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An Automatic Screening Approach for Obstructive Sleep Apnea Diagnosis Based on Single-Lead Electrocardiogram Lili Chen, Xi Zhang, and Changyue Song

Abstract—Traditional approaches for obstructive sleep apnea (OSA) diagnosis are apt to using multiple channels of physiological signals to detect apnea events by dividing the signals into equal-length segments, which may lead to incorrect apnea event detection and weaken the performance of OSA diagnosis. This paper proposes an automatic-segmentation-based screening approach with the single channel of Electrocardiogram (ECG) signal for OSA subject diagnosis, and the main work of the proposed approach lies in three aspects: (i) an automatic signal segmentation algorithm is adopted for signal segmentation instead of the equal-length segmentation rule; (ii) a local median filter is improved for reduction of the unexpected RR intervals before signal segmentation; (iii) the designed OSA severity index and additional admission information of OSA suspects are plugged into support vector machine (SVM) for OSA subject diagnosis. A real clinical example from PhysioNet database is provided to validate the proposed approach and an average accuracy of 97.41% for subject diagnosis is obtained which demonstrates the effectiveness for OSA diagnosis. Note to Practitioners—Automatic diagnosis of obstructive sleep apnea based on physiological signals is critical for healthcare service improvement. Equal-length segmentation of signals is adopted in current OSA diagnosis, in which each segment of signal requires inferences from physicians to determine the apnea events. However, this equal-length segmentation may bring possible misdetected apnea events, and finally lead to an incorrect diagnosis. This paper aims to reduce the number of misdetected apnea events by proposing an automatic segmentation rule with consideration of reasonable physiological interpretation. An OSA severity index which can be obtained from signal segments of each subject is designed. An SVM is employed to implement the final diagnosis. To fully implement this approach, it is necessary (i) to preprocess the RR intervals and eliminate unexpected signal points; (ii) to embed individual information of OSA suspects into an SVM. A real world case study has shown that the proposed diagnosis approach provided a satisfactory diagnosis accuracy.

Index Terms—Obstructive sleep apnea, RR interval, signal segmentation, support vector machine.

Manuscript received May 09, 2014; revised July 02, 2014; accepted July 16, 2014. This paper was recommended for publication by Associate Editor J. Li and Editor L. Shi upon evaluation of the reviewers’ comments. This work was supported by Peking University under Research Seed Grant BME-201215. The authors are with the Department of Industrial Engineering and Management, College of Engineering, Peking University, Beijing 100871, China (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASE.2014.2345667

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I. INTRODUCTION

BSTRUCTIVE SLEEP APNEA SYNDROME (OSAS) is a repeated, temporary cessation or reduction of breathing during sleep caused by physically complete or partial intermittent airway obstruction in breath. Generally, the occurrence of an apnea event involves a cessation of airflow for at least 10s while a hypopnea is defined as an airflow reduction for at least 10s with a blood oxygen desaturation of 4% or a neurological arousal [1]. The risk factors for developing OSAS are complicated and various which may include anatomical defects, obesity, alcohol abuse, smoking, etc. It has been reported that OSAS affects around 4% of men and 2% of women of the general middle age population in USA, which greatly influences people’s health and quality of life [2]. In clinical applications, the apnea-hypopnea index (AHI) is pervasively used to evaluate the severity of OSA subjects. A suspect with a value of AHI exceeding 5, is generally diagnosed as an OSA subject. The calculation of AHI involves the acquisition of around 16 major physiological signals including Electrocardiogram (ECG), Electroencephalogram (EEG), respiratory effort, airflow signal and oxygen saturation . The acquired signals are analyzed to obtain AHI by measuring the average number of apnea and hypopnea events per hour during sleep [3]. This procedure is known as Polysomnography (PSG) study [4]. Currently, PSG has been recognized as the most popular and effective tool for OSA diagnosis. However, the implementation of PSG requires OSA suspects to sleep in a sleep center over one or two nights with special equipment and careful nursing, which results in a time-consuming, and expensive process. Moreover, acquisition of all the physiological signals requires OSA subjects to be connected with many wires and electrodes, which makes subjects very uncomfortable. Thus, the inconvenience, expensiveness and discomfort of PSG set a barrier to its extensive acceptance in public. To overcome this problem, growing attention has been focused on the development of convenient OSA detection techniques. These techniques are established based on the analysis of a decreased number of physiological signals that could be easily acquired rather than all channels of signals collected by the PSG. Among these studies, methods based on signals such as ECG [5]–[9], [10]–[13], snoring signal [14], [15], respiratory sound signal [16], thoracic effort signal [17], EEG [18] and combined signals [1], [19] have been proposed for OSA detection. Through these physiological signals, various features such as time domain features and frequency domain features are

