Open Journal of Obstetrics and Gynecology, 2011, 1, 84-89
doi:10.4236/ojog.2011.13015 Published Online September 2011 (
Published Online September 2011 in SciRes.
Optimization of a novel three dimensional risk calculation
model for software-based aneuploidy screening in early
Cindy Hörmansdörfer1*, Michael Golatta2, Bernhard Vaske3, Alexander Scharf 4, Peter Schmidt4
1Klinikum Oldenburg gGmbH, Department of General and Visceral Surgery, Oldenburg, Germany;
2University of Heidelberg, Department of Gynecology and Obstetrics, Heidelberg, Germany;
3Medical University of Hannover, Department of Medical Statistics and Biometry, Hannover, Germany;
4Institute for Prenatal Health, Wolfenbüttel, Germany.
E-mail: *
Received 17 June 2011; revised 11 July 2011; accepted 18 July 2011.
Introduction: A novel three dimensional approach for
aneuploidy screening in the first trimester of preg-
nancy was developed in which risk assessment derives
directly from comparing the plotted data of nuchal
translucency, pregnancy associated plasma protein A
(PAPP-A), and free β-human chorionic gonadotropin
(fβ-hCG) of an examined fetus with similar coordi-
nates of fetuses with already known health status.
Under this approach, it is possible to utilize either a
‘box’ or a ‘sphere’ model. In either case, optimal
volume sizes and the benefits of adopting a ‘minimum
number of required fetuses’ (MNR) have not yet been
investigated; and for the box model, two modifica-
tions, called ‘empty box results positive’ (EB+) and
‘simulation’ (SIM), provide additional options. It was
the aim of this study to analyze which of the two mo-
dels and their variants provides the best test perfor-
mance. Methods: The study cohort was divided into a
reference collective (n = 10,954) and a test collective
(n = 4239). The test collective was examined repeat-
edly, with another model and modification used on
each occasion. Test performances were compared by
the area under curve (AUC) of receiver operating
characteristics (ROC) curves. Results: The sphere
model was inferior to the box model when optimal vo-
lumes were used with the latter and combined with
the modifications EB+ and Sim. EB+ increased the
number of assessable fetuses while Sim improved the
test performance. MNR improved neither the box nor
the sphere model. Conclusion: A new, optimized mo del
in line with the obtained results should be developed
and tested in further studies.
Keywords: Aneuploidy; Down Syndrome; First
Trimester Screening; Nuchal Translucency; Trisomy
In order to detect fetal aneuploidies in early pregnancy, a
non-invasive software-based screening for chromosomal
aberrations in the first trimester (12th to 14th pregnancy
week) has become the worldwide standard in recent de-
cades [1,2]. Individual risk assessments for aneuploidies
are obtained from the comprehensive interpretation of
the fetal nuchal translucency thickness in mm according
to the crown-rump-length (NT), which is measured by
ultrasound, and the maternal blood serum concentration
of pregnancy associated plasma protein A (PAPP-A), and
free β-human chorionic gonadotropin (fβ-hCG) [3]. Dif-
ferent methods have been developed for risk calculation
[3-7]. Recent studies suggested the potential of a novel
computer model called “Advanced First Trimester Scr-
eening three dimensional (AFS-3D)” [8-10] in which
each parameter is assigned to one axis in a three dimen-
sional coordinate system (Figure 1). It could be demon-
strated that most healthy fetuses accumulate around each
parameter’s mean values, whereas most trisomy 21 cases
are found to have elevated fβ-hCG in Multiple of Median
(MoM), lowered PAPP-A (MoM) and increased NT
values. Fetuses with trisomy 18 or 13 also typically pre-
sent lower PAPP-A and increased NT values, but in con-
trast to trisomy 21 cases, fβ-hCG is found in reduced
concentrations (Figure 2) [11]. Consequently, risk as-
sessment could directly derive from comparing the mea-
sured values of each examined fetus with similar co-
ordinates of fetuses with an already known health status
(reference fetuses).
In a pilot study, the three dimensional space was di-
vided into several cubes [8]. Only reference fetuses
whose plotted data fell within these designated cubes
C. Hörmansdörfer et al. / Open Journal of Obstetrics and Gynecology 1 (2011) 84-89 85
Figure 1. Example for the presentation of the fetal
measurement values NT, PAPP-A and fβ-hCG in a
three dimensional scatter plot.
