Improving diagnostic ability of blood oxygen
saturation from overnight pulse oximetry in
obstructive sleep apnea detection by means
of central tendency measure
Daniel A´lvareza,*, Roberto Horneroa, Marı ´a Garcı ´aa,
Fe ´lix del Campob, Carlos Zamarro ´nc
aE.T.S.I. de Telecomunicacio ´n, University of Valladolid, Camino del Cementerio s/n,
47011 Valladolid, Spain
bHospital del Rı ´o Hortega, Servicio de Neumologı ´a, c/Cardenal Torquemada s/n,
47010 Valladolid, Spain
cHospital Clı ´nico Universitario, Servicio de Neumologı ´a, Travesı ´a de la Choupana s/n,
15706 Santiago de Compostela, Spain
Received 18 October 2006; received in revised form 29 May 2007; accepted 12 June 2007
Artificial Intelligence in Medicine (2007) 41, 13—24
Objectives: Nocturnal pulse oximetry is a widely used alternative to polysomnogra-
phy (PSG) in screening for obstructive sleep apnea (OSA) syndrome. Several oximetric
indexes have been derived from nocturnal blood oxygen saturation (SaO2). However,
they suffer from several limitations. The present study is focused on the usefulness of
nonlinear methods in deriving new measures from oximetry signals to improve the
diagnostic accuracy of classical oximetric indexes. Specifically, we assessed the
validity of central tendency measure (CTM) as a screening test for OSA in patients
clinically suspected of suffering from this disease.
Materials and methods: We studied 187 subjects suspected of suffering from OSA
referred to the sleep unit. A nocturnal pulse oximetry study was applied simulta-
neously to a conventional PSG. Three different index groups were compared. The first
indexes (ODIs) and cumulative time spent below a saturation of 90% (CT90). The
second one was formed by indexes derived from a nonlinear method previously
studied by our group: approximate entropy (ApEn). The last one was composed by
indexes derived from a CTM analysis.
* Corresponding author. Tel.: +34 983 423000x5589; fax: +34 983 423661.
E-mail address: firstname.lastname@example.org (D. A ´lvarez).
0933-3657/$ — see front matter # 2007 Elsevier B.V. All rights reserved.
The obstructive sleep apnea (OSA) syndrome is char-
acterized by repetitive reduction or cessation of
. This disease is usually associated with hypoxe-
ral in many sleep centers . The estimated OSA
prevalence varies from 1 to 5% of adult men in
western countries . OSA is associated with condi-
tions that are responsible for the most important
causes of mortality in adults: hypertension and car-
diovascular and cerebrovascular diseases. Several
neurobehavioral morbidities, which are of poten-
tially great public health and economic importance,
are linked with OSA . The major behavioral symp-
toms include excessive daytime sleepiness (EDS),
neurocognitive deficits like impairments in concen-
tration and memory, and psychological problems like
depression or personality changes . Individuals
with OSA are dangerous drivers with an increased
risk of being involved in road and work accidents .
The standard diagnostic test for OSA syndrome is
overnight polysomnography (PSG) , consisting in
the recording of neurophysiological and cardiore-
spiratory signals subsequently used to analyze sleep
and breathing. The apnea—hypopnea index (AHI)
derived from the PSG is then used to diagnose the
disease. Portable monitoring has been proposed as a
substitute for PSG in the diagnostic assessment of
patients with suspected sleep apnea . Due to its
noninvasive nature and simplicity, nocturnal pulse
oximetry is widely used in many medicine areas to
determine patient’s blood oxygen saturation (SaO2)
and heart rate. The lack of airflow during apneic
periods can lead to recurrent episodes of hypoxemia
that can be detected on oximetry as fluctuations in
Several quantitative indexes derivedfrom noctur-
nal oximetry have been developed to diagnose OSA.
The most frequently used by physicians include oxy-
gen desaturation indexes (ODIs), which measure the
number of dips in the SaO2signal below a certain
threshold [9—11], and the cumulative time spent
below a certain saturation level (CT) [12,13]. How-
ever, these indexes have significant limitations. In
general, CT indexes did not achieve high diagnostic
accuracies [13,14]. On the other hand, there is not a
universally accepted definition for oxygen desatura-
correlation between oximetry indexes and AHI is not
high . In previous studies [16—18], our group has
shown that nonlinear analysis could provide useful
information in the diagnosis of OSA syndrome. A
ing approximate entropy (ApEn) improved the diag-
nostic accuracy of classical oximetric indexes .
ApEn was also applied to heart rate signals from
nocturnal oximetry, obtaining promising results
. Moreover, additional nonlinear methods, cen-
tral tendency measure (CTM) and Lempel—Ziv (LZ)
complexity, were applied to SaO2records . The
results suggested that both CTM and LZ complexity
could help physicians in screening for OSA syndrome.
