Measures of overnight oxygen saturation to characterize sleep apnea severity and predict postoperative respiratory depression

Abstract

Background

Sleep apnea syndrome, characterized by recurrent cessation (apnea) or reduction (hypopnea) of breathing during sleep, is a major risk factor for postoperative respiratory depression. Challenges in sleep apnea assessment have led to the proposal of alternative metrics derived from oxyhemoglobin saturation (SpO₂), such as oxygen desaturation index (ODI) and percentage of cumulative sleep time spent with SpO₂ below 90% (CT90), as predictors of postoperative respiratory depression. However, their performance has been limited with area under the curve of 0.60 for ODI and 0.59 for CT90. Our objective was to propose novel features from preoperative overnight SpO₂ which are correlated with sleep apnea severity and predictive of postoperative respiratory depression.

Methods

Preoperative SpO₂ signals from 235 surgical patients were retrospectively analyzed to derive seven features to characterize the sleep apnea severity. The features included entropy and standard deviation of SpO₂ signal; below average burden characterizing the area under the average SpO₂; average, standard deviation, and entropy of desaturation burdens; and overall nocturnal desaturation burden. The association between the extracted features and sleep apnea severity was assessed using Pearson correlation analysis. Logistic regression was employed to evaluate the predictive performance of the features in identifying postoperative respiratory depression.

Results

Our findings indicated a similar performance of the proposed features to the conventional apnea–hypopnea index (AHI) for assessing sleep apnea severity, with average area under the curve ranging from 0.77 to 0.81. Notably, entropy and standard deviation of overnight SpO₂ signal and below average burden showed comparable predictive capability to AHI but with minimal computational requirements and individuals’ burden, making them promising for screening purposes. Our sex-based analysis revealed that compared to entropy and standard deviation, below average burden exhibited higher sensitivity in detecting respiratory depression in women than men.

Conclusion

This study underscores the potential of preoperative SpO₂ features as alternative metrics to AHI in predicting postoperative respiratory.

Background

Sleep apnea syndrome, a common respiratory disorder during sleep, is a major risk factor for postoperative respiratory depression [1,2,3,4,5]. Its prevalence is estimated to range from 9 to 38% in general population [6,7,8] and 18–67.6% among surgical patients [1, 9]. Sleep apnea syndrome is characterized by repeated interruptions in breathing during sleep, known as apneas (complete pauses in breathing) and hypopneas (partial reductions in airflow) [10]. These interruptions in breathing lead to intermittent hypoxemia (decreased blood oxyhemoglobin level), which is strongly associated with cardiovascular disorders such as hypertension and stroke [8]. The breathing irregularities of sleep apnea syndrome are exacerbated postoperatively [11] due to the respiratory-depressing effects of pain medications (mainly opioids). The consequence is the increased risk of cardiovascular complications [5], respiratory depression, cardiorespiratory arrest [1], and mortality [12]. Preoperative assessment of respiratory irregularities associated with sleep apnea syndrome is crucial to ensure optimal perioperative care and to prevent adverse outcomes.

Diagnosing and assessing the severity of sleep apnea syndrome have several challenges which limits its predictive power for postoperative respiratory depression. The gold standard technique for diagnosing sleep apnea syndrome is lab-polysomnography (PSG) where more than 10 signals, including brain activity (EEG), eye movement (EOG), muscle activity (EMG), heart rate (ECG), blood oxygenation (SpO₂), nasal pressure (airflow), and respiratory efforts are recorded to assess respiration and apneas and hypopneas during sleep [13]. The severity of sleep apnea syndrome is assessed using the apnea–hypopnea index (AHI), which is the number of apneas and hypopneas per hour of sleep. PSG is uncomfortable, has long wait times, and requires expert knowledge [8, 14]. Moreover, the assessment of AHI through the analysis of multiple signals demands proficiency and entails a laborious and time-intensive process. Home sleep apnea testing (HSAT) is a recent alternative to PSG to evaluate sleep apnea syndrome at home using a subset of airflow, respiratory effort, and blood oxygenation signals, which sensors can be applied by the individual with minimal training [8]. HSAT has high false negatives [13] and screening questionnaires, such as STOP Bang, have low to moderate specificities [15, 16]. Thus, there is an unmet need for alternative metrics which are predictive of postoperative respiratory depression.

