## 3 Results  
We recruited 16 male participants 40-76 years of age. Table 1 shows the demographic and main characteristics of the participants. The data from the sleep instruments indicated that our sample had a mean insomnia severity index of 10.3, reflecting sub-clinical insomnia on average. Five participants reported difficulties falling asleep, while eight participants reported difficulties staying sleep and four participants reported waking up too early. The average Epworth sleepiness scale was normal, with a mean score of 8.2. Additionally, the average score of the Pittsburg sleep index was 5.4, reflecting poor sleep quality. Based on the items of the Pittsburgh sleep quality index four participants had difficulties falling asleep and 11 participants endorsed difficulties staying asleep or early awakening. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Continuous Variables**} \\ \hline  & **Mean** & **SD** & **Median** & **Range** \\ \hline Age, years & 59.7 & 9.4 & 60.8 & 43.9 & 76.59 \\ Years of education & 16.4 & 3.9 & 16.5 & 6.0 & 22.0 \\ Body mass index, kg/m\({}^{2}\) & 29.9 & 4.5 & 29.4 & 22.4 & 36.4 \\ Insonnia severity index & 10.3 & 4.7 & 8.0 & 6.0 & 19.0 \\ Epworth sleepiness scale & 8.2 & 5.9 & 8.0 & 0.0 & 23.0 \\ Pittsburgh sleep quality index & 5.4 & 4.8 & 3.5 & 1.0 & 17.0 \\ Depression score & 2.5 & 2.9 & 2.0 & 0.0 & 10.0 \\ Anxiety score & 29.3 & 5.9 & 28.5 & 21.0 & 42.0 \\ Apnea-hypopnea index & 52.6 & 28.2 & 53.4 & 15.7 & 119.0 \\ Average night-time oxygen saturation, \% & 91.4 & 6.9 & & & \\ Oxygen saturation nadir, \% & 75.1 & 11.4 & & & \\ Time with less than 90\% oxygen saturation, minutes & 32.9 & 35.6 & & & \\ \hline \multicolumn{6}{c}{**Categorical Variables**} \\ \hline Language & \% & - & - & - & - \\ English & 41\% & - & - & - & - \\ Spanish & 53\% & - & - & - & - \\ Hispanic background & 71\% & - & - & - & - \\ Hypertension & 59\% & - & - & - & - \\ Diabetes Mellitus & 24\% & - & - & - & - \\ Coffee, cups per day & & - & - & - & - \\ None & 18\% & - & - & - & - \\
1–2 cups & 65\% & - & - & - & - \\
3–5 cups & 12\% & - & - & - & - \\ Current tobacco & 6\% & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sample characteristics of treatment, naïve patients with moderate to severe sleep apnea. We observed a bivariate correlation between the insomnia severity index with the Epworth sleepiness scale, (r = 0.68, \(p\) = 0.0037), and with the average oxygen saturation (r = \(-\)0.53, \(p\) = 0.036). The insomnia severity index had a negative correlation with attention score (r = \(-\)0.66, \(p\) = 0.015), adjusting for education and multiple comparison. The insomnia severity index did not correlate with other cognitive domains. Of interest, the apnea-hypopnea index correlated with memory (r = \(-\)0.70, \(p\) = 0.01), while the Epworth sleepiness scale was negatively correlated with attention (r = \(-\)0.69, \(p\) = 0.02), adjusting for education and multiple comparisons. We also observed that average oxygen saturation during sleep had positive correlation with memory (r = 0.64), attention (r = 0.69) and global cognition (r = 0.57), but these were attenuated when adjusting for years of education. We also evaluated differences in verbal and visual memory subdomains and their relationships with the apnea-hypopnea index. We observed that visual memory had a statistically significant inverse correlation with apnea-hypopnea index (rho = \(-\)0.65, \(p\) < 0.01), but not with verbal memory functioning. The Pittsburgh sleep quality index did not correlate with the different cognitive domains. _Correlations between the Insomnia Severity Index and Sleep Variables with Brain Volumes_  
After adjusting for age and multiple comparisons, the insomnia severity index had negative correlations with the caudal anterior cingulate cortex (r = 0.31, \(p\) = 0.04) and the inferior parietal gyrus (r = \(-\)0.75, \(p\) = 0.01); while the Epworth sleepiness scale correlated with the lateral ventricles (r = 0.83, \(p\) = 0.002).