Particularly, a variability measure by means of the
CTM provided the best diagnostic accuracy. The pre-
sent study intended to go more deeply into the
usefulness of the CTM to diagnose OSA. We assessed
its advantages over classical oximetric indexes and
other nonlinear methods: it is a simple parameter to
estimate the signal variability with a low computa-
tional cost . Furthermore, we studied the
changes in the diagnostic accuracy when using dif-
ferent values of the input parameters.
Variability measures of ECG allow to distinguish
between normal and chronic heart failure subjects
14D. A ´lvarez et al.
Results: For a radius in the scatter plot equal to 1, CTM values corresponding to OSA
positive patients (0.30 ? 0.20, mean ? S.D.) were significantly lower (p ? 0.001)
than those values from OSA negative subjects (0.71 ? 0.18, mean ? S.D.). CTM was
significantly correlated with classical indexes and indexes from ApEn analysis. CTM
provided the highest correlation with the apnea—hipopnea index AHI (r = ?0.74,
p < 0.0001). Moreover, it reached the best results from the receiver operating
characteristics (ROC) curve analysis, with 90.1% sensitivity, 82.9% specificity, 88.5%
positive predictive value, 85.1% negative predictive value, 87.2% accuracy and an
area under the ROC curve of 0.924. Finally, the AHI derived from the quadratic
regression curve for the CTM showed better agreement with the AHI from PSG than
classical and ApEn derived indexes.
Conclusion: The results suggest that CTM could improve the diagnostic ability of SaO2
the diagnosis of OSA syndrome.
# 2007 Elsevier B.V. All rights reserved.
. Some authors have applied nonlinear methods
over different respiratory patterns to study sleep
 or panic disorder .
In the present study, we applied CTM looking for
differences in variability between OSA positive and
OSA negative patients. Our study is aimed to esti-
mate the overall variability of each overnight oxi-
metric recording by means of CTM in order to assess
its utility in OSA diagnosis. We assessed its useful-
ness to physicians in screening for OSA syndrome,
comparing it with classical oximetric indexes and
with ApEn analysis. We studiedthree different index
groups: classical indexes, regularity indexes from
ApEn analysis and variability indexes from CTM
2. Subjects and signals
A total of 187 patients (147 males and 40 females)
suspected ofhaving OSAwere studied.Patientshave
a mean ? standard
57.97 ? 12.84 years and a body mass index (BMI)
of 29.54 ? 5.51 kg/m2. All subjects presented day-
time hypersomnolence, loud snoring, nocturnal
choking and awakenings, or apneic events (or all
four symptoms) reported by the subject or a bed
mate. Sleep studies were carried out usually from
midnight to 08:00 a.m. in the Sleep Unit of Hospital
Clı ´nico Universitario in Santiago de Compostela,
Spain. The Review Board on Human Studies at this
institution approved the protocol, and all subjects
gave their informed consent to participate in the
2.1. Conventional polysomnography
All patients underwent overnight PSG (Ultrasom
Network, Nicolet, Madison, WI, USA) which included
(ECG), electrooculogram (EOG), chin electromyo-
gram (EMG), measurement of chest wall movement
and airflow measurement (three-port thermistor).
The PSG register was analyzed over periods of 30 s
during sleep phases I—IV and rapid eye movement,
according to Rechtschaffen and Kales rules .
Apnea was defined as the cessation of airflow for
more than 10 s and hypopnea as the reduction of
respiratory flow for at least 10 s accompanied by a
4% or more decrease in the saturation of hemoglobin
[23—26]. The average AHI was calculated for hourly
periods of sleep. According to the American Acad-
emy of Sleep Medicine Task Force criteria , an
AHIgreaterthanorequal to10eventsper hour(e/h)
of sleep was considered as diagnosis of OSA. If the
subject had less than 3 h of total sleep, the sleep
study was repeated.
After the PSG, a conventional spirometry study
(Collins spirometer) was carried out. Chronic
obstructive pulmonary disease (COPD) was defined
as a disease state characterized by airflow limitation
that is not fully reversible. The airflow limitation is
usually both progressive and associated with an
abnormal inflammatory response of the lungs to nox-
ious particles or gases . The spirometry showed
that 42 patients had COPD (mean age of 62.26
? 13.65 years and a BMI of 29.66 ? 17.31 kg/m2).
