Variable Selection in Functional Linear Cox Model

TL;DR

This paper introduces a new variable selection method for functional linear Cox models that effectively handles high-dimensional physiological signals and identifies key predictors related to mortality.

Contribution

It develops a spline-based semiparametric estimation with a group MCP penalty and an efficient algorithm for variable selection in complex survival models.

Findings

Accurate variable selection demonstrated in simulations

Identified key physical activity patterns linked to mortality

Provides an automated method for tuning parameters

Abstract

Modern biomedical studies frequently collect complex, high-dimensional physiological signals using wearables and sensors along with time-to-event outcomes, making efficient variable selection methods crucial for interpretation and improving the accuracy of survival models. We propose a novel variable selection method for a functional linear Cox model with multiple functional and scalar covariates measured at baseline. We utilize a spline-based semiparametric estimation approach for the functional coefficients and a group minimax concave type penalty (MCP), which effectively integrates smoothness and sparsity into the estimation of functional coefficients. An efficient group descent algorithm is used for optimization, and an automated procedure is provided to select optimal values of the smoothing and sparsity parameters. Through simulation studies, we demonstrate the method's ability to perform accurate variable selection and estimation. The method is applied to 2003-06 cohort of the National Health and Nutrition Examination Survey (NHANES) data, identifying the key temporally varying distributional patterns of physical activity and demographic predictors related to all-cause mortality. Our analysis sheds light on the intricate association between daily distributional patterns of physical activity and all-cause mortality among older US adults.