Elastic functional Cox regression model with shape predictors.

Phase variability in functional data can obscure prominent geometric features, e.g. local extrema, and deteriorate predictive performance of regression models with functional predictors. We propose an elastic functional Cox regression model (EFCRM) that captures the association between a time-to-event outcome and the shape of a functional predictor. As such, EFCRM accounts for phase variation in the functional predictor via registration, which is supervised by the survival outcome. The model is fit using an iterative algorithm that alternates between removal of phase variation and estimation of the regression coefficient function. To improve convergence of the estimation procedure, we use a small number of separate gradient-based updates at each iteration for the two steps. The model is assessed based on estimation accuracy and predictive performance using a simulation study. We additionally apply the proposed framework to two real-world datasets. Overall, we show that the EFCRM is robust to misspecification of the number and type of basis functions used to approximate the coefficient function and results in comparable or better estimation accuracy and predictive ability than competitors.