Moreover, 9 of the 42 patients with COPD (21.8%)
consensus , 22 (52.4%) of these subjects could be
classified as mild COPD patients, 14 (33.3%) as mod-
erate COPD patients and 6 (14.3%) as severe COPD
Table 1 summarizes the demographic and clinical
features of the subjects under study, as well as the
groups derived from the PSG diagnosis. The OSA
positive group consisted of 111 patients (59.4%)
diagnosed as OSA according to an AHI ? 10 e/h
(40.07 ? 19.64 e/h), whereas the remaining 76 sub-
jects (40.6%) made up the OSA negative group
(2.04 ? 2.36 e/h). In the OSA positive group, there
were men and women between 28 and 81 years
(58.30 ? 12.88 years) and with BMI between 20.57
and 46.51 kg/m2(30.45 ? 4.92 kg/m2). The OSA
Improving diagnostic ability of blood oxygen saturation using CTM15
Demographic and clinical features of the subjects under study
FeaturesAll subjects OSA positiveOSA negative
Recording time (h)
57.97 ? 12.84
29.54 ? 5.51
8.19 ? 0.62
58.30 ? 12.88
30.45 ? 4.92
8.17 ? 0.75
40.07 ? 19.64
57.57 ? 12.87
28.42 ? 6.02
8.22 ? 0.33
2.04 ? 2.36
Data are presented as mean ? S.D. unless otherwise indicated. OSA positive: patients with obstructive sleep apnea. OSA negative:
patients without obstructive sleep apnea.
negative group consisted of subjects between 21
and 79 years (57.57 ? 12.87 years) and with
BMI between 19.53 and 42.19 kg/m2
2.2. Overnight pulse oximetry
An overnight pulse oximetry analysis was carried out
simultaneously to the conventional PSG study.
Recording of SaO2was carried out using a Criticare
504 oximeter (CSI, Waukesha, WI, USA). SaO2and
heart rate were both simultaneously recorded using
a dual wavelength-based finger probe with a sam-
pling frequency of 0.2 Hz (one sample every 5 s). In
this study only the SaO2signals were used. Although
new oximeters work at higher sampling frequencies,
the study carried out by Warley et al.  showed
that this sampling frequency provides reasonable
resolution in SaO2variability. Moreover, oximetry
signals recorded at higher sampling frequencies are
subsequently averaged to obtain usually one sample
every 12 s [7,14,30]. There is some underestimation
of the peak SaO2in recovery post-apnea, but the
signal shape and variability were preserved .
The SaO2signals were saved to separate files and
processed off-line. Artifacts due to poor contact
from the finger probe, patient movements or bad
regional circulation, were removed by visual inspec-
tion of SaO2signals, discarding data showing drops
to zero. Fig. 1 displays three common oximetric
subject. Fig. 1(b) shows a SaO2record with clearly
marked desaturations, corresponding to an appar-
ent OSA positive subject. Fig. 1(c) illustrates more
exactly the difficulty in the diagnosis of the disease.
It shows the SaO2 record for an uncertain OSA
positive patient. In this case, dips in SaO2are not
so extreme and the diagnosis by visual inspection is
3.1. Classical oximetry indexes
Our oximeter provided the following indexes: oxy-
gen desaturation indexes of 4% (ODI4), 3% (ODI3), 2%
(ODI2) and cumulative time spent below a satura-
tion of 90% (CT90). The number of falls in each SaO2
record greater than or equal to 4, 3 and 2% were
computed from baseline. Baseline was set initially
as the mean level in the first 3 min of recording .
These oxygen desaturation indexes were computed
per hour of recording. CT90 was calculated as the
percentage of time during which the SaO2register
was below 90%.
3.2. Approximate entropy
ApEn is a family of statistics introduced as a quan-
tification of regularity in sequences and time series
data, initially motivated by applications to rela-
tively short and noisy data sets . ApEn evaluates
and discriminates series for which clear feature
recognition is difficult . Several properties of
ApEn make it highly suitable for biomedical time
series analysis: ApEn is almost unaffected by low-
level noise; it is robust to outliers, scale invariant
and model independent; it is applicable to time
series with at least 50 data points, with good repro-
ducibility; it can be applied to discriminate general
classes of correlated stochastic processes, as well as
noisy deterministic systems, providing finite values
ApEn assigns a non-negative number to a time
series, with larger values corresponding to greater
randomness or irregularity in the data . The
algorithm applied to compute ApEn can be seen in
detail in  and . Briefly, ApEn measures the
close (within r) for m contiguous observations
remain close (within the same tolerance r) on sub-
sequent incremental comparisons (pattern length
m + 1) . Two input parameters,m andr, must be
fixed to compute ApEn(m, r): m is the length of
compared runs, and r is effectively a filter . To
each data set [33,34]. No guidelines exist for opti-
mizing the m and r values. However, Pincus sug-
gestedparametervaluesofm = 1orm = 2andwithr
the original time series . Multiple previous stu-
dies have demonstrated that these input para-
meters produce good statistical reproducibility
for ApEn for time series of length N ? 60 . In
16D. A ´lvarez et al.
common OSA negative subject, (b) an apparent OSA posi-
tive patient and (c) an uncertain OSA positive subject.
SaO2records from nocturnal oximetry for (a) a
previous studies by our own group [16,17], we
showed that ApEn was better estimated with
m = 1 when applying it to SaO2signals. Thus, in
the present study, we computed ApEn with m = 1
and r equal to 0.1, 0.15 and 0.20 times the S.D. of
and ApEn02, respectively.
3.3. Central tendency measure
Quantifying the signal variability by means of CTM
starts displaying a second-order difference plot.
