Statistical analysis of actigraphy data with generalised additive models

There is a growing interest in the use of physical activity data in clinical studies, particularly in diseases that limit mobility in patients. High-frequency data collected with digital sensors are typically summarised into actigraphy features aggregated at epoch level (e.g., by minute). The statistical analysis of such volume of data is not straightforward. The general trend is to derive metrics, capturing specific aspects of physical activity, that condense (say) a week worth of data into a single numerical value. Here we propose to analyse the entire time-series data using Generalised Additive Models (GAMs). GAMs are semi-parametric models that allow inclusion of both parametric and non-parametric terms in the linear predictor. The latter are smooth terms (e.g., splines) and, in the context of actigraphy minute-by-minute data analysis, they can be used to assess daily patterns of physical activity. This in turn can be used to better understand changes over time in longitudinal studies as well as to compare treatment groups. We illustrate the application of GAMs in two clinical studies where actigraphy data was collected: a non-drug, single-arm study in patients with amyotrophic lateral sclerosis, and a physical-activity sub-study included in a phase 2b clinical trial in patients with chronic obstructive pulmonary disease.