## 4 Discussion  
In this study, we proposed a new sleep indicator named Hsi that reflects the regularity of respiratory frequency by quantifying the degree of HF power concentration on a narrow frequency range. In the analysis of polysomnographic data in 141 subjects, we observed that Hsi discriminates NREM sleep from wake and REM sleep segments with an AUC of ROC curve of 0.86, which was significantly greater than those of other HRV indices, scaling exponents, and ABM that have been used as indicators to detect sleep or estimate sleep stages in earlier studies [7; 8; 9; 10; 11; 12; 13; 14; 15]. With a cutoff criterion of \(>\) 70%, Hsi detected NREM sleep with 77% sensitivity, 80% specificity, 79% accuracy, and a Cohen's kappa coefficient of 0.57. These observations indicate that Hsi is a powerful univariate marker of NREM sleep. Hsi is expected to improve the performance of sleep and sleep stage estimations by R-R intervals of ECG and other heartbeat signals obtained by wearable sensors. There are a plenty of earlier studies on the estimations of sleep and sleep stage using ECG [8; 9; 10; 11]. In a study of 78 subjects undergoing polysomnography, [PERSON] et al. [8] analyzed HRV indices (mean R-R interval, SD of R-R interval, VLF, LF, HF, and LF/HF) and scaling exponents for 5-min consecutive segments whose sleep stage was defined as that continued for \(>\)3 min in the segment. They reported 85% accuracy for sleep stage separation by a discriminant model consisting of mean and SD of R-R intervals and scaling exponents. In a study using 18 polysomnographic data in the MIT/BIH \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **AUC (SE)** & **95\%CI** & \(p\) **vs. Hsi** \\ \hline his & 0.79 (0.0031) & 0.78–0.79 & - \\ Heart rate & 0.54 (0.0036) & 0.53–0.55 & \(<\)0.0001 \\ VLF power & 0.69 (0.0032) & 0.68–0.69 & \(<\)0.0001 \\ LF power & 0.56 (0.0036) & 0.56–0.57 & \(<\)0.0001 \\ HF power & 0.61 (0.0036) & 0.61–0.62 & \(<\)0.0001 \\ HF peak power & 0.70 (0.0035) & 0.69–0.70 & \(<\)0.0001 \\ LF/HF & 0.74 (0.0030) & 0.73–0.74 & \(<\)0.0001 \\ \(\alpha_{30-60}\) & 0.76 (0.0029) & 0.76–0.77 & \(<\)0.0001 \\ \(\alpha_{60-300}\) & 0.63 (0.0034) & 0.63–0.64 & \(<\)0.0001 \\ ABM & 0.76 (0.0028) & 0.76–0.77 & \(<\)0.0001 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Discriminant performance of NREM stage from wake and REM stages per epoch. Figure 5: Receiver-operating characteristic (ROC) curves for discriminating NREM from wake and REM stages. AUC for Hsi is greater than those of other HRV indices, scaling exponents, and ABM and is comparable to that for the Hsi of respiration (Table 3). Polysomnographic Database, [PERSON] et al. [9] reported 80% accuracy and a Cohen's kappa of 0.41 for the classification of wake and sleep of 30-s epochs with the 10 features of HRV and heart rate dynamics selected by the support vector machine recursive elimination system. In a study of 48 polysomnographic data in healthy adults, [PERSON] et al. [10] reported 80% accuracy and a kappa of 0.56 in the classification of 30-s epochs of wake, NREM sleep, and REM sleep with 80 features selected from 142 feature of ECG and thoracic respiratory effort. Finally, in a study of 20 young healthy subjects, [PERSON] et al. [11] reported 76% accuracy and a kappa of 0.52 for the classification of 5-min segment of REM and NREM sleep by HRV and nonlinear heart rate dynamics. Although the discriminant accuracy of Hsi we observed in this study seems comparable to those reported in these earlier studies, it should be noted that Hsi achieved that with a univariate model, while those in earlier studies were achieved by multivariate models. This suggests that the discriminant performance may be further improved by combination of Hsi and other indices. In fact, we observed that ABM effectively distinguishes between REM and wake stages after NREM had been separated by Hsi, suggesting the usefulness of the combination of Hsi and ABM for the classification of wake, NREM, and REM stages (Figure 4).