Hypoxemia, a common consequence of sleep apnea syndrome, can be assessed based on the changes in SpO₂ levels which can be recorded continuously and affordably using a pulse oximeter from the finger. ODI, defined as the number of episodes with over 4% drops in SpO₂ level per hour of sleep, and CT90 were shown to be predictive of postoperative adverse outcomes [17]. However, the performance of these metrics was limited to the area under the curve of 0.6 for ODI and 0.59 for CT90 [17]. To enable investigating more temporal and frequency domain characteristics of SpO₂ signal, we have previously developed algorithms for automatic segmentation of SpO₂ signal and extracting features from desaturation episodes. We validated our algorithm in a preliminary analysis using data from 50 individuals and we investigated the association of four features with AHI [18]. Our results showed that compared to AHI, measures of area under the curve of preoperative overnight desaturation episodes with ≥ 3% drops were more correlated with postoperative respiratory depression [18]. However, the sample size was limited, and we did not investigate the performance of the extracted measures to predict postoperative respiratory depression. Therefore, the primary aim of this study was to assess the effectiveness of SpO₂ measures in predicting postoperative respiratory depression, building upon our prior research by enlarging both the sample size and the range of features examined.

Results

In this retrospective analysis, we analyzed preoperative SpO₂ signals from surgical patients to derive seven distinct features aimed at predicting postoperative respiratory depression (Table 1). The primary outcome of postoperative respiratory depression was defined as having at least one hypoxemia episode where SpO₂ was less than 85% for more than 3 min [4]. Additionally, we examined the association of the extracted features with traditional assessment measures of sleep apnea syndrome, that is AHI (number of apneas and hypopneas per hour of sleep), total arousal index (the average of arousals per hour of sleep), and respiratory-related arousal index (the hourly average of arousals associated with apneas or hypopneas).

Table 1 Extracted SpO₂ measures

Participants demographics

Out of 158 individuals whose data were included in the analysis, 27 individuals (17%) had postoperative respiratory depression. Characteristics of individuals with and without postoperative respiratory depression are presented in Table 2. While there were equal number of men and women in the study, the proportion of men and women differed between those with and without postoperative respiratory depression (p = 0.02). In individuals with postoperative respiratory depression, the proportion of women were significantly higher than men (70.37% women vs. 29.63% men, p = 0.032). No significant difference was observed between women and men among individuals without respiratory depression (45.80% women vs. 54.20% men, p = 0.336). Compared to individuals without respiratory depression, BMI, AHI, total arousal index, respiratory-related arousal index, and SpO₂ measures (SpO₂ STD, SpO₂ ENT, BAB, ODB AVG, ODB STD, ODB ENT, NDB) were significantly higher in individuals with respiratory depression (p < 0.01 for all). Moreover, the prevalence of moderate to severe sleep apnea syndrome (AHI ≥ 15) was significantly higher in individuals with postoperative respiratory depression than those without respiratory depression (74.07% vs. 46.56%, p = 0.009).

Table 2 Patients’ demographics

Our sex-based analysis showed that in individuals with postoperative respiratory depression, the prevalence of moderate to severe sleep apnea syndrome was higher in women than men (12 vs. 8) while the severity was lower (average AHI: 40.63 h⁻¹ vs. 50.06 h⁻¹, average total arousal: 34.53 h⁻¹ vs. 38.70 h⁻¹, average respiratory-related arousal: 26.56 h⁻¹ vs. 34.19 h⁻¹). In individuals without postoperative respiratory depression, the prevalence and severity of moderate to severe sleep apnea syndrome was lower in women than men (prevalence: 23 in women vs. 38 in men, average AHI: 25.63 h⁻¹ in women vs. 33.43 h⁻¹ in men, average total arousal: 21.31 h⁻¹ in women vs. 27.60 h⁻¹ in men, average respiratory-related arousal: 13.65 h⁻¹ in women vs. 20.62 h⁻¹ in men).

