This retrospective analysis is based on data collected in the context of two prior studies. The Sleep Analysis of Depressive Burden (SADB) study (ClinicalTrials.gov Identifier: NCT04232267) and the Sleep Signal Analysis for Current Major Depressive Episode (SAMDE) study (ClinicalTrials.gov Identifier: NCT05708222) are both cross-sectional, naturalistic, single-arm, multicenter trials sponsored by Medibio Ltd (Minnesota, USA). Participant recruitment for SADB occurred from December 2019 to February 2022 across multiple U.S. sites, including sleep clinics in Ohio and Minnesota, while SAMDE recruitment took place from June 2023 to July 2024 across additional sites in Texas, North Carolina, South Carolina, Florida, Minnesota, and Ohio. Inclusion criteria encompassed adults aged 18–75 (SADB) and 22–75 (SAMDE), able to provide informed consent and adhere to study procedures. Exclusion criteria differed slightly, with SADB excluding active substance abuse and SAMDE excluding pacemaker recipients, heart transplant patients, and those undergoing CPAP titration studies. Psychotropic medication use was permitted to enhance sample representativeness. Preliminary findings on depression prevalence in both cohorts have been reported in earlier publications (Daccò et al., 2023, 2025).

Both SADB and SAMDE studies adopted a harmonized protocol to ensure data comparability across sites and studies. Upon enrollment, participants completed self-administered forms capturing demographic and clinical variables, followed by the PHQ-9 to assess depressive symptom severity. Additionally, SAMDE participants completed a fully structured diagnostic interview using the Mini International Neuropsychiatric Interview for major depressive episode diagnosis (Sheehan et al., 1998).

PSG recordings in both studies adhered strictly to AASM guidelines (American Academy of Sleep Medicine, 2023), utilizing identical EEG derivations including six recommended channels (F4-A1, C4-A1, O2-A1) and backup channels (F3-A2, C3-A2, O1-A2). These standardized recording protocols and sleep staging criteria were applied uniformly, enabling reliable pooling and comparative analyses of sleep variables relevant to depressive burden.

Collected covariates included age, sex, medical history, comorbidities, and current medications, allowing control for confounding factors during analyses. The consistent methodology across multiple U.S. clinical sites—including those overlapping between SADB and SAMDE in Minnesota and Ohio—facilitated robust, generalizable insights into the relationship between sleep characteristics and depression.

The PHQ-9 (Kroenke and Spitzer, 2002; Kroenke et al., 2001) is a validated 9-item self-report questionnaire widely used in depression assessment (Maurer et al., 2018). Its 9 items align with the 9 DSM-5 criteria for a Major Depressive Episode (American Psychiatric Association, 2022). Item response options for each item range from “not at all” (score of 0) to “several days” (score of 1), “more than half the days” (score of 2), and “nearly every day” (score of 3), reflecting how often each symptom has bothered the respondent over the past 2 weeks. The PHQ-9 total score for the nine items ranges from 0 to 27. The scores 5, 10, 15, and 20 represent the cutoffs for mild, moderate, moderately severe, and severe depression symptoms, respectively.

A cutoff of 10 or greater is a widely used threshold to screen for current Major Depressive Episode (cMDE). A recent and comprehensive Individual Participant Data Meta-analysis (Negeri et al., 2021), including approximately 44,500 participants, evaluated the accuracy of PHQ-9 to detect a cMDE through comparisons with the reference standard. Compared to reference standards, sensitivity and specificity for a cut-off of ≥ 10 ranged from 0.67 to 0.88 and from 0.86 to 0.88, respectively. Specifically, compared to semi-structured psychiatric diagnostic interviews, sensitivity and specificity for a cutoff of ≥ 10 (95% CI) were 0.88 (0.82–0.92) and 0.86 (0.82–0.88). For fully structured interviews, sensitivity and specificity ranged from 0.67 (0.57–0.76) to 0.75 (0.66–0.82), and from 0.86 (0.80–0.90) to 0.88 (0.84–0.91). Overall, PHQ-9 demonstrated satisfactory accuracy in depressive episode detection. Consistently, a score of ≥ 10 has been associated with an increased risk of major depression more than 2.6 times (Kroenke et al., 2001). Overall, based on the large body of scientific evidence concerning PHQ-9, this cutoff threshold (≥ 10) approach is advised as the most reliable for screening use in clinical practice and clinical trials (He et al., 2020).

