Analysis of Active/Inactive Patterns in the NHANES Data using Generalized Multilevel Functional Principal Component Analysis

Between 2011 and 2014 NHANES collected objectively measured physical activity data using wrist-worn accelerometers for tens of thousands of individuals for up to seven days. Here we analyze the minute-level indicators of being active, which can be viewed as binary (because there is an active indicator at every minute), multilevel (because there are multiple days of data for each study participant), functional (because within-day data can be viewed as a function of time) data. To extract within- and between-participant directions of variation in the data, we introduce Generalized Multilevel Functional Principal Component Analysis (GM-FPCA), an approach based on the dimension reduction of the linear predictor. Scores associated with specific patterns of activity are shown to be strongly associated with time to death. In particular, we confirm that increased activity is associated with time to death, a result that has been reported on other data sets. In addition, our method shows the previously unreported finding that maintaining a consistent day-to-day routine is strongly associated with a reduced risk of mortality (p-value < 0.001) even after adjusting for traditional risk factors. Extensive simulation studies indicate that GM-FPCA provides accurate estimation of model parameters, is computationally stable, and is scalable in the number of study participants, visits, and observations within visits. R code for implementing the method is provided.