Nonparametric Time Series Summary Statistics for High-Frequency Actigraphy Data from Individuals with Advanced Dementia

Actigraphy data has been widely used to measure activity and the circadian rhythm of individuals across the health sciences, in particular with people with advanced dementia. Modern actigraph devices can record continuous observations on a single individual for several months at a sampling frequency of the order of one hertz. Such rich and lengthy data sets provide new opportunities for statistical insight, but also pose challenges in selecting from a wide range of possible summary statistics, and how the calculation of such statistics should be optimally tuned and implemented. In this paper, we build on existing approaches, as well as propose new summary statistics, and detail how these should be implemented with high frequency actigraphy data. We test and validate our methods on an observed data set from 40 participants: 26 of which are from individuals with advanced dementia, and 14 of which are individuals without dementia. We study four metrics: Interdaily stability (IS), intradaily variability (IV), Hurst parameter estimation via detrended fluctuation analysis (DFA), and a novel nonparametric estimator which we call the proportion of variance (PoV), which calculates the strength of the circadian rhythm using spectral density estimation. We perform a detailed analysis indicating how the time series should be optimally subsampled to calculate IV, and recommend a subsampling rate of approximately 5 minutes. In addition, we propose the use of Hurst parameter estimation separately for daytime and nighttime, to further separate effects between individuals. We compare the relationships between all these methods and show that they effectively capture different features of the time series.