Functional Linear Cox Regression Model with Frailty

TL;DR

This paper introduces a novel functional linear Cox regression model incorporating frailty to better analyze survival data with unobserved heterogeneity, improving estimation and prediction in high-dimensional settings.

Contribution

It develops a new model combining scalar, functional covariates, and frailty, estimated via functional PCA and penalized likelihood, with demonstrated superior performance.

Findings

Outperforms traditional models in simulation studies.

Identifies significant links between physical activity and mortality.

Provides an R package for practical implementation.

Abstract

This paper presents a functional linear Cox regression model with frailty to tackle unobserved heterogeneity in survival data with functional covariates. While traditional Cox models are common, they struggle to incorporate frailty effects that represent individual differences not captured by observed covariates. Our model combines scalar and functional covariates with a frailty term to address these unmeasured influences, creating a robust framework for high-dimensional survival analysis. We estimate parameters using functional principal component analysis and apply penalized partial likelihood for the frailty structure. A simulation study shows that our model outperforms traditional approaches in estimation accuracy and predictive capacity, especially with high frailty. We also analyze data from the National Health and Nutrition Examination Survey, highlighting significant links between physical activity and mortality in frail subpopulations. Our findings demonstrate the model's effectiveness in managing complex survival data, with potential applications in biomedical research related to unobserved heterogeneity. The method is available as an R package.