Joint and Individual Representation of Domains of Physical Activity, Sleep, and Circadian Rhythmicity

Abstract

Developments in wearable technology have enabled researchers to continuously and objectively monitor various aspects and physiological domains of real life including levels of physical activity, quality of sleep, and strength of circadian rhythm in many epidemiological and clinical studies. Current analytical practice is to summarize each of these three domains individually via a standard inventory of interpretable features, and explore individual associations between the features and clinical variables. However, the features often exhibit significant interaction and correlation both within and between domains. Integration of features across multiple domains remains methodologically challenging. To address this problem, we propose to use joint and individual variation explained, a dimension reduction technique that efficiently deals with multivariate data representing multiple domains. In this paper, we review the most frequently used features to characterize the domains of physical activity, sleep, and circadian rhythmicity and illustrate the approach using wrist-worn actigraphy data from 198 participants of the Baltimore Longitudinal Study of Aging.

Appendix

A Functional PCA

Functional PCs for circadian rhythmicity domain, for each subject, 1440-min activity profile were averaged across valid days which resulted in an average daily profile that is representative. Then functional PCA using sandwich smoother for covariance matrix smoothing was applied [78]. The first 10 principal components explained more than 90% of total variation. Figure 11 shows the first 10 functional PCs.

B Results from the Two-Step Alternative Approach

We considered an alternative two-step approach by first performing PCA to each domain individually, and then applying JIVE to the joint truncated data from all three domains.

Fig. 15

Cross-correlations between features and JIVE/PC scores, for S1, where median is used to impute missing data

Fig. 16

Cross-correlations between features and JIVE/PC scores, for S2, where days with more than 7% were removed

Fig. 17

Cross-correlations between features and JIVE/PC scores, for S3, where all subject days with missing values were removed

In order to keep as much joint variation as possible, we considered in the first step (i.e., individual PCA) to keep 5 and 8 PCs from each domain. When 5 PCs were kept in each domain, JIVE selected joint rank to be 4, and 1, 2, and 5 as the individual ranks for PA, SL, and CR, respectively. Meanwhile, when 8 PCs were kept in each domain, JIVE selected joint rank to be 4 as well, but individual ranks to be 2, 2, and 7 for domains for PA, SL, and CR, respectively. Figure 12 shows the proportion of variation explained. Even though it seems like there are more joint variation recovered, but we have to keep in mind that potentially useful information may have been removed, and the proportion here is with respect to the remained variation in the truncated data.

Figures 13 and 14 show the relationships between JIVE results from the main analysis (denoted by (A)) and the alternative analysis with 5 PCs selected (denoted by (B1)), and with 8 PCs selected (denoted by (B2)). The first joint PCs between (A) and (B1)/(B2) are highly correlated, which shows high consistency between the two approaches. There is also certain level of correlation between JT-PC2 from the two approaches. The individual PCs from the two approaches are highly correlated.

C Results for the Sensitivity Analyses

This section contains the results from the sensitivity analyses described in Sect. 4.4 where we considered 3 other ways to handle missing data in activity profiles. In sensitivity analysis 1 (S1), missing data were imputed using median of the specific time within each subject instead of mean. We still have 198 subjects contributed by 1134 days (with mean 5.72 days and standard deviation of 0.62). In sensitivity analysis 2 (S2), instead of using $5\%$ of the threshold, we consider removing days with more than $7\%$ of missing data (101 min per day). We have 198 subjects contributed by 1163 days (with mean 5.76 days and standard deviation of 0.59). In sensitivity analysis 3 (S3), we considered the most aggressive approach which is to remove all subject days with missing values. This approach left us 189 subjects contributed by 986 days (with mean 5.22 days and standard deviation of 0.98).

The patterns are quite similar to what we observed from the main analysis. In S1, joint structure explains 68.1%, 20.1%, and 25.8% of total variation in PA, SL, and CR domains, respectively. Individual structures explain 26.1%, 74.5%, and 38.5% of total variation in PA, SL, and CR domains, respectively. And there are only 5.8%, 5.3%, and 35.7% of variation that cannot be explained in PA, SL, and CR respectively. In S2, joint structure explains 69.0%, 18.7%, and 25.9% of total variation in PA, SL, and CR domains, respectively. Individual structures explain 25.2%, 76.2%, and 38.6% of total variation in PA, SL, and CR domains, respectively. And there are only 5.7%, 5.2%, and 35.5% of variation that cannot be explained in PA, SL, and CR respectively. Finally, in S3, joint structure explains 63.6%, 20.7%, and 27.2% of total variation in PA, SL, and CR domains, respectively. Individual structures explain 30.5%, 73.0%, and 35.3% of total variation in PA, SL, and CR domains, respectively. And there are only 6.0%, 6.3%, and 37.5% of variation that cannot be explained in PA, SL, and CR, respectively. The cross-correlation plots between features and JIVE/PC scores are shown in Figs. 15, 16, and 17.