In both men and women, AHI, total arousal index, respiratory-related arousal index, and SpO₂ measures, except for ODB ENT and NDB, were significantly higher in individuals with postoperative respiratory depression (p < 0.05 for all) (Fig. 1). The significance was stronger (p was lower) in men than women except for the total arousal index. In individuals with postoperative respiratory depression, AHI, total arousal index, respiratory-related arousal index, and SpO₂ measures were higher in men than women. The difference was significant for NDB (7.99 ± 4.85 in men vs. 3.55 ± 3.43 in women, p = 0.009). In individuals without postoperative respiratory depression, AHI (20.97 ± 18.89 h⁻¹ in men vs. 13.1 ± 12.35 h⁻¹ in women, p = 0.014), total arousal index (21.43 ± 13.72 h⁻¹ in men vs. 14.64 ± 9.40 h⁻¹ in women, p = 0.001), respiratory-related arousal index (13.11 ± 13.30 h⁻¹ in men vs. 7.17 ± 9.21 h⁻¹ in women, p < 0.001), ODB ENT (4.75 ± 0.86 in men vs. 4.28 ± 0.97 in women, p = 0.007), and NDB (2.92 ± 2.03 in men vs. 2.01 ± 1.70 in women, p = 0.005) were significantly higher in men than women.

Fig. 1

Sex-differences of sleep apnea and SpO₂ measures in patients with and without postoperative respiratory depression. a apnea–hypopnea index (AHI), b total arousal index, c respiratory-related arousal index, d standard deviation of overnight SpO2 signal (SpO₂ STD), e entropy of overnight SpO₂ signal (SpO₂ ENT), f below average burden (BAB), g average of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB AVG), h standard deviation of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB STD), i entropy of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB ENT), j Overall nocturnal desaturation burden (NDB). RD: respiratory depression. Values show p-values

Prediction of postoperative respiratory depression

Figure 2 presents the performance of SpO₂ measures as well as AHI, total arousal index, and respiratory-related arousal index in predicting postoperative respiratory depression in total and between sexes, using logistic regression model. Our results showed that SpO₂ STD, SpO₂ ENT, BAB, ODB AVG, ODB STD, ODB ENT, and NDB were able to predict postoperative respiratory depression with average area under the receiver operating curve (AUC-ROC) of 0.81, 0.80, 0.81, 0.80, 0.79, 0.77, and 0.81, respectively. Except for ODB ENT, AUC-ROC of models with SpO₂ measures were similar to the models with AHI, total arousal index, and respiratory-related arousal index. Specificity of the models with total (0.75) and respiratory-related (0.74) arousal index were significantly higher than AHI (0.70). Among SpO₂ measures, SpO₂ STD (0.73) and BAB (0.72) had highest specificities which were similar to the highest specificities of total arousal index and respiratory-related arousal index. The sensitivity of the models with SpO₂ ENT (0.73) and ODB ENT (0.72) were higher than AHI (0.70), total arousal index (0.70), and respiratory arousal index (0.67). However, the differences were not significant. In summary, our sex-based analysis showed that in general the performance of the models is lower for women than men. Only in the models with total arousal index and BAB, average sensitivity was higher in women than men.

