Regularized scalar-on-function regression analysis to assess functional association of critical physical activity window with biological age

Abstract

Accelerometry data enables scientists to extract personal digital features useful in precision health decision making. Existing analytic methods often begin with discretizing physical activity (PA) counts into activity categories via fixed cutoffs; however, the cutoffs are validated under restricted settings and cannot be generalized across studies. Here we develop a data-driven approach to overcome this bottleneck in the analysis of PA data in which we holistically summarize an individual’s PA profile using occupation-time curves that describe the percentage of time spent at or above a continuum of activity levels. The resulting functional curve is informative to capture time-course individual variability of PA. We investigate functional analytics under an ${\mathit{L}}_0$ regularization approach, which handles highly correlated micro-activity windows that serve as predictors in a scalar-on-function regression model. We develop a new one-step method that simultaneously conducts fusion via change-point detection and parameter estimation through a new ${\mathit{L}}_0$ constraint formulation, which is evaluated via simulation experiments and a data analysis assessing the influence of PA on biological aging.