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extracted to characterize the clinical conditions of suspects, and meanwhile a large number of classification methods have been employed to improve the detection performance based on those extracted features. Accomplishments using the advanced classification methods include linear/quadratic discriminant classifiers [15], support vector machine [5], [19]–[21] and neural networks [22], [23]. In contrast to PSG, the main purpose of these approaches is to utilize the extracted features to establish a principle for automatic condition monitoring and severity evaluation, i.e. developing an alternative procedure which is able to detect the apnea events based on specific physiological signals and corresponding extracted features. However, one critical issue in current research should be addressed. Most of the aforementioned methods follow a similar strategy in signal preprocessing which implement equal-length segmentation on collected physiological signals before further diagnosis [5]–[21]. The physiological signals are divided into equal-length segments in which OSA diagnosis could be implemented based on those segments. This strategy may lead to incorrect detection and may even weaken the performance of OSA diagnosis. For instance, different equal-length segmentation strategies were tried in the research [24], [25] and the results were quite discrepant. Since the apnea events can happen in any duration, equal-length segmentation strategy distorts the apnea event effect. The detailed reason could be elaborated by an example in Fig. 1. In the upper panel, the actual durations of apnea events are shown by the rectangles colored in blue. It can be observed that there are five segments labeled as apnea events during time between 2880 and 3840 seconds in terms of actual apnea event lists from the PSG of an OSA suspect. Compared to the upper panel, only four apnea events are detected by the equal-length segmentation rule of 30 seconds in the lower panel. One apnea event between 3081 to 3094 (the rectangle in red) is misdetected because this period is split into two parts (one part with length of 9 seconds and the other with 4 seconds) by the equal-length segmentation rule. These two successive segments are not recognized as the apnea events since the durations of both apnea events do not reach the threshold of 10 seconds, which has been widely accepted as the criterion of the occurrence of an apnea event clinically. Thus, a segment with actual apnea event is misrepresented as a normal event due to limitation of the equal-length segmentation rule. Consequently, the classifiers based on features extracted from the signals of those segments could not correctly characterize the conditions of OSA suspects, and this possibly leads to an incorrect OSA diagnosis. It also should be addressed that this problem does not only occur in a 30-second equal-length segmentation but may also exist in various types of equal-length segmentation rules, e.g. a minute-by-minute segmentation. Thus, an appropriate segmentation method is necessary for the OSA diagnosis to reduce the number of undetected apnea events. At the same time, a physiological signal should be appropriately selected. In other words, segmentation should be established on a representative signal with clinical explanation of apnea events for OSA diagnosis. Among all the PSG signals, ECG signal has been considered as one of the most extensively studied physiological signals. The RR intervals (R wave

Fig. 1. Example of missed detected apnea events.

Fig. 2. Example of RR intervals on ECG signal.

