Joint regression modelling of intensity and timing of accelerometer counts

Accelerometers are commonly used in human medical and public health research to measure physical movement, which is relevant in a wide range of studies, from physical activity and sleep behaviours studies, to identification of movement patterns in people affected by diseases of the locomotor system and prediction of risk of injury in high performance sports. The accelerometer output provides the intensity (activity count) and timing (timestamp) of the movement, which can be used to define bouts of activity (periods of sustained movement of a given intensity). In some contexts, it may be important to include both dimensions to obtain a broader and deeper understanding of the phenomenon under study. Such is the case of a large-scale epidemiological investigation on the daily and weekly physical activity behaviours of school-aged children enrolled in the UK Millennium Cohort Study, which has motivated the present article. I present a statistical approach to joint modelling of intensity and timing of activity bouts that takes advantage of the circular nature of the timing. The model, which accounts for the longitudinal structure of the observations, is remarkably simple to implement using standard statistical software.