Regularized logistic regression for obstructive sleep apnea screening during wakefulness using daytime tracheal breathing sounds and anthropometric information

Abstract

Obstructive sleep apnea (OSA) is a prevalent health problem. Developing a technology for quick OSA screening is momentous. In this study, we used regularized logistic regression to predict the OSA severity level of 199 individuals (116 males) with apnea/hypopnea index (AHI) ≥ 15 (moderate/severe OSA) and AHI < 5 (non-OSA) using their tracheal breathing sounds (TBS) recorded during daytime, while they were awake. The participants were guided to breathe through their nose, and then through their mouth at their deep breathing rate. The least absolute shrinkage and selection operator (LASSO) feature selection approach was used to select the discriminative features from the power spectra of the TBS and the anthropometric information. Using a five-fold cross-validation procedure, five different training sets and their corresponding blind-testing sets were formed. The average blind-testing classification accuracy over the five different folds was found to be 79.3% ± 6.1 with the sensitivity (specificity) of 82.2% ± 7.2% (75.8% ± 9.9%). The accuracy for the entire dataset was found to be 81.1% with sensitivity (specificity) of 84.4% (77.0%). The feature selection and classification procedures were intelligible and fast. The selected features were physiologically meaningful. Overall, the results show that TBS analysis can be used as a quick and reliable prediction of the presence and severity of OSA during wakefulness without a sleep study.

Appendix 1. Classification using simple logistic regression

In this study, as we had 2 classes of participants (non-OSA and moderate/severe OSA). Thus, we also applied the binomial logistic regression classifier to the features selected by the LASSO penalized logistic regression for classification purpose. The classification of the entire 164 non-OSA and moderate/severe participants showed 80.5% accuracy with sensitivity and specificity of 82.2% and 78.4%, respectively. The average of the results between the 5 training sets showed accuracies of 82.0% ± 1.8% and 78.1% ± 7.7% for training and testing, respectively. The sensitivity (specificity) was 83.0% ± 3.1% (80.8% ± 2.2%) for training and 78.9% ± 11.4% (77.1% ± 9.9%) for testing, respectively. The AUC, associated with ROC curve calculated using all non-OSA and moderate/severe participants, was shown to be 80.3. In addition, the average of the AUC values between the 5 training sets was shown to be 81.9 ± 1.7. For the dataset containing all 164 non-OSA and moderate/severe OSA participants, 32 were misclassified, out of which, 16 were from non-OSA and 16 were from moderate/severe OSA group. In addition, 17 out of 35 subjects in the gap range were assigned to the non-OSA group and the remaining 18 subjects to the moderate/severe group.

The reason for achieving the better result for regularized logistic regression classification than the simple logistic regression is that as there is still some correlation between the selected features, the regularization term can improve the generalization performance (performance on new data) by reducing the variance of parameter estimates.

1.1 Appendix 2. Computational complexities

The computation cost of our proposed algorithm is relatively low. For the feature extraction part, the computational cost was estimated for a typical TBS with length N after normalization. The feature extraction phase consisted of 2 main parts: LogVar estimation and PSD estimation. The LogVar and PSD calculated for each segment, defined as the window with length L which moves along the signal with 50% overlap. Thus, the total number of overlapping windows within each TBS is approximately$\frac{2N}{L}$ . The computational cost of calculating LogVar within one segment is L; thus, the total number of operations to calculate the LogVar of each TBS is as follows:

$$ L\times \frac{2N}{L}=O(N). $$

(10)

For the PSD estimation, the fast Fourier transform (FFT) of each segment was calculated and averaged. The computational cost of calculating FFT of each segment is L log(L); thus, the total cost of PSD estimation for each TBS is as follows:

$$ O\left(\frac{2N}{L}\times L\ \log (L)\right)=O\left(\mathrm{Nlog}(L)\right). $$

(11)

The feature extraction part is from O(k),where K is the number of extracted features from each TBS signal. As we have 16 signals for each participant (for mouth/nose breathing maneuvers, inspiratory/expiratory phases, summation/subtraction of phases, and normal/logarithmic scale), therefore, the total cost of feature extraction from n participant is as follows:

$$ 16n\times \left(O(N)+O\left(\mathrm{Nlog}(L)\right)+O(k)\right)\approx 16n\times O\left(\mathrm{Nlog}(L)\right). $$

(12)

Feature reduction part of this study consists of applying t test and LASSO. As each t test has the computational cost of O(n), therefore, the overall t tests for all p features have the computational cost of p × O(n). On the other hand, in this study, we ran the LASSO with the Glmnet package of R, which uses the coordinate descent algorithm to find the optimum solution. The computational cost of this method is reported to be O(pn) for each iteration of the optimization [32]. Besides, as three features were selected as the best feature set of each training set, thus, the computational cost of logistic regression classification using the LASSO penalty is O(3n). Therefore, the total computational cost of our proposed method can be written as follows:

$$ 16n\times O\left(\mathrm{Nlog}(L)\right)+p\ O(n)+O\left(\mathrm{pn}\right)+O(3n)\approx 16n\times O\left(\mathrm{Nlog}(L)\right)+O\left(\mathrm{pn}\right) $$

(13)

which is linear in terms of n, p.

Glossary

AHI

Apnea/hypopnea index

AUC

Area under the curve

CI

Confidence interval

FFT

Fast Fourier transform

LASSO

Least absolute shrinkage and selection operator

LogVar

Logarithm of the sound’s variance

MANOVA

Multivariate analysis of variance

OSA

Obstructive sleep apnea

PSD

Power spectrum density

PSG

Polysomnography

ROC

Receiver operating characteristic

S_aO₂

Oxygen saturation level of blood

SVM

Support vector machine

TBS

Tracheal breathing sounds

UA

Upper airway