Multiple imputation approaches for epoch-level accelerometer data in trials

Clinical trials that investigate physical activity interventions often use accelerometers to measure step count at a very granular level, for example in 5-second epochs. Participants typically wear the accelerometer for a week-long period at baseline, and for one or more week-long follow-up periods after the intervention. The data is aggregated to provide daily or weekly step counts for the primary analysis. Missing data are common as participants may not wear the device as per protocol. Approaches to handling missing data in the literature have defined missingness on the day level using a threshold on daily weartime, which leads to loss of information on the time of day when data are missing. We propose an approach to identifying and classifying missingness at the finer epoch-level and present two approaches to handling missingness using multiple imputation. Firstly, we present a parametric approach which accounts for the number of missing epochs per day. Secondly, we describe a non-parametric approach where missing periods during the day are replaced by donor data from the same person where possible, or data from a different person who is matched on demographic and physical activity-related variables. Our simulation studies show that the non-parametric approach leads to estimates of the effect of treatment that are least biased while maintaining small standard errors. We illustrate the application of these different multiple imputation strategies to the analysis of the 2017 PACE-UP trial. The proposed framework is likely to be applicable to other digital health outcomes and to other wearable devices.