Generalized Functional Linear Models for Right-Censored Time-to-Event Data

Music City Center 

Interpreting real-time data from wearable devices, such as continuous glucose monitors (CGM), to inform long-term adverse event risk is a central objective of digital health and precision medicine. We address a gap in existing regression-based methods for modeling scalar responses with functional predictors by developing a generalized functional linear model for a right-censored scalar response that incorporates both functional and scalar covariates. We consider a direct binomial model in which a binary outcome indicates the survival of a subject past a fixed time horizon. We approximate the random functional predictors using a truncated Karhunen-Loève expansion, with the truncation parameter permitted to increase with sample size. Inverse probability of censoring weights are used to obtain unbiased effect size estimates in the presence of censoring. By establishing asymptotic normality, we construct confidence intervals for both the scalar coefficients and the parameter function. We illustrate our method by modeling the survival probability of over 2,000 veterans with type 2 diabetes using CGM data and their baseline scalar characteristics.

functional regression

right censoring

generalized linear model

digital health

wearable devices 

Lifetime Data Science Section