Estimating Physical Activity in 7-year-old British School Children: A Statistical Approach to Modelling Accelerometer Data Using Functional Analysis of Variance

Background Accelerometers measure levels of physical activity (PA) objectively, and they are being increasingly used to obtain information on PA in children.

Functional Data Analysis (FDA) is a statistical method that can be used to better characterise continuous activity patterns and their variation over time.

The objective of this study is to evaluate the potential of FDA to model daily and seasonal trajectories of accelerometer-based PA measurements.

Methods Between May 2008 and August 2009 seven-year old children participating in the longitudinal Millennium Cohort Study were asked to wear an Actigraph GT1M accelerometer for seven consecutive days during waking hours. We analysed data of 6,247 children with at least one observed day, contributing 21,927 daily minute-by-minute PA profiles. We used the R package fda to fit Functional Analysis of Variance (FANOVA) models in order to analyse the effects of day of the week, weekend and season on the functional response consisting of accelerometer trajectories modelled through smoothing splines.

Results FANOVA provided evidence of temporal patterns in PA. During weekdays, PA levels peaked around 10:50, 13:00, 14:30 and 15:30. Also, overall PA levels in weekends were higher as compared to weekdays between 9:00 and 15:30. The highest peaks of PA were observed during spring, while the lowest levels were observed during winter, especially after 15:30.

Conclusions Functional models enable temporal trajectories obtained through accelerometers to be characterised and analysed in large population-based datasets of PA measurements. This approach can be extended to analyse factors operating at child, family and broader social and environmental levels.