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doi:10.1378/chest.06-1624
(Chest. 2007; 131:750-757)
© 2007 American College of Chest Physicians
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Smoothed Periodogram of Oxyhemoglobin Saturation by Pulse Oximetry in Sleep Apnea Syndrome*

An Automated Analysis

Chung-Ching Hua, MD and Chung-Chieh Yu, MD

* From Chang Gung Memorial Hospital, Keelung, Republic of China.

Correspondence to: Chung-Ching Hua, MD, Chang Gung Memorial Hospital, Keelung, 222 MaiChi Rd, Keelung 204, Taiwan, Republic of China; e-mail: hc2008{at}adm.cgmh.org.tw

Abstract

Background: Variability of oxyhemoglobin saturation (SpO2) during sleep has been utilized as a diagnostic index for sleep apnea. Spectral analysis with its graphical presentation, the periodogram, is an approach for measuring such variability. This work examined the parameters on a smoothed periodogram created from series data for SpO2 obtained by pulse oximetry during a sleep study.

Design and results: SpO2 was recorded during polysomnography study of 273 subjects. Clinical data of subjects were collected retrospectively. A novel automated algorithm was created to measure the low-frequency (< 0.1 Hz) peak and the slope of spectral density vs frequency in the frequency region of 0.1 to 0.5 Hz (slope0.1–0.5). Two successive modified Daniell smoothers with span lengths of 3 to 121 in odd numbers were applied to determine the effect of smoothing on these parameters. slope0.1–0.5 was least affected by smoothing and had a sensitivity of 78% and a specificity of 80% in diagnosing sleep apnea defined by a value of apnea-hypopnea index ≥ 5. Combining slope0.1–0.5 with parameters of the low-frequency peak enlarged the area under the receiver operating characteristic curve. A composite indicator comprised of slope0.1–0.5 and ratio of the area under the curve of the low-frequency peak to that of whole periodogram (AUCratio) had a positive likelihood ratio of 15.25 in identifying patients with moderate-to-severe obstructive sleep apnea. The algorithm was validated in another 206 patients undergoing polysomnographic studies.

Conclusions: These analytical results demonstrate that the smoothed periodogram of SpO2 is a useful tool for screening subjects with sleep apnea.

Key Words: apnea hypopnea index • pulse oximetry • sleep apnea • smoothed periodogram • spectral analysis

Obstructive sleep apnea is associated with reduced-caliber upper airway and acute repetitive events of apneas and hypopneas with resulting oxyhemoglobin desaturation, decrease in intrathoracic pressure, and CNS arousal. Attended, in-laboratory polysomnography is the "gold standard" for diagnosing obstructive sleep apnea.1 However, this method is costly and time-consuming. Nocturnal pulse oximetry has been applied with varying success to screen for and predict sleep apnea using several indexes.2

Irregular episodes of apnea and hypopnea during sleep apnea produce oxyhemoglobin desaturation and result in fluctuations in oxyhemoglobin saturation (SpO2). Desaturation accompanied by hypercapnia stimulates ventilation via the chemoreflex, the sensitivity of which is high in patients with obstructive sleep apnea.3 Rapid increases in ventilation cause resaturation and shorten the duration of apnea and hypopnea. Consequently, the record of SpO2 in obstructive sleep apnea typically has small irregular fluctuations.

As noted by Suki,4 irregular fluctuations represent information that can be evaluated using particular probability density distributions. Spectral analysis is one of the several methods of conducting variability analysis.5 Few studies have utilized spectral analysis and its graphical presentation, the periodogram, to examine the variability of SpO2 in a sleep study. A spectrum peak between period boundaries of 30 to 70 s has been proposed as a diagnostic marker for sleep apnea by Zamarron et al67; however, these studies have used three observers to evaluate the periodogram by visual inspection and have not addressed the possible contribution of the regions outside the period boundary.

A raw or smoothed periodogram is graphical presentations of the spectral analysis, a method to describe the variability of series data.5 This study presents a novel algorithm for locating the low-frequency (< 0.1 Hz) peaks in a periodogram and determining automatically the slope in a high-frequency (0.1 to 0.5 Hz) region. Various degrees of smoothing were utilized to determine the effect of smoothing on periodogram parameters and their diagnostic capabilities. The effects of combined parameters on diagnostic effectiveness were also investigated.

