Between 2006 and 2016, 1,115 children were recruited from the Louisville and Chicago areas. Children from Louisville were recruited through collaboration with public schools, and children in Chicago were recruited through community announcements and distribution of materials across the University of Chicago medical center. All children were between 5 and 10 years of age, and most had reported some form of sleep pathology. Demographic characteristics of the sample are outlined in Table 1. Some participants had missing information on one or more of the cognitive measures used, most often due to time constraints in assessments or data entry, and were, therefore, excluded in certain analyses. Resulting sample sizes for each model are indicated in the descriptions below. This study was carried out in accordance with the recommendations of University of Louisville and University of Chicago medical centers’ Institutional Review Boards, both of which approved all data collection and procedural elements of this research. Written informed consent from all children and/or their parents was obtained in accordance with the Declaration of Helsinki.

Behavioral measures were chosen to obtain a wide coverage of behavioral pathology using a small number of clinically validated measures. These included the Hyperactivity, Psychosomatic, and Inattention subscales of the Conners’ Parent Rating Scales-Revised [CPRS-R; (28)], and the Internalizing and Externalizing index scores of the child behavior checklist-revised [CBCL; (29)]. Both scales utilize parent ratings to determine the occurrence and severity of a variety of problematic behaviors and psychiatric concerns in children. The internalizing score from the CBCL is a partial summary score that combines subscale scores from items measuring withdrawn, somatic complaints, and anxious-depressed symptomology. Similarly, the CBCL externalizing score reflects aggression and conduct problems subscale scores.

Both the CBCL and CPRS-R have shown acceptable psychometric properties upon examination. Estimates of internal consistency are strong for all subscales of the CPRS-R [0.77–0.93; (28)] and the CBCL [0.71–0.89; (30)]. Since both scales were designed as screens for clinical use, a wealth of research has examined, and generally supported, their use at detecting a variety of childhood conditions involving emotional or behavioral problems, including autism, disruptive behavior disorders, and bipolar disorder [e.g., Ref. (31–34)]. A recent meta-analysis has also suggested moderately strong pooled sensitivity of 0.75 and 0.77 and specificity of 0.75 and 0.73 for the CPRS-R and CBCL, respectively, for detecting attention deficit hyperactivity disorder in children and adolescents (35).

Intellectual functioning was assessed by both verbal and non-verbal cluster scores on the Differential Ability Scale [DAS; (36)]. We also included individual subtest scores from both the NEPSY and the NEPSY-II (37) to capture potential deficits in a variety of neurocognitive domains, including attention/executive-functioning, language ability, and visuospatial processing. These included the design copying, phonological processing, speeded naming, arrows, and comprehension of instructions subtests from the NEPSY-II, as well as the visual attention and tower subtests from the original NEPSY.

Estimates of internal reliability for the DAS are over 0.70 for all subtests, and estimates of inter-rater reliability are greater than 0.90 (36). In addition, clinical utility of overall cluster scores has been demonstrated (38, 39), and DAS performance is moderately-to-strongly associated with other intellectual functioning measures, such as the Kaufman and Wechsler instruments (38). Research has also supported the overall psychometric properties of the NEPSY, with internal consistency and reliability estimates ranging from 0.79 to 0.91, and inter-rater reliability estimates above 0.97 (40, 41). Subtests also relate well with relevant subtests of other commonly utilized measures, such as Wechsler intelligence tests and the Delis–Kaplan executive functions system, and the utility of the NEPSY in identifying childhood cognitive functioning problems with various clinical samples across several domains has also been supported (41).

All children were assessed overnight through standard nocturnal polysomnogram (NPSG). Estimates for AHI were scored according to current American Association of Sleep Medicine guidelines by pediatric sleep experts, and refer to the number of sleep disruptions per hour of sleep. Scorers were blind to behavioral test results and, similarly, the developmental neuropsychologists performing the behavioral and cognitive battery assessments were unaware of the sleep study findings. Parent reports were utilized to obtain snoring information. Snoring status was reported by a parent as “never,” “rarely (once per week),” “occasionally (twice per week),” “frequently (three times per week),” and “almost always (more than four times per week)” as part of a validated and commonly used questionnaire that has demonstrated convergence with objective measures of snoring (25, 26, 42).

Mediation models were examined using behavioral problems as a mediator of the relationship between SDB and cognitive functioning (see Figure 1). We adjusted for age, sex, BMI, race, and asthma status in both the outcome and mediation models for all analyses, as all are commonly found to be associated with both SDB status and behavioral or cognitive functioning in children [e.g., Ref. (5, 43)]. Due to some skewness in cognitive and behavioral measures, a Box-Cox transformation was utilized for all measures (44). Initial exploration also indicated that relationships between SDB and both behavior and cognition overall domain scores were significant at p < 0.05.¹ To reflect empirical and clinical differences in the assessment of SDB and to determine whether differences in mediation exist based on changes in these characterizations, SDB status was dichotomized in two different ways in separate analyses. A description and explanation of each follows.