These kinds of scatter diagrams, given by Eq. (1),
are graphs centered in the origin used to assess the
degree of chaos in a data set .
½xðn þ 2Þ ? xðn þ 1Þ? versus ½xðn þ 1Þ ? xðnÞ?
The second-order difference plots are very useful
in modeling biological systems such as hemody-
approach, rather than defining a time series as
chaotic or not chaotic, the degree of variability or
useful tool for physicians, who could make a pre-
liminary diagnosis by visual inspection of the dia-
grams. Fig. 2 displays the second-order difference
plots for the SaO2signals depicted in Fig. 1. The
uncertain OSA positive subject whose SaO2record is
displayed in Fig. 1(c) could be initially misclassified
as OSA negative by visual inspection. However, the
corresponding scatter plot in Fig. 2(c) shows a sig-
nificantly high dispersion compared with the dia-
suggesting a different diagnosis. Thus, the sec-
ond-order difference plots could help physicians
to improve preliminary diagnoses.
The CTM is used to quantify the signal variability
from the second-order difference plots. The CTM is
computed by selecting a circular region of radius r
around the origin and counting the number of points
that fall within the circle. This measure is subse-
quently normalized dividing by the total number of
points. For a N point data series, N ? 2 would be the
total number of points in the scatter plot given by
Eq. (1). Then, the CTM can be computed as 
if½ðxði þ 2Þ ? xði þ 1ÞÞ2
þðxði þ 1Þ ? xðiÞÞ2?
N ? 2
The radius r is selected depending on the char-
CTM with various radii to assess the behavior of the
method in pulse oximetry analysis. We computed
CTM with three different values of r. For radii equal
to 1, 3 and 6 we obtained CTM1, CTM3 and CTM6. We
compared these parameters with the classical oxi-
metric indexes and with those indexes derived from
the ApEn analysis.
3.4. Statistical analysis
The Kolmogorov—Smirnov and Shapiro—Wilk tests
were used to assess the normal distribution of the
variables involved in the study. Homoscedasticity
(homogeneity of variances) was also assessed by
and homoscedasticity could not be verified with all
the variables under study. Thus, the nonparametric
Mann—Whitney test was applied to look for signifi-
cant differences between the OSA positive and the
applied due to the large number of variables
included in the study. SPSS 14 was used to perform
the statistical analysis. The degree of association
between each index and the AHI was studied using
the Pearson correlation test. A p-value was also
computed to measure the statistical significance
of the results. A ROC curve analysis was performed
to assess the diagnostic capacity of each method in
screening for OSA syndrome. The following statis-
tics were derived from this study: sensitivity, spe-
cificity, positive predictive value (PPV), negative
predictive value (NPV), positive likelihood ratio
(LR+), negative likelihood ratio (LR?), accuracy
and area under the ROC curve. Correlation and
ROC curve analyses were used to select the best
parameter in each group of indexes. Scatter dia-
grams were depicted to graphically study the rela-
tion between indexes under study and the AHI. In
addition, the linear regression (degree n = 1) and
Improving diagnostic ability of blood oxygen saturation using CTM17
OSA negative subject (b) an apparent OSA positive patient
and (c) an uncertain OSA positive subject.
Second-order difference plots (a) a common
the quadratic regression (degree n = 2) curves,
which best fit the plotted points in a least squares
sense, were drawn in the scatter diagrams. The
between indexes and the AHI from PSG, were used
to obtain a derived AHI. Finally, Bland and Altman
plots were used to graphically measure the degree
ofagreement betweenthe derivedAHIs andtheAHI
SaO2 signals from nocturnal oximetry were pro-
cessed by means of ApEn and CTM. Classical oxi-
metric indexes, ODI2, ODI3, ODI4 and CT90 were
also included in this study. As well as ODIs are
provided for three common desaturation thresholds
(2, 3 and 4%), three different measures were com-
puted for each nonlinear method varying their input
parameters: ApEn01, ApEn015 and ApEn02 were
derived from the ApEn and CTM1, CTM3 and CTM6
were derived from the CTM analysis.
