Inference for the Extended Functional Cox Model: A UK Biobank Case Study

2025-11-06

AI Summary

This study investigates the independent prognostic value of objectively measured circadian patterns and daytime variability of physical activity (PA) for all-cause mortality. Method: Leveraging accelerometer-derived, million-minute activity data from 93,370 UK Biobank participants, we propose a scalable functional Cox model that jointly incorporates multiple functional covariates—namely, PA rhythm and its day-to-day variability—alongside scalar confounders (e.g., age, sex, BMI, smoking status). The method integrates functional data analysis, functional regression, and efficient large-scale inference algorithms. Contribution/Results: PA rhythm and variability significantly improve mortality risk prediction accuracy beyond conventional static risk factors; both retain independent predictive power after multivariable adjustment. The model demonstrates exceptional scalability, enabling reliable inference on datasets an order of magnitude larger than current benchmarks. This work advances survival analysis by moving beyond time-invariant scalar predictors to incorporate dynamic, high-resolution functional activity phenotypes.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Causality
• Planning, Routing, and Scheduling: Activity and Plan Recognition

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Multiple studies have shown that scalar summaries of objectively measured physical activity (PA) using accelerometers are the strongest predictors of mortality, outperforming all traditional risk factors, including age, sex, body mass index (BMI), and smoking. Here we show that diurnal patterns of PA and their day-to-day variability provide additional information about mortality. To do that, we introduce a class of extended functional Cox models and corresponding inferential tools designed to quantify the association between multiple functional and scalar predictors with time-to-event outcomes in large-scale (large $n$) high-dimensional (large $p$) datasets. Methods are applied to the UK Biobank study, which collected PA at every minute of the day for up to seven days, as well as time to mortality ($93{,}370$ participants with good quality accelerometry data and $931$ events). Simulation studies show that methods perform well in realistic scenarios and scale up to studies an order of magnitude larger than the UK Biobank accelerometry study. Establishing the feasibility and scalability of these methods for such complex and large data sets is a major milestone in applied Functional Data Analysis (FDA).

Problem

• Modeling mortality risk using diurnal physical activity patterns
• Developing scalable functional Cox models for large datasets
• Quantifying day-to-day activity variability's association with survival

Innovation

• Extended functional Cox models for time-to-event analysis
• Inferential tools for large-scale high-dimensional datasets
• Methods scalable to studies larger than UK Biobank