B, Rigshospitalet,. University of Copenhagen,. Copenhagen. 2100; and. Department of. Clinical. Chemistry,. Central. Hospital,. Hillerod. 3400,. Denmark; and.
CLIN.
CHEM.
22/4,
422428
Method
(1976)
for Monitoring
Concentrations
Per Winkel,
Plasma
Progesterone
in Pregnancy
Preben
Gaede,
and J#{216}rgenLyngbye
We present a timeseries model for monitoring concentrations in plasma of hormones produced in the placenta, progesterone being chosen as an example. The model, which is based on the assumption that variations in plasma progesterone concentration in pregnant subjects mainly reflect variations in the growth rate of the placenta, was applied to eight series of progesterone values measured during pregnancy in eight subjects. In the model, which was found to fit the data, it is assumed that progesterone concentration is proportional
to the size
of the
placenta
and that
the growth
rate of the placenta varies at random, with a mean value a. The variation of a was of the same magnitude among and within the subjects. If the average of many subjects’ a values is used, a single subject may be used as her own reference, based on only one previous observation. When two observations are available, an individual’s own a value may be estimated and used for the prediction. The predictive power of the new method was found to be far superior to the conventional in which a single sample reference material Furthermore, one need not know the gestational
order
method is used. age in
to use the method.
Additional
Keyphrases:
hormones
in plasma
cental
growth
#{149}
In evaluating ence group
#{149} pregnancy,
the
result
values
during
test
data from an is often used.
purposes
subject
changes
of a laboratory
based on subjects
monitoring
using
and predicting
for #{149} pla
fetal status
the
interval of healthy
For
monitoring
(e.g.)
as his or her
much
own
in
a group
for
to elimi
the
subject
as his
(or
her)
own
Departmentsof Clinical University of Copenhagen,
Chemistry Copenhagen
Clinical Chemistry, Central Institute of Mathematical Denmark.
Hospital, Statistics,
Address Chemistry
correspondence A, Rigshospitalet,
hagen, DK 2100, Received June 422
CLINICAL
to
,
A and B, 2100; and Hillerod 3400,
University
P.W. at the 9 Blegdamsvej,
Vol.
can
use
reference.
Copenhagen 0, Denmark. 25, 1975; accepted Jan. CHEMISTRY.
we
for
15, 1976.
22. No. 4. 1976
of Clinical of Copen
comparison,
obtained
we
progesby using
from
healthy
of pregnancy.
with
from
each
of 324
data
were
menstrual
calculating Plasma was reliable
the nonparametric sampled from menstrual
All
blood
vein into In all
data
were
samples
were
at one
to 42. The
infants’
Analytical
Method in
(Mallinckrodt, (1500 ,fl) instead (2000
,l)
plasma
antecubital with
perorally,
high
each
Statistical The
obtained the
period in week 2500
by
38 g.
a corn
we slightpetroleum ether an aliquot ether frac
precision. serum
taken
from
of postmenopausal of estrogen
for
antecubital
eight
(4 mg
the
women of estradiol,
days).
Methods
from
following
(a) During pregnancythe
of the
doses
day
in
), which
with
used
subject as her own if a simple exponential
data
(1
we took petroleum
the
blood
place
estimated
“Nanograde”) of the whole
venous
treated
was
we
the
all exceeded
method extraction
protein,
basis
interval. women
neonatal
took
weights
to improve
As binding
the
birth
birth
the
to threeweek
from
tubes. and
and
women
as
A total of 72 samples series study (Figure 1).
drawn
heparinized glass cases, pregnancy
uncomplicated
pregnant used
reference eight pregnant
tervals during their pregnancy. were used in the consecutive
model of
Denmark; and of Copenhagen,
Department University
samples
reliable
the Rigshospitalet, Department
in
and Methods
Plasma with
med
before
a time
changes pregnancy
Materials
ries
is necessary
For
samples
Progesterone
by
subjects.
stages
petitive proteinbinding ly modified: after
is gained
such
time course of plasma during pregnancy,
single
at various
Material
we used
intraindividual concentration during
average
concentrations
subjects
analyze
of healthy the
values
tion
data
investigation
terone
nate interindividual variation from the comparison. This requires the presence of one or more previous observations, obtained during a period when it was known that the subject was in a stable state, e.g., in “good health.” But it is also necessary to know how to use these observations to predict what the values for future observations should be if the former stable state still exists. Thus a study of a chronological Seof biological
present
model to progesterone
computed
a refer
appropriate
reference,
In the series plasma
placenta
the
same
assumptions
except time
for
subject.
and
exam
could With
fit this
made:
after the 12th value reflects
biological
(t) after is proportional
first
curve
are
later pregnancyi.e., plasma progesterone
tion. (b) At any given rate of the placenta attained.
We
reference: growth
analytical
week of the size
varia
the 12th week the growth to the size it has already
Progesterone
nmol/i
plasma
weeks I
15
Consecutive pregnant women Fig.
plasma
1.
progesterone
I
16
17
w.#{149}ks of pregoncy
I
observed
values
values
0 predicted
values
in eight
of pregnancy
U
Fig. 3. A comparison of the prediction of plasma progesterone values in a pregnant subject by use of the regression line of Figure 2 and the method of the present study The
segment
are taken
Progesterone
line and the corresponding
of the regression
from
Figure
observed
values
2
I plasma 100
80 50
(c) The slope between consecutive progesterone values in such a semilogarithmic system reflects the growth rate over that period; i.e., we assume that the remaining biological and analytical variation is negligible in this context.
40
It should
20
of
pregnancy
10 12
16
20
2’.
28
be noted
to be valid nancy. We
32
Fig. 2. Plasma progesterone values of a healthy subject as a function of duration of pregnancy
pregnant
The regression line depicting the logarithm of the plasma progesterone as a function of time is also shown. Note that the scale of the ordinate arithmic. The framed part of the figure is reproduced in Figure 3
value is log
between
consecutive
average
slope
from
the
one
If the
plasma
terone tion that ure
progesterone
size of placenta, equation where level
at
of this the log 2 shows
function
we X(t)
time
equation of X(t) the log
of time
for
t:
values the
based
dX(t)/dt
=
kX(t).
to
differenprogesThe
solu
one
of the
eight
healthy
pregnant
line corresponding that the data points
to are
We
on the
considerably. therefore
following
Thus choose
the another
model
did
model
the
point,
one
the not.
not
fit
that
is
line.
closer
draws
to
the
2.1
computed. the
apart
a line that
observed
the
the
Figure
4 shows
that
of the
previous to the folone data
average
slope
value
is found
that
are
on much
is the
regression
the
points
shown
how
the
average
we are only means
in time,
on
slope
using that
the
a
as compared 3 we have
points
than
on 2 and
all
This are
focus
point from
predicted
almost
observation.
observations
the
this value
us
slopes
points
for
use
in Figure
one data Starting predicted
is true
It appears last
Let behaves In Figure
having
The
and
progesterone
shown
from follows.
It is seen
This
Figure and
curve
assumed
week of pregof all slopes
values new
of all the
mentioned.
is only
observed.
average
The prediction is done as
line.
a
previously
curve. lowing
this
model
and 36th an average
this type of prediction of the regression line.
we just
at random around the regression line and slope between consecutive progesterone
varies data.
is proportional following the plasma
is X(t) = Aeut. This implies is a linear function of time. Figof the plasma progesterone as a
subjects. The regression data is also shown. Note scattered that the
value have the signifies
predict of the
computed
the tial
the
the 12th compute progesterone
to
smallersegment see how to that
that
between may now
the
the better
is
first
further we
are
able to estimate the average slope. This is an important quality of the model in that it implies that if one observation is obtained during early pregnancy one can age
always slope.
get The
the best possible slopes then vary
estimate of the averat random around a
assumptions:
(a) The plasma progesterone concentration reflects the size of placenta. (b) The growth rate of the placenta is proportional to the size it has already attained; however, the proportionality constant varies at random over time, a growth model first studied by Lewontin and Cohen in 1969 (2). The model implies that the slope of the log of plasma progesterone depicted as a function of time will vary with time.
1
We
submit
that
our
comparison
between
the
regression
model
and the present model does not allow us to draw any definite conclusions, because it was only based on one example where the sample size was sufficiently large for the performance of a detailed comparison between the two models. However, our main reason for choosing the present model is that we think that the assumptions upon which this model is based are more realistic than those upon which the regression model is based.
CLINICAL
CHEMISTRY.
Vol.
22.
No.
4,
1976
423
y(t) C >,
0
(aa7a7o/o,)/5=(2O4)/
95
9o 0 we0
20
.::: 15
l
7#{176} 60
>50
u
40
.
0 :,
‘2
20
0’
8 0.5
value
‘
.
2
4,
t
Fig. 5. Empirical the consecutive
e
2
I
3
5
4
The figure
6