The first characterization of SDB compared SDB of any type (n = 871) to controls (n = 145). A child who snored “occasionally” or more frequently or had an AHI >1/h TST was determined to suffer from SDB. Although some debate exists regarding the use of the AHI of 1/h TST, this cut off is commonly used in research and clinical practice [e.g., Ref. (45)]. This characterization allowed for a comparison of control children who do not snore regularly with children who suffer from SDB and ignored any severity or classification variations within those who suffer from SDB, although AHI was incorporated into this categorization.

The second characterization defined SDB purely based on snoring status and attempted to compare children who snore regularly (n = 701) with those who do not (n = 194). Regular snoring was defined as “occasionally” or more frequent. AHI was ignored in this characterization, based on prior research that suggested that snoring status serves as a more effective predictor of cognitive and behavioral pathology (11). Furthermore, the correlation between snoring status and AHI was significant but not particularly strong in this sample (r_s = 0.24, p < 0.01), suggesting that this characterization could meaningfully differ from the first in identification of pathology and associations with outcomes.

Three analytic methods were utilized for mediation analysis to ensure robustness of the findings under slightly different procedures and identification assumptions. All three approaches attempted to test the theory that behavioral and psychiatric problems mediate the relationship between SDB and cognitive functioning problems. These mediation analytic methods are capable of assessing direct effects of SDB status on cognitive functioning, as well as indirect effects of SDB status on cognition through behavioral and psychiatric problems. Determining direct and indirect effects is typically accomplished through fitting two linear models. The first model predicts the outcome using an exposure or treatment variable, a mediator, and any relevant covariates. The second predicts the mediator using the exposure variable and any relevant covariates. Direct and indirect effects of an exposure variable on an outcome are traditionally estimated using coefficients obtained through these models, as discussed in reviews elsewhere [e.g., Ref. (46, 47)]. However, unlike typical SEM-based analyses, the resampling approach (RBM) and RMPW methods utilized here are also capable of assessing SDB-by-mediator interactions. Such interactions can determine whether any effect of behavioral pathology on cognitive functioning differs depending on child’s SDB status, which is both novel to this field and of potential interest in this analysis.

Our first analytic method utilized a traditional SEM-based approach to examine a latent behavioral problems variable as a mediator of the relationship between SDB and cognitive functioning. This approach involves assessing the potential structural relationships between both measured variables and latent variables. In our current work, cognition and behavior problems, which are assessed through various measurements, are hypothesized to comprise aspects of the underlying constructs they represent. This approach allowed for examination of direct and indirect effects of SDB on a latent cognition variable while assessing loadings of measured variables onto the latent behavior and cognition domains, as well as overall fit of the structural model. All five behavioral measures were included as measured variables for the latent behavioral problems domain, and all nine cognitive measures were included for the cognitive functioning domain. Full information maximum likelihood estimation (FIML) was utilized for SEM estimation due to the presence of some missing values.²

The second analytic method utilized a resampling-based mediation (RBM) approach introduced by Imai and colleagues (47–50). This approach generates linear models for the outcome and mediator as outlined above, followed by repeated simulations estimating potential values of both models and appropriate levels of statistical uncertainty through bootstrapping or Monte Carlo approximations. This is a flexible approach that easily extends to non-parametric estimation and sensitivity analysis. We utilized 100 simulations and determined SEs for significance testing using bootstrapping with at least 1,000 resamples for all mediation analyses using this approach. Additional benefits of this approach include the ability to examine SDB-by-mediator interactions and the existence of a readily available method of conducting sensitivity analyses using existing software.

Our third analytic mediation approach used RMPWs (51, 52). This involved first fitting propensity-score based inverse-probability-of-treatment weights in an attempt to balance the covariates noted above across SDB groups. Ratio-of-mediator-probability weights were then generated based on conditional probabilities of mediator values under alternative SDB conditions. Weighted analyses were next conducted for the mediator and outcome models to assess any direct or indirect effects of SDB, as well as SDB–mediator interaction. Due to some remaining imbalance in covariates across SDB groups, we further adjusted for age, sex, BMI, race, and asthma status in the outcome model that generated direct and indirect effects estimates. At least 1,000 bootstrapped samples were utilized to determine SEs for significance testing for all RMPW analyses. This new propensity score-based approach may rely on fewer model assumptions than the SEM or resampling approach (46).