Sleep staging was performed using an automated system implemented via the STAGER software (Medibio Limited, Savage, MN, USA). This tool processes polysomnographic recordings stored in EDF format by focusing on EEG signals from six pre-selected channels. The recordings are first segmented into 30-s epochs, during which a detailed spectral analysis is performed to compute absolute and relative power values across key frequency bands. These features are then input into a pipeline of machine learning and deep learning algorithms. Initially, a convolutional neural network and gradient-boosting machine learning algorithms are used, followed by two additional temporal-aware models, such as recurrent neural networks. An ensemble method integrates the outputs from these classifiers to assign each epoch to one of the five standard sleep stages (wake, N1, N2, N3, and REM) in accordance with the American Academy of Sleep Medicine (AASM) guidelines (American Academy of Sleep Medicine, 2023). Prior to analysis, the software requires the entry of lights-off and lights-on times to accurately delineate the sleep period. The performance of STAGER has been validated in a recent study (Grassi et al., 2023). In 40 clinical PSGs, STAGER's automatic staging achieved an overall percentage agreement of 83.8% (95 % CI = 82.3%−85%) vs. the majority vote of three AASM-certified technicians, with a Cohen's κ of 0.78 (substantial agreement). Stage-specific positive-percent-agreement was 90.7% for REM, 89.7% for N2, 87.3% for N3, 81.6% for Wake, and 51% for N1; except for a modest drop in Wake sensitivity, these values were statistically comparable to or higher than those obtained by individual human scorers.

The odds ratio product (ORP) is a continuous metric that quantifies sleep depth and wake propensity on a scale from 0 (indicative of very deep sleep) to 2.5 (reflecting full wakefulness). Unlike conventional sleep staging, which classifies sleep in discrete 30-s epochs, ORP is computed every 3 s from EEG recordings, allowing for a much more refined temporal resolution of sleep dynamics (Younes, 2023). In brief, the method initially applies a fast Fourier transform to brain wave bands from 0.33 Hz to 60 Hz in non-overlapping 3-s epochs. Then, the power across four frequency bands (Alpha 7.3–14.0 Hz, Beta 14.3–35.0 Hz, Delta 0.3–2.3 Hz, and Theta 2.7–6.3 Hz) is evaluated. For each band, the power is ranked into deciles based on a normative dataset derived from a broad array of clinical polysomnograms. These decile scores are then concatenated to form a unique four-digit “bin” number for each epoch. A lookup table, constructed from the frequency of these patterns during wake and arousal, converts the bin number into a probability that is normalized (by dividing by 40) to yield an ORP value between 0 and 2.5.

This continuous measure enables the detection of subtle transitions between sleep and wake states that are not discernible with traditional, categorical staging. In addition, because ORP captures variations in sleep depth within the same conventional stage, it provides an enriched depiction of the sleep architecture. For example, a strong association between ORP values and the probability of spontaneous arousal in the subsequent epoch has been found, underscoring its validity as a sensitive indicator of sleep stability and depth (Younes et al., 2015). ORP can be graphically displayed as an epoch-by-epoch trace across the night, or summarized as average values within traditional sleep stages, and even as the percentage of total recording time spent in defined ORP ranges. These features offer significant advantages, particularly in clinical research, where they can help identify subtle sleep abnormalities that may underlie various sleep disorders or predict therapeutic outcomes.

In our study, the ORP value was computed for each non-overlapping 3-s epoch throughout the entire polysomnographic recording, from lights-off to lights-on, using the central EEG channels (C4-A1 and C3-A2) among the six channels recommended by the AASM guidelines (Younes, 2023). These computations were performed via the API provided by Cerebra Medical LTD. (Winnipeg, CA).

For the entire polysomnographic recording, the mean ORP and its standard deviation were computed and used in the statistical analyses. Additionally, the mean and standard deviation of ORP for each sleep stage (Wake, N1 + N2, N3, and REM) were also calculated and incorporated into the analyses. N1 has been incorporated into N2 (sometimes collectively referred to as light sleep). Algorithmically, despite merging N1 and N2, the STAGER software can differentiate each stage by identifying the presence of spindle bands and K-complex.

