THE NORMAL FETAL HEART RATE STUDY:
ANALYSIS PLAN
M. Daumer
, M. Scholz
, A.-L. Boulesteix
, S. Pildner von Steinburg
,
S. Schiermeier
§
, W. Hatzmann
§
, K.T.M. Schneider
September 11, 2007
Abstract
Recording of fetal heart rate via CTG monitoring has been routinely per-
formed as an important part of antenatal and subpartum care for several decades.
The current guidelines of the FIGO (ref 1) recommend a normal range of the fetal
heart rate from 110 to 150 bpm. However, there is no agreement in the medical
community whether this is the correct range (ref 2). We aim to address this ques-
tion by computerized analysis (ref 3) of a high quality database (HQDb, ref 4)
of about one billion electronically registered fetal heart rate measurements from
about 10,000 pregnancies in three medical centres over seven years. In the present
paper, we lay out a detailed analysis plan for this evidence-based project in the
vein of the validation policy of the Sylvia Lawry Centre for Multiple Sclerosis
Research (ref 5) with a split of the database into an exploratory part and a part
reserved for validation. We will perform the analysis and the validation after pub-
lication of this plan in order to reduce the probability of publishing false positive
research findings (ref 6-7).
Sylvia Lawry Centre for MS Research, Munich, Germany
Trium Analysis Online GmbH, Munich, Germany
Department of Obstetrics and Gynecology, Technical University of Munich, Germany
§
Department of Obstetrics and Gynecology, University Witten/Herdecke, Germany
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Nature Precedings : doi:10.1038/npre.2007.980.2 : Posted 29 Oct 2007
1
INTRODUCTION
Recording of fetal heart rate via CTG monitoring has been routinely performed as
an important part of antenatal and subpartum care for several decades. As stated by
Massaniev (ref 2),
"baseline rate provides valuable information
on which we plan our further actions."
However, he also notes that
"a survey of some well-established obstetric textbooks
in Britain and abroad shows that there is no agreement
on a normal term fetus's baseline heart rate."
The most frequently cited intervals are 110-150 bpm and 120-160 bpm, whereas 115-
160 bpm and 110-160 bpm are used by a smaller number of clinicians. In the present
study, we address this crucial issue from the point of view of clinical informatics,
based on about one billion individual fetal heart rate measurements. Such an accurate
definition of the normal fetal heart rate should allow to better detect abnormal fetal
heart rates that may reveal bad condition of the fetus and necessitate intervention and
to reduce the false alarm rate and the associated unnecessary interventions.
Previous research
Based on 250,000,000 individual fetal heart rate measurements, a preliminary study
using the data from the hospital "Rechts der Isar" (Munich, Germany) for 2000 and
2001 revealed that the currently recommended normal ranges [110, 150 bpm] (ref
8) are inappropriate and should be shifted to [115, 160 bpm]. This might reduce the
number of false alarms, a big problem in clinical practice. Our preliminary results were
presented at the German Perinatal Congress (ref 9).
History of this analysis plan
This analysis plan is an improved version of an analysis plan draft written in March
2007. Besides small unimportant changes (typos, presentation, etc), the following sub-
stantial changes were carried out.
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· It is now specified explicitly that confidence intervals are derived via the boot-
strap method.
· The three validation data sets are now explicitly defined.
· Mixed models are now included.
· The analyses with the other parameters are now explained in more details.
· Separate analyses for each year are now included.
Criteria of inclusion of the CTGs
Only the CTGs of singleton pregnancies that are longer than 30 minutes will be in-
cluded in the analysis.
Investigated variables
The following variables will be analyzed.
· Non-averaged raw fetal heart rate without accelerations and decelerations
(FHR). Statistical unit = data point.
· Non-averaged baseline (BL) as computed by the CTG online algorithm (ref 3).
Statistical unit = data point.
· Averaged raw fetal heart rate without accelerations and decelerations (AFHR).
Statistical unit = CTG.
· Averaged baseline (ABL) as computed by the CTG online algorithm. Statistical
unit = CTG.
Formulation of the normal fetal heart rate range
The main analysis will be based on the non-averaged baseline (BL). The normal in-
terval for the fetal heart rate will be expressed as an interval of the form [z
, z
1-
],
where z
denotes the -quantile. Values ending with 0 or 5 will considerably simplify
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the practical application of the (new) normal heart rate range and improve its accep-
tance by clinicians. Because a width smaller than 40 bpm would further increase the
false alarm rate and a width greater than 45 bpm would possibly put some fetuses in
jeopardy, the admissible widths are 40 and 45 bpm.
