Functional Time Transformation Model with Applications to Digital Health

TL;DR

This paper introduces a flexible functional time transformation model for survival analysis with wearable sensor data, addressing limitations of traditional Cox models and demonstrating superior predictive performance in health-related case studies.

Contribution

It develops a novel monotone transformation-based survival model using Bernstein polynomials and sieve maximum likelihood estimation for functional and scalar covariates.

Findings

The model performs well in simulations for estimation and inference.

Application to NHANES accelerometer data reveals links between activity patterns and mortality.

Application to diabetic CGM data shows improved prediction over traditional biomarkers.

Abstract

The advent of wearable and sensor technologies now leads to functional predictors which are intrinsically infinite dimensional. While the existing approaches for functional data and survival outcomes lean on the well-established Cox model, the proportional hazard (PH) assumption might not always be suitable in real-world applications. Motivated by physiological signals encountered in digital medicine, we develop a more general and flexible functional time-transformation model for estimating the conditional survival function with both functional and scalar covariates. A partially functional regression model is used to directly model the survival time on the covariates through an unknown monotone transformation and a known error distribution. We use Bernstein polynomials to model the monotone transformation function and the smooth functional coefficients. A sieve method of maximum likelihood is employed for estimation. Numerical simulations illustrate a satisfactory performance of the proposed method in estimation and inference. We demonstrate the application of the proposed model through two case studies involving wearable data i) Understanding the association between diurnal physical activity pattern and all-cause mortality based on accelerometer data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014 and ii) Modelling Time-to-Hypoglycemia events in a cohort of diabetic patients based on distributional representation of continuous glucose monitoring (CGM) data. The results provide important epidemiological insights into the direct association between survival times and the physiological signals and also exhibit superior predictive performance compared to traditional summary based biomarkers in the CGM study.