Page 1

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

http://www.intl.elsevierhealth.com/journals/aiim

KEYWORDS

Central tendency

measure;

Nonlinear methods;

Blood oxygen

saturation;

Oximetry;

Obstructive sleep

apnea

Summary

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

onewascomposedbyclassicalindexesprovidedbyouroximeter:oxygendesaturation

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: dalvgon@gmail.com (D. A ´lvarez).

0933-3657/$ — see front matter # 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.artmed.2007.06.002

Page 2

1. Introduction

The obstructive sleep apnea (OSA) syndrome is char-

acterized by repetitive reduction or cessation of

airflowduetopartialorcompleteairwayobstruction

[1]. This disease is usually associated with hypoxe-

mia,bradycardia,arousalsandfragmentedsleep[2].

Nowadays,OSAisthemostcommonrespiratoryrefer-

ral in many sleep centers [3]. The estimated OSA

prevalence varies from 1 to 5% of adult men in

western countries [4]. 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 [4]. 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 [5]. Individuals

with OSA are dangerous drivers with an increased

risk of being involved in road and work accidents [3].

The standard diagnostic test for OSA syndrome is

overnight polysomnography (PSG) [6], 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 [7]. 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

SaO2records [8].

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-

tion.Moreover,thereisnotaconsensusonathreshold

todiagnoseOSA basedonODIs[14,15].Furthermore,

correlation between oximetry indexes and AHI is not

high [13]. In previous studies [16—18], our group has

shown that nonlinear analysis could provide useful

information in the diagnosis of OSA syndrome. A

regularitymeasurefromSaO2signalsobtainedapply-

ing approximate entropy (ApEn) improved the diag-

nostic accuracy of classical oximetric indexes [16].

ApEn was also applied to heart rate signals from

nocturnal oximetry, obtaining promising results

[17]. Moreover, additional nonlinear methods, cen-

tral tendency measure (CTM) and Lempel—Ziv (LZ)

complexity, were applied to SaO2records [18]. 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 [19]. 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

signalsrecordedfromportablemonitoring.CTMcouldbeausefultoolforphysiciansin

the diagnosis of OSA syndrome.

# 2007 Elsevier B.V. All rights reserved.

Page 3

[19]. Some authors have applied nonlinear methods

over different respiratory patterns to study sleep

stagesandthecoordinationbetweenbrainandlungs

[20] or panic disorder [21].

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

analysis.

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

study.

deviation(S.D.)ageof

2.1. Conventional polysomnography

All patients underwent overnight PSG (Ultrasom

Network, Nicolet, Madison, WI, USA) which included

electroencephalogram(EEG),

(ECG), electrooculogram (EOG), chin electromyo-

gram (EMG), measurement of chest wall movement

electrocardiogram

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 [22].

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 [27], 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 [28]. 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%)

presentedrespiratoryfailure.Accordingtotheglobal

initiativeforchronicobstructivelungdisease(GOLD)

consensus [28], 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

patients.

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

Table 1

Demographic and clinical features of the subjects under study

FeaturesAll subjectsOSA positiveOSA negative

Subjects (n)

Age (years)

Males (%)

BMI (kg/m2)

Recording time (h)

AHI (e/h)

COPD (n)

187

57.97 ? 12.84

78.61

29.54 ? 5.51

8.19 ? 0.62

111

58.30 ? 12.88

84.68

30.45 ? 4.92

8.17 ? 0.75

40.07 ? 19.64

22

76

57.57 ? 12.87

69.74

28.42 ? 6.02

8.22 ? 0.33

2.04 ? 2.36

20 42

Data are presented as mean ? S.D. unless otherwise indicated. OSA positive: patients with obstructive sleep apnea. OSA negative:

patients without obstructive sleep apnea.

Page 4

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

6.02 kg/m2).

(28.42 ?

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. [29] 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 [29].

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

recordings.Fig.1(a)depictsacommonOSAnegative

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

not evident.

3. Methods

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 [31].