Fig. 2

Performance of the sleep apnea and SpO₂ measures in predicting postoperative respiratory depression. AHI: apnea–hypopnea index, SpO₂ STD: standard deviation of overnight SpO₂ signal, SpO₂ ENT: entropy of overnight SpO₂ signal, BAB: below average burden, ODB AVG: average of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops, ODB STD: standard deviation of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops, ODB ENT: entropy of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops, NDB: Overall nocturnal desaturation burden. All models included sex, BMI, and pre-existing cardiorespiratory disorders (arterial hypertension, coronary artery disease, stroke, angina, myocardial infarction, heart failure, coronary revascularization, asthma, chronic obstructive pulmonary disease) to adjust for patients’ demographics. The error bars show the 95% confidence interval

Assessment of severity of sleep apnea syndrome

The correlation between the SpO₂ measures and AHI, total arousal index, and respiratory-related arousal index are presented in Figs. 3, 4, and 5. Our results indicated that SpO₂ measures were significantly correlated with AHI, total arousal index, and respiratory-related arousal index (p < 0.001, for all). The correlation was stronger with AHI and respiratory-related arousal index than total arousal index and NDB had the highest correlation with AHI, total and respiratory-related arousal indices. AHI was correlated strongly with NDB (r = 0.85) and moderately with SpO₂ STD (r = 0.73), SpO₂ ENT (r = 0.73), BAB (r = 0.72), ODB AVG (r = 0.76), ODB STD (r = 0.64), and ODB ENT (r = 0.77). Total arousal index was correlated moderately with NDB (r = 0.69) and fairly with SpO₂ STD (r = 0.53), SpO₂ ENT (r = 0.55), BAB (r = 0.54), ODB AVG (r = 0.57), ODB STD (r = 0.42), and ODB ENT (r = 0.59). Respiratory-related arousal index was correlated strongly with NDB (r = 0.80), fairly with ODB STD (r = 0.51), and moderately with SpO₂ STD (r = 0.63), SpO₂ ENT (r = 0.62), BAB (r = 0.63), ODB AVG (r = 0.68), and ODB ENT (r = 0.66). Our sex-based analysis showed that except for the SpO₂ ENT and ODB ENT, the correlation between the SpO₂ measures with AHI was higher in women than men; the correlation between the SpO₂ measures and total arousal index was lower in women than men; and except for NDB, the correlation between the SpO₂ measures and respiratory-related arousal index was lower in women than men. Nonetheless, the difference was not significant.

Fig. 3

Correlation between apnea–hypopnea index (AHI) and SpO₂ Measures. a standard deviation of overnight SpO2 signal (SpO₂ STD), b entropy of overnight SpO₂ signal (SpO₂ ENT), c below average burden (BAB), d average of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB AVG), e standard deviation of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB STD), f entropy of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB ENT), g Overall nocturnal desaturation burden (NDB). h correlation values

Fig. 4

Correlation between total arousal index and SpO₂ Measures. a standard deviation of overnight SpO₂ signal (SpO₂ STD), b entropy of overnight SpO₂ signal (SpO₂ ENT), c below average burden (BAB), d average of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB AVG), e standard deviation of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB STD), f entropy of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB ENT), g Overall nocturnal desaturation burden (NDB).) correlation values

Fig. 5

Correlation between respiratory-related arousal index and SpO₂ Measures. a standard deviation of overnight SpO₂ signal (SpO₂ STD), b entropy of overnight SpO₂ signal (SpO₂ ENT), c below average burden (BAB), d average of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB AVG), e standard deviation of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB STD), f entropy of normalized desaturation burdens of overnight desaturation episodes with ≥ 3% drops (ODB ENT), g Overall nocturnal desaturation burden (NDB). h correlation values

Discussion

In this paper, we presented measures of variation of preoperative overnight SpO₂ and burden of desaturation episodes which were significantly correlated with the severity of sleep apnea syndrome and predictive of postoperative respiratory depression. Our results showed that the predictive power of the introduced measures was similar to those of AHI and arousal indices, with average AUC-ROC values ranging from 0.77 to 0.81. Notably, standard deviation, entropy, and below average burden of overnight oxygen saturation demonstrated predictive power comparable to that of traditional indices like AHI and arousal indices. Moreover, these measures can be computed with minimal computational resources, making them attractive options for screening purposes. Additionally, we observed that the below average burden of overnight SpO₂ exhibited higher sensitivity in detecting respiratory depression among women compared to men, in contrast to entropy and standard deviation.