Materials and Methods

Subjects
A learning set of 273 consecutive patients and a validation set of another 206 consecutive patients suspected of having sleep apnea syndrome clinically were referred to Chang Gung Memorial Hospital for polysomnographic evaluation. Epworth sleepiness scale score was recorded before the polysomnography. Clinical data were collected retrospectively. The study was approved by the Institutional Review Board at Chang Gung Memorial Hospital.

Polysomnographic Study
Overnight polysomnography (Embla N7000; Medcare; Reykjavik, Iceland) was performed between 10 PM and 6 AM. Polysomnography comprised continuous polygraphic recording from surface leads for EEG, electrooculography, electromyography, ECG, cannula/pressure sensor for nasal airflow, thoracic and abdominal impedance belts for respiratory effort, pulse oximetry for oxyhemoglobin level, and sensors to detect the body position during sleep. Polysomnographic records were staged manually using the criteria developed by Rechtschaffen et al.8 Respiratory events were scored according to American Academy of Sleep Medicine criteria: apnea was defined as complete cessation of airflow lasting ≥ 10 s, and hypopnea was defined as either a ≥ 50% reduction in airflow for ≥ 10 s or a < 50% and discernible reduction in airflow accompanied either by a decrease in SpO2 of > 3% or arousal. Severity of obstructive sleep apnea-hypopnea syndrome (OSAHS) was measured based on the following frequencies of apnea-hypopnea episodes: mild, 5 to 15/h; moderate, 15 to 30/h; and severe, > 30/h.9

Beat-to-beat values without averaging or slewing of SpO2 during polysomnography were obtained via a finger pulse oximeter (Xpod 3012; Nonin Medical; Plymouth, MN) with a sampling frequency of 3 Hz. Averaging was done off-line. Nonartifactual data in three samplings per second were averaged, and the integer nearest to the mean or zero, in case all three samplings were artifacts, was used as the representative. In the data series averaged per second, the data of zero were replaced by the integer nearest to the mean of nonzero data.

Smoothed Periodogram
Development of the proposed algorithm (Fig 1 ) was completed using the R statistical package (R Foundation for Statistical Computing; Vienna, Austria).10 SpO2 recordings for subjects were first transformed into a format for time series data. For each subject, fast Fourier transformation with two successive modified Daniell smoothers was performed on time series data by a "spectrum" function to acquire the estimated spectral densities and corresponding frequencies, which were then utilized to plot smoothed periodograms (Fig 2 ). Two successive modified Daniell smoothers with same span length of 3 to 121 in odd numbers were employed to have at least one peak in the low-frequency region (0 to 0.1 Hz) of the periodogram. An automated algorithm was then utilized to define the low-frequency peak. First, a turning point was defined as the point at which a downward curve turned upward. All the turning points with frequencies < 0.1 Hz were identified. When a curve was initially upward, the leftmost point was adopted as the first turning point. For each turning point, the frequency period was gated between frequency of the turning point and that of the rightmost point whose spectral density was larger than or equal to that of the turning point, or 0.1 Hz when the frequency of the rightmost point was > 0.1 Hz. The point with maximal spectral density for each gated frequency period was documented, and the difference in spectral density with corresponding turning points was derived. The frequency period with the largest spectral density difference was adopted as the period in which the peak occurred. For the peak, the point with largest spectral density was considered as the "top" point and the turning point was adopted as the "base" point. The frequency at the top point, the frequency at the base point, and the difference in frequency at the top vs the base were calculated, as were the spectral frequency at the top point, the spectral density at the base point, and the difference between the top and base density. Spectral density-related parameters were corrected according to the range of all estimated spectral densities. The ratio of the area under the curve (AUC) of the peak to that of the whole periodogram (AUCratio) was calculated, as was the slope of spectral density vs frequency obtained by a linear regression in the frequency region > 0.1 Hz (slope0.1–0.5).