to R wave intervals, see Fig. 2), inverse of heart rate derived from ECG signals, are highly related to physiological manifestation of apnea events which has been demonstrated in the literature [26], [27]. The apnea/hypopnea elicits changes in both parasympathetic and sympathetic cardiac activities which cause the fluctuation of RR intervals. Hence, the concealed information in ECG signals can be employed to detect the apnea/hypopnea events. In addition, with the fast development of advanced sensor technologies, the acquisition of ECG signals is quite convenient and reliable by remote biosensors and the derived RR intervals can be easily extracted from ECG signals by appropriate algorithms. In previous research on OSA detection based on RR interval analysis, a large amount of attention has been received on extraction and selection of various features from segmented RR intervals to obtain a higher screening rate for apnea event detection. These features include time domain features [8], frequency domain features [7], and nonlinear measures [6]. Among all these features, ratio of low frequency (LF, 0.04–0.15 Hz) to high frequency (HF, 0.15–0.4 Hz) has been the most frequently used and explainable feature for apnea event detection. LF component reflects the interaction of sympathetic and parasympathetic tones and HF component has been clinically shown to be related to parasympathetic control of RR intervals [27]. Hence, the degree of control from sympathetic and parasympathetic tones could be well indicated by the combining effect of LF and HF. Literature has indicated that the ratio of low frequency to high frequency (LF/HF) is an appropriate indicator to the activity

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of sympathetic system and provides valuable information and significant power in discriminating apnea and non-apnea events since activity of sympathetic tone predominates the activity of parasympathetic tone during apnea [27]. Thus, LF/HF is applied in this paper to characterize the activity of apnea event. To fill the research gap mentioned above, this paper proposes a systematic OSA subject diagnosis approach based on an automatic signal segmentation algorithm for apnea event detection to reduce the possibility of misdetected apnea events. The contributions lie in three aspects: First, the proposed approach applies an iterated cumulative sums of squares (ICSS) algorithm to detect apnea state of RR intervals instead of equal-length segmentation. Since RR intervals present an increased cyclic variation during apnea and the variation changes are not obvious according to our preliminary studies, the ICSS algorithm applied in this paper is capable of automatically conducting segmentation of RR intervals based on variation changes, and most of the misdetected cases are expected to be eliminated. Moreover, this algorithm is convenient to operate and easy to be understood. Second, a local median filter is designed for RR interval preprocessing. The segmentation performance of ICSS algorithm will be greatly influenced by unexpected data spikes and deviations in original RR intervals and these unexpected data points are usually caused by the signal misreading from original ECGs or some other sensing errors during signal collections. The designed median filter is effective to eliminate the unexpected data spikes. Additionally, an apnea severity index based on segmentation results and LF/HF is then designed to evaluate the apnea severity of an OSA suspect. Afterwards, the severity index and other critical admission information of OSA suspects are plugged into support vector machine for OSA subject screening and detection. This proposed approach is effective to discriminate the OSA subjects from the heathy subjects with high accuracy. To our knowledge, this is the first study to segment the physiological signals by detecting the potential apnea events and perform the OSA diagnosis according to the segmentation results. The rest of this paper is organized as follows. Section II provides details of proposed OSA diagnosis approach based on ICSS algorithm. Meanwhile, the improved local median filter is also introduced in this part for signal preprocessing. In Section III, a real case is studied to validate the effectiveness of our proposed approach and conclusion is drawn in Section IV. II. OBSTRUCTIVE SLEEP APNEA DIAGNOSIS APPROACH The scheme of the proposed OSA diagnosis approach is shown in Fig. 3. The original RR intervals extracted from ECG signals are firstly preprocessed by the local median filter. The filtered RR intervals are then applied for potential apnea event detection with the iterated cumulative sums of squares algorithm [28]. After segmentation, frequency analysis is employed to extract LF/HF from segmented RR intervals for each subject, followed by a thresholding technique to derive the OSA severity index. Finally, the severity index and the critical admission information of each subject are used as predictors for OSA subject diagnosis.

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Fig. 3. Scheme of proposed OSA diagnosis approach.