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 [32]. ApEn evaluates

bothdominantandsubordinantpatternsinthedata,

and discriminates series for which clear feature

recognition is difficult [32]. 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

forbothstochasticanddeterministicprocesses[32].

ApEn assigns a non-negative number to a time

series, with larger values corresponding to greater

randomness or irregularity in the data [32]. The

algorithm applied to compute ApEn can be seen in

detail in [16] and [17]. Briefly, ApEn measures the

logarithmiclikelihoodthatrunsofpatternsthatare

close (within r) for m contiguous observations

remain close (within the same tolerance r) on sub-

sequent incremental comparisons (pattern length

m + 1) [32]. 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 [33]. To

ensureappropriatecomparisonsbetweendatasets,

allinputparametersm,randNmustbethesamefor

each data set [33,34]. No guidelines exist for opti-

mizing the m and r values. However, Pincus sug-

gestedparametervaluesofm = 1orm = 2andwithr

afixedvaluebetween0.1and0.25timestheS.D.of

the original time series [32]. Multiple previous stu-

dies have demonstrated that these input para-

meters produce good statistical reproducibility

for ApEn for time series of length N ? 60 [32]. In

16D. A ´lvarez et al.

Figure 1

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

Page 5

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

theoriginaltimeseries,obtainingApEn01,ApEn015

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 [19].

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-

namicsand heart rate

approach, rather than defining a time series as

chaotic or not chaotic, the degree of variability or

chaosisevaluated[19].Suchscatterplotscouldbea

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-

gramfora common

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

(1)

variability.Withthis

OSA negativesubject,

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 [35]

PN?2

where

if½ðxði þ 2Þ ? xði þ 1ÞÞ2

þðxði þ 1Þ ? xðiÞÞ2?

0otherwise

CTM ¼

i¼1dðdiÞ

N ? 2

8

>

The radius r is selected depending on the char-

acterofthedata.Inthepresentstudy,wecomputed

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.

(2)

dðdiÞ ¼

1

1=2<r

>

:

<

(3)

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

meansoftheLevene’stest.Thenormaldistribution

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

OSAnegativegroups.TheBonferronicorrectionwas

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

Figure 2

OSA negative subject (b) an apparent OSA positive patient

and (c) an uncertain OSA positive subject.

Second-order difference plots (a) a common

Page 6

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

polynomials,which defined

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

from PSG.

the relationship

4. Results

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.

Table 2

study

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

ODI2

ODI3

ODI4

CT90

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

ApEn01

ApEn015

ApEn02

CTM1

CTM3

CTM6

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.

Table3

metric indexes and AHI from PSG

Pearsoncorrelationcoefficientsbetweenoxi-

Classical oximetric indexes

ODI2ODI3ODI4CT90

r

p

0.608

<0.0001

0.617

<0.0001

0.603

<0.0001

0.280

<0.001

Regularity indexes from ApEn analysis

ApEn01ApEn015ApEn02

r

p

0.577

<0.0001

0.579

<0.0001

0.606

<0.0001

Variability indexes from CTM analysis

CTM1CTM3CTM6

r

p

?0.738

<0.0001

?0.684

<0.0001

?0.561

<0.0001

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.

Figure 3

index group in terms of diagnostic accuracy and correla-

tion with AHI.

ROC curves for the best parameter of each

Page 7

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

value,85.1%negativepredictivevalue,87.2%accu-

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

indexgroup,ApEn02from theApEnindexgroupand

CTM1 from the CTM index group. The ROC curves

illustrate the variation of sensitivity and specificity

andhence,thediagnosis,whendifferentthresholds

Improving diagnostic ability of blood oxygen saturation using CTM 19

Table 4

Test results for the optimum decision threshold from the ROC curve analysis

ThSE PPVNPV LR+LR?

