Method for Monitoring Plasma Progesterone ... - Clinical Chemistry

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B, Rigshospitalet,. University of Copenhagen,. Copenhagen. 2100; and. Department of. Clinical. Chemistry,. Central. Hospital,. Hillerod. 3400,. Denmark; and.

CLIN.

CHEM.

22/4,

422-428

Method

(1976)

for Monitoring

Concentrations

Per Winkel,

Plasma

Progesterone

in Pregnancy

Preben

Gaede,

and J#{216}rgenLyngbye

We present a time-series 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 pregnancy-the

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 three-week

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 protein-binding ly modified: after

is gained

such

time course of plasma during pregnancy,

single

at various

Material

we used

intra-individual concentration during

average

concentrations

subjects

analyze

of healthy the

values

tion

data

investigation

terone

nate inter-individual 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 pregnancy-i.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=(2O-4)/

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 normal-probability

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 f-values

mean

V-value

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

Single-sample 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

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