facts,
Three
were
sets
chosen
from
populations
with
standard
deviations
of the
300, and
420
of concentrations
mg/liter,
tested
respecvaried
mean
were
randomly
chosen,
for each of
from a normal
population
of er-
equal
to zero
and
standard
test
and
correct
statistic
S values
only
Table 4. Effect
was
with
at
CV
the
=
mean
of Choosing
=
applied
to
0.05.
This
value,
CV
1.20
resulis, of
case
stability
is 38 (Table
maximum
choice
serum
samples
could
coast-to-coast
od was chosen
mailing
since
days.
stability
for
that
tested
by
The
in the
experience
room
summer
long
enough
creatine
temperature
(30
onto
the
methanol
sides
of a test tube
immersed
or the equivalent,
was necessary.
0
by
defining
#{176}C
was
gave
rolling
and
in solid
CO2/
stability
(1000
Additive
error
proportional
Stable,
E(Z) = 0
as % of total
tested with
T. S.
Unstable,
=
1 CV
E(Z)
Av.
SD
Range
18
93-153
97
95
95
95
120
30
71-175
97
94
91
96
120
42
50-197
95
93
80
97
CHEMISTRY,
and
serum
120
CLINICAL
inused
extremely
the
detecting
by Simulation
Unstable,
E(Z) = 1 SD
Correct
decisions,
arrive
kinase
mailing)
or in a freezer
Quick-freezing,
penin-
held
at -20
#{176}C
by placing
them
on solid
with
to permit
specimens
indicate
results.
Evaluated
One
U. S. A. A four-day
in this laboratory
variable
for
tech-
Figure
1. This
experconditions
by which
room-temperature
CO2
the
laboratory.
Quick-frozen
samples
Samples
frozen
slowly
error tested
additive
T.S.
5. In
run to
be nec-
and
t5,
in our
all mailed
results
both
use
be stored
substantially
technique
proposal
might
casually
Our
in
effect
in Figure
must
be
of a, /3, and
is given
in Table
2 and
was designed
to test
the
that
in this
pattern
that
example
iment
g/liter.
Stable,
E(Z) =
central
number
result
The
is intermediate
used
were
in four
any
patterns
nique
dicates
getting
5).
definition,
also
by making
a = 0.005
With
25, respectively.
pattern
is 15; the
the
Figure
5
M,
neces-
size,
affected
before
of the
0.05)
is the
the minimum
prove
the Wrong Test Statistic
(T.S.)
Experiments
per Case)
chosen
run
The
essary
Proportional
Concns.
be
/3 on
by
stringent.
is 120 and
4 #{176}C
storage.
proved
stable.
a system1. Then
the
the
=
to simulate
deviation
case
may
cases
a and
With
a = 0.05 and /3 = 0.10
12. However,
the
maximum
19.
=
M
/3 on breadth
/3
(2a
twofold.
proportional
F
the
M
of
is little
or less
significance.
The
the
equal
to 60 mg/liter.
For the unstable
atic change
was chosen
such that
E(Z)
tant
by
case. The results
exactly
those
for
using
The
180,
range
in its
expo-
generated
two
of a and
logarithmic
taking
concentrations
three
Additive
errors
these concentrations,
rors
The
by
realized
tested
g/liter.
were
the
SD.
numbers
glucose
of 1.20
of
obtained
proportional
was
0.01,
larger),
=
choices
test
is illustrated
minimum
sample
more
that
these
were
various
stability
criteria
and /3
(10-fold
ex-
model
as the additive
case duplicated
the
simulated
proportional
was
the additive
case
(as we
after
trying
it).
The
effect
of mistakenly
in
Such
37.
prove
number
the
errors
same
basic
algorithm
for the proportional
when
16 at Nd
be repeated.
tests
of
nentials
of the
of
sequential
general,
the
Vol.
22,
No.
2, 1976
181
Table
5. Coordinates
Making Graph,
of Boundaries
Assuming 2a
and.5
=
A1
=
Curved
ja
Abscissas,
7.275
+
-7.275
-
boundaries
Ordinates,
±0
15
16
17
±0.2
±1.6
±2.2
± 3.0
±
Note that the abscissas
and ordinates from Table 4 of ref. 2 have been multiby 2 and ±2. respectIvely,
to yield the abscissas
and ordinates
in this
figure
has
as a prerequisite
a specific
tion of acceptable
question.
