High-dimensional partially linear functional Cox models.

The article focuses on developing a high-dimensional partially linear functional Cox model to analyze time-to-event data with functional predictors, addressing limitations of the classical functional Cox model that assumes linearity between functional principal component (FPC) scores and hazard rates. Motivated by the study of long-term survival in kidney transplant recipients, where post-transplant renal function measured by estimated glomerular filtration rate (eGFR) serves as a functional predictor, the proposed model allows for nonlinear effects of FPC scores and incorporates diverging numbers of scalar predictors and FPCs as sample size grows. The authors employ a penalized partial likelihood estimation using smoothly clipped absolute deviation (SCAD) penalties for variable selection and B-spline approximations for smooth function estimation, demonstrating consistency, sparsity, and asymptotic normality of estimators. Simulation studies confirm the method’s effectiveness in selecting relevant predictors and estimating nonlinear effects, and application to kidney transplant data identifies significant nonlinear associations between eGFR trajectories and survival, as well as key scalar covariates influencing long-term outcomes.