Supplementary Material from Hidden Markov models for monitoring circadian rhythmicity in telemetric activity data

Wearable computing devices allow collection of densely sampled real-time information on movement enabling researchers and medical experts to obtain objective and non-obtrusive records of actual activity of a subject in the real world over many days. Our interest here is motivated by the use of activity data for evaluating and monitoring the circadian rhythmicity of subjects for research in chronobiology and chronotherapeutic healthcare. In order to translate the information from such high-volume data arising we propose the use of a Markov modelling approach which (i) naturally captures the notable square wave form observed in activity data along with heterogeneous ultradian variances over the circadian cycle of human activity, (ii) thresholds activity into different states in a probabilistic way while respecting time dependence and (iii) gives rise to circadian rhythm parameter estimates, based on probabilities of transitions between rest and activity, that are interpretable and of interest to circadian research.