Figure 2. Estimated distribution of measurement val-
ues from healthy fetuses (centre) and cases with tri-
somy 21, respectively trisomy 18 or 13 (left).
were considered for risk assessment (Figure 3). The re-
sults showed an excellent test performance with a sensi-
tivity of 81.61% and a false positive rate of 2.27%. How-
ever, in discussions it was considered likely that the uti-
lized model could still be further optimized.
Two additional modifications to the box model were
proposed that could be applied either separately or in
combination: 1) Empty box results positive (EB+): Ane-
uplodies are more likely to be located in cubes which
may be empty. Therefore, in order not to miss aneuplo-
dies the test should always record a positive result if a
cube contains no reference points. 2) Simulation (Sim):
One healthy and one affected fetus are artificially added
to the result in each cube. This was thought likely to lead
to a reduction in the random error of boxes with very low
numbers of reference points: If a box contained a few
healthy fetuses, but would due to its location probably
Figure 3. Schematic picture of the AFS-3D box model. The
surrounding space is divided into cubes. Only reference
cases within the box of the examined fetus are considered
for risk assessment. T = fetus of the Test Collective; R = fe-
tuses of the Reference Collective; NR = not referenced fe-
tuses, as lying outside the box.
contain an affected fetus in a future examination, then
this probability would already be taken into account in
the simulation result. At the same time, in cubes with a
large number of known fetuses, this addition would not
markedly affect the result.
In addition to the box model, the potential benefits of a
sphere model were considered (Figure 4). Due to the
discrete positioning of the reference volumes in the box
model, an examined fetus might be positioned close to a
border. However, the adjacent box is not considered until
the three dimensional plot crosses its edge. The result is a
sudden ‘jump’ in relation to reference boxes when mov-
ing a test-plot along one axis: imprecision occurs when
considering reference fetuses that are closely distributed
in one direction along the axis of NT, PAPP-A or
fβ-hCG. It was thought that this might probably nega-
tively affect risk assessment. In contrast, in the innova-
tive approach of the sphere model the data of the ob-
served fetus is placed at the centre of a sphere whose
radius is augmented until the plotted values of a certain
number of reference fetuses are found within the bubble.
It is thought that the positioning at the centre of the ref-
erence volume could compensate the impact of the fur-
ther plotted reference fetuses since these are bilaterally
Independent from the model, the optimal volume size
has not yet been established. Within the box model, the
cube size is referred to in terms of the number of divi-
sions per ‘length of the edge’ (LE) of the whole sur-
rounding space (Figure 5). In contrast, the bubble size in
the sphere model is equal to the number of referenced
opyright © 2011 SciRes. OJOG
C. Hörmansdörfer et al. / Open Journal of Obstetrics and Gynecology 1 (2011) 84-89
Figure 4. Schematic picture of the AFS-3D sphere model.
The data of the observed fetus is placed at the centre of a
sphere. T = fetus of the Test Collective; R = fetuses of the
Reference Collective; NR=Not Referenced fetuses, as ly-
ing outside the sphere.
Figure 5. Illustration of divisions per ‘length of the edge’
(LE) in the box model. In this example, the LE equals 14.
fetuses contained within the sphere. The larger the box,
or the bubble, the more reference fetuses are considered
and, as a result, statistical evidence improves. At the
same time however, as the volume increases the mea-
surement values of the control group tend to differ more
from the values of examined fetuses, and risk assessment
may become more imprecise.
If, in contrast, smaller volumes are chosen, a large
number of boxes that only take very similarly positioned
reference fetuses into account emerge. On the one hand,
this results in superior discriminatory power. However,
on the other hand, the number of empty boxes in which
few or no references are found rises and, as a result, there
are more cases in which a risk assessment cannot be ob-
tained. Accordingly, the ideal volume size both attains a
high discriminatory power and ensures that enough re-
ference fetuses are located in each box.
Finally, it was also suggested that each box or sphere
should contain a minimum number of healthy as well as
affected fetuses (minimum number of required references,
MNR) in order to improve statistical robustness.
It was the aim of this study to analyze which of the
two models and its variations provided the best test per-
The data of 15,193 combined first trimester screenings
(FTS) with known fetal outcomes were collected be-
tween May 1, 2000 and December 12, 2007 in seven
German centers for prenatal diagnostics. The women vo-
luntarily requested a FTS on the basis of information
about this procedure from their gynecologist/obstetrician,
the media or family members/friends. All examiners
were trained and certified by the Fetal Medicine Founda-
tion (FMF) and measurement of the nuchal translucency
strictly followed FMF criteria. Biochemical analyses
were performed with Brahms Kryptor systems (Brahms
GmbH, Hennigsdorf, Germany).