Epochs in which the Cerebra API identified problems in the EEG signal (e.g., artifacts, noise, lack of signal) that prevented a correct ORP calculation, as well epochs the STAGER software staged as non-classified (U) for similar problems in the EEG signal, were excluded from the analysis.

We conducted statistical analyses to assess the associations between the mean and standard deviation of ORP during the whole PSG and two depression outcome measures: the total PHQ-9 score (continuous variable), and a dichotomized PHQ-9 score based on the conventional cut-off of 10 (that is, ≥10). We applied linear regression for the continuous PHQ-9 score and logistic regression for the PHQ-9 cut-off of 10.

To account for potential non-linear relationships, both linear and quadratic terms for the ORP variables were included in the analyses. Age and sex were included as covariates in all models to adjust for potential confounding effects and isolate the residual association between ORP and depression measures. The independent variables were mean-centered prior to model fitting, and quadratic terms were computed after centering. This approach reduces multicollinearity between the linear and quadratic terms and enhances the interpretability of regression coefficients of the ORP variables.

If a subject never exhibited a particular sleep stage or if EEG signal problems during certain epochs made it impossible to calculate the ORP, then the ORP variables for that sleep stage were deemed uncalculable for that individual. Consequently, these instances were excluded from the analysis of the ORP variable for those epochs. As a result, the overall number of epochs for certain sleep stages may be smaller than the total sample size used in the analysis of the entire PSG.

Data were collected from multiple sleep centers, each of which potentially differed in equipment, protocols, and patient characteristics. Therefore, we evaluated both fixed-effects and mixed-effects models to determine if center-related variability should be incorporated into our analyses. To this end, we developed a grouping variable by aggregating centers based on their state location and management by the same organization, as centers under the same organization typically followed similar protocols and utilized the same PSG system. One exception was a Texas center (TX) where a subset of PSG recordings was performed using an alternative system; these recordings were assigned a distinct level within the grouping variable (TA). Because both SADB and SAMDE employed naturalistic recruitment and shared similar protocols, the study of origin was not treated as a separate factor in this grouping.

For each independent-dependent variable combination, we evaluated four model structures: 1) Fixed-effects model (no random effects); 2) Mixed-effects model with a random intercept; 3) Mixed-effects model with a random intercept and a random slope for the independent variable; 4) Mixed-effects model with random effects for the intercept, independent variable, and covariates. All mixed-effects models were initially fitted using Maximum Likelihood (ML) to ensure comparability between models, including the fixed-effects model. For mixed-effects models with more than one random effect (models 3 and 4), we tested three different covariance structures for the random effects: independent, diagonal, and full covariance matrix. Model selection was guided by the Akaike Information Criterion (AIC), which balances model complexity against goodness-of-fit by penalizing unnecessary parameters. The model with the lowest AIC was considered the most parsimonious and best-fitting for each independent-dependent variable pairing. If a mixed-effects model was selected as the best model, it was refitted using Restricted Maximum Likelihood (REML) to obtain more accurate estimates of variance components.

To assess the association between each ORP independent variable and the total PHQ-9 score (linear regression), statistical significance was evaluated using the t-test for the regression coefficient. The regression coefficient itself was used to quantify the direction of the association, while the standardized regression coefficient (β coefficient) was computed to facilitate the interpretation of the magnitude of the effect. We also quantified the additional variance explained by the ORP terms as the change in the coefficient of determination (ΔR²), calculated by subtracting the R² of the covariate-only model from the R² of the full model that included both covariates and the two ORP terms (ΔR² = R²_full – R²_covariates).

For the association between each ORP independent variable and the PHQ-9 cut-off 10 outcomes (logistic regression), statistical significance was assessed using the z-test for the regression coefficient. Also in this analysis, the regression coefficient itself was used to quantify the direction of the association, while the standardized regression coefficient (β coefficient) was computed to facilitate the interpretation of the magnitude of the effect. We also assessed the gain in discriminative ability by computing the change in the area under the receiver-operating characteristic curve (ΔAUC), defined as the difference between the AUC of the full model (covariates + ORP terms) and that of the covariate-only model.