Notation for the local median filter, and ICSS algorithm is as follows: is a RR intervals series of length • • is the centralized RR interval series of length • is the half window size for the local median filter and are lower bound and upper bound of RR in• tervals for the local median filter • is the cumulative sum of squares of at in ICSS algorithm • is the normalized cumulative at where in ICSS sum of squares of algorithm is the normalized cumulative sum of • squares on the range over in ICSS algorithm is the designed statistic to monitor changes of • in ICSS algorithm (follows Wiener process asymptotically under variance homogeneity as shown in Appendix) is the asymptotic critical value of at confi• dence level of in ICSS algorithm • is the number of change points found before Step 4 in ICSS algorithm is the vector of all the possible change points found • before Step 4 in ICSS algorithm. Define the two extreme and . values A. An Improved Local Median Filter for RR Interval Correction Due to the poor quality in the R waves generated from ECG signals, the RR interval sequences might contain unexpected data points such as data spikes and large deviations which could not be physiologically interpreted. Some of research works apply the median filter proposed by [29] to overcome this

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problem. However, this median filter implements RR interval correction in a local window, and the corrected value is highly affected by the local estimate (e.g. the median). Since there exist successive abnormal RR intervals within a window frame, the abnormal RR intervals could not be distinguished. Thus, the median filter in [29] is necessary to be improved for RR interval correction in this paper. The basic principle is to detect and correct the abnormal RR intervals through a sliding window with the constraints of setting a lower bound and an upper bound. Since the suspected abnormal RR intervals can be generated due to spurious R wave and detection or missed R wave detection, a lower bound are determined respectively according to an upper bound physiological range of RR intervals to discriminate these two types of uninterpretable data points. For abnormal RR intervals due to spurious R wave detection, RR intervals in the sliding window are compared to the lower bound and corrected using either averaging or merging strategies. For abnormal RR intervals due to missed R wave detection, RR intervals in current window are divided into several equal values or averaged with the neighbor according to the designed criteria. Compared to the original median filter in [29], the proposed local filter is capable to correct the successive abnormal RR intervals. Details of the improved local median filter are illustrated as follows: as the minimum value of a RR interval • Step 1: Denote series . If , then go to Step 3; otherwise, go to Step 2. which • Step 2: Specify the window centering at contains points. Denote the window as . The median of RR intervals within the window is calculated and two absolute distances are computed as follows: 1) The absolute distance by comparing the sum of and the neighbor with a smaller value to is given by (1) 2) The absolute distance by comparing the average of and the neighbor with a larger value to is given by

(2) If , choose the neighbor of with the smaller value and merge them together into a single value; otherwise average and the associated neighbor with the larger value. Go to Step 1. . • Step 3: Select the maximum value of , denoted as , stop the algorithm; otherwise go to Step 4. If which con• Step 4: Specify the window centering at tains points. Calculate the median of the window. Similarly, two absolute distances are computed as below:

Fig. 4. An example of comparison of original and filtered RR intervals.

1) The absolute distance between given by

and

is

(3) where 2) The absolute distance between and the average of and the neighbor with smaller value is given by

(4) If , divide by to form a series of new RR intervals; otherwise average and the neighbor with the smaller value. Go to Step 3. The algorithm is implemented until all RR intervals are examined. Fig. 4 shows an example of RR interval sequence before and after filtering. A significant improvement can be observed with an elimination of abnormal RR intervals after implementing this improved local median filter. B. Apnea Event Detection Using Iterated Cumulative Sums of Squares In this subsection, the filtered RR intervals are segmented by the iterated cumulative sums of squares (ICSS) algorithm [28] to detect the potential apnea state change points. According to previous studies, RR intervals during apnea would slightly change the oscillation pattern and the changes are not obviously observed [27]. The iterated cumulative sums of squares (ICSS) aims to search the small variation changes in time series and is effective to discriminate the state changes [28]. Therefore, ICSS algorithm is applied in this paper for potential apnea event detection and segmentation of RR intervals. The details of the algorithm are shown as below: • Step 1: Let

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• Step 2: Calculate point at which

