A global kernel estimator for partially linear varying coefficient additive hazards models.

We study kernel-based estimation methods for partially linear varying coefficient additive hazards models, where the effects of one type of covariates can be modified by another. Existing kernel estimation methods for varying coefficient models often use a "local" approach, where only a small local neighborhood of subjects are used for estimating the varying coefficient functions. Such a local approach, however, is generally inefficient as information about some non-varying nuisance parameter from subjects outside the neighborhood is discarded. In this paper, we develop a "global" kernel estimator that simultaneously estimates the varying coefficients over the entire domains of the functions, leveraging the non-varying nature of the nuisance parameter. We establish the consistency and asymptotic normality of the proposed estimators. The theoretical developments are substantially more challenging than those of the local methods, as the dimension of the global estimator increases with the sample size. We conduct extensive simulation studies to demonstrate the feasibility and superior performance of the proposed methods compared with existing local methods and provide an application to a motivating cancer genomic study.