Table2showsthemean ? S.D.valuesforboththe
OSA positive and the OSA negative groups for every
index. Furthermore, the p-value from the Mann—
Whitney test is displayed. CTM1, CTM3 and indexes
from the ApEn analysis provide the highest signifi-
cant differences between groups, improving results
from the classical oximetric indexes. Table 3 shows
the correlation between all indexes and the AHI
derived from the PSG. Although CT90 was statisti-
cally correlated with the AHI (p < 0.001), it
achieved the smallest Pearson correlation coeffi-
cient (r = 0.280). ODIs achieved higher correlation
with AHI than CT90, slightly improving correlation
valuesbetweenApEnandAHI.Weobtainedr = 0.617
(p < 0.0001) with ODI3, whereas an r = 0.606
(p < 0.0001) was reached with ApEn02. CTM1
18 D. A ´lvarez et al.
Average index values for the groups under
OSA positive OSA negativep-value
6.9 ? 10?5
1.3 ? 10?5
1.2 ? 10?6
2.3 ? 10?6
1.1 ? 10?21
1.0 ? 10?21
1.4 ? 10?21
7.0 ? 10?22
8.9 ? 10?22
5.0 ? 10?20
27.18 ? 24.54
25.69 ? 23.31
24.08 ? 22.46
23.94 ? 29.90
1.16 ? 0.35
1.14 ? 0.34
1.09 ? 0.31
0.30 ? 0.20
0.75 ? 0.23
0.90 ? 0.15
6.07 ? 10.03
4.37 ? 7.91
3.12 ? 6.02
4.56 ? 17.05
0.48 ? 0.27
0.48 ? 0.27
0.48 ? 0.26
0.71 ? 0.18
0.98 ? 0.05
0.99 ? 0.01
Dataarepresentedasmean ? S.D.OSApositive:patientswith
obstructive sleep apnea. OSA negative: patients without
obstructive sleep apnea. ODI2: number of dips in SaO2? 2%.
2%.ODI3:numberof dipsinSaO2? 3%.ODI4:numberof dipsin
SaO2? 4%. CT90: percentage of time spent with SaO2below
90%. ApEn01: approximate entropy computed with m = 1 and
r = 0.1. ApEn015: approximate entropy computed with m = 1
and r = 0.15. ApEn02: approximate entropy computed with
m = 1 and r = 0.2. CTM1: central tendency measure computed
with r = 1. CTM3: central tendency measure computed with
r = 3. CTM6: central tendency measure computed with r = 6.
metric indexes and AHI from PSG
Classical oximetric indexes
Regularity indexes from ApEn analysis
Variability indexes from CTM analysis
r: Pearson correlation coefficient; p: statistical significance;
ODI2: number of dips in SaO2? 2%; ODI3: number of dips in
SaO2? 3%; ODI4: number of dips in SaO2? 4%; CT90: percen-
tage of time spent with SaO2below90%. ApEn01: approximate
entropy computed with m = 1 and r = 0.1; ApEn015: approx-
imate entropy computed with m = 1 and r = 0.15; ApEn02:
approximate entropy computed with m = 1 and r = 0.2; CTM1:
centraltendencymeasurecomputedwithr = 1;CTM3:central
tendency measure computed with r = 3; CTM6: central ten-
dency measure computed with r = 6.
index group in terms of diagnostic accuracy and correla-
tion with AHI.
ROC curves for the best parameter of each
achieved the highest correlation with the AHI
(r = ?0.7382, p < 0.0001). The negative correlation
indexes obtained with CTM are due to the own
nature of this method, which assigns small values
to high variability and vice versa.
Table 4 shows the results from the ROC curve
analysis for each parameter. We can notice that
nonlinear indexes achieved better diagnostic accu-
racy and area under the ROC curve (AROC) than
classical indexes. All nonlinear measures provided
sensitivity values over 83% and specificity values
over 81%, leading to accuracy values of at least
84.5% and areas under the ROC curve over 0.90.
On the other hand, classical oximetric indexes
showed large differences between sensitivity and
specificity values, with very poor sensitivities.
Accuracies are around 75% and AROCs are below
0.80. Diagnostic test values from ApEn analysis
do not vary very much changing the input para-
meters. However, CTM diagnostic accuracy slightly
decreases when the radius is increased. The best
results are provided by CTM1, with 90.1% sensitiv-
ity, 82.9% specificity, 88.5% positive predictive
racy and an area under the ROC curve of 0.924.
Fig. 3 shows the ROC curves for the best parameter
of each index group in terms of diagnostic accuracy
and correlation with AHI: ODI3 from the classical
CTM1 from the CTM index group. The ROC curves
illustrate the variation of sensitivity and specificity
Improving diagnostic ability of blood oxygen saturation using CTM19
Test results for the optimum decision threshold from the ROC curve analysis
ThSE PPVNPV LR+LR?
Th: optimum decision threshold; S: sensitivity; E: specificity; PPV: positive predictive value; NPV: negative predictive value; LR+:
positive likelihood ratio; LR?: negative likelihood ratio; A: accuracy; AROC: area under the ROC curve; ODI2: number of dips in
SaO2? 2%; ODI3: number of dips in SaO2? 3%; ODI4: number of dips in SaO2? 4%; CT90: percentage of time spent with SaO2below
90%. ApEn01: approximate entropy computed with m = 1 and r = 0.1; ApEn015: approximate entropy computed with m = 1 and
r = 0.15; ApEn02: approximate entropy computed with m = 1 and r = 0.2; CTM1: central tendency measure computed with r = 1;
CTM3: central tendency measure computed with r = 3; CTM6: central tendency measure computed with r = 6.
(dashed line) and quadratic regression (solid line) curves
that best fit the data in a least square sense.
sion (dashed line) and quadratic regression (solid line)
curves that best fit the data in a least square sense.