These
oratory
that
known
conditions
undertakes
stability
should
if it is not,
increase
be specific
then
one
in interfering
precision
of
the
method
clinical-utility
between
tion
ods
standpoint.
standard
should
be
36
37
±19.4
±21.6
as follows.
is surprisingly
nase in Figure
2.
We made
four
this
stated,
study.
are
not
chemical
methods
cision
is measured
tions.
No attempt
tionship
required
is
at
is
by
not
be
analyte
information
perhaps
implied
by
(b)
on
the
concentra-
CHEMISTRY,
as
literature
precision
ki-
a result
obvious,
of
once
or
of
22,
No. 2, 1976
Usually
from
multiplied
CV
26.2
Schneiderman
by
and
SD
statements
as they
do,
data.
Accurate
more
work
than
(c)
by
clinical
very incomplete.
Typically,
preone or perhaps
two concentramade
to get the complete
nelathe technique
described
in this
Vol.
been
were alternative
of ascribing,
2 and
±2,
and
Armitage’s
respectively.
are
given
as though
of the same
quite
different
measurements
one usually
if one
were
each,
could
the
measured
differ
by almost
test
level.
(4) would
reject
Thus
statements
to run
two
they
thing
instead
properties
to
more
work
theoretical
for
of SD
is willing
on CV require
to apply.
Even
series
of 20 replicate
values
50%
of the
respective
before
the variance
specimens
them
as unlikely
at
of SD on CV to more
significant
figure
frequently
data
they come from.
(d)
Reliable
demonstrations
stability
CLINICAL
4 (2) have
±
ordinates
the
meth-
for cneatine
are
the
and
to
signifi-
about
paper.
182
enough
Table
abscissas
is useful
relafrom
(e.g.)
a
observations
they
practice.
general,
data
good
±
37.82
aThe
a cumulative
substances.
The
It is shown
general
Although
they
conventional
(a) In
sparse.
laboratory
and to be
time.
The
in question;
should
and
Such
12.0
±15.2
±16.4
±17.8
of the art permits.
The
That
is, the relationship
deviation
known.
±11.2
±14.0
be
It
8.6
±
33
34
35
stability
that
degree
of change
poorer
than
the state
should
be known.
±
9.4
±10.2
27
28
29
32
analyte
should
about
7.0
7.8
of detenmina-
studies,
the
±
±
26
5.6
6.4
for the analyte
in
be met in any lab-
may be measuring
or inhibiting
provide
knowledge
tive to the acceptable
cantly
precision
for
±
5.0
±13.0
The method
should
have
been
used
in the
long enough
to have
unchanging
precision
known
to be free of “drift”
of values
with
method
±
30
31
method
precision
should
±
22
23
24
25
and minimum
3.6
±4.2
21
Fig. 5. Relationships
of a and
to maximum
sample size for the truncated sequential test
Aja
14.94
19
20
NUMBER, I
I
0.05
/2
18
SAMPLE
1/2
=
boundaries
1ZAi
Lower
j3
1.0SD
=
Straight-line
Upper
of Decision=
then
one
treatment
usually
a single
time
has
are
oveninterpreting
of
stability
is willing
to apply.
shown,
one cannot
period
to the
rather
SD’s
ratio
the
than
0.05
one
the
require
As our
prove
gener-
U)
a:
U-0
li,,
LU
2>
U)
0.1-
0
I.U)
F-
0u
zo
U-
U)
Liz
FU)
OW
U)
LU
o
F-
K=I
L&.
SAMPLE
z
Fig. 7. Graphical
presentation
test for K = 1 1.5, 2
NUMBER
of truncated
normal
sequential
,
ACCEPTABLE
SD
Fig. 6. Relationship
tion acceptable
minimum
between
in deciding
number
stability
AMOUNT
OF CHANGE_
METHOD
OF ANALYTICAL
amount
of change
for stability
of sample
pairs required
.
in concentra-
(expressed
as K), and
to demonstrate
decisions
will
used,
When
if it exists
the
limits
blind-pairs
we
of data
by conventional
Setting
K
propose
by the
tests.