Definition of the mathematical optimization problem
To sum up, we aim to find an interval of the form [~
z
, ~
z
1-
] with:
· ~
z
and ~
z
1-
ending with 0 or 5,
· ~
z
and ~
z
1-
being as close as possible to the non-rounded quantiles z
and z
1-
,
respectively,
· ~
z
1-
- ~
z
= 40 or 45.
For (z
-
, z
+
) R
2
+
and < 0.5, we define the optimality criterion C(, z
-
, z
+
) as
C(, z
-
, z
+
) = (z
+
- z
1-
)
2
+ (z
-
- z
)
2
.
For a fixed width W (e.g., W = 40 or W = 45), let (
(W ),z
-
(W ),z
+
(W )) be the
solution of the corresponding three-dimensional minimization problem:
C(
(W ), z
-
(W ), z
+
(W )) = min
,z
-
,z
+
(C(, z
-
, z
+
))
under the two following constraints:
1. z
+
(W ) - z
-
(W ) = W
2. z
-
(W ) and z
+
(W ) are multiples of 5.
It is to expect that this solution will be unique in practice. If not, we will choose the
solution that is most similar to the FIGO recommendation (ref 1).
Finally, C(
(40), z
-
(40), z
+
(40)) and C(
(45), z
-
(45), z
+
(45)) will be com-
pared. The width W
yielding the minimal C will be selected as the final width and
the normal fetal heart rate range will be defined as
[ z
-
(W
) , z
+
(W
) ].
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Training and validation
Validation of the results on an independent data set is a crucial step to avoid false
research findings (ref 5-6). Both temporal validation (based on data collected later
than the training data) and external validation (based on data collected in another
medical center) are known to be important (ref 10). Hence, we adopt the following
validation procedure.
Training data set
· data from the hospital "Rechts der Isar" (MRI), 2000-2004
Three validation data sets:
· data from the hospital "Rechts der Isar", 2005-2006 (temporal validation)
· data from the Marien-Hospital Witten (external validation, university hospital)
· data from the Achern hospital (external validation, non-university hospital)
First, all the analyses described below will be performed using the training data
set only, without even opening the validation data sets. The main analysis (Part IA)
will then be validated based on the three validation data sets. We will consider the
results as completely validated if all three validation data sets yield the same range
[z
-
(B
), z
+
(B
)]. If the result is different for at least one of the validation data sets,
we will pool all four data sets and use them to suggest an interval (based on the same
methodology) that will have to be validated in further research.
Part I: Estimation of the "normal" interval for the fetal
hearth rate
A. Main analysis with BL
With BL only, we will determine the normal fetal heart rate range as described above
using the following algorithm.
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1. Determining z
and z
1-
for different values of
For all m {100, . . . , 125}, determine n such that
^
F (m - 1) + ^
F (m) (1 - ^
F (n)) + (1 - ^
F (n - 1)),
with ^
F denoting the empirical distribution function of the fetal heart rate.
2. Minimizing C for W = 40
For each pair of quantiles found in step 1, find the pair (z
-
, z
+
) of multiples of 5
minimizing C. Select the pair of quantiles yielding the smallest C and store the
corresponding interval [z
-
(40), z
+
(40)].
3. Minimizing C for W = 45
Repeat step 2 for W = 45 instead of W = 40.
4. Selecting the final range
Select the interval ([z
-
(40), z
+
(40)] or [z
-
(45), z
+
(45)]) minimizing C as the
final normal fetal heart rate.
The validation of this analysis will be performed as outlined in the introduction.
B. Complementary analyses
For FHR, BL, AFHR and ABL, the following analyses will be carried out based on the
training data only.
1. Estimate of the 0.5%, 1%, 2.5%, 5%, 10%, 50%, 90%, 95%, 97.5%, 99%, 99.5%
quantiles.
2. Estimate the 95% confidence interval and standard deviation of the 0.5%, 1%,
2.5%, 5%, 10%, 90%, 50%, 95%, 97.5%, 99%, 99.5% quantiles based on 100
(for FHR and BL) or 10000 bootstrap samples (for AFHR and ABL).
The validation of these analyses will be performed as follows. After all analyses
with the training data are completed, step 1 will be repeated for all three validation
data sets successively. A quantile computed with the training data will be considered
as validated if the estimates based on all three validation data sets are located in the
confidence interval derived from the training data set.
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Part II: Association between fetal hearth rate and weeks
of gestation
These analyses are based on the (comparatively small) subset of CTGs for which the
week of gestation (WG) is known. Only training data are used.