All statistical analyses were performed using Python (version 3.12.1; Python Software Foundation, 2024). Statistical significance was set at α = 0.05.

Of the 864 PSG initially available for this study, 829 were finally included in the analysis (292 from the SADB study, 232 from the SAMDE Phase 1 study, and 305 from the SAMDE Phase 2 study; Figure 1). Thirty-two were excluded from the analysis because the Sex was not provided by the subject (29 from the SAMDE Phase 1 study) or was indicated by the subjects as “other” (2 from the SAMDE Phase 2 study and 1 from the SAMDE Phase 1 study). Moreover, three additional subjects were excluded because age was missing (2 from the SADB study and 1 from the SAMDE Phase 1 study). Descriptive statistics for the entire sample are summarized in Table 1.

Participants were grouped into seven distinct groups based on their recruitment centers, which have been used in the random-effect models: Minnesota (MN) with 262 subjects, South Carolina (SC) with 202 subjects, Texas (TX) with 121 subjects, North Carolina (NC) with 113 subjects, Ohio (OH) with 107 subjects, the alternative PSG machine in Texas (TA) with 14 subjects, and Florida (FL) with 10 subjects. Descriptive statistics stratified by recruitment center are summarized in Supplementary Tables S2 and S3 in the Supplementary materials.

Descriptive statistics for the entire sample and stratified by recruitment center are summarized in Table 1.

To assess the appropriateness of including age and sex as covariates, we first examined their association with depressive symptoms. In all models tested—including linear regression models using the PHQ-9 total score as the dependent variable and logistic regression models using a dichotomized PHQ-9 cutoff of 10—both age and sex were significantly associated with depression outcomes (all p-values < 0.001). Age was negatively associated with depressive symptoms, indicating a decrease in symptom severity with increasing age. Furthermore, female participants exhibited higher levels of depressive symptoms compared to males. Full results are available in the Supplementary materials (Supplementary Tables S4–S9).

The analysis examined the associations between the mean and standard deviation of ORP during the whole PSG and depression severity, as measured by the PHQ-9 total score (linear regression) and the dichotomized PHQ-9 based on a conventional cut-off score of 10 (logistic regression). Linear regression models were applied to the continuous PHQ-9 score, while logistic regression models were used for the dichotomized PHQ-9 outcome.

For all analyses, model selection based on the Akaike Information Criterion (AIC) consistently favored the fixed-effects model over the mixed-effects alternatives. Despite data being collected from multiple sleep centers, the variability between centers did not seem to substantially influence the associations between ORP and PHQ-9 outcomes. The lack of a significant center effect indicates that the relationships observed are robust across different clinical settings and are unlikely to be driven by site-specific differences in equipment, protocols, or patient populations. Complete results, including the AIC values for all models, are provided in the Supplementary materials (Supplementary Tables S6 and S7).

For the linear regression models, the mean ORP during the whole PSG (from light-off to lights-on) showed no significant linear association with PHQ-9 total scores (β = 0.022, p = 0.521). However, a significant positive quadratic relationship was detected (β_quadratic = 0.078, p = 0.001), suggesting that the relationship follows a U-shaped or convex pattern (Figure 2). Since the variables were mean-centered, this indicates that individuals with either higher (shallower sleep) or lower (deeper sleep) mean ORP values across the night were more likely to experience higher depression scores than individuals with average mean ORP values during the whole PSG.

When considering specific sleep stages, mean ORP during N1 + N2 also exhibited a non-significant linear relationship (β = 0.016, p = 0.625), but a positive significant quadratic effect was present (β_quadratic = 0.073, p = 0.003) that indicates a similar U-shaped relationship as observed above. Instead, the mean ORP in N3 showed a significant positive linear association with PHQ-9 scores (β = 0.12, p = 0.004), but no significant quadratic relationship (β_quadratic = 0.0, p = 0.991), signifying that as the mean ORP in N3 increases indicating shallower sleep in N3, individuals are expected to have higher PHQ-9 total scores (Figure 3). These findings suggest that ORP levels in N3 sleep might follow a more straightforward linear association with depression severity, whereas the relationship follows a quadratic trajectory for N1 + N2 and overall sleep stages. Finally, no significant association resulted for the mean ORP during the REM stage and during Wake epochs with the PHQ-9 total score.