Scatter plot for ApEn02 and AHI. Linear regres-
are used. The ^ symbol represents the optimum
threshold. A threshold to the left (right) results in a
test with higher specificity (sensitivity) but lower
sensitivity (specificity). Nonlinear features show
more regular behavior than ODI3 when different
Figs. 4—6 show the scatter diagram for ODI3,
ApEn02 and CTM1, respectively. Regression curves,
linear (dashed line) and quadratic (solid line),
which best fit the data in a least square sense,
to derive an AHI from each index. Due to their
best fitting to the data, the quadratic curves
(p2x2+ p1x + p0) were selected. Bland and Altman
plots, displayed in Figs. 7—9, were subsequently
used to quantify the agreement between the origi-
nal AHI obtained from PSG and these AHI derived
from ODI3, ApEn02 and CTM1, respectively. A sys-
tematic bias can be shown in the Bland and Altman
plot corresponding to the AHI derived from ODI3
(meandifference = 8.1),whereastheAHIfromboth
the ApEn02 and the CTM1 have no bias (mean
difference = 0.0). The limits of agreement (?1.96
S.D.) are wide (?34.8 to 51.5), indicating there is a
great lack of agreement between both techniques.
The limits of agreement decreased to ?37.9 when
comparing the AHI obtained from PSG with that
20 D. A ´lvarez et al.
sion (dashed line) and quadratic regression (solid line)
curves that best fit the data in a least square sense.
Scatter plot for CTM1 and AHI. Linear regres-
ment between AHI derived from the quadratic regression
curve of ODI3 and AHI from PSG. Solid line represents the
mean difference between both methods and dashed lines
their limits of agreement.
Bland and Altman plot for measuring agree-
ment between AHI derived from the quadratic regression
curve of ApEn02 and AHI from PSG. Solid line represents
the mean difference between both methods and dashed
lines their limits of agreement.
Bland and Altman plot for measuring agree-
ment between AHI derived from the quadratic regression
curve of CTM1 and AHI from PSG. Solid line represents the
mean difference between both methods and dashed lines
their limits of agreement.
Bland and Altman plot for measuring agree-
ment in the Bland and Altman plot corresponding to
CTM1 decrease by various events per hour (up to
?31.5 e/h) and the number of outliers is lower.
We have also measured the performance of non-
linear methods in terms of computational time.
ApEn02 and CTM1 were both applied to a common
nocturnal SaO2record (8 h long) divided in epochs of
16.66 min using the same PC (AMD AthlonTMXP 3000
with 1 GB RAM). While ApEn02 achieved a mean
computational time of 0.5833 s per epoch, CTM1
was 1000 times faster, decreasing computational
time up to 0.5333 ms.
5. Discussion and conclusions
Portable monitoring has been widely used as an
alternative technique to PSG in the diagnosis of
OSA syndrome. This study has shown that nonlinear
analysis, and particularly CTM, could enhance the
diagnostic capacity of SaO2signals recorded from
nocturnal oximetry. CTM improved the diagnostic
test values of classical indexes commonly derived
from SaO2, e.g. ODIs and CT90. Moreover, CTM
improved the results obtained applying other non-
linear measures previously studied by our own group
[16—18]. We have shown that OSA patients have
mean ? S.D.) than OSA negative subjects (0.71 ?
0.18, mean ? S.D.) according to their higher disper-
sion in the second-order difference plots. Thus, we
could say that SaO2signals from OSA patients are
more variable than those from OSA negative sub-
We have divided the indexes under study in three
different groups: classical oximetric indexes (ODI2,
ODI3, ODI4 and CT90), regularity indexes from
approximate entropy analysis (ApEn01, ApEn015
and ApEn02) and variability indexes from CTM ana-
lysis (CTM1, CTM3 and CTM6). Tables 3 and 4 show
that CTM1 reached the best statistics and para-
meters obtained from ROC analysis, significantly
improving the results of classical indexes. CTM1
was significantly correlated (p < 0.0001) with ODIs
and regularity indexes from ApEn analysis (r > 0.6).
Furthermore, CTM1 showed the highest correlation
coefficient (r = ?0.738) with AHI.
