Analysing longitudinal wearable physical activity data using Non-stationary Time Series models

Background: Wearable devices have emerged as a new technology for monitoring physical activity over time. Conventional approaches to wearable physical activity data have tended to ignore temporal changes and, instead, have typically analysed summative measures and/or snapshots (e.g., averages over a specific period). In this report, we aimed to develop a novel statistical method to analyse longitudinal physical activity data accounting for the temporal structure in the data. Methods: This research used secondary data from the Multidimensional Individualised Physical Activity (MIPACT) randomized controlled trial. Physical activity data over the 12-week intervention for 80 participants (28 women) aged between 43 and 70 years old met the criteria for inclusion in this analysis. We modelled the temporal dynamic of each participant using a Trend Locally Stationary Wavelet model, and we introduced the Time in Reference Region of Variability (TIRRV) to assess individual changes relative to baseline. Results: The analysis of wearable physical activity data poses an important challenge for traditional statistical methods, which often fail to account for dependency between sequential data points and varying characteristics. In this work we demonstrate the effectiveness of a Trend Locally Stationary Wavelet model (TLSW) approach in analysing hourly resolution data from a 12-week intervention, enhancing the understanding of physical activity data, and providing meaningful insights at both individual and group levels. The TLSW considers the time dependency and structure of the data, enabling detailed trend and point-wise confidence intervals analysis. In addition to trends, the newly-developed TIRRV represents a baseline-informed metric to assess the success of individuals and groups over time. The application of these methods produce robust and readily understandable insights about the effect of interventions. Conclusions: The TLSW-based approach is a novel method for analysing physical activity collected using high-resolution wearable technology. The TLSW trends robustly characterize individual and group behaviour over extended periods of time. This novel approach enables researchers, clinicians, and patients to understand temporal changes in device-measured physical activity data in a way that was not possible previously.