1. Repeat the analyses from Part 1B for WG<28 (if there are more than 50 CTGs),
WG in [28,31], WG in [32,36], WG37.
2. Carry out linear regression with WG as predictor and AFHR or ABL as response
(statistical unit = CTG).
3. Carry out linear regression with categorized WG (same thresholds as in A) as
predictor and AFHR or ABL as response (statistical unit = CTG).
4. Carry out a mixed model analysis with WG as predictor and AFHR or ABL as
response (statistical unit = CTG). This approach takes into account that some
CTGs come from the same woman.
The validation of these analyses will be performed as follows. The models 2,3,4 will
be fitted again to all three validation data sets successively. A significant p-value (i.e.,
p <0.05) obtained with the training data set will be considered as validated if it is also
significant with all three validation data sets.
Part III: Association between fetal hearth rate and age
of the mother
These analyses are based on the (comparatively small) subset of CTGs for which the
age of the mother and the week of gestation (WG) are known. Only training data are
used.
1. Carry out linear regression with age of the mother as predictor and AFHR or
ABL as response (statistical unit = CTG).
2. Carry out a mixed model analysis with WG and age of the mother as predictors
and averaged FHR and averaged BL as response (statistical unit = CTG). This
approach takes into account that some CTGs come from the same woman.
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Nature Precedings : doi:10.1038/npre.2007.980.2 : Posted 29 Oct 2007
These analyses will be validated using the approach outlined in Part II.
Part IV: Evolution of the fetal hearth rate
1. Perform the analyses from Part 1B with MRI data from 2000-2001 only (already
published data).
2. Perform the analyses from Part 1B with MRI data for each year
(2000,2001,2002,2003,2004) separately.
Appendix: Additional explorative analyses
Further questions related to the fetal heart rate may be investigated in future research,
provided that the corresponding data are available. Among others:
1. Perform the analyses from Part 1B with ante partu CTGs only.
2. Perform the analyses from Part 1B with sub partu CTGs only.
3. Perform the analyses from Part 1B for all CTGs excepting fetuses with acidosis
or amniotic infection.
4. Perform the analyses from Part 1B for sub partu CTGs with acidosis.
5. Perform the analyses from Part 1B for sub partu CTGs with amniotic infection.
6. Perform the analysis from Part 3 (1-2) with the sex of the fetus as additional
predictor.
Acknowledgment
We thank Dr. Christian Lederer for helpful comments and Dr. Thomas Fšusslin for
making the data from the Achern hospital available. This work was partially supported
by the Porticus Foundation in the context of the International School for Technical
Medicine and Clinical Bioinformatics.
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Bibliography
1. FIGO: "Guidelines for the use of fetal monitoring", International Journal of Gy-
necology and Obstetrics 25:1159-1167, 1987.
2. Manassiew N: "What is the normal heart rate of a term fetus?", British Journal
of Obstetrics and Gynecoloy 103:1269-1273, 1996.
3. Schindler T: "Delayed Moving Window Algorithm for Online Cardiotocogram
Analysis - A Comparison of Computurized CTG Analysis", 1. Auflage, 120
Seiten, Paperback, ISBN 3-86130-300-0, 2002.
4. Noseworthy JH: "The challenge of long-term studies in multiple sclerosis: use of
pooled data, historical controls and observational studies to determine efficacy",
in Multiple Sclerosis Therapeutics (3rd edition), by Cohen JA and Rudick RA
(eds), Informa Healthcare, 2007.
5. Daumer M, Held U, Ickstadt K, Heinz M, Schach S, Ebers G: "Reducing the
probability of false positive research findings by pre-publication validation", Na-
ture Precedings, http://precedings.nature.com/documents/433/version/1, 2007.
6. Ioannidis J: "Why most published research findings are false", PloS Medicine
2:e124, 2005.
7. Rubin DB: "The design versus the analysis of observational studies for causal
effects: parallels with the design of randomized trials", Statistics in Medicine
26(1):20-36.
8. Schneider KTM, Butterwegge M, Daumer M, Duddenhausen J, Feige A, Gonser
M, Hecher K, Jensen A, Koepcke E, Kšunzel W, Roemer VM, Schmidt S, Vetter
K: "Application of CTG during pregnancy and delivery", 24 Seiten, Deutsche
Gesellschaft fšur Gynšakologie und Geburtshilfe, 2004.
9. Daumer M, Harner N, Pildner v. Steinburg S, Fischer T, Schneider KTM: "Can
we use large CTG databases to determine the normal heart rate of a term fetus?"
Poster, German Perinatal Congress, 2005.
