Modeling Circadian Influences on Actigraphy Data With Zero-inflatet Poisson Distribution

Abstract

ABSTRACT BODY: Introduction : Actigraphy is commonly used as a non-invasive method to study sleep/wake patterns. We decided to explore two aspects of actigraphy data. (1) We investigated whether there were circadian rhythms in actigraphy counts independent of prior wake or sleep duration. For this we used data from inpatient forced desychrony (FD) studies in which sleep and wake were evenly distributed across all circadian phases. (2) Since understanding the underlying statistical distribution and correlation structure of the activity data is required for performing appropriate statistics, we applied a Zero-Inflated Poisson (ZIP) regression model to analyze the longitudinal count data that contain extra zeros and correlated data from the same individual. Methods : Fifty healthy young (19-34 years; 16F) participants with no medical, psychological or sleep disorders and using no medications or caffeine were studied in inpatient FD protocols with sleep/wake cycle (T) durations: T=20 hr (Wyatt 1999), T=28 hr (Gronfier 2007), T=42.85 hr (Wyatt 2004, Grady 2010) with a 2:1 wake:sleep ratio and T=42.85hr (Cohen 2010) with a 3.3:1 wake:sleep ratio. Participants wore an actiwatch on the non-dominant wrist at all times. Data were divided into ~4-hr circadian bins (adjusted for each individual’s circadian period estimated from melatonin data). Actigraphy data were tested for statistically Normal, Poisson and ZIP distributions. Twelve participants from this dataset are included here. Light level (illuminance) was tested as a covariate. Results : The distribution of activity counts was not statistically Normal or Poisson, whereas the zero-Inflated Poisson (ZIP) model provided an appropriate fit. There was a difference in activity between circadian bins (P<0.0001), with the lowest levels at the time of the fitted melatonin maximum, independent of sleep/wake state or prior wake or sleep duration. Light level also had a positive influence on activity counts (P<0.0001). Conclusion: Results from ZIP models suggest that the distribution of activity counts is zero-inflated and there is strong circadian variation. This model provides a useful statistical tool to analyze circadian rhythms in such activity count data. Summary statistics (e.g., mean and standard deviation) based on statistically Normal distributions should not be used on actigraphy data, since the results may be misleading. Future work will include: (i) adding data from more participants; and (ii) analysis of the effects of prior time awake or sleep on actigraphy counts.