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

ABSTRACT Technological advancements in wearable devices and medical imaging often lead to high‐dimensional physiological signals in the form of images or surfaces. To address these data structures, we develop a novel survival on image regression model with a specific focus on partially functional distributional representation of wearable data. The existing approaches for functional data and survival outcomes have been primarily developed for uni‐dimensional functional predictors. Drawing on recent developments in distributional data analysis, we model temporally varying distributional patterns of physical activity (PA) as a partially functional distributional predictor within a semiparametric Cox model framework. We use tensor product splines to model the smooth bivariate functional coefficients, and a penalized partial likelihood is employed for estimation. A large sample approximation of the posterior distribution from an equivalent Bayesian formulation is used for uncertainty quantification. Numerical analysis through simulations illustrates a satisfactory and competitive finite sample performance of the proposed method in estimation. We demonstrate the application of the proposed method using data from the National Health and Nutrition Examination Survey (NHANES) 2011–2014, where we investigate the relationship between temporally varying PA distribution and all‐cause mortality. The results highlight a protective effect of having a higher reserve of PA during the daytime, while subjects having disrupted sleep could be at an increased risk of mortality. Our findings provide important insights for developing time‐of‐day and intensity‐specific PA interventions. Software implementation of the proposed method is provided in R.