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Nature Precedings : doi:10.1038/npre.2007.980.2 : Posted 29 Oct 2007
10. Kšonig I, Malley JD, Weimar C, Diener HC, Ziegler A: "Practical experiences on
the necessity of external validation", submitted, 2007.
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Nature Precedings : doi:10.1038/npre.2007.980.2 : Posted 29 Oct 2007
Amendment to
"THE NORMAL FETAL HEART RATE STUDY:
ANALYSIS PLAN"
M. Daumer
, M. Scholz
, A.-L. Boulesteix
, S. Pildner von Steinburg
,
S. Schiermeier
§
, W. Hatzmann
§
, K.T.M. Schneider
October 29, 2007
1
Modification of the optimality criterion
As stated in the first version of our analysis plan, we seek an interval [~
z
, ~
z
1-
] with
· ~
z
and ~
z
1-
ending with 0 or 5,
· ~
z
and ~
z
1-
being as close as possible to non-rounded quantiles z
and z
1-
,
respectively,
· ~
z
1-
- ~
z
= 40 or 45.
We now simplify the corresponding optimality criterion which was described in the
subsection "Definition of the mathematical optimization problem" in the first version
of our analysis plan by skipping the computation of the quantiles and assessing the
symmetry of the candidate intervals directly. The procedure is as follows.
Sylvia Lawry Centre for MS Research, Munich, Germany
Trium Analysis Online GmbH, Munich, Germany
Department of Obstetrics and Gynecology, Technical University of Munich, Germany
§
Department of Obstetrics and Gynecology, University Witten/Herdecke, Germany
1
Nature Precedings : doi:10.1038/npre.2007.980.2 : Posted 29 Oct 2007
· Let us consider the following candidate intervals:
z
(1)
lower
= 110
z
(1)
upper
= 150
z
(2)
lower
= 110
z
(2)
upper
= 155
z
(3)
lower
= 115
z
(3)
upper
= 155
z
(4)
lower
= 115
z
(4)
upper
= 160
z
(5)
lower
= 120
z
(5)
upper
= 160
· For each candidate interval i = 1, . . . , 5, we measure the asymmetry of the
interval as the squared difference between the lower and upper tails:
A(z
(i)
lower
, z
(i)
upper
) =
^
F (z
(i)
lower
) - (1 - ^
F (z
(i)
upper
))
2
,
where ^
F is an estimator of the (continuous) distribution function of the fetal
heart rate expressed as the number of beats per minute. Since the fetal heart
rate is given as an integer in our database, we have to correct for continuity as
follows. If a denotes an integer (such as a = 110, a = 115, etc) and x
1
, . . . , x
n
the n observed integer fetal heart rates from our database, we define ^
F as
^
F (a) =
1
n
n
i=1
I(x
i
a) -
1
2
n
i=1
I(x
i
= a)
,
with I denoting the indicator function (I(A) = 1 if A is true, I(A) = 0 other-
wise). The underlying assumption is that the density function is constant within
the interval [a - 0.5, a + 0.5].
· We choose the interval minimizing A as the correct normal heart rate interval:
Normal fetal heart rate interval = [z
(i
)
lower
, z
(i
)
upper
],
where
i
= arg min
i=1,...,5
A(z
(i)
lower
, z
(i)
upper
).
2
Results of the training steps and hypotheses
Based on our results obtained using the training data from the hospital "Rechts der
Isar" for the years 2000 to 2004, we formulate the hypotheses that have to be validated
as follows.
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1. The lower bound is 115 or 120 bpm.
2. The upper bound is 160 bpm.
Note that increasing the lower bound from 110 bpm to 115 bpm or more would also
decrease the risk of misinterpreting the pulse of a tachycardic mother as the fetal pulse,
a situation which is potentially highly dangerous for the fetus. In this respect, 120 bpm
would be preferable to 115 bpm. However, 120 bpm would also yield higher false
alarm rates, possibly leading medical staff to ignore alarms and thus oversee dangerous
events (ref 1). According to the results of the training step, the choice between 115
bpm and 120 bpm will be difficult and cannot at this stage be satisfactorily supported
by empirical data. Multivariate analyses involving fetal and maternal outcome data
will probably be needed to overcome these limitations.
Acknowledgment
We thank Christian Lederer for very helpful comments and suggestions.
Bibliography
1. Lawless ST: "Crying wolf: false alarms in a pediatric intensive care unit", Crit
Care Med 22(6):981-985.
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Nature Precedings : doi:10.1038/npre.2007.980.2 : Posted 29 Oct 2007