. Let

be the is obtained, and let

(5) , consider there is a change point at and proceed to Step 3a. Otherwise, no evidence of state changes in the series. The algorithm stops. • Step 3a: Let . Calculate . That is, to calculate the centered cumulative sums of squares which is applied only to the beginning of the series up to . If , a new change point is . Othdetected and repeat Step 3a until erwise it is considered that there is no evidence of change points within interval and the first state change point . is • Step 3b: Conduct the same procedure starting from the first change point found in Step 2, toward the end of the series. Assign a new value for by letting . Calculate . If , a new change point is detected and repeat Step . Otherwise, it is considered 3b until that no change points can be found in interval . Let . , there is only one change point. • Step 3c: If The algorithm stops here. If , preserve both points as possible change points and repeat Step 1 and Step 2 on the signal segment between these two change points; and . Each time when that is, Steps 3a and 3b are repeated, one or two more points can be obtained. • Step 4: If there are two or more possible change points, the points should be arranged in an increasing order. Check each possible change point by calculating , . If , keep the point; otherwise, eliminate it. Repeat Step 4 until the number of change points does not change and the points found in each new step are approximate to those in the previous step. It should be pointed out that the implementation of this algorithm may require a large amount of time before convergence. Hence the number of iterations is usually limited to avoid this situation in practice. Empirically, 100 iterations are sufficient to find all change points. If

C. Feature Extraction and Severity Index Calculation Since activity of sympathetic tone predominates the activity of parasympathetic tone during apnea and LF/HF is a well indicator of the activity of sympathetic system [27], LF/HF is utilized to characterize the activity of apnea events in this paper. For each segment, low frequency (LF, 0.04–0.15 Hz) and high frequency (HF, 0.15–0.4 Hz) are obtained by Fast Fourier Transform (FFT) as the integral of frequency ranges of 0.04–0.15

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and 0.15–0.4 of power spectrum density. The ratio of LF to HF (LF/HF) is then calculated. After extraction of LF/HFs from RR segments of each subject, a severity index is designed in present study to evaluate the severity of subjects. A varying thresholding method is applied to calculate different severity indexes under different thresholds for subjects. Given a range of potential thresholds in an ascending order, the severity index under for subject , is calculated threshold , as (6) where indicates the total number of subjects, denotes total is the time length number of segments of subject and is a Heaviside of th segment for subject . step function. The most appropriate severity index and the corresponding threshold can be obtained by maximizing the correwith the AHI using (7). The lation between designed severity index can be interpreted as the total time for a subject within apnea state during 7 to 8 hours’ sleeping. (7) D. Support Vector Machine for Subject Classification In this study, a support vector machine (SVM) [30] is applied to classify OSA (OSA+) and non-OSA (OSA-). The derived and some critical subject admission informaseverity index tion (age, body mass index and sex) are plugged into the SVM. The principle of SVM is to minimize the structural risk and maximize the geometric margin between classes which leads to high performance in practical application. Empirical evidence shows that it performs well in many real learning problems [31]. The theory of SVM can be represented as follows: with each input Consider a training set and the associated output . Each input is transformed into a higher dimension feature space via a nonlinear mapping function . When the training samples are linearly separable in , there exists a vector and a that define the separating hyperplane as scalar (8) The margin of separation between two classes is defined as and by maximizing this margin, SVM constructs an optimum separation hyperplane (OSH) as the one that minimizes under the constraints of (8). The optimal hyperplane is decided by maximizing a quadratic programming (QP) problem which involves constructing a Lagrangian formulation and transforming into a dual problem:

(9)

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where is the nonnegative Lagrangian multiplier. The samples corresponding to which lie along the margins of the decision boundary are the support vectors. is the regularization parameter which is a constant and determines the tradeoff between the maximum margin and minin (9) can be imum classification error. The term computed through a kernel function instead of directly obtaining and . The formula could be transformed as follows:

TABLE I COMPARISON OF RR CORRECTION EFFECTS

(10) After determining the optimum , the optimum solution for the vector is given by (11) For any test sample