1 in the
with
fewer
sequential
than
15
technique
or 26
mens
expression
K X SD
strongly
to that
degree
of change.
Figure
6 shows
one practical
the
amount
relationship
of work
ists.
This
ingK
=
required
K
probability
other
prove
the
than
the
to
stability,
1 alter
reaching
be used
if it ex-
the
shape
values
of
the
stability
test
to
chosen
formed
its,
with
and
In any
generally
provided
given
/3
at 2a
accepted
situation,
if one
presented
limits
If the
(Figure
that
is incorrect,
usefulness
of the
too large.
logarithms
The ease
required
led
method
SD
this
they
lim-
confidence
in the
required
maximum
to reach
not
little
if the
range
vary
us to recommend
in this paper.
We
the
think
single
that
with
effect
routhe
and finnegligi-
overall
time
period
may
traditional
time
periods
a stability
experiment
frequently
of any
design
the
is already
experiment
ends
quickly.
2. Schneiderman,
quential
procedures.
3. Aitchison,
Cambridge
a
con-
on
of values
of using
SD and thus
for the
proportional
quite
a study
is almost
experimental
avoiding
case
the
is not
the
test
test statistic
few incorrect
C.
0. E., Automation
In Automation
Symposia
1965; L. T. Skeggs
N. Y. 10017, 1966, p 417.
length.
higher
does
and
do
the
1. Hagebusch,
tory medicine.
con-
confidence
of convenient
has
and
because
we
in the
Although
such
load
the
the
one
Stewart
(CDC,
and constructive
Atlanta,
advice
Georgia)
during
the
for
de-
References
4.
Davies,
ments,
5.
assumption
that
than
We thank
Dr. Charles
several
valuable
discussions
velopment
of this work.
de-
5).
centration
statistic
presented
because
wants
found
longer
ex-
only
clear,
runs
studies.
starting
the work
for
for
already
daily
ex-
analyspeci-
ones,
data
it is not
stability
the
and
When
(abnormal
to collect
the
at any
that
stability.
statistic
95%
experiments
the
price
to be paid
is reflected
number
of samples
that
may
be
decision
for
between
be long,
hand
only
increase
K
for
whatever
0.05
obtain
using
elapsing
it can
to design
techniques
be interrupted
provided
In case
laboratory
rather
sired.
For example,
one can choose
an acceptable
degree
of change
in terms
of concentration
and relate
that
to K x SD to determine
the appropriate
K value
to use. a and /3 are also arbitrary
numbers
and were
arbitrarily
at a time.
duration,
of the
to
is
ranges.
recommended
be possible
recommend
taken
of choos-
a decision
with
determine
difficult
We have
be much
statistic
regarding
handling
remain
unchanged.
time
ishing
ble.
not
K,
minimum
practicality
increasing
of
7 can
Figure
here
in choosing
and
this
concentration
may
freely,
tine
at
of
significantly;
the
to
illustrates
K
1.
Values
graph
figure
aspect
between
the
of data
it may
specimen
i5
is using
conditions
sample
are
ample),
when
reasonable
resumed
perimental
sis of each
is an
namely
one
and
arbitrary
choice.
Whether
K should
be chosen
smallen on larger
depends
only on the degree
of change
acceptable
in deciding
for stability,
and fitting
K X SD
=
encountered
accumulation
time
ous-sounding
be
if one chooses
0.
Hafner
Dixon,
Analysis,
6. Lindley,
2, Cambridge
7. Mandel,
terscience,
8. Sobel,
choosing
a normal
J.,
Univ.
W.
3rd
M.
A.,
and
Biometrika
in the
in
private
Analytical
et al.,
practice
of labora-
Technicon
Chemistry,
Eds.,
Mediad,
Inc.,
Armitage,
P., A family
49, 41 (1962).
L., The Design
Pub.
Co., New
and
Analysis
York,
N. Y.,
J., and Massey,
ed., McGraw-Hill,
F. J., Jr., Introduction
New York,
N. Y.,
D. V., Introduction
to Probability
Univ.
Press,
Cambridge,
U. K.,
Analyses
1964,
chap.
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