Multiple methods were chosen for this analysis to ensure robustness of conclusions despite differing assumptions inherent to each analytic method described above [for review see Ref. (46)]. Both RBM and RMPW are based on the counterfactual (potential outcomes) framework for causal inference, which has been effectively described elsewhere [e.g., Ref. (46, 48, 53)]. To complete RBM and RMPW analyses, which unlike SEM do not traditionally utilize latent variables, factor scores were created to obtain individual scores for overall behavioral problems and overall cognitive functioning. These scores were created using maximum likelihood estimation (FIML), and included all five behavioral outcomes and nine cognitive outcomes.³ All SEM models utilized 1,097 participants due to the ability of FIML methods to accommodate missing data. Both RBM and RMPW analyses utilized sample sizes of 623 participants. All analyses were conducted using Stata version 14 and R statistical software.

Using an SDB cut-off value that compared children suffering from SDB (AHI >1 or snoring status at least occasional) with control children, indirect effects of SDB on cognitive functioning through behavior problems were significant (p < 0.01) though direct effects of SDB on cognition were not (p = 0.05; see Table 2). The same trend existed when characterizing SDB exclusively based on snoring status; the indirect effect of SDB through behavioral problems was significant (p < 0.01), but not the direct effect of SDB on cognition (p = 0.13). Both direct and indirect effects of SDB were negative, reflecting that children with SDB had lower overall cognitive functioning, though it appears that this effect is primarily mediated through behavior problems. Although the primary purpose for this analysis was examination of direct and indirect effects rather than construction of a comprehensive model of SDB effects, fit indices for the SEM model likely reflect adequate model fit (54, 55): snoring and AHI model: χ²(148) = 987.79, RMSEA = 0.07; snoring model: χ²(148) = 994.33, RMSEA = 0.07, though no modifications were made to the hypothesized model based on modification or fit indices.

When characterizing SDB based on both snoring and AHI, average direct effects of SDB on cognitive functioning were again non-significant (p = 0.30) though average indirect effects of SDB through behavioral problems were significant (p < 0.01; see Table 2). Characterizing SDB exclusively based on snoring status also yielded a significant average indirect effect of SDB through behavioral problems (p < 0.01), though again the direct effect of SDB on cognition was not statistically significant (p = 14). Both direct and indirect effects were negative, reflecting that children with SDB had lower overall cognitive functioning, though much like the findings observed in the SEM analysis, these effects appeared to be primarily mediated by behavioral problems. No evidence of SDB by behavior interaction effects existed for either characterization of SDB (ps > 0.05), suggesting that any effects of behavior problems on cognitive functioning did not differ based on the child SDB status.

Results using the RMPW approach were consistent with those reported using the SEM and RBM approaches. When characterizing SDB based on both snoring and AHI, the indirect effect of SDB on cognitive functioning through behavior was significant (p < 0.01) but the direct effect of SDB was not (p > 0.05). Similarly, when characterizing SDB exclusively relying on snoring status, the indirect effect of SDB through behavioral problems was significant (p < 0.01), but the direct effect of SDB on cognition was not (p > 0.05). As observed in the SEM and RBM approaches, both direct and indirect effects suggest that children with SDB had lower cognitive functioning. SDB by behavior interaction effects were again non-significant for both models (ps > 0.05), suggesting consistent effects of behavior on cognition across SDB status groups.

Causal interpretations of direct and indirect effects require that the sequential ignorability assumption for causal inference has been met. This assumption holds that, conditional measured covariates, the exposure and mediator variables can be viewed as randomized. This implies that no unmeasured confounding of the relationship between SDB and behavioral pathology, the relationship between behavioral pathology and cognitive functioning, or the relationship between SDB and cognitive functioning exists. This assumption is often very difficult to ascertain in observational and cross-sectional research studies, such that results regarding causation in such studies should always be interpreted with caution. To determine the plausibility of this assumption, sensitivity analyses were conducted for both characterizations of SDB using the procedure outlined by Imai and colleagues (48). This involved obtaining a sensitivity parameter (r) and determining the strength of a hypothesized unmeasured confounder or proportion of unexplained variance accounted for by said unmeasured confounders that would be needed to convert the average mediation effects to zero. Our results suggested that an unobserved confounder would need to account for approximately 3% of the overall variability in the mediator or outcome, or 4% of the unexplained variability, to fully negate our average mediation effect findings. Although such values cannot necessarily be interpreted in isolation, they likely indicate that the existence of a moderately strong unobserved confounder could potentially negate the effects observed here. Though this is certainly possible, it appears unlikely when considering that the combined effect of variables often cited as important, including age, sex, BMI z-score, race, and asthma status accounted for slightly under 3% of the total variance in behavioral functioning, and only race alone accounted for more than 2% of the variability in cognitive functioning.