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Additive Functional Cox Model.

Erjia Cui1, Ciprian M Crainiceanu1, Andrew Leroux2

  • 1Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, USA.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|December 13, 2021
PubMed
Summary
This summary is machine-generated.

We introduce the Additive Functional Cox Model to analyze how complex health data, like physical activity patterns, impacts survival. This new statistical tool reveals non-linear associations with mortality risk.

Keywords:
accelerometryfunctional datasurvival analysiswearable devices

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Area of Science:

  • * Biostatistics and Survival Analysis
  • * Statistical Modeling of Health Data

Background:

  • * Traditional survival models often assume linear relationships, limiting their ability to capture complex associations.
  • * Functional data, representing measurements over time or space, present unique challenges in survival analysis.
  • * Existing methods may struggle with model identifiability and interpretation when dealing with sparse functional covariate data.

Purpose of the Study:

  • * To propose the Additive Functional Cox Model (AFCM) for flexible quantification of associations between functional covariates and time-to-event data.
  • * To extend the linear functional proportional hazards model by allowing non-linear associations in both the functional domain and covariate values.
  • * To introduce critical transformations and a novel estimation procedure to address model identifiability and enhance interpretation.

Main Methods:

  • * Development of the Additive Functional Cox Model (AFCM) with non-linear association capabilities.
  • * Introduction of critical transformations for functional covariates to improve model identifiability.
  • * Implementation of a novel estimation procedure that directly incorporates identifiability constraints.
  • * Application to the National Health and Nutrition Examination Survey (NHANES) 2003-2006 accelerometry data.
  • * Development of a simulation framework for survival data with functional predictors.

Main Results:

  • * Quantification of novel, interpretable circadian patterns of physical activity associated with all-cause mortality using NHANES data.
  • * Demonstrated the model's ability to capture complex, non-linear relationships between functional covariates and hazard rates.
  • * Validated the effectiveness of the proposed transformations and estimation procedure through simulations and real-world data.

Conclusions:

  • * The Additive Functional Cox Model provides a flexible and powerful tool for analyzing time-to-event data with functional predictors.
  • * The model successfully identified interpretable associations between physical activity patterns and mortality risk.
  • * The developed R software offers a fast, open-source, and reproducible solution for researchers in biostatistics and epidemiology.