We defined respiratory depression based on its most common adverse outcome, that is hypoxemia [1]. Hypoxemia and subsequent hypercapnia significantly increase the risk of cardiorespiratory arrest [1]. Identifying individuals with postoperative hypoxemia will enable early interventions which can significantly alleviate the subsequent cardiorespiratory complications.

The main novelty of our proposed method is that unlike AHI and arousal indices which require recording of several signals, computation of our proposed SpO₂ measures is only dependent on one signal. Monitoring of SpO₂ offers a 3-fold advantage: 1) recording of SpO₂ is facile, cost-effective, automatic, and uninterrupted with minimal training of the patient or the caregiver, whether in the comfort of one's home or within a medical facility; 2) SpO₂ measures can be automatically extracted using the developed algorithms with minimal expert knowledge; 3) the algorithms can be embedded in pulse oximeter devices for automatic screening of patients. In particular, SpO₂ STD and SpO₂ ENT can be computed without a complex algorithm or expert knowledge. Thus, they can be used as simple alternatives to AHI in predicting postoperative respiratory depression.

The advantage of our SpO₂ processing technique is that it detects desaturation episodes automatically based on signal derivatives. This eliminates the need for manual annotations to identify event start and end points, thus broadening its applicability beyond respiratory events that strictly adhere to > 10 s duration criteria for apneas and hypopneas. Furthermore, our prediction algorithm incorporates major risk factors for respiratory depression, such as sex, BMI, and pre-existing cardiorespiratory disorders, in the model to enhance the model’s clinical relevance and effectiveness.

Sleep apnea syndrome is a major risk factor for postoperative respiratory depression. Our results showed that more than 74% of patients with postoperative respiratory depression had moderate to severe sleep apnea syndrome. Due to the limitations of lab-PSG, HSAT, and questionnaires, sleep apnea syndrome is highly undiagnosed or overestimated, which may misguide the pre- and postoperative care of patients. Previously, it has been shown that ODI, CT90 [19], and sleep apnea specific hypoxic burden (SSHB) defined as the area under the curve of desaturation episodes of apneas and hypopneas [20], are significantly correlated with AHI (r = 0.89, 0.60, 0.7, respectively). Our results showed that the correlation between AHI and SpO₂ STD, SpO₂ ENT, ODB AVG, ODB STD, and NDB were higher than CT90 and SSHB. While the correlation of ODI and AHI was higher, the SpO₂ measures extracted in this study were more predictive of postoperative respiratory depression (AUC-ROC: ≥ 0.79 for SpO₂ measures vs. 0.6 for ODI).

Our sex-based analysis showed that the prevalence of moderate to severe sleep apnea syndrome was higher and the severity was lower in women than men in patients with postoperative respiratory depression. Seventy percent of patients with postoperative respiratory depression were women among whom 63% had moderate to severe sleep apnea syndrome. Since the ventilatory responses and cardiovascular consequences of hypoxemia is stronger in women than men [21, 22], women with sleep apnea syndrome are at higher risk of respiratory depression. We observed that there was a trend for stronger correlation between the SpO₂ measures and AHI in women than men and stronger correlation between the SpO₂ measures and arousal indices in men, albeit these differences were not significant. Moreover, our results showed that the models with total arousal index and BAB had higher sensitivity in predicting postoperative respiratory depression in women.