Figure 1
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  		Figure 1.. Flow chart to determine parameters on a smoothed periodogram. freq-top = frequency at the top point; freq-base = frequency at the base point; freq-top – base = difference between frequency at the top and frequency at the base; spec-top = spectral density at the top point; spec-base = spectral density at the base point; spec-top – base = difference between spectral density at the top and spectral density at the base.

 

Figure 2
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  		Figure 2.. Smoothed periodogram with a smoother span of 121 in a patient with severe obstructive sleep apnea. The shaded angle is the largest low-frequency (< 0.1 Hz) peak. The top ({downarrow}) and base (->) of the peak are marked. The base is also one of the three turning points ({uparrow}) that are detected at the point where direction of the downward curve turns in the low-frequency region.

 
Receiver Operating Characteristic Curve Analysis
Based on staging severity, the cutoff value for the apnea-hypopnea index (AHI) was set at 5, 15, or 30. Parameter performance derived from the smoothed periodogram was assessed by the AUC of the receiver operating characteristic (ROC) curve for each cutoff value. The effects of the smoother spans on the parameters and their performances were determined via linear regression. The span of smoother of 121 was utilized to compare parameters among different groups with different severity and their performances at different cutoff values. At each cutoff value, the parameter in the low-frequency (< 0.1 Hz) region with the largest AUC for the ROC curve was combined with slope0.1–0.5 to generate a composite indicator. Performance of the composite indicator at different cutoff values was also analyzed.

Data Analysis
Linear regression analysis was used to find the effect of smoothing on the AUC. The Kruskal-Wallis and Mann-Whitney U tests or the one-way analysis of variance with Bonferroni multiple comparison test were applied to compare variables between groups with different severity of AHI. Logistic regression analysis was employed to determine the weight of each component of a composite indicator for each cutoff value. Student t test was used to compare variables between the misclassified subset and the whole in the learning set. {chi}2 analysis or Fisher exact test were used to compare discrete variables in the learning set. A value of p < 0.05 was considered statistically significant. For the ROC curve, the point with largest sum of sensitivity and specificity was chosen as a threshold in the learning set.

Results

Table 1 shows the demographic characteristics of subjects in both the learning and validation sets. All patients received a diagnosis of OSAHS by polysomnography. Referring departments and clinical indications for polysomnography were listed on Table 1s (see Supplementary Data).


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  		Table 1.. Demographic Characteristics of the Learning and Validation Sets*

 
Table 2 shows the effects of smoothing on the parameters of smoothed periodograms. slope0.1–0.5 had smallest change, and spectral density at the top point was the parameter least subjected to the effect of smoothing in the low-frequency region. As the degree of smoothing increased, the low-frequency peak became shifted right and upward, widened at the base, and decreased in amplitude with a small AUCratio.


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  		Table 2.. Effects of Smoothing on Mean of Parameters in the Learning Set*

 
Table 3 presents the effects of smoothing on the AUC for the ROC curves at different cutoff values. slope0.1–0.5 was least affected by smoothing for all three cutoff values and for the low-frequency parameters; AUCratio and the difference between frequency at the top and frequency at the base were least affected by smoothing.


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  		Table 3.. Effects of Smoothing on the AUC of the ROC Curves in the Learning Set*

 
Two successive modified Daniell smoothers were applied, each with a span of 121. Table 4 shows the parameters of the smoothed periodogram in groups with different severity of AHI. Table 5 shows the AUC for the ROC curves using different parameters at three cutoff values. As the severity of sleep apnea increased, the peak in low-frequency region shifted left and upward, widened at the base, and increased in amplitude with a large AUCratio. The negative value of slope0.1–0.5 increased as severity increased. For the AUC of the ROC curves, slope0.1–0.5 had the largest value, excluding the AHI cutoff value of 15; among the low-frequency parameters, AUCratio had the largest AUC value, with the exception of the AHI cutoff value of 30. Composite indicators, which combined slope0.1–0.5 and best performer in low-frequency region, yielded AUC values ≥ 0.9 that were better than that of any single parameter at all three cutoff values.


