Handling missing data in rest-activity time series measured by actimetry

A handling procedure of off-wrist episodes in actimetry time series of motor activity is presented using two records (regular vs. irregular sleep-wake cycle and daytime activity) of 14 consecutive days sampled in 1-minute epochs. We generated single missing value (NA) intervals of 1 h, 2 h, 4 h, 6 h, 12 h, and 24 h as well as random NA episodes following probabilistic rules to simulate real-life off-wrist episodes. Then, we replaced these episodes with "zeroes" (i.e., the default of immobility records), mean or median of the remaining 13 days corresponding to the missing bins. Single missing episodes of up to 12 h resulted in less than 5% variation from the original values. The irregular series showed higher variability in acrophase, MESOR, L5, M10 and RA compared to the regular series. Random missing allocation simulating real-life off-wrist episodes resulted in significant changes in most parameters, and the imputation of zeroes significantly increased the variance; however, replacing NA with mean or median resulted in patterns similar to those of NA. We recommend replacing 'zeroes' with NA whenever possible, given the risk of inflating invariance using zeroes. If the parameters cannot be computed in the presence of NA, we recommend using the weekly mean of corresponding timepoints.