One of the limitations of our study is that we studied a limited number of features and examined their predictive power of postoperative respiratory depression separately. Further studies are required to investigate other features from SpO₂ as well as a proper feature selection technique for the classification model. Moreover, it is important to note that in this study, only individuals without oxygen therapy or CPAP treatment were included in the analysis, as these interventions can significantly affect oxygen saturation levels. Recognizing that SpO₂ is not reliable in assessing hypoxemia and respiratory depression in these individuals, future studies should explore other monitoring modalities such as respiratory rate, end-tidal CO₂, or transcutaneous CO₂ modalities to assess changes in respiration and the risk of respiratory depression in these individuals.

Conclusion

Diagnosis and assessing the severity of sleep apnea syndrome is important in surgical patients for incorporating proper perioperative care to reduce the adverse outcomes. In this study, we proposed several measures of variations of preoperative overnight SpO₂ and burden of desaturation episodes, which were highly correlated with the severity of sleep apnea syndrome and can predict postoperative respiratory depression with high sensitivity and specificity. These measures provide unique insights into the respiratory health of surgical patients, enabling tailored perioperative management strategies to mitigate complications. Notably, measures such as standard deviation, entropy, and below average burden of preoperative overnight SpO₂, which require minimal computational resources, are favorable options for screening purposes. The developed algorithms facilitate automated SpO₂ data extraction, allowing seamless integration into pulse oximeters or smartwatches for simplified and effortless patient screening. The predictive algorithm empowers physicians to readily identify high-risk respiratory depression cases, optimizing perioperative care.

Methods

Participants

We analyzed data from 235 surgical patients retrospectively. Participants were adults of 18 years and older who were of American Society of Anesthesiologists physical status I–IV undergoing non-cardiac procedures at a tertiary hospital in Toronto [11, 23]. Data from 77 individuals were excluded for the following reasons: 1) being on chronic opioids, 2) missing data of demographics, comorbidities, SpO₂ recordings, or the severity of sleep apnea syndrome, 3) having oxygen therapy pre- or postoperatively or missing the information regarding oxygen therapy, 4) being on continuous positive airway pressure (CPAP) therapy pre- or postoperatively for sleep apnea syndrome or missing the information regarding CPAP therapy, 5) having SpO₂ recordings of less than an hour, or 6) having SpO₂ with more than 50% of signal being invalid (i.e. SpO₂ = 0). The study was approved by the Research Ethics Board of the University Health Network (IRB: #17-5495).

Measurements

Participants’ demographics (age, sex, body mass index [BMI]) and pre-existing cardiorespiratory comorbidities (arterial hypertension, coronary artery disease, stroke, angina, myocardial infarction, heart failure, coronary revascularization, asthma, and chronic obstructive pulmonary disease) were collected preoperatively. Participants underwent overnight sleep studies at home or in hospital preoperatively and on the third night after surgery [11, 23]. Sleep studies were performed using a HSAT (Embletta X100, Embla, Broomfield, CO), which included SpO₂ recordings with a sampling frequency of 3Hz and a sampling resolution of 1%. Sleep studies were scored by a certified sleep technologist according to the guideline of American Academy of Sleep Medicine (2007) [24]. Apnea was defined as a decrease in airflow signal by over 90% and a duration of more than 10 s. Hypopnea was defined as reduction in the airflow signal by more than 50% and a duration of more than 10 s which was associated with either more than 3% oxygen desaturation or an arousal from sleep. Moderate to severe sleep apnea syndrome was defined as AHI ≥ 15 events per hour (hr⁻¹) [25].

Data processing

The processing pipeline included signal processing, feature extraction, prediction model development, and statistical analysis. Python 3.7 and JMP Pro 16 were used for data processing and statistical analysis, respectively.

Signal processing: included 1) preprocessing the signals to remove the noises related to setting up or removing the device, movement, or sampling resolution, including excluding the first and last 15 min of overnight signals and applying a median filter (window = 10 s) [18], 2) detecting desaturation episodes with ≥ 3% drops in preoperative SpO₂ signals in 2 steps of finding the drops and the recovery phases [18], and 3) detecting respiratory depression episodes using a 85% threshold in postoperative SpO₂ signals [18]. A drop phase initiated upon the onset of SpO₂ decline, continuing till the minimum level. A recovery phase ensued as SpO₂ began to increase, lasting until SpO₂ returned to its initial level at the start of the desaturation. If desaturation episode did not recover to the SpO₂ level at the start of the drop, the end of the desaturation was set as the time of maximum SpO₂ within two minutes after the end of the drop.

