Measuring Variability in Rest-Activity Rhythms from Actigraphy with Application to Characterizing Symptoms of Depression

The twenty-four hour sleep-wake pattern known as the rest-activity rhythm (RAR) is associated with many aspects of health and well-being. Researchers have utilized a number of interpretable, person-specific RAR measures that can be estimated from actigraphy. Actigraphs are wearable devices that dynamically record acceleration and provide indirect measures of physical activity over time. One class of useful RAR measures are those that quantify variability around a mean circadian pattern. However, current parametric and non-parametric RAR measures used by applied researchers can only quantify variability from a limited or undefined number of rhythmic sources. The primary goal of this article is to consider a new measure of RAR variability: the log-power spectrum of stochastic error around a circadian mean. This functional measure quantifies the relative contributions of variability about a circadian mean from all possibly frequencies, including weekly, daily, and high-frequency sources of variation. It can be estimated through a two-stage procedure that smooths the log-periodogram of residuals after estimating a circadian mean. The development of this measure was motivated by a study of depression in older adults and revealed that slow, rhythmic variations in activity from a circadian pattern are correlated with depression symptoms.