Figure 1
Data flow for one subject. Plot (a) shows weekdays ordered Monday through Friday from top to bottom, with the time of day indicated on the X and the height of the spike indicating the raw activity level on the Y axis. The plot (b) shows the activity averaged at each minute over the 5 days (black points) and the Fourier expansion representing this patient's circadian activity pattern (red solid line).
Figure 2
Smoothed activity of 8 subjects fitted by Fourier expansion and shown in separate plots with time recorded on the X axis, and activity level on the Y axis. The top 4 plots show the high apnea subjects and the bottom 4 plots show the low apnea subjects.
Figure 3
FLM result for 8 subjects. Plot (a) shows the 8 individual circadian activity patterns with blue and red line for high and low apnea groups, respectively. The overall mean circadian activity pattern is the solid black line and the mean circadian activity patterns for the high and low apnea groups are thick blue and red line, respectively. Plot (b) shows F-test result the red solid curve represents the observed statistic F(t) at each time point, the blue dashed and dotted lines correspond to a global and point-wise test of significance at significant level α = 0.05, respectively.
Table 1
Demographic information and sample characteristics
| Variable | N (%) Mean ± std (N Total 395) | |
|---|---|---|
| Female | 196(49.87%) | |
| Race | African-American | 134 (35.08%) |
| Caucasian | 237 (62.04%) | |
| Presenting Symptoms | Snoring | 279 (70.63%) |
| Gasping | 93 (23.54%) | |
| Morning headache | 67 (16.96%) | |
| RLS symptoms | 26 (6.58%) | |
| PLMS | 3 (0.76%) | |
| Witnessed apneas | 146 (36.96%) | |
| Insomnia | 42 (10.63%) | |
| Excessive day sleepiness | 91 (23.04%) | |
| Nonrestorative sleep | 9 (2.28%) | |
| Mallampati score | Class 4 | 145 (41.55%) |
| Class 3 | 136 (38.97%) | |
| Class 2 | 53 (15.19%) | |
| Class 1 | 15 (4.30%) | |
| Diagnosis Result | OSA | 292 (73.92%) |
| RLS | 5 (1.27%) | |
| Insomnia | 8 (2.03%) | |
| Hypersomnia | 20 (5.06%) | |
| BMI > 30 | 241 (60.86%) | |
| BMI | 34.66 ± 8.88 (Median = 34) | |
| Age(years) | 47.9 ± 14.8 | |
| apnea | 22.11 ± 28.11 (Median = 12.95) | |
Figure 4
Smoothed Activity for individuals as black solid curves and overall mean as red curves.
Table 2
Three Functional Linear Models
| Model 1 | apnea Main Effect Only | Activityk(t) = β0(t) + βAHI(t) × AHIk + εk(t) |
|---|---|---|
| Model 2 | BMI Main Effect Only | Activityk(t) = β0(t) + βBMI(t) × BMIk + εk(t) |
| Model 3 | apnea+BMI+interaction | Activityk(t) = β0(t) + βAHI(t) × AHIk + βBMI(t) × BMIk +βAHI × BMI (t) × AHIk × BMIk + εk(t) |
Figure 5
FLM result for apnea main effect model. Plot (a) is estimated activity patterns for two apnea groups and 95% confidence band. Plot (b) is F-test result for this model.
Figure 6
FLM result for BMI main effect model. Plot (a) is estimated activity patterns for two BMI groups and 95% confidence band. Plot (b) is F-test result for this model.
Table 3
Sample size for apnea, BMI mode
| apnea Low (< 10.75) | apnea High (> = 10.75) | Total | |
|---|---|---|---|
| BMI > = 30 | 61 | 94 | 155 |
| BMI < 30 | 55 | 22 | 77 |
| Total | 116 | 116 | 232 |
Figure 7
FLM result for apnea and BMI model. Plot (a) is estimated activity patterns for the four groups and 95% confidence band. Plot (b) is F-test result for this model.
Figure 8
FLM result for BMI model treating BMI as continuous. Plot (a) is estimated activity patters for BMI groups. Plot (b) is F-test result for this model.