Measuring the impact of apnea and obesity on circadian activity patterns using functional linear modeling of actigraphy data

Abstract

Background: Actigraphy provides a way to objectively measure activity in human subjects. This paper describes a novel family of statistical methods that can be used to analyze this data in a more comprehensive way.

Methods: A statistical method for testing differences in activity patterns measured by actigraphy across subgroups using functional data analysis is described. For illustration this method is used to statistically assess the impact of apnea-hypopnea index (apnea) and body mass index (BMI) on circadian activity patterns measured using actigraphy in 395 participants from 18 to 80 years old, referred to the Washington University Sleep Medicine Center for general sleep medicine care. Mathematical descriptions of the methods and results from their application to real data are presented.

Results: Activity patterns were recorded by an Actical device (Philips Respironics Inc.) every minute for at least seven days. Functional linear modeling was used to detect the association between circadian activity patterns and apnea and BMI. Results indicate that participants in high apnea group have statistically lower activity during the day, and that BMI in our study population does not significantly impact circadian patterns.

Conclusions: Compared with analysis using summary measures (e.g., average activity over 24 hours, total sleep time), Functional Data Analysis (FDA) is a novel statistical framework that more efficiently analyzes information from actigraphy data. FDA has the potential to reposition the focus of actigraphy data from general sleep assessment to rigorous analyses of circadian activity rhythms.

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.

Figure 4

Smoothed Activity for individuals as black solid curves and overall mean as red curves.

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.

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.