# Functional varying-coefficient Cox model and its application

## TL;DR

This paper introduces a new survival model that handles complex data by combining varying-coefficient and functional covariates, tested on Alzheimer's data.

## Contribution

The novel functional varying-coefficient Cox model improves adaptability for survival analysis with complex covariates.

## Key findings

- The model effectively handles survival data with varying-coefficient and functional covariates.
- Simulation studies confirm the model's performance improvements.
- Application to ADNI data demonstrates practical utility in Alzheimer's research.

## Abstract

When data become increasingly complex, desirable models are required to be more flexible for analyzing survival data. Building upon the existing functional Cox model, we introduce a novel functional varying-coefficient Cox model and the corresponding estimation algorithms are proposed in this article. The proposed model can simultaneously handle survival data with varying-coefficient covariates and functional covariates, thereby significantly enhancing the adaptability of survival models. The model performance is evaluated by simulation studies, and a real application using Alzheimer’s disease neuroimaging initiative (ADNI) data is used to illustrate the practicality of the proposed model.