, the output is given by

(12) The construction of SVMs involves selecting a kernel function which might affect the performance of SVM. The Gaussian radial basis function (RBF) kernel is the most widely used kernel in practice owing to its universal approximation [32]. Thus, RBF is adopted in our approach for OSA subject classification. The polynomial kernel is also tested in this paper to illustrate the performance of the proposed approach. III. A REAL CASE STUDY A. Data Description 1) Physionet Apnea-ECG Database: 70 records of RR intervals have been obtained from an open database at Physionet.org [33], [34], and the AHI of these subjects ranges between 0 and 83. The age of those subjects is between 27 and 63 years (mean: 45 10 years) with body mass index (BMI) between 19.2 and (mean: ). Recordings vary in 45.33 duration from slightly less than 7 hours to nearly 10 hours each. 2) St. Vincent’s University Hospital/University College Dublin (SVUH/UCB) Sleep Apnea Database: The sleep apnea database from SVUH/UCB is also contained in the present study for validation1 which includes full overnight polysomnograms from subjects with suspected sleep-disordered breathing. The age of these 25 recordings (4 females and 21 males) varies 9.55 years) with between 28 and 68 years (mean: 49.96 weights between 59.8 and 128.6 kg (mean: 95.02 14.70 kg). It should be pointed out that three subjects in the first database and two subjects in the second database are not considered in our study due to existence of a large amount of physiologically uninterpretable heartbeats. Thus, a total of 90 subjects are 1http://www.physionet.org/physiobank/database/ucddb/

Fig. 5. Corrected RR with original median filter and improved median filter.

included in this study. An independent sampling scheme is employed to evaluate the generalization ability of the diagnosis system. B. Results 1) Data Preprocessing: Since the physiological range of RR intervals is [0.6, 1.2] (heart rate 50 bmp–100 bmp), the lower bound and upper bound for the local median filter were chosen as 0.4 and 2 (heart rate 30 bmp–150 bmp) respectively to reduce the individual effects and random noises. The half window size for the local median filter was chosen as 5 in accord with the research [29]. The comparison studies in terms of abnormal beat rates (percentage of RR intervals which satisfy and ) for ten exemplary subjects were performed among original RR intervals, corrected RR intervals with median filter in [29] and with the improved median filter in this paper. The results are shown in Table I. Compared to both original RR intervals and corrected RR intervals with original median filter, the proposed median filter in present study was effective to eliminate a large number of unexpected points. To further demonstrate the performance of the improved median filter, an example of corrected RR intervals with the original median filter and improved median filter for a subject was given in Fig. 5. In the upper panel, an abnormal RR interval still exists by the original median filter. However, this abnormal RR

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Fig. 6. Kernel densities of adjacent segments for a subject.

interval was eliminated with the improved median filter in the lower panel. 2) Results of ICSS Segmentation: After preprocessing, ICSS algorithm was implemented for potential apnea event detection for each subject. Fig. 6 shows an example of the kernel densities of three successive segments. The density curves of different segments are marked with square, triangular and circular symbols respectively. It can be observed that the shapes of these three densities are distinct and the peaks stand discrepantly. Kolmogorov-Smirnov test also demonstrated significant differences in variance among these segments at a significance level of 5%. After change point detection, LF/HFs were extracted from segmented RR intervals. Example of the extracted LF/HF series of two selected subjects (AHI 69.6 and 39.1) are given in Fig. 7. The horizontal axis is the time and the vertical axis represents magnitude of LF/HF. The duration of each detected state is denoted by the length of the corresponding horizontal line. The graph depicts that LF/HF varies dramatically over different segments. More specifically, it can be seen that segments with large value of LF/HF tend to possess short durations. Since the durations of apnea events are short in most clinical cases, the segments with large value of LF/HF might indicate the potential apnea events. 3) Severity Index Calculation: After extraction of LF/HF for each subject, a range of potential thresholds 1.4 to 20 with an increment of 0.1 were applied to the LF/HFs series to calculate severity indexes by (6). The optimum severity index with corresponding threshold was obtained by searching the maximum correlation. Two examples of severity indexes under different thresholds are displayed in Fig. 8. Severity index for subject A decreases rapidly as the threshold increases and it decreases to zeros when the threshold increases to 8. Comparatively, the severity index for subject B decreases slowly and reduces to zero until the threshold reaches 18. The results of selecting maximum correlation are provided in Fig. 9 and a maximum correlation of 0.6297 was found at . Fig. 9 indicated that the severity index at the threshold of 2.1 was highly correlated with AHI. According to the definition of derived severity index , it can be interpreted

Fig. 7. LF/HF for subjects with different severities. (a) . (b)

.

