Tests of the functional coefficients in the varying-coefficient cox proportional hazard model

Cox proportional hazard model is one of the most celebrated models for analyzing lifetime data. There exists one problem when we replace the covariate effects with varying-coefficient functions. That is whether this replacement is reasonable or partially reasonable. In this paper, we propose a hypothesis testing based on the asymptotic distribution of the normalized maximum deviations, for this problem, whether the parametric components are known or unknown. We also conducted simulation studies to evaluate finite-sample properties of our proposed methods.