Penalized estimation for varying coefficient additive hazards models

Varying coefficient models are commonly used to capture intricate interaction effects among covariates in regression models, allowing for the modification of one covariate's effect by another. Although these models offer increased flexibility, they also introduce greater estimation and computational complexity as a trade-off. This complexity is particularly evident in genomic studies, where the covariates are often high-dimensional, rendering conventional estimation methods inapplicable. In this paper, we study a penalized estimation method for the varying coefficient additive hazards model. We adopt the group lasso penalty along with the kernel smoothing technique to estimate the varying coefficients. In contrast to existing kernel methods, which only use a "local" neighborhood of subjects to estimate the varying coefficient function at any given point, the proposed method takes a "global" approach that incorporates all subjects and is more efficient. Through extensive simulation studies, we demonstrate that the proposed method produces interpretable results with satisfactory predictive performance. We provide an application to a major cancer genomic study.