distribution plasma
was drawn
of residual 2
I
0
of the normalized
progesterone
residuals
in
series
on normalprobability
paper
Fig. 4. A constructed example where Y(t) symbolizes the log of the plasma progesterone value and t symbolizes the dura
tion of pregnancy The
example
slopes
illustrates
of the
result
of the last and the first ing fvalues
mean
Vvalue
of the
also
divided
the tn
from
the
that used
servations
in estimating
time
are of
used
the
period
model
t
(t+1
=
data
(see
may
t1)

, and
the
the
ized
the
residuals and
common
to
change over
from
one
Singlesample from the single pregnant
by
published
observed Y) of consec

its vandeviation of the model of all normalwith
mean
analysis
method
pre
by one of us (3).
of
the
normalized residuals for the eight subjects terone data;
values that
on all the nificantly are 424
depicted CLINI(AL
were
empirical
distribution
of
showed that for whom
the model consecutive
adopted proges
available
is to say,
the
adequately empirical
described distribution
(HEMISTRY
5. Evidently Vnl.
22
Nm
there 4
19Th
the
the based
72 normalized residuals did not differ from the theoretical. The two distributions in Figure
21
6
4.02
35
2
18
7
4.02
18 61
3
24
5
3.96
4
17
6
2.81
5
23
7
2.86
16
6
20
7
4.26
14
7
19
7
2.57
4
8
19
18
3.02
9
3.46
17.1
Weighted averages
correspondence between shows the estimates of a
the and
females. The autocorrelation cases where we were able
to
differ
significantly
The
showed
(x27
is very
siggood
of
6
P
among order
common 3.46 X Based
the
centage
increase
The
coefficients calculate them
they
variances were
for
subjects
to the estimate
first
in did
the
significantly
was
9
i0’,
X
as within
those not
(Table in the
plasma
is of the
subjects.
17.1
X
tables the
The
iO
and
were
con
minimal
per
progesterone
number
of weeks
elapsed
obtained
by
the
pooling
the large variation
which
2) relates
eight
different
the
estimates of y2 and a were 102, respectively. on these two estimates, two The
2
the
of magnitude
structed.
Table 1 of the eight