Within this study collective, the first 10,954 data sets
collected served as a reference collective with which the
3D model was established. 4239 subsequently collected
data sets from a medical practice served as a low risk test
collective. This test collective was examined in multiple
ways, with each recalculation exploring another model
and modification as set out in Figure 6. For this purpose
the working group designed and developed specific cal-
culation software. Since the test performance could theo-
retically change markedly depending upon the model and
variant used, all combinations of all modifications were
As valid cut off values were not available for these
new methods, receiver operating characteristics (ROC)
curves were generated in order to determine the areas
under curve (AUC): The better the sensitivity at a given
specificity, the greater the AUC. The statistical approach
was validated by the Department of Medical Statistics
and Biometry, Medical University of Hannover, Ger-
3.1. Study Population
The maternal age of the reference group ranged from 15
opyright © 2011 SciRes. OJOG
C. Hörmansdörfer et al. / Open Journal of Obstetrics and Gynecology 1 (2011) 84-89 87
Figure 6. Flowchart for the analysis of the different models and
their modifications.
to 46 years, the arithmetic mean being 31.6 years. The
(low risk) test group ranged from 16 to 46 years, with an
arithmetic mean of 31.2 years. 1.07% of pregnancies in
the reference group and 0.96% of pregnancies in the test
cohort were affected by an abnormal karyotype. Figure 7
displays the age distribution curves of both study co-
3.2. Box Model—Size
In this study the optimal size was found to be LE = 1/14,
in which the best compromise between a high discrimi-
natory power and enough reference fetuses in each box
was attained.
3.3. Box Model—MNR
When applying the MNR concept no improvement was
attained by increasing the MNR per box. The number of
appraisable fetuses declined from 4225 to 4156 in set-
tings with a minimum of five required cases. Simultane-
ously, the AUC dropped from 0.8916 to 0.8864 in higher
minimum count settings.
3.4. Box Model—Modification I (EB+)
Modification I did not change the AUC (0.9287 with and
without EB+), but all fetuses from the test group could
be analyzed when this additional function was applied,
even if the respective box contained no fetus from the
control group.
3.5. Box Model—Modification II (Sim)
Modification II improved the test performance, as the
AUC increased from 0.9287 to 0.9331. However, risk
could only be assessed in 4.225 out of 4.239 fetuses. In
the remaining cases, not enough reference data was
Figure 7. Age distribution of study cohorts.
3.6. Box Model—Modification I + II (EB+ and
By combining modification I and modification II, the
advantages of both modifications were obtained: The
number of appraisable fetuses was 4.239 (= all fetuses),
the same as with the exclusive application of modifica-
tion I. In addition an elevated AUC of 0.9331 was regi-
stered, which is equivalent to the exclusive application of
modification II. Again, utilization of MNR together with
modification I or IIeither separately or in combination
did not improve test performance.
3.7. Box versus Sphere Model
In contrast to our theoretical considerations, the box
model generally offered better ROC values in this study
than the sphere model.
3.8. Sphere Model—MNR
The application of MNR tended to result in an improved
test performance in smaller bubbles. In larger bubbles
however, MNR 3 slightly worsened the test perfor-
mance. At MNR = 3, for example, the observed values
ranged from an improvement of AUC by +7.04% (sphere
size 100) to a worsening of AUC by –0.92% (sphere size
1500). Nevertheless, the AUC was generally higher in
larger spheres: The highest AUC (0.9166) was found at a
sphere size of 1.900 reference fetuses. The AUC was also
high (0.9164) at sphere sizes 1.500, 3.400, and 3.500.
4.1. Comparability of the Populations
Both the aneuploidy rate and the mean maternal age were
(slightly) lower in the low risk test cohort. This had been
anticipated, as medical practices attend to more young
women and women without anterior miscarriages and/or
aneuploidies than prenatal centers do. Nevertheless, in
both study cohorts (high and low risk) aneuploidies were
found more often than is usually expected in pregnancies
at this stage (0.20% in the normal population in Germany)
[12]. A possible explanation concerning this observation
opyright © 2011 SciRes. OJOG
C. Hörmansdörfer et al. / Open Journal of Obstetrics and Gynecology 1 (2011) 84-89
is the increased inclusion of women who wished to get
first trimester screening due to an individually perceived
higher risk of chromosomal aberrations, for example due
to higher maternal age or anterior miscarriages. Although
this might have led to a higher risk assessment, it was of
negligible impact for the study results, as these were
strictly focused on a comparison of the different AFS-3D
models and their modifications. At the same time several
studies describe a demographic change in the maternal
age structure in industrialized countries in recent years.
