Using hidden Markov models with raw, triaxial wrist accelerometry data to determine sleep stages

Accelerometry is a low-cost and noninvasive method that has been used to discriminate sleep from wake, however, its utility to detect sleep stages is unclear. We detail the development and comparison of methods which utilise raw, triaxial accelerometry data to classify varying stages of sleep, ranging from sleep/wake detection to discriminating rapid eye movement sleep, stage one sleep, stage two sleep, deep sleep and wake. First- and second-order hidden Markov models (HMMs) with time-homogeneous and time-varying transition probability matrices, along with continuous acceleration observations in the form of a Gaussian-observation HMM and K-means classified acceleration in a discrete-observation HMM were explored. In addition, generalised linear mixed models (GLMMs) with binary and multinomial responses and logit link functions were considered as was whether incorporating adjoining acceleration information into the models improved prediction. Model predictions were compared to the reference-standard in sleep detection (polysomnography) and outcome accuracies were calculated. Consistently, HMMs yielded greater sleep stage detection than GLMMs but there was little difference between first- and second-order HMMs. Varying degrees of difference were observed when comparing Gaussian-observation HMMs to discrete-observation HMMs, and time-varying HMMs yielded greater discrimination than time-homogeneous HMMs, as did models which considered adjoining acceleration information. These results suggest that wrist-worn accelerometry data may be able to detect sleep stages but that further investigation is required to optimise classification accuracy.