Survival on Image Regression with Application to Partially Functional Distributional Representation of Physical Activity

Music City Center 

We develop a novel survival on image regression model with partially functional distributional predictors. Technological advancements in wearables and medical imaging leads to high-dimensional physiological signals in the forms of images. The existing approaches for functional data and survival outcomes have been primarily developed for uni-dimensional functional predictors. Recent developments in distributional data analysis enables us to model temporally varying distributional representation of physical activity (PA) as a partially functional predictor and investigate its association with survival using a semiparametric Cox model. We use tensor product splines to model the smooth bivariate functional coefficients. A penalized partial likelihood is employed for estimation. Numerical analysis through simulations illustrates a satisfactory finite sample performance of the proposed method in estimation. The application of the proposed method is demonstrated in understanding the association between temporally varying distributional representation of physical activity and all-cause mortality based on the National Health and Nutrition Examination Survey (NHANES) 2011-2014. The results provide important insights for developing time-of-day and intensity specific PA interventions.

Functional Cox Model

Partially Functional Distributional Data

Physical Activity

NHANES