Feature extraction: seven measures were extracted from preoperative SpO₂ signals (Table 1): entropy (SpO₂ ENT) and standard deviation (SpO₂ STD) of overnight SpO₂ signal; below average burden (BAB) which was defined as the area under the overnight average of SpO₂ divided by total recording time in seconds; average (ODB AVG), standard deviation (ODB STD), and entropy (ODB ENT) of normalized overnight desaturation burdens; and overall nocturnal desaturation burden (NDB). Desaturation burden was defined as the area under the curve of desaturation episodes with respect to the maximum SpO₂ level within 100 s before SpO₂ starts rising again. Normalization was performed by dividing the burden to the duration of desaturation episode in seconds. NDB was defined as the cumulative overnight desaturation burdens divided by the total recording time in seconds.

Prediction model development: for each extracted measure, a logistic regression model (regularization: L2, optimization: LBFGS) was trained on 80% of the data (training set) for predicting postoperative respiratory depression (binary classification). Validation set, comprising 20% of the data, was used to assess performance of the model. We selected logistic regression as our prediction model to enable comparison with previously proposed metrics [17].

To mitigate the challenges associated with imbalanced datasets, we incorporated techniques like stratified sampling, class weights, and using appropriate evaluation metrics, such as AUC-ROC, sensitivity, and specificity, rather than accuracy. The training and validation sets were selected based on a stratified randomization process to make sure that they are matched in terms of sex, BMI, and the ratio of the respiratory depression cases. Since the age of participants with and without respiratory depression was similar, age was not included in the stratification process and model development. Class weights were added to the model to address the dataset imbalance during training. As for evaluation metrics, AUC-ROC is the probability curve of sensitivity with respect to 1-specificity for different classification thresholds and it presents the ability of the classifier in distinguishing the classes. Sensitivity is calculated as $\frac{TP}{TP+FN}$ and specificity is calculated as $\frac{TN}{TN+FP}$. TP is true positive, FN is false negative, TN is true negative, and FP is the false positive, considering 0.5 as the classification threshold.

To assess the robustness, generalizability, and reproducibility of the model, this process was repeated 100 times, and the average performance was reported. All models included sex, BMI, and pre-existing cardiorespiratory conditions (arterial hypertension, coronary artery disease, stroke, angina, myocardial infarction, heart failure, coronary revascularization, asthma, chronic obstructive pulmonary disease (COPD)) to adjust for individuals’ demographics. We opted for 100 runs over traditional cross-validation due to the imbalance in the data and the challenges associated with maintaining the same distribution of both classes in cross-validation in all runs. Our approach ensures robust evaluation, considering the imbalanced nature of the dataset, and minimizes bias in model performance estimation.

Statistical analysis: to compare the characteristics of patients with and without postoperative respiratory depression or within sexes, t-test or Mann–Whitney U test were used for numerical variables based on normality test. Chi-squared test was used for categorical variables. Pearson’s correlation was employed to investigate the relationship between the SpO₂ measures and AHI, total arousal index, and respiratory-related arousal index. Correlations r  0.8, 0.6 ≤ r < 0.8, and 0.3 ≤ r < 0.6 are considered strong, moderate, and fair, respectively [26]. To investigate whether the correlations are significantly different between sexes, the 95% confidence interval of correlations were used. If the confidence intervals of correlations for men and women overlapped, the difference was assumed to be non-significant. Retrospective power analysis was performed and only the results where the statistical power was more than 70% were reported. p-value < 0.05 were considered statistically significant.