All significant associations in the linear regression models could be interpreted as of small magnitude based on the conventional effect size interpretations that consider a β of 0.1 as indicative of a small effect (Cohen, 1988).

For the logistic regression models, in which a dichotomized PHQ-9 total score as above or below the threshold of 10 was used as the dependent variable, mean ORP during the whole PSG did not exhibit a significant linear relationship with increased depression risk (β = 0.042, p = 0.589), though a significant positive quadratic association was observed (β_quadratic = 0.248, p = 0.001), indicating a potential U-shaped relationship. This indicates that individuals with either higher or lower mean ORP values are at a higher risk of having a PHQ-9 total score above the threshold of 10 than individuals with average mean ORP values during the whole PSG.

Similarly, for N1+N2, the linear effect was non-significant (β = 0.02, p = 0.793), whereas a significant positive quadratic effect was found (βquadratic = 0.233, p = 0.002) that indicates a U-shaped relationship as observed above. In contrast, mean ORP in N3 showed a significant linear association with higher odds of having PHQ-9 scores above 10 (β = 0.255, p = 0.020), but the quadratic term was not significant (βquadratic = 0.041, p = 0.668).

All significant associations in the logistic regression models could be interpreted as having a small magnitude based on conventional standards, as a β below 0.3 is usually indicative of a small effect (Cohen, 1988).

These results highlight a complex relationship between mean ORP and PHQ-9. While ORP in deep sleep (N3) shows a more direct association with depression scores, ORP in lighter sleep stages (N1 + N2) and during the whole PSG exhibits non-linear, U-shaped patterns. Complete results are reported in Tables 2, 3.

For the standard deviation of ORP, the results were more nuanced. For the linear regression models, the standard deviation of ORP during the whole PSG exhibited a significant negative linear association with PHQ-9 total score (β = −0.104, p = 0.002), indicating that lower variability in ORP during the whole PSG was associated with higher depression severity. However, no significant quadratic relationship was found (β_quadratic = −0.019, p = 0.422). When examining specific sleep stages, the standard deviation of ORP in N1 + N2 showed no significant linear (β = −0.031, p = 0.380) or quadratic (β_quadratic = −0.022, p = 0.393) association with PHQ-9 total score. In contrast, the standard deviation of ORP in N3 displayed a significant positive linear association with PHQ-9 total score (b = 0.095, p = 0.020), indicating that lower variability in ORP during N3 was associated with lower depression. No quadratic relationship was found (β_quadratic = −0.001, p = 0.949). Finally, no significant association resulted for the standard deviation of ORP during the REM stage and during Wake epochs with PHQ-9 total score.

As for mean ORP, all significant associations in the linear regression models for the standard deviation of ORP could be interpreted as of small magnitude based on the conventional effect size interpretations that consider a b of 0.1 as indicative of a small effect (Cohen, 1988).

For the logistic regression models, a significant negative linear association of small magnitude (Cohen, 1988) was observed with the standard deviation of ORP during the whole PSG (β = −0.227, p = 0.005), indicating that higher variability in ORP was associated with a lower likelihood of depression scores above 10. However, no quadratic association was found (β_quadratic = −0.077, p = 0.333). For N1 + N2, N3, REM, and Wake, no significant associations were found for either the linear or quadratic terms.

These findings underscore a nuanced association between the variability of ORP and depression. Specifically, the standard deviation of ORP during the whole PSG was significantly and negatively associated with PHQ-9 scores in linear regression models, suggesting that greater overall variability is linked to lower depression severity, albeit with a small effect size. In contrast, variability during deep sleep (N3) showed a trend toward a positive association with depression, while no significant associations emerged in lighter sleep stages (N1 + N2), REM, or Wake periods, and no quadratic effects were observed in any model. Consistent with these findings, logistic regression revealed a significant negative linear association during the whole PSG. Complete results are reported in Tables 2, 3.