Incorporating Heterogeneity in Mixed Hidden Markov Models With an Application to the Sleep‐Wake Cycle

The sleep-wake cycle plays an important and far-reaching role in health. By utilizing personal physical activity monitors (PAMs), inferences about the sleep-wake cycle can be made. Hidden Markov models (HMMs) have been applied in this area as an accurate unsupervised approach. To account for heterogeneity in activity levels, we developed a mixed HMM that allows for individual differences. Through extensive simulations, we quantified the added gains relative to a standard HMM from using a mixed HMM to account for heterogeneity across several realistic scenarios. We found that mixed HMMs are often more accurate than standard HMMs when follow-up times are shorter. In situations with many repeated measurements per individual, a standard and mixed HMM have similar levels of accuracy, although a standard HMM is faster and easier to implement. Afterward, we applied our HMMs to actigraphy data from the National Health and Nutrition Examination Survey. We present results on sleep summary statistics by age and BMI. Summary statistics about the sleep-wake cycle extracted by the standard and mixed HMM were qualitatively similar. Differences in results, however, were likely driven by the heterogeneity in physical activity due to BMI and age, which we identified using a post hoc investigation of the data-driven clusters produced by the mixed HMM.