Fig. 8. Severity index series under different thresholds.

Fig. 9. Correlations under different thresholds with maximum correlation analysis.

as the measurement of the total time of a subject within apnea state. 4) OSA Diagnosis With SVM: SVMs were applied to OSA subject diagnosis with the derived severity index and the related admission information (age, BMI, sex) to demonstrate the discriminating power of the proposed OSA diagnosis approach. Subjects can be classified into two categories according to the

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TABLE II SUBJECT LABEL FOR CLASSIFICATION

TABLE III INDEPENDENT SAMPLING SCHEME FOR PERFORMANCE EVALUATION

TABLE IV PERFORMANCE MEASURES OF SVM FOR OSA SUBJECT DIAGNOSIS

clinical principle as shown in Table II. 90 subjects were divided into training set and testing set using the independent sampling method. The training set included randomly selected 59 subjects and the remaining 31 subjects were used for testing. The details are provided in Table III. The overall accuracy, sensitivity and specificity were employed to evaluate the performance of proposed approach and calculated based on 10000 independent trials. Results of independent trials on classification performance are summarized in Table IV. Comparisons were also conducted to evaluate the performance of the SVMs for different kernel functions and different regularization parameters. Mean accuracy achieved up to 97.03% with mean sensitivity 99.16% and mean specificity 90.91% in polynomial kernel of degree 1 for and 97.41% with mean sensitivity 98.99% and mean specificity 92.87% in RBF kernel . Comparatively, the performance of the RBF kernel with different values was relatively consistent. Besides the parameter combinations shown in this paper, other parameter settings were also tested in this study and similar results could be obtained. In practice, RBF kernels can be applied for OSA diagnosis due to its consistency. In order to demonstrate the performance of our proposed approach, results of recent related works for OSA subject diagnosis are listed in Table V. Compared to logistic regression (LR), linear/quadratic discriminant analysis (LDA/QDA), -nearest neighbor (KNN) and probabilistic neural network (PNN), the proposed OSA diagnosis approach achieved a satisfactory result in terms of sensitivity, specificity and accuracy.

IV. CONCLUSION This paper presented a systematic route for OSA diagnosis based on an automatic signal segmentation algorithm. Rather than the equal-length segmentation of physiological signals required by conventional approaches, the proposed approach was able to reduce the chances of misdetected apnea events and improve the identification performance by monitoring a single channel of ECG signals. To appropriately use this approach, a local median filter was improved to reduce the unexpected data points with an interpretable range before signal segmentation. The designed severity index and the critical subject admission information were plugged into the SVM for OSA diagnosis. To validate it, the RR intervals from 90 subjects were used to evaluate the performance by independent test method. The results demonstrated a competitive performance for the OSA suspect diagnosis. It is worth noting that the proposed approach only requires the RR intervals derived from ECG signals of OSA suspects, which is easier to access by some advanced remote biosensors (e.g. strapless heart rate monitors) compared to traditional invasive PSG monitoring approach. Hence, by appropriate improvement, this approach could be applied for OSA screening and home diagnosis. Meanwhile, this signal-based diagnosis approach has a great potential for other cardiac disease screening and detection by combining associated pathological knowledge.

APPENDIX PROOF OF FOLLOWING WIENER PROCESS ASYMPTOTICALLY UNDER VARIANCE HOMOGENEITY Let Let

where

, so

and

. By Donsker’s theorem, . Let

.

, so . Then

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TABLE V PERFORMANCE COMPARISON AMONG DIFFERENT APPROACHES FOR SUBJECT DIAGNOSIS

