## 3 Results
### The Effect of CBT-I, versus Control, on Subjective-Objective Discrepancy  
There was no significant group by time interaction on total sleep time SOSD (Figure 3; F(1, 135) = 0.156, \(p\) = 0.693). There were also no significant group by time interactions on sleep onset latency, wake after sleep onset, or sleep efficiency SOSD (all interaction \(p\geq\) 0.347). There was a significant main effect of time on total sleep time SOSD indicating that discrepancy reduced from baseline (M = \(-\)51.78, 95%CI = \(-\)66.29, \(-\)37.27) to 6-week  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Total** & **Control** & **CBT-I** & **_p_ \\  & _(\(n\) = 145)_ & _(\(n\) = 73)_ & _(\(n\) = 72)_ & \(p\) \\ \hline Age & 58.2 (9.9) & 57.3 (9.9) & 59.1 (9.9) & 0.279 \\ Sex, \% & 55.2\% male, & 54.8\% male, & 55.6\% male, & 0.927 \\  & 44.8\% female & 45.2\% female & 44.4\% female & * \\ BMI (kg\(\cdot\)m\({}^{-2}\)) & 35.1 (6.4) & 35.9 (6.6) & 34.4 (6.1) & 0.171 \\ AHI (events/h) & 34.5 (21.9) & 35.8 (23.9) & 33.2 (19.8) & 0.471 \\ Insomnia severity index & 18.2 (5.0) & 17.9 (4.7) & 18.5 (5.4) & 0.497 \\ Flinders fatigue scale & 15.9 (6.3) & 15.9 (5.8) & 16.0 (6.8) & 0.969 \\ Epworth sleepiness scale & 9.3 (4.8) & 9.7 (4.5) & 8.9 (5.0) & 0.335 \\ Daytime feelings and functioning scale & 17.4 (8.3) & 17.8 (8.5) & 16.9 (8.0) & 0.551 \\ DBAS & 59.4 (17.0) & 58.6 (15.4) & 60.3 (18.5) & 0.549 \\ Depression & 14.6 (12.1) & 14.6 (12.8) & 14.5 (11.4) & 0.959 \\ Anxiety & 9.6 (8.3) & 8.9 (7.9) & 10.2 (8.8) & 0.352 \\ Stress & 15.4 (9.6) & 15.6 (9.8) & 15.1 (9.5) & 0.792 \\ One-week diary & & & & \\ Total sleep time (min) & 348.4 (77.5) & 350.6 (9.5) & 346.2 (8.8) & 0.730 \\ Sleep onset latency (min) & 53.0 (42.9) & 49.6 (4.1) & 56.6 (5.9) & 0.326 \\ Wake after sleep onset (min) & 96.9 (66.5) & 99.3 (8.5) & 94.5 (7.1) & 0.665 \\ Sleep efficiency (\%) & 67.4 (13.4) & 68.0 (1.7) & 66.7 (1.5) & 0.582 \\ \hline \hline \end{tabular}  
* AHI, apnoea\(-\)hypopnoea index; BMI, body mass index; DBAS, dysfunctional beliefs and attitudes about sleep scale. *, Chi\({}^{2}\) test.  
\end{table}
Table 1: Baseline participant characteristics (M (SD); or \(n\) (%)).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Subjective** & **Objective** & **Cohen’s _d_** & \(p\) & **SOSD** \\ \hline Total sleep time (min) & 314.9 (98.0) & 366.7 (86.7) & 0.56 & \(<\) 0.001 & \(-\)51.9 (94.1) \\ Sleep onset latency (min) & 65.2 (80.7) & 30.1 (50.3) & 0.52 & \(<\) 0.001 & 34.5 (86.1) \\ Wake after sleep onset (min) & 91.8 (69.6) & 95.6 (57.1) & 0.06 & 0.524 & \(-\)4.2 (76.9) \\ Sleep efficiency (\%) & 64.9 (18.1) & 74.7 (13.0) & 0.62 & \(<\) 0.001 & \(-\)9.6 (18.3) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Baseline subjective and objective sleep parameters, and discrepancy (SOSD) for total sleep time, sleep onset latency, wake after sleep onset, and sleep efficiency.  
follow-up for both groups (M = -21.40, 95%CI = -36.15, -6.65; F(1,135) = 11.93, \(p\) = 0.001). There were also main effects of time on sleep onset latency SOSD and sleep efficiency SOSD, but not for wake after sleep onset SOSD. There was no significant main effect of group on total sleep time SOSD, indicating that total sleep time SOSD did not differ between the CBT-I group and the control group when collapsed over time (F(1, 135) = 1.98, \(p\) = 0.162). There were also no significant main effects of group on sleep onset latency SOSD, wake after sleep onset SOSD, or sleep efficiency SOSD (see Supplementary Materials).