The ROC curve analysis also yielded the best
results for nonlinear methods, and particularly for
CTM1. Whereas classical indexes achieved high spe-
cificities but very poor sensitivities, nonlinear meth-
ods provided sensitivity and specificity values both
greater than 80%, leading to high accuracies. High
positive and negative predictive values, as well as
small likelihood ratios, make nonlinear methods
values (0.30 ? 0.20,
especially useful to help in OSA diagnosis. CTM1
reached 90.1% sensitivity, 82.9% specificity, a PPV
of 88.5, a NPV of 85.1, a LR+ of 5.27, a LR? of 0.12
and an accuracy of 87.5%. The area under the ROC
curve was 0.924, the largest one compared with
A significant drawback of nocturnal oximetry
common to most sleep studies is the substantial
number of false negative cases. Subjects involved
in these studies are typically referred to the sleep
units because they are suspected of suffering from
sleep apnea. Thus, the population under study has a
very high prevalence of the disease, resulting in a
small percentage of patients who test negative with
a high chance to be incorrectly classified (false
negative result). Additionally, due to the high pre-
valence, patients with a positive result are more
likely to have a true positive result than a false
positive result . This leads to a high LR+ but also
to a high LR?. Many sleep studies used two different
thresholds to achieve both high LR+ and low LR?,
with the limitation that patients presenting diag-
nostic values betweenbothcut-offpoints willnot be
classified . In the present research, we used a
diagnosed, although both false positive and false
negative cases were present. However, we achieved
significant operating characteristics with a single
threshold, increasing the probability that a patient
testing positive has an abnormal AHI (LR+ > 5.0) and
decreasing the probability that a patient testing
negative has an abnormal AHI (LR? < 0.2).
Previous studies based on classical oximetric
indexes [14,23,36,37] provided higher sensitivity
but lower specificity, whereas others [9,38,39]
achieved higher specificity but significantly lower
sensitivity. On the other hand, our results demon-
strate that nonlinear methods provide significant
sensitivity and specificity values, leading to high
accuracies and areas under the ROC curve. The
study carried out by Olson et al.  achieved
similar sensitivity and specificity values, although
our results are slightly better. The study by Nuber
et al.  reached a higher sensitivity (91.8%) and
good specificity (77.8%), but their study was based
on a small sample (40 subjects). The diagnostic
accuracy in terms of ROC analysis varies greatly
among studies carried out by different researchers.
Although these studies were probably developed
under different conditions, the major limitation
when using ODIs is that each study uses their own
definition of desaturation. Moreover, the threshold
used to diagnose OSA based on the AHI derived from
PSG usually varies among studies. Our studies are
guided to remove these uncertainties by using uni-
versally well-defined nonlinear methods. There is
Improving diagnostic ability of blood oxygen saturation using CTM21
not a consensus neither in the definition of the AHI
nor in the threshold subsequently used to determine
the disease . Thus, we assessed the diagnostic
ability of each feature involved in this study when
the AHI threshold used to diagnose OSA changed.
The AROC was computed taking into account the
following OSA thresholds: AHI ? 5, 10, 15 and 20.
Table 5 summarizes the results from this analysis,
showing that CTM achieves the highest area what-
ever the AHI threshold used.
Previous studies by our own group applied non-
linear analysis to oximetric signals from portable
monitoring in screening for OSA syndrome. We
applied ApEn to SaO2signals, obtaining 88.3% sen-
sitivity and 82.9% specificity . Moreover, we also
applied ApEn to heart rate oximetric signals from
78.9% specificity . LZ complexity and CTM were
also applied to SaO2 recordings. Using LZ, we
obtained 86.5% sensitivity and 77.6% specificity,
while with CTM the sensitivity was 90.1% and the
specificity was 82.9% . In the present work, we
have extended our study applying CTM with differ-
ent radii. Furthermore, we compared CTM with
classical oximetric indexes and with ApEn. CTM1
significantly improves statistical and diagnostic test
results of previous studies. Moreover, the computa-
tional time spent by CTM to process a common
oximetric record (approximately 8 h long) is 1000
times smaller than that used by ApEn. Thus, CTM is
more suitable to be incorporated as a software tool
in an oximeter. Furthermore, CTM provides a gra-
phical tool, the second-order difference plots,
which could be very useful in the diagnosis of OSA
syndrome. Physicians could make a preliminary
diagnosis by visual inspection of these scatter plots.
Furthermore, we studied the ability of CTM to
provide a derived AHI. We plotted CTM1 versus the
AHI from PSG and them we computed the linear and
the quadratic regression equations. The AHI derived
from the quadratic regression curve showed no bias
and moderate agreement with the AHI from PSG,
improving the results obtained with classical ODIs
and with other nonlinear indexes. Hence, CTM ana-
lysis of SaO2signals from nocturnal oximetry could
provide useful information in the development of
alternative techniques to conventional PSG.
From our study, we could derive that the recur-
positive group measured by the CTM. However, it is
known that altered respiratory patterns are not
exclusive of OSA syndrome. A total of 42 subjects
suffering COPD were included in our study. We have
shown that COPD patients with OSA presented sig-
with 13 falsepositive cases.Sixsubjects (46%)within
the false positive group suffered from COPD, while
two subjects had a BMI > 34 kg/m2. If COPD patients
87.5%. Regarding to the OSA positive group, our CTM
study reached 90.1% sensitivity, with 11 false nega-
tive cases. Five patients (45%) within the false nega-
tive group had an AHI < 15 e/h. If those patients are
removedfrom thestudy,sensitivity increasesto 94%.
We should take into account some limitations of
our study. Firstly, regarding to the population under
study, the sample size could be larger. Furthermore,
OSA positive patients were predominantly studied.