In this respect, the data of this study could represent the
quotidian situation over the next five to ten years [13-
4.2. Impact of MNR on the Test Performance
In the box model, the MNR concept did not improve test
performance. The AUC was identical or worse in all
analyses. Furthermore, in a large number of test cases a
risk assessment could not be obtained due to empty re-
ference boxes or too small a number of reference fetuses.
In the sphere model, the MNR showed mixed results. At
small sphere sizes up to 500 Units the best results were
obtained if a certain number of reference fetuses were
considered, including a minimum number of healthy and
affected fetuses. Since larger spheres over 1000 Units
probably contain enough healthy and affected fetuses
anyway, the impact of MNR was low or non-existent.
Summarizing the results, MNR does not improve ei-
ther the box or the sphere model and should not be ap-
plied in developing improved methods in future.
4.3. Optimal Model
Considering the results of this study, the best test per-
formance is reached when the model comprises the fol-
lowing characteristics:
1) It is a box model.
2) The box size equals LE = 1/14.
3) Modifications I (EB+) and II (Sim) are applied in
4.4. Importance of This Model
In comparison to the established approach to first trime-
ster screening, this innovative model does not take ma-
ternal age into account, as previous studies have shown
that this would increase the number of falsenegative
cases in younger mothers and the number of false-posi-
tive cases in older mothers without significantly improv-
ing the detection rate [5,6]. However, the most important
innovation is the direct assessment of the risk of fetal
aneuploidy through the assessment of the three-dimen-
sional spatial arrangement of plotted data from screening
data instead of the sequential multiplication of estimated
risk from each of the measurements taken. Preliminary
test runs with the new methodology suggest that in com-
parison to the classic model and at an identical sensiti-
vity rate a reduction of the false positive rate by up to
70% is realistic. The expected advantage of this model
would therefore be much greater precision in the calcula-
tion of risk.
4.5. Utility of This Screening Method
In view of current demographic trends it is important to
develop a screening test which performs as precisely as
possible in relation to the higher maternal age groups.
However, recent studies have shown that the classic first
trimester screening procedure produces test positive rates
that approach 100% in women over 40 years of age, with
false-positive rates which are almost as high [16,17].
This means that the classic screening method is inevita-
bly of very limited utility in respect to these age groups,
as most or all women are subsequently referred for fur-
ther invasive testing. At the same time these women are
the number one target group for FTS. AFS-3D has been
developed to solve this dilemma as it would allow for
meaningful routine screening in this age group, thus re-
ducing the risk of adverse outcomes of invasive testing,
such as hemorrhage, infection and iatrogenic abortion.
4.6. Alternative Model Variant
The results of this study are not conclusive. Further im-
provement could potentially be reached by modifying the
sphere model. The floating positioning of the reference
space under the sphere model is theoretically superior to
the discrete positioning within the box model. Conse-
quently, a model with static sized spheres could be deve-
loped. This approach would combine the invariant size of
the boxes with the centered test volume around the ex-
amined fetus. EB+ and Sim would also be applicable in
such a model.
Further studies are needed. In particular, the AFS-3D
algorithm has still to prove its worth in clinical studies
and comparative trials with other risk assessment algo-
rithms that are already available on the market.
[1] Krampl, E., Wertaschnigg, D. and Husslein, P. (2002)
Down-syndrom-screening im ersten trimenon. Geburt-
shilfe Frauenheilk, 62, 843-848.
[2] Wapner, R., Thom, E., Simpson, J.L., Pergament, E.,
Silver, R., Filkins, K., Platt, L., Mahoney, M., Johnson,
A., Hogge, W.A., Wilson, R.D., Mohide, P., Hershey, D.,
Krantz, D., Zachary, J., Snijders, R., Greene, N., Sabba-
gha, R., MacGregor, S., Hill, L., Gagnon, A., Hallahan, T.
and Jackson, L. (2003) First-trimester screening for tri-
somy-21 and 18. The New England Journal Medicine,
349, 1405-1413. doi:10.1056/NEJMoa025273
[3] Snijders, R.J.M., Sundberg, K., Holzgreve, W., Henry, G.
opyright © 2011 SciRes. OJOG
C. Hörmansdörfer et al. / Open Journal of Obstetrics and Gynecology 1 (2011) 84-89
Copyright © 2011 SciRes.
and Nicolaides, K.H. (1999) Maternal age and gestation-
specific risk for trisomy 21. Ultrasound Obstetrics and
Gynecology, 14, 167-170.
