Using functional principal component analysis (FPCA) to quantify sitting patterns derived from wearable sensors

Abstract

Background: Sedentary behavior (SB) is a recognized risk factor for many chronic diseases. ActiGraph and activPAL are two commonly used wearable accelerometers in SB research. The former measures body movement and the latter measures body posture. The goal of the current study is to quantify the pattern and variation of movement (by ActiGraph activity counts) during activPAL-identified sitting events, and examine associations between patterns and health-related outcomes, such as systolic and diastolic blood pressure (SBP and DBP).

Methods: The current study included 314 overweight postmenopausal women, who were instructed to wear an activPAL (at thigh) and ActiGraph (at waist) simultaneously for 24 hours a day for a week under free-living conditions. ActiGraph and activPAL data were processed to obtain minute-level time-series outputs. Multilevel functional principal component analysis (MFPCA) was applied to minute-level ActiGraph activity counts within activPAL-identified sitting bouts to investigate variation in movement while sitting across subjects and days. The multilevel approach accounted for the nesting of days within subjects.

Results: At least 90% of the overall variation of activity counts was explained by two subject-level principal components (PC) and six day-level PCs, hence dramatically reducing the dimensions from the original minute-level scale. The first subject-level PC captured patterns of fluctuation in movement during sitting, whereas the second subject-level PC delineated variation in movement during different lengths of sitting bouts: shorter (< 30 minutes), medium (30 -39 minutes) or longer (> 39 minute). The first subject-level PC scores showed positive association with DBP (standardized $\hat{\beta }$ : 2.041, standard error: 0.607, adjusted p = 0.007), which implied that lower activity counts (during sitting) were associated with higher DBP.

Conclusion: In this work we implemented MFPCA to identify variation in movement patterns during sitting bouts, and showed that these patterns were associated with cardiovascular health. Unlike existing methods, MFPCA does not require pre-specified cut-points to define activity intensity, and thus offers a novel powerful statistical tool to elucidate variation in SB patterns and health.

Trial registration: ClinicalTrials.gov NCT03473145; Registered 22 March 2018; https://clinicaltrials.gov/ct2/show/NCT03473145 ; International Registered Report Identifier (IRRID): DERR1-10.2196/28684.

Keywords: Accelerometer; Functional Principal Component Analysis (FPCA); Multilevel FPCA; Sedentary Behavior (SB).

Fig. 1

Example of one participant’s profile for one day of VM counts/minute within ordered sitting bouts. Vertical grey lines indicated all possible sitting bout lengths from 1 minute to 60 minutes. The corresponding horizontal axis at bottom was the cumulative sum of the top bout lengths and the maximum value of the bottom axis was ${\sum }_{b=1}^{60}b=1830$ minutes, which implied $t\in [1,1830]$ with increment of 1 minute. t = 1 at the bottom was mapping to 1-minute sitting bout at the top; t = 2 and 3 at bottom were mapping to the first minute and second minute of the 2-minute sitting bout at the top; t = 4 to 6 at the bottom would be the 3-minute bout at the top, etc. If the top bout length was 8 minutes, the corresponding bottom values would span from ${\sum }_{b=1}^{7}b=28$ to ${\sum }_{b=1}^{8}b=36$; if the top bout length was 60 minutes, the bottom values would span from ${\sum }_{b=1}^{59}b=1770$ to 1830. Each minute of the bottom axis held a VM count value or a missing value. Black dots represent VM counts/minute within sitting bouts

Fig. 2

Histogram of sitting bouts from 1 minute to 60 minutes among all participant-days (1776)

Fig. 3

Participant-level eigenfunctions (top) and mean function $\mu (t)$ (red) with addition (blue) or subtraction (green) of square root of two eigenvalues multiplying corresponding eigenfunctions (bottom)

Fig. 4

Example fitting profiles in different participants on different days of MFPCA curves tracing the observed VM counts/minute (black dots) within sitting bouts by adding one element at a time based on model Eq. 1: 1. $\mu (t)$; 2. $\mu (t)+{\eta }_j(t)$; 3. $\mu (t)+{\eta }_j(t)+{\sum }_{k=1}^2{\xi }_{\mathit{ik}}{\varphi }_k^{(1)}(t)$; 4. $\mu (t)+{\eta }_j(t)+{\sum }_{k=1}^2{\xi }_{\mathit{ik}}{\varphi }_k^{(1)}(t)+{\sum }_{l=1}^6{\zeta }_{\mathit{ijl}}{\varphi }_l^{(2)}(t)$. a was the same participant-day from Fig. 1 where a majority of VM counts were below 1000 cpm with notable size of those close to 0; b was a different participant on a different day where a large number of VM counts were still above 1000 cpm and fewer VM counts were close to 0