The compositional isotemporal substitution model: A method for estimating changes in a health outcome for reallocation of time between sleep, physical activity and sedentary behaviour.

How people use their time has been linked with their health. For example, spending more time being physically active is known to be beneficial for health, whereas long durations of sitting have been associated with unfavourable health outcomes. Accordingly, public health messages have advocated swapping strategies to promote the reallocation of time between parts of the time-use composition, such as "Move More, Sit Less", with the aim of achieving optimal distribution of time for health. However, the majority of research underpinning these public health messages has not considered daily time use as a composition, and has ignored the relative nature of time-use data. We present a way of applying compositional data analysis to estimate change in a health outcome when fixed durations of time are reallocated from one part of a particular time-use composition to another, while the remaining parts are kept constant, based on a multiple linear regression model on isometric log ratio coordinates. In an example, we examine the expected differences in Body Mass Index z-scores for reallocations of time between sleep, physical activity and sedentary behaviour.