0.39

0.39

0.44

0.36

0.13

0.13

0.14

0.12

0.19

0.17

A AROC

ODI2

ODI3

ODI4

CT90

ApEn01

ApEn015

ApEn02

CTM1

CTM3

CTM6

10

10.3

13

1

0.679

0.679

0.679

0.583

0.966

0.997

66.7

65.1

58.7

73.0

89.2

89.2

88.3

90.1

83.8

85.6

84.9

88.7

94.3

75.5

81.6

81.6

82.9

82.9

85.5

82.9

84.0

87.2

92.5

78.0

87.6

87.6

88.3

88.5

89.4

88.0

68.2

68.1

65.8

70.2

83.8

83.8

82.9

85.1

78.3

79.7

4.42

5.75

10.38

2.98

4.84

4.84

5.16

5.27

5.79

5.00

75.0

75.9

75.0

74.1

86.1

86.1

86.1

87.2

84.5

84.5

0.743

0.761

0.785

0.774

0.923

0.923

0.921

0.924

0.923

0.903

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.

Figure4

(dashed line) and quadratic regression (solid line) curves

that best fit the data in a least square sense.

ScatterplotforODI3andAHI.Linearregression

Figure 5

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-

Page 8

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

cut-offpointsareusedtodeterminethepresenceof

OSA.

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,

arealsodepicted.Weusedtheregressionequations

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.

Figure 6

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-

Figure 7

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-

Figure 8

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-

Figure 9

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-

Page 9

derivedfromApEn02.Furthermore,limitsofagree-

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

significantlylowerCTM

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-

jects.

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

other indexes.

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 [7]. 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 [7]. In the present research, we used a

singlethreshold.Allsubjectsinthedatasetcouldbe

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. [40] achieved

similar sensitivity and specificity values, although

our results are slightly better. The study by Nuber

et al. [11] 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 CTM 21

Page 10

not a consensus neither in the definition of the AHI

nor in the threshold subsequently used to determine

the disease [14]. 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 [16]. Moreover, we also

applied ApEn to heart rate oximetric signals from

thesamepopulation,obtaining71.2%sensitivityand

78.9% specificity [17]. 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% [18]. 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-

renceoftheapneaeventstypicalofOSAwererespon-

sibleforthehighvariabilityofSaO2signalsintheOSA

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-

nificantlyhigherCTMvaluesthanCOPDpatientswith-

outOSA.TheCTManalysisprovided82.9%specificity,

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

wereremovedfromthestudy,specificityincreasesto

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. [41] showed that low sampling

rates provide SaO2recordings with a low number of

artifacts.However,lowsamplingfrequenciespoten-

22 D. A ´lvarez et al.

Table 5

feature varying the AHI used to diagnose OSA syndrome

Area under the ROC curve for each diagnostic

AHI ? 5

0.706

0.723

0.740

0.729

0.898

0.896

0.894

0.905

0.898

0.879

AHI ? 10

0.743

0.761

0.785

0.774

0.923

0.923

0.921

0.924

0.923

0.903

AHI ? 15

0.711

0.720

0.737

0.730

0.885

0.885

0.883

0.915

0.914

0.905

AHI ? 20

0.742

0.745

0.756

0.743

0.855

0.885

0.853

0.889

0.891

0.883

ODI2

ODI3

ODI4

CT90

ApEn01

ApEn015

ApEn02

CTM1

CTM3

CTM6

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

SaO2below90%.ApEn01:approximateentropycomputedwith

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.

Page 11

tially reduce the sensitivity and increase the speci-

ficity of a diagnostic test [7]. Although the study

carried out by Warley et al. [29] 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

shouldbementioned.Thermistorishighlyreliablein

detecting static respiratory events (apneas). How-

ever, it is less effective with dynamic respiratory

events (hypopneas) [42]. The use of nasal cannula

can improve the detection of hypopneas [43].

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 [27]. 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 [44]. However, thermistor is the most common

method for defining breathing events based on a

flow measurement [7]. 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

pointwilltestpositive,resultinginsensitivityvalues

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 [45]. 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 [46].

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 [47]. 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

preliminarydiagnosisbyvisualinspection,whileCTM

provides a quantitative measure from those scatter

diagrams, making both interrelated techniques sui-

table to be incorporated in the oximeters.

Acknowledgements

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

Patologı ´a Respiratoria).

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