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  		Table 4.. Parameters in the Group with Different Severity by AHI in the Learning Set*

 

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  		Table 5.. AUC of the ROC Curve by Smoothed Periodogram Parameters in the Learning Set*

 
Table 2s (see Supplementary Data) shows the parameters of the raw periodogram and the raw SpO2 data with different severity of AHI. Figure 1s (see Supplementary Data) shows good agreements between AHI and slope0.1–0.5 or the composite indicator for AHI cutoff of 15 via a modified Bland-Altman plot.

Table 6 shows the sensitivities, specificities, predictive values, and likelihood ratios for slope0.1–0.5 and the composite indicators. Table 7 shows the AUCs of the ROC curves of slope0.1–0.5 and the composite indicators in the validation set. The AUCs of the ROC curves of the validation set were very similar to those of the learning set. Table 3s (see Supplementary Data) shows the characteristics of the misclassified subjects in the learning set. Ratios of misclassification in subjects with separate comorbidity were not different from those of the whole.


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  		Table 6.. Usefulness of Smoothed Periodogram Parameters in the Diagnosis of OSAHS in the Learning Set

 

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  		Table 7.. AUC of ROC by Smoothed Periodogram Parameters in the Validation Set (n = 206)

 
Discussion

Spectral analysis of SpO2 during sleep has been identified as an effective approach for diagnosing sleep apnea.7 This study presented a novel algorithm that automates parameter analyses in a smoothed periodogram, which plots the estimated spectral density against frequency. Two successive modified Daniell smoothers with odd numbered span lengths of 3 to 121 were utilized to evaluate the effects of smoothing on parameters. The degree of smoothing changed the parameters or their performances in diagnosing sleep apnea by using the AUC for the ROC curve. Although the effects of smoothing varied, slope0.1–0.5 was the one least affected in both its value and diagnosing performance. With a span length of 121, all the parameters identified differences among subjects grouped by AHI. For diagnostic performance at different cutoff values, slope0.1–0.5 achieved the largest AUC with the exception of cutoff value of 15. The diagnostic performance improved further by combining slope0.1–0.5 with other parameters. The algorithm was showed to have similar performances in the validation set.

Full polysomnography is the "gold standard" for the diagnosis of OSAHS.1 However, full polysomnography is time consuming and expensive. Additional approaches for diagnosing sleep apnea have been developed, such as indirect measurement of peripheral vasoconstriction and transient tachycardia using a finger plethysmograph, analysis of very-low-frequency components in heart rate variability, and the measurement of the change in pulse.11 Transcutaneous nocturnal pulse oximetry is increasingly being utilized for initial screening for OSAHS, as it is inexpensive and is simply applied and interpreted.12 The sensitivity of nocturnal pulse oximetry in diagnosing of OSAHS is 31 to 98%, with a specificity of 41 to 100%.11 The parameters reported vary widely and include the total number of desaturation events, oxyhemoglobin desaturation index, desaturation events per hour, and highest, lowest, and mean SpO2.11 In studies measuring episodic desaturation during sleep, diagnostic performances vary according to parameters and criteria used by authors.1314151617

Since the oxygen saturation data recorded in sleep is a time series with considerable fluctuation, diagnostic values of parameters for variability have been examined. For a {Delta} index threshold at 0.6, the sensitivity of oximetry for diagnosing OSAHS was 98% and the specificity was 46%.18 With a {Delta} index threshold at 0.4, the sensitivity of oximetry for diagnosing OSAHS was 88% and the specificity was 70%.19 {Delta} index was a superior predictor to oxyhemoglobin desaturation index; however, the difference between the two was small.2 Zamarron et al7 used spectral analysis to assess power density of SpO2 using the fast Fourier transformation of the oximetric signal. The peak amplitude and the ratio of the area enclosed in the 30 to 70 s peak to the total area of the spectrum have been proved effective in diagnosing OSAHS; presence of a peak has a sensitivity of 78% and a specificity of 89%. Using a threshold of 0.15 for the ratio of the area enclosed in the 30 to 70 s peak to the total area of the spectrum, the sensitivity was 91% and the specificity was 67%. By evaluating SaO2 and heart rate variability simultaneously, the presence of a peak in the periodogram in either signal has a sensitivity of 94% and a specificity of 82%.6 Variability indexes are reported to be good indicators for diagnosing OSAHS in these studies.