[4] Scharf, A., Schmidt, P., Seppelt, M., Maul, H., Wüste-
mann, M. and Sohn, C. (2003) Comparison of risk calcu-
lation for trisomy 21 by Nicolaides with a novel software:
Retrospective analysis of 744 cases. Geburtshilfe Frauen-
heilk, 63, 148-152.
[5] Schmidt, P., Rom, J., Maul, H., Vaske, B., Hillemanns, P.
and Scharf, A. (2007) Advanced first trimester screen-
ing (AFS): An improved test strategy for the individual
risk assessment of fetal aneuploidies and malformations.
Arch Gynecology and Obstetrics, 276, 159-166.
[6] Schmidt, P., Hörmansdörfer, C., Pruggmayer, M., Schütte,
C., Neumann, A., Gerritzen, A., Vaske, B., Hillemanns, P.
and Scharf, A. (2008) Improved prenatal aneuploidy scr-
eening using the novel “advanced first trimester scree-
ning” algorithm—A multicenter study of 10,017 pregnan-
cies. Journal of Clinical Ultrasound, 36, 397-402.
[7] Merz, E. (2007) First trimester screening—A new algorithm
for risk calculation of chromosomal anomalies developed
by FMF Germany. Ultraschall in Medecine, 28, 270-272.
[8] Schmidt, P., Hörmansdörfer, C., Oehler, K., Hertel, H.,
Hillemanns, P. and Scharf, A. (2008) Dreidimensionale
scatterplotanalyse zur risikoeinschätzung für fetale an-
euploidien—eine weiterentwicklung des ersttrimester
screenings. Z Geburtsh Neonatol, 212, 127-135.
[9] Schmidt, P., Dormeier, J., Hörmansdörfer, C., Golatta, M.,
Scharf, A. and Hillemanns, P. (2008) Vorstellung einer
neuen methodik zur visualisierung typischer befund kons-
tellationen für euploide und aneuploide feten—Common
bubbles im AFS-3D-Verfahren. Geburtsh Frauenheilk, 68,
[10] Schmidt, P. and Dormeier, J. (2008) How to skin a scatter
plot. Geburtsh Frauenheilk, 68, S1-194.
[11] Wald, N.J. and Hackshaw, A.K. (1997) Combining ultra-
sound and biochemistry in first-trimester screening for
down’s syndrome. Prenatal Diagnosis, 17, 821.
[12] Hassold, T. and Schwartz, S. (2003) Chromosomen-
aberrationen. In: Dietel, M., Dudenhausen, J. and Suttorp,
N., Eds., Harrisons innere medizin—Dt. ausgabe der 15.
Auflage in zusammenarbeit mit der charité. ABW-
Wissenschaftsverlag, Berlin, 406.
[13] Wellesley, D., Boyle, T., Barber, J. and Howe, D.T.
(2002) Retrospective audit of different antenatal screen-
ing policies for down’s syndrome in eight district general
hospitals in one health region. British Medical Journal,
325, 15. doi:10.1136/bmj.325.7354.15
[14] Olsen, C.L. (2003) Down syndrome: Interaction between
culture, demography and biology in determining the pre-
valence of a genetic trait. Human Biology, 75, 503-520.
[15] Kuppermann, M. and Norton, M.E. (2005) Prenatal test-
ing guidelines: Time for a new approach? Gynecology
and Obstetrics Investegation, 60, 6-10.
[16] Gebb, J. and Dar, P. (2009) Should the first-trimester
aneuploidy screen be maternal age adjusted? Screening
by absolute risk versus risk adjusted to maternal age.
Prenatal Diagnosis, 29, 245-247.
[17] Hörmansdörfer, C., Golatta, M., Scharf, A., Hillemanns,
P. and Schmidt, P. (2011) Age-independent first trimester
screening for down syndrome: Analysis of three modified
software programs with 6508 pregnancies. Arch Gyne-
cology and Obstetrics, 283, 749-754.