Variable Selection in Functional Linear Cox Model

2025-06-03

AI Summary

This paper addresses the challenge of variable selection for functional covariates in joint modeling of high-dimensional physiological time-series signals from wearable devices and survival outcomes. We propose a group-sparse and smooth joint estimation framework for functional linear Cox models. Our method innovatively integrates group minimax concave penalty (group MCP) with spline-based semiparametric estimation, simultaneously enforcing smoothness constraints and group-wise sparsity on functional coefficients. It enables joint selection of multiple functional covariates (e.g., activity time-distribution curves) and scalar covariates. Through spline basis expansion, grouped coordinate descent optimization, and automatic dual-parameter tuning, our approach identifies statistically significant associations between daily activity patterns and all-cause mortality in the NHANES 2003–06 cohort—particularly among older adults. Empirical evaluation demonstrates superior variable selection accuracy and coefficient estimation precision compared to state-of-the-art methods.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Develop variable selection for functional linear Cox model
• Integrate smoothness and sparsity in functional coefficients
• Identify key physical activity patterns linked to mortality

Innovation

• Spline-based semiparametric estimation for functional coefficients
• Group minimax concave penalty integrating smoothness and sparsity
• Automated selection of smoothing and sparsity parameters