Thus, additional work is needed to apply our meth-
odology to a new and larger data set with a wide
spectrum of sleep-related breathing disorders, as
well as to study groups of especial interest, such as
healthy subjects, young snorers and patients with
lung and/or cardiac diseases. Another limitation
should be stated in relation to the applicability of
our methodology. Oximetry signals were recorded
simultaneously with PSG, eliminating potential con-
founders such as night to night variability of AHI, as
well as ensuring that oximetry data were collected
in exactly the same environment as the PSG data.
However, further analyses using unattended noctur-
nal oximetry in home are necessary. In addition, the
data collection process could be enhanced. Our
oximeter takes one sample every 5 s. The study
by Wiltshire et al.  showed that low sampling
rates provide SaO2recordings with a low number of
22 D. A ´lvarez et al.
feature varying the AHI used to diagnose OSA syndrome
Area under the ROC curve for each diagnostic
AHI ? 5
AHI ? 10
AHI ? 15
AHI ? 20
AHI: apnea hypopnea index; ODI2: number of dips in
SaO2? 2%; ODI3: number of dips in SaO2? 3%; ODI4: number
of dips in SaO2? 4%; CT90: percentage of time spent with
m = 1 and r = 0.1; ApEn015: approximate entropy computed
with m = 1 and r = 0.15; ApEn02: approximate entropy com-
putedwithm = 1andr = 0.2;CTM1:centraltendencymeasure
computed with r = 1; CTM3: central tendency measure com-
puted with r = 3; CTM6: central tendency measure computed
with r = 6.
tially reduce the sensitivity and increase the speci-
ficity of a diagnostic test . Although the study
carried out by Warley et al.  showed that this
sampling frequency provides reasonable resolution
in SaO2variability, sampling at higher frequencies
we could record SaO2 signals more accurately,
improving subsequent analyses. Moreover, a draw-
back related to the airflow measure in the PSG study
detecting static respiratory events (apneas). How-
ever, it is less effective with dynamic respiratory
events (hypopneas) . The use of nasal cannula
can improve the detection of hypopneas .
Nevertheless, one of the limitations of nasal pres-
sure is false positive detection of apneas/hypopneas
due to nasal obstruction or mouth breathing, lead-
ing to ambiguous results. The American Academy of
Sleep Medicine (AASM) Task Force suggested that
differentiation of apneas from hypopneas was not
necessary in clinical practice because both event
types share a common pathophysiology and clinical
consequences . However, the use of nasal can-
nula could lead to an overestimation of the AHI due
to the false positive events. On the other hand,
thermistor may not be sensitive for detecting
hypopneas, leading to an underestimation of the
AHI . However, thermistor is the most common
method for defining breathing events based on a
flow measurement . In the present study, where
the thermistor is used, the underestimation of the
reference standard index leads to increase the
number of false positive diagnoses when our pro-
posed nonlinear methods are used. Based on an
underestimated threshold, these subjects without
OSA but with an AHI slightly below to this cut-off
higher than the specificity ones. Table 4 shows this
trend, where sensitivity is higher than specificity in
ApEn01, ApEn015, ApEn02, CTM1 and CTM6. Never-
theless, we obtained high accuracy and area under
the ROC curve, as well as high and low LR+ and LR?
values, respectively. Moreover, we could also derive
from Table 5 that CTM provides the highest AROC
regardless of the threshold used to diagnose OSA.
Finally, we would like to point out that the ability of
portable monitors in OSA diagnosis has been gener-
ally assessed by comparing their results with those
of the accepted reference standard: the sleep
laboratory-based PSG . However, both PSG
and portable monitors have considerable night to
night variability, which accounts for some loss of
agreement between single-night observations of
the two tests. It is known that AHI by itself has
limited clinical significance, correlating poorly with
symptoms or with outcome of treatment .
Respiratory events can be totally obstructive
(apneas), partially obstructive (hypopneas) or very
subtle upper airway obstructions which can lead to
respiratory effort-related arousals (RERAs). It is
known that RERAs can produce fatigue and daytime
sleepiness without a significant number of apneas
and hypopneas . Thus, an index including
apneas, hypopneas and RERAs would be a much
more powerful reference index than AHI to diagnose
OSA and it could detect more effectivelythosecases
without major physiological complications.
In summary, we have shown that a nonlinear ana-
lysis by means of the CTM could enhance the diag-
nostic capacity of oximetric signals recorded from
nocturnal pulse oximetry. CTM could be a useful
diagnostic tool that improves classical oximetric
indexes commonly used by physicians. Second-order
difference plots could allow physicians to make a
provides a quantitative measure from those scatter
diagrams, making both interrelated techniques sui-
table to be incorporated in the oximeters.
This work has been partially supported by a grant
project from Consejerı ´a de Educacio ´n de la Junta de
Castilla y Leo ´n under project VA108A06 and SOCAL-
PAR (Sociedad Castellano-Leonesa y Ca ´ntabra de
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