Additive Functional Cox Model

Abstract

We propose the additive functional Cox model to flexibly quantify the association between functional covariates and time to event data. The model extends the linear functional proportional hazards model by allowing the association between the functional covariate and log hazard to vary nonlinearly in both the functional domain and the value of the functional covariate. Additionally, we introduce critical transformations of the functional covariate which address the weak model identifiability in areas of information sparsity and discuss their impact on interpretation and inference. We also introduce a novel estimation procedure that accounts for identifiability constraints directly during model fitting. Methods are applied to the National Health and Nutrition Examination Survey 2003–2006 accelerometry data and quantify new and interpretable circadian patterns of physical activity that are associated with all-cause mortality. We also introduce a simple and novel simulation framework for generating survival data with functional predictors which resemble the observed data. The accompanying inferential R software is fast, open source, and publicly available. Our data application and simulations are fully reproducible through the accompanying vignette. Supplementary materials for this article are available online.

Keywords:

• Accelerometry
• Functional data
• Survival analysis
• Wearable devices

Supplementary Materials

vignette_afcm.Rmd The vignette (designed for rnhanesdata package) containing code and instructions to reproduce all results shown in the article. (.Rmd file)

vignette_afcm.html The HTML version of the vignette. (.html file)

process_data.R The R code to process and organize raw NHANES data into a data frame. Please follow the instructions in the vignette and do not run it separately. (.R file)

supplementary_materials.pdf Additional discussion about estimability and identifiability, comparison of methods that impose identifiability constraints, sample R code for simulating survival data, and additional simulation results. (.pdf file)

Disclosure Statement

Dr. Crainiceanu is consulting with Bayer and Johnson and Johnson on methods development for wearable devices in clinical trials. The details of the contracts are disclosed through the Johns Hopkins University eDisclose system and have no direct or apparent relationship with this article.

Additional information

Funding

This work was supported by the National Institute of Neurological Disorders and Stroke under grant number R01 NS060910; and the National Institute on Aging under grant number T32 AG000247.