Note that

Thus

As

,

and

Therefore

By the law of large numbers,

, so

. ACKNOWLEDGMENT The authors gratefully acknowledge the editor and the reviewers for their insightful comments and valuable suggestions that led to a marked improvement of the article. The authors appreciate Hongyu He and Liqing Zhang for their valuable suggestions. REFERENCES [1] B. Xie and H. Minn, “Real-time sleep apnea detection by classifier combination,” IEEE Trans. Inf. Technol. Biomed., vol. 16, no. 3, pp. 469–477, 2012. [2] T. Young, L. Finn, D. Austin, and A. Peterson, “Menopausal status and sleep-disordered breathing in the Wisconsin sleep cohort study,” Am. J. Respir. Crit. Care. Med., vol. 167, no. 9, pp. 1181–1185, 2003. [3] A. S. Shamsuzzaman, B. J. Gersh, and V. K. Somers, “Obstructive sleep apnea,” JAMA, vol. 290, no. 14, pp. 1906–1914, 2003. [4] K. E. Bloch, “Polysomnography: A systematic review,” Technol. Health Care, vol. 5, no. 4, pp. 285–305, 1997. [5] A. H. Khandoker, M. Palaniswami, and C. K. Karmakar, “Support vector machines for automated recognition of obstructive sleep apnea syndrome from ECG recordings,” IEEE Trans. Inf. Technol. Biomed., vol. 13, no. 1, pp. 37–48, 2009.

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[25] B. Koley and D. Dey, “Adaptive classification system for real-time detection of apnea and hypopnea events,” in Proc. 2013 IEEE PHT, 2013, pp. 42–45. [26] A. Voss, S. Schulz, R. Schroeder, M. Baumert, and P. Caminal, “Methods derived from nonlinear dynamics for analysing heart rate variability,” Philos. T. Roy. Soc. A, vol. 367, no. 1887, pp. 277–296, 2009. [27] F. Chouchou, V. Pichot, J.-C. Barthélémy, H. Bastuji, and F. Roche, “Cardiac sympathetic modulation in response to apneas/hypopneas through heart rate variability analysis,” PloS One, vol. 9, no. 1, p. e86434, 2014. [28] C. Inclan and G. C. Tiao, “Use of cumulative sums of squares for retrospective detection of changes of variance,” JASA, vol. 89, no. 427, pp. 913–923, 1994. [29] P. De Chazal, C. Heneghan, E. Sheridan, R. Reilly, P. Nolan, and M. O’Malley, “Automated processing of the single-lead electrocardiogram for the detection of obstructive sleep apnoea,” IEEE Trans. Biomed. Eng., vol. 50, no. 6, pp. 686–696, 2003. [30] C. Cortes and V. Vapnik, “Support-vector networks,” Machine Learning, vol. 20, no. 3, pp. 273–297, 1995. [31] T. Hastie, R. Tibshirani, and J. J. H. Friedman, The Elements of Statistical Learning. New York, NY, USA: Springer, 2001, vol. 1. [32] A. R. Webb, Statistical Pattern Recognition. New York, NY, USA: Wiley, 2003. [33] T. Penzel, G. Moody, R. Mark, A. Goldberger, and J. Peter, “The apnea-ECG database,” in IEEE Computers in Cardiology 2000, 2000, pp. 255–258. [34] G. B. Moody, R. G. Mark, and A. L. Goldberger, “PhysioNet: A webbased resource for the study of physiologic signals,” IEEE Eng. Med. Biol. Mag., vol. 20, no. 3, pp. 70–75, 2001. Lili Chen received the B.S. degrees in Industrial Engineering from Nankai University, Tianjin, China, in 2011. Currently she is a Ph.D. candidate at the Department of Industrial Engineering and Management, Peking University. Her research interests are focused on statistically modeling of physiological data and complex system.

Xi Zhang received the B.S. degrees in Mechanical Engineering and Automation from Shanghai Jiaotong University, Shanghai, China, in 2006, and the Ph.D. degree in Industrial Engineering from the University of South Florida, Tampa, 2010. Currently, he is an assistant professor at the Department of Industrial Engineering and Management, Peking University, Beijing. His research interests are focused on data-driven modeling and analysis for complex dynamic systems including physiological-data-driven analysis for healthcare delivery. Dr. Zhang is a member of INFORMS and IIE.

Changyue Song received the B.S. degrees in Industrial Engineering from Tsinghua University, Beijing, China, in 2012. Currently, he is a graduate student at the Department of Industrial Engineering and Management, Peking University. His research interests are focused on statistically modeling of physiological data.