Measured physiologic data invariably fluctuate, often carry information about the underlying processes.4 The respiratory system during sleep, like other biological systems, is complex. The properties of the complex system are distinct from the properties of the parts, and they depend on the integrity of the whole.5 Focusing on the events, such as desaturation during sleep, may not reflect the status of complex system. The spatial and temporal organization of complex system can be analyzed by its connectivity and variability.20 Analyzing the variability of physiologic signals may facilitate an improved ability to differentiate between clinically distinct groups of patients.5 Spectral analysis, which examines the relation of spectral density with corresponding frequency following Fourier transformation of physiologic signals, is an approach to assess variability and has been successfully applied to analyze heart rate variability under numerous clinical conditions.2122232425262728

The studies of Zamarron et al67 demonstrate the utility of using spectral analysis when diagnosing OSAHS by pulse oximetry. However, questions regarding the effect of smoothing on the periodogram and the contribution of regions outside the period boundary of 30 to 70 s remained to be answered. In spectral analysis, smoothing is necessary to reduce leakage that is caused by side lobes in the spectral window and to obtain the optimal estimator of spectral density.2930 However, incremental increases in smoother span elevate bandwidth and consequently decrease resolution. To quantify the parameters and determine the effect of smoothing, this work utilized a novel algorithm by using a free statistical package, R, to automate the analyses. Two successive Daniell smoothers were used to obtain stable estimates of spectral densities and to avoid the appearance of rectangles on the periodogram that cause difficulty in analyzing the low-frequency peak.30 Smoothing significantly affected the values and diagnostic powers of parameters in the low-frequency region. As the degree of smoothing increased, the low-frequency peak shifted rightward and upward, and decreased in size. A small peak certainly affects the judgment of visual inspection that was used by Zamarron et al.67 The diagnostic power, presented as the AUC for the ROC curve, was also affected by smoothing. In the low-frequency peak, AUCratio has diagnostic power that only minimally affected by smoothing with the AUC of the ROC curves ≥ 0.8 for all three AHI cut-off values. A similar parameter, the ratio of the area enclosed in the 30 to 70 s peak to the total area of the spectrum, which was used in the study by Zamarron et al,7 also had good diagnostic power.

Among all the parameters, slope0.1–0.5 and its diagnostic power were the least affected by smoothing with the AUC for ROC curve all ≥ 0.84. Calculation of slope0.1–0.5 was also easier than that for other parameters. These analytical findings suggest slope0.1–0.5 alone is a better indicator than any other parameter in frequency region ≤ 0.1 Hz. Combining slope0.1–0.5 with other parameters further increased the diagnostic power, as evidenced by the increased positive likelihood ratio. Notably, combining slope0.1–0.5 and AUCratio at an AHI cutoff value 15 had positive likelihood ratio of 15.25. This composite indicator can help to identify the patients with moderate-to-severe OSAHS who need full polysomnography most. However, this indicator is also subjected to the effect of smoothing due to the presence of AUCratio.

Aided by automated analyses, this study demonstrated that smoothing significantly affects the low-frequency peak in spectral analysis of oximetric data during sleep. As it has a stable diagnostic power and minimally affected by smoothing, slope0.1–0.5 is a superior parameter for diagnosing OSAHS. By combining slope0.1–0.5 with other parameters for low-frequency peak, diagnostic ability was further enhanced.

Footnotes

Abbreviations: AHI = apnea-hypopnea index; AUC = area under the curve; AUCratio = ratio of the AUC of the low-requency peak to that of the whole periodogram; OSAHS = obstructive sleep apnea-hypopnea syndrome; ROC = receiver operating characteristic; slope0.1–0.5 = slope of spectral density vs frequency in the frequency region of 0.1 to 0.5 Hz; SpO2 = oxyhemoglobin saturation

This study was supported by a grant from Chang Gung Memorial Hospital (CMRPG240151).

The authors have no conflicts of interest to disclose.

Received for publication